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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
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<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgb9e4bbf">1. Experimental conditions</a></li> <li><a href="#org20cd7af">1. Experimental conditions</a></li>
<li><a href="#orgbe7bf59">2. Measurements procedure</a></li> <li><a href="#org4b136ea">2. Measurements procedure</a></li>
<li><a href="#org3337380">3. Measurement Files</a></li> <li><a href="#org7a4e10c">3. Measurement Files</a></li>
<li><a href="#orgc59cdd1">4. Data Analysis</a> <li><a href="#orgc4e4e05">4. Data Analysis</a>
<ul> <ul>
<li><a href="#org97ea2b9">4.1. Loading of the data</a></li> <li><a href="#org8e48582">4.1. Loading of the data</a></li>
<li><a href="#org55d35ad">4.2. Pre-processing of the data</a></li> <li><a href="#orgdef23af">4.2. Pre-processing of the data</a></li>
<li><a href="#org409f95e">4.3. X-direction FRF</a></li> <li><a href="#org9329022">4.3. X-direction FRF</a></li>
<li><a href="#org5ca4365">4.4. Y-direction FRF</a></li> <li><a href="#orgf143ff0">4.4. Y-direction FRF</a></li>
<li><a href="#org491a242">4.5. Z-direction FRF</a></li> <li><a href="#org69dd2ae">4.5. Z-direction FRF</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgf03bfb4">5. Results</a></li> <li><a href="#orgdfa9254">5. Results</a></li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orgb9e4bbf" class="outline-2"> <div id="outline-container-org20cd7af" class="outline-2">
<h2 id="orgb9e4bbf"><span class="section-number-2">1</span> Experimental conditions</h2> <h2 id="org20cd7af"><span class="section-number-2">1</span> Experimental conditions</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
@ -326,19 +90,19 @@ Dynamics of the station is evaluated using instrumented hammer and accelerometer
<li>The granite is not glued to the floor</li> <li>The granite is not glued to the floor</li>
<li>The Y-Translation stage is powered and in closed-loop</li> <li>The Y-Translation stage is powered and in closed-loop</li>
<li>The spindle is not powered</li> <li>The spindle is not powered</li>
<li>Mass is placed on top of the Hexapod (<b>how much?</b>) (figure <a href="#orgb5022d9">1</a>).</li> <li>Mass is placed on top of the Hexapod (<b>how much?</b>) (figure <a href="#orge99c284">1</a>).</li>
<li>Made by Marc Lesourd on the 17th of November 2017</li> <li>Made by Marc Lesourd on the 17th of November 2017</li>
</ul> </ul>
<div id="orgb5022d9" class="figure"> <div id="orge99c284" class="figure">
<p><img src="./figs/accelerometers.png" alt="accelerometers.png" width="500px" /> <p><img src="./figs/accelerometers.png" alt="accelerometers.png" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Accelerometers position</p> <p><span class="figure-number">Figure 1: </span>Accelerometers position</p>
</div> </div>
<div id="orgaaf63dd" class="figure"> <div id="org363f97a" class="figure">
<p><img src="./figs/instrumented_hammer.png" alt="instrumented_hammer.png" width="500px" /> <p><img src="./figs/instrumented_hammer.png" alt="instrumented_hammer.png" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Instrumented Hammer used</p> <p><span class="figure-number">Figure 2: </span>Instrumented Hammer used</p>
@ -346,11 +110,11 @@ Dynamics of the station is evaluated using instrumented hammer and accelerometer
</div> </div>
</div> </div>
<div id="outline-container-orgbe7bf59" class="outline-2"> <div id="outline-container-org4b136ea" class="outline-2">
<h2 id="orgbe7bf59"><span class="section-number-2">2</span> Measurements procedure</h2> <h2 id="org4b136ea"><span class="section-number-2">2</span> Measurements procedure</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<b>3-axis Accelerometers</b> (specifications table <a href="#org2f4877d">1</a>) are glued on (see figure <a href="#orgb5022d9">1</a>): <b>3-axis Accelerometers</b> (specifications table <a href="#org3aa8e2c">1</a>) are glued on (see figure <a href="#orge99c284">1</a>):
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Marble</li> <li>Marble</li>
@ -359,7 +123,7 @@ Dynamics of the station is evaluated using instrumented hammer and accelerometer
<li>top of Hexapod</li> <li>top of Hexapod</li>
</ul> </ul>
<table id="org2f4877d" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org3aa8e2c" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Pieozoelectric acc. 356b18 - 3 axis</caption> <caption class="t-above"><span class="table-number">Table 1:</span> Pieozoelectric acc. 356b18 - 3 axis</caption>
<colgroup> <colgroup>
@ -396,7 +160,7 @@ Dynamics of the station is evaluated using instrumented hammer and accelerometer
</table> </table>
<p> <p>
The structure is excited using an <b>instrumented hammer</b> with impacts on (see figure <a href="#orgaaf63dd">2</a>): The structure is excited using an <b>instrumented hammer</b> with impacts on (see figure <a href="#org363f97a">2</a>):
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Marble</li> <li>Marble</li>
@ -405,8 +169,8 @@ The structure is excited using an <b>instrumented hammer</b> with impacts on (se
</div> </div>
</div> </div>
<div id="outline-container-org3337380" class="outline-2"> <div id="outline-container-org7a4e10c" class="outline-2">
<h2 id="org3337380"><span class="section-number-2">3</span> Measurement Files</h2> <h2 id="org7a4e10c"><span class="section-number-2">3</span> Measurement Files</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
Two measurements files are: Two measurements files are:
@ -415,7 +179,7 @@ Two measurements files are:
<li><code>id31_microstation_2017_11_17_frf.mat</code> that contains: <li><code>id31_microstation_2017_11_17_frf.mat</code> that contains:
<ul class="org-ul"> <ul class="org-ul">
<li><code>freq_frf</code> the frequency vector in Hz</li> <li><code>freq_frf</code> the frequency vector in Hz</li>
<li>Computed frequency response functions (see table <a href="#org71ee83c">2</a>)</li> <li>Computed frequency response functions (see table <a href="#org2cde1ca">2</a>)</li>
</ul></li> </ul></li>
<li><code>id31_microstation_2017_11_17_coh.mat</code> <li><code>id31_microstation_2017_11_17_coh.mat</code>
<ul class="org-ul"> <ul class="org-ul">
@ -424,10 +188,10 @@ Two measurements files are:
</ul> </ul>
<p> <p>
For each of the measurement, the measured channels are shown on table <a href="#org1bf8383">3</a>. For each of the measurement, the measured channels are shown on table <a href="#org6601586">3</a>.
</p> </p>
<table id="org71ee83c" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org2cde1ca" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Description of the location of direction of the excitation for each measurement</caption> <caption class="t-above"><span class="table-number">Table 2:</span> Description of the location of direction of the excitation for each measurement</caption>
<colgroup> <colgroup>
@ -446,44 +210,44 @@ For each of the measurement, the measured channels are shown on table <a href="#
</thead> </thead>
<tbody> <tbody>
<tr> <tr>
<td class="org-left">frf<sub>hexa</sub><sub>x</sub></td> <td class="org-left">frf_hexa_x</td>
<td class="org-left">Hexapod</td> <td class="org-left">Hexapod</td>
<td class="org-left">X</td> <td class="org-left">X</td>
</tr> </tr>
<tr> <tr>
<td class="org-left">frf<sub>hexa</sub><sub>y</sub></td> <td class="org-left">frf_hexa_y</td>
<td class="org-left">Hexapod</td> <td class="org-left">Hexapod</td>
<td class="org-left">Y</td> <td class="org-left">Y</td>
</tr> </tr>
<tr> <tr>
<td class="org-left">frf<sub>hexa</sub><sub>z</sub></td> <td class="org-left">frf_hexa_z</td>
<td class="org-left">Hexapod</td> <td class="org-left">Hexapod</td>
<td class="org-left">Z</td> <td class="org-left">Z</td>
</tr> </tr>
<tr> <tr>
<td class="org-left">frf<sub>marble</sub><sub>x</sub></td> <td class="org-left">frf_marble_x</td>
<td class="org-left">Marble</td> <td class="org-left">Marble</td>
<td class="org-left">X</td> <td class="org-left">X</td>
</tr> </tr>
<tr> <tr>
<td class="org-left">frf<sub>marble</sub><sub>y</sub></td> <td class="org-left">frf_marble_y</td>
<td class="org-left">Marble</td> <td class="org-left">Marble</td>
<td class="org-left">Y</td> <td class="org-left">Y</td>
</tr> </tr>
<tr> <tr>
<td class="org-left">frf<sub>marble</sub><sub>z</sub></td> <td class="org-left">frf_marble_z</td>
<td class="org-left">Marble</td> <td class="org-left">Marble</td>
<td class="org-left">Z</td> <td class="org-left">Z</td>
</tr> </tr>
</tbody> </tbody>
</table> </table>
<table id="org1bf8383" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org6601586" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 3:</span> Description of each measurement channel</caption> <caption class="t-above"><span class="table-number">Table 3:</span> Description of each measurement channel</caption>
<colgroup> <colgroup>
@ -599,63 +363,63 @@ For each of the measurement, the measured channels are shown on table <a href="#
</div> </div>
</div> </div>
<div id="outline-container-orgc59cdd1" class="outline-2"> <div id="outline-container-orgc4e4e05" class="outline-2">
<h2 id="orgc59cdd1"><span class="section-number-2">4</span> Data Analysis</h2> <h2 id="orgc4e4e05"><span class="section-number-2">4</span> Data Analysis</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
</div> </div>
<div id="outline-container-org97ea2b9" class="outline-3"> <div id="outline-container-org8e48582" class="outline-3">
<h3 id="org97ea2b9"><span class="section-number-3">4.1</span> Loading of the data</h3> <h3 id="org8e48582"><span class="section-number-3">4.1</span> Loading of the data</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-4-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/id31_microstation_2017_11_17_coh.mat'</span>,<span class="org-underline">...</span> <pre class="src src-matlab">load(<span class="org-string">'./raw_data/id31_microstation_2017_11_17_coh.mat'</span>,...
<span class="org-string">'coh_hexa_x'</span>,<span class="org-underline">...</span> <span class="org-string">'coh_hexa_x'</span>,...
<span class="org-string">'coh_hexa_y'</span>,<span class="org-underline">...</span> <span class="org-string">'coh_hexa_y'</span>,...
<span class="org-string">'coh_hexa_z'</span>,<span class="org-underline">...</span> <span class="org-string">'coh_hexa_z'</span>,...
<span class="org-string">'coh_marble_x'</span>,<span class="org-underline">...</span> <span class="org-string">'coh_marble_x'</span>,...
<span class="org-string">'coh_marble_y'</span>,<span class="org-underline">...</span> <span class="org-string">'coh_marble_y'</span>,...
<span class="org-string">'coh_marble_z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-string">'coh_marble_z'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/id31_microstation_2017_11_17_frf.mat'</span>,<span class="org-underline">...</span> load(<span class="org-string">'./raw_data/id31_microstation_2017_11_17_frf.mat'</span>,...
<span class="org-string">'freq_frf'</span>,<span class="org-underline">...</span> <span class="org-string">'freq_frf'</span>,...
<span class="org-string">'frf_hexa_x'</span>,<span class="org-underline">...</span> <span class="org-string">'frf_hexa_x'</span>,...
<span class="org-string">'frf_hexa_y'</span>,<span class="org-underline">...</span> <span class="org-string">'frf_hexa_y'</span>,...
<span class="org-string">'frf_hexa_z'</span>,<span class="org-underline">...</span> <span class="org-string">'frf_hexa_z'</span>,...
<span class="org-string">'frf_marble_x'</span>,<span class="org-underline">...</span> <span class="org-string">'frf_marble_x'</span>,...
<span class="org-string">'frf_marble_y'</span>,<span class="org-underline">...</span> <span class="org-string">'frf_marble_y'</span>,...
<span class="org-string">'frf_marble_z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-string">'frf_marble_z'</span>);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org55d35ad" class="outline-3"> <div id="outline-container-orgdef23af" class="outline-3">
<h3 id="org55d35ad"><span class="section-number-3">4.2</span> Pre-processing of the data</h3> <h3 id="orgdef23af"><span class="section-number-3">4.2</span> Pre-processing of the data</h3>
<div class="outline-text-3" id="text-4-2"> <div class="outline-text-3" id="text-4-2">
<p> <p>
The FRF data are scaled with the sensitivity of the accelerometer and integrated two times to have the displacement instead of the acceleration. The FRF data are scaled with the sensitivity of the accelerometer and integrated two times to have the displacement instead of the acceleration.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">accel_sensitivity = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">102</span>; <span class="org-comment">% [V/(m/s2)]</span> <pre class="src src-matlab">accel_sensitivity = 0.102; <span class="org-comment">% [V/(m/s2)]</span>
w = <span class="org-constant">j</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf; <span class="org-comment">% j.omega in [rad/s]</span> w = <span class="org-constant">j</span><span class="org-type">*</span>2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf; <span class="org-comment">% j.omega in [rad/s]</span>
frf_hexa_x = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_hexa_x<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-1">(</span>w<span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; frf_hexa_x = 1<span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_hexa_x<span class="org-type">./</span>(w<span class="org-type">.^</span>2);
frf_hexa_y = <span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_hexa_y<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-1">(</span>w<span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; frf_hexa_y = <span class="org-type">-</span>1<span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_hexa_y<span class="org-type">./</span>(w<span class="org-type">.^</span>2);
frf_hexa_z = <span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_hexa_z<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-1">(</span>w<span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; frf_hexa_z = <span class="org-type">-</span>1<span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_hexa_z<span class="org-type">./</span>(w<span class="org-type">.^</span>2);
frf_marble_x = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_marble_x<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-1">(</span>w<span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; frf_marble_x = 1<span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_marble_x<span class="org-type">./</span>(w<span class="org-type">.^</span>2);
frf_marble_y = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_marble_y<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-1">(</span>w<span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; frf_marble_y = 1<span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_marble_y<span class="org-type">./</span>(w<span class="org-type">.^</span>2);
frf_marble_z = <span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_marble_z<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-1">(</span>w<span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; frf_marble_z = <span class="org-type">-</span>1<span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_marble_z<span class="org-type">./</span>(w<span class="org-type">.^</span>2);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org409f95e" class="outline-3"> <div id="outline-container-org9329022" class="outline-3">
<h3 id="org409f95e"><span class="section-number-3">4.3</span> X-direction FRF</h3> <h3 id="org9329022"><span class="section-number-3">4.3</span> X-direction FRF</h3>
<div class="outline-text-3" id="text-4-3"> <div class="outline-text-3" id="text-4-3">
<div id="org5d69ec3" class="figure"> <div id="orgc62d27f" class="figure">
<p><img src="figs/marble_x_frf.png" alt="marble_x_frf.png" /> <p><img src="figs/marble_x_frf.png" alt="marble_x_frf.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Response to a force applied on the marble in the X direction</p> <p><span class="figure-number">Figure 3: </span>Response to a force applied on the marble in the X direction</p>
@ -663,7 +427,7 @@ frf_marble_z = <span class="org-type">-</span><span class="org-highlight-numbers
<div id="orgf472153" class="figure"> <div id="org6bfc7a4" class="figure">
<p><img src="figs/hexa_x_frf.png" alt="hexa_x_frf.png" /> <p><img src="figs/hexa_x_frf.png" alt="hexa_x_frf.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Response to a force applied on the hexa in the X direction</p> <p><span class="figure-number">Figure 4: </span>Response to a force applied on the hexa in the X direction</p>
@ -671,18 +435,18 @@ frf_marble_z = <span class="org-type">-</span><span class="org-highlight-numbers
</div> </div>
</div> </div>
<div id="outline-container-org5ca4365" class="outline-3"> <div id="outline-container-orgf143ff0" class="outline-3">
<h3 id="org5ca4365"><span class="section-number-3">4.4</span> Y-direction FRF</h3> <h3 id="orgf143ff0"><span class="section-number-3">4.4</span> Y-direction FRF</h3>
<div class="outline-text-3" id="text-4-4"> <div class="outline-text-3" id="text-4-4">
<div id="org8581a20" class="figure"> <div id="org1460e50" class="figure">
<p><img src="figs/marble_y_frf.png" alt="marble_y_frf.png" /> <p><img src="figs/marble_y_frf.png" alt="marble_y_frf.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Response to a force applied on the marble in the Y direction</p> <p><span class="figure-number">Figure 5: </span>Response to a force applied on the marble in the Y direction</p>
</div> </div>
<div id="orgdea2e62" class="figure"> <div id="org50bc3da" class="figure">
<p><img src="figs/hexa_y_frf.png" alt="hexa_y_frf.png" /> <p><img src="figs/hexa_y_frf.png" alt="hexa_y_frf.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Response to a force applied on the hexa in the Y direction</p> <p><span class="figure-number">Figure 6: </span>Response to a force applied on the hexa in the Y direction</p>
@ -690,18 +454,18 @@ frf_marble_z = <span class="org-type">-</span><span class="org-highlight-numbers
</div> </div>
</div> </div>
<div id="outline-container-org491a242" class="outline-3"> <div id="outline-container-org69dd2ae" class="outline-3">
<h3 id="org491a242"><span class="section-number-3">4.5</span> Z-direction FRF</h3> <h3 id="org69dd2ae"><span class="section-number-3">4.5</span> Z-direction FRF</h3>
<div class="outline-text-3" id="text-4-5"> <div class="outline-text-3" id="text-4-5">
<div id="org525b297" class="figure"> <div id="orga24d122" class="figure">
<p><img src="figs/marble_z_frf.png" alt="marble_z_frf.png" /> <p><img src="figs/marble_z_frf.png" alt="marble_z_frf.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Response to a force applied on the marble in the Z direction</p> <p><span class="figure-number">Figure 7: </span>Response to a force applied on the marble in the Z direction</p>
</div> </div>
<div id="orgf376c05" class="figure"> <div id="orge608125" class="figure">
<p><img src="figs/hexa_z_frf.png" alt="hexa_z_frf.png" /> <p><img src="figs/hexa_z_frf.png" alt="hexa_z_frf.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Response to a force applied on the hexa in the Z direction</p> <p><span class="figure-number">Figure 8: </span>Response to a force applied on the hexa in the Z direction</p>
@ -709,10 +473,10 @@ frf_marble_z = <span class="org-type">-</span><span class="org-highlight-numbers
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgf03bfb4" class="outline-2"> <div id="outline-container-orgdfa9254" class="outline-2">
<h2 id="orgf03bfb4"><span class="section-number-2">5</span> Results</h2> <h2 id="orgdfa9254"><span class="section-number-2">5</span> Results</h2>
<div class="outline-text-2" id="text-5"> <div class="outline-text-2" id="text-5">
<div class="important"> <div class="important" id="orgbd89935">
<ul class="org-ul"> <ul class="org-ul">
<li>Resonances have been identified at 45Hz and 75Hz</li> <li>Resonances have been identified at 45Hz and 75Hz</li>
<li>However, the quality of the measurements are bad at low frequency</li> <li>However, the quality of the measurements are bad at low frequency</li>
@ -725,8 +489,7 @@ frf_marble_z = <span class="org-type">-</span><span class="org-highlight-numbers
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-14 mar. 23:06</p> <p class="date">Created: 2020-11-12 jeu. 10:26</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -258,26 +22,26 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org27cbd90">1. Experimental conditions</a></li> <li><a href="#orgf7b0b7a">1. Experimental conditions</a></li>
<li><a href="#orgf2bb684">2. Measurements procedure</a></li> <li><a href="#org01526bf">2. Measurements procedure</a></li>
<li><a href="#org604de72">3. Measurement Channels</a></li> <li><a href="#org5428c6f">3. Measurement Channels</a></li>
<li><a href="#orgee6f009">4. Experiments</a></li> <li><a href="#org083916b">4. Experiments</a></li>
<li><a href="#orgc91528e">5. Data Analysis</a> <li><a href="#orga6855fa">5. Data Analysis</a>
<ul> <ul>
<li><a href="#org64c9d55">5.1. Loading and pre-processing of the data</a></li> <li><a href="#orgf4e2716">5.1. Loading and pre-processing of the data</a></li>
<li><a href="#org528d8bd">5.2. X-direction FRF</a></li> <li><a href="#orged9d5af">5.2. X-direction FRF</a></li>
<li><a href="#orgb043f14">5.3. Y-direction FRF</a></li> <li><a href="#orgc5bca15">5.3. Y-direction FRF</a></li>
<li><a href="#org63f36f4">5.4. Z-direction FRF</a></li> <li><a href="#org281b6fd">5.4. Z-direction FRF</a></li>
<li><a href="#org9fd4cff">5.5. Save the processed data</a></li> <li><a href="#org79b392d">5.5. Save the processed data</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orge5ef1a0">6. Results</a></li> <li><a href="#orgfbc6e27">6. Results</a></li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org27cbd90" class="outline-2"> <div id="outline-container-orgf7b0b7a" class="outline-2">
<h2 id="org27cbd90"><span class="section-number-2">1</span> Experimental conditions</h2> <h2 id="orgf7b0b7a"><span class="section-number-2">1</span> Experimental conditions</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
@ -328,12 +92,12 @@ Obtain better coherence at low frequency.
</div> </div>
</div> </div>
<div id="outline-container-orgf2bb684" class="outline-2"> <div id="outline-container-org01526bf" class="outline-2">
<h2 id="orgf2bb684"><span class="section-number-2">2</span> Measurements procedure</h2> <h2 id="org01526bf"><span class="section-number-2">2</span> Measurements procedure</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<b>Geophones</b> <b>Geophones</b>
L-28LB geophones (table <a href="#org27c9f01">1</a>) are placed on L-28LB geophones (table <a href="#orgef0c0ef">1</a>) are placed on
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Marle</li> <li>Marle</li>
@ -341,7 +105,7 @@ L-28LB geophones (table <a href="#org27c9f01">1</a>) are placed on
<li>Top of Hexapod</li> <li>Top of Hexapod</li>
</ul> </ul>
<table id="org27c9f01" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="orgef0c0ef" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> L-28LB Geophone characteristics</caption> <caption class="t-above"><span class="table-number">Table 1:</span> L-28LB Geophone characteristics</caption>
<colgroup> <colgroup>
@ -377,10 +141,10 @@ The structure is excited using an <b>instrumented hammer</b> with impacts on
</div> </div>
</div> </div>
<div id="outline-container-org604de72" class="outline-2"> <div id="outline-container-org5428c6f" class="outline-2">
<h2 id="org604de72"><span class="section-number-2">3</span> Measurement Channels</h2> <h2 id="org5428c6f"><span class="section-number-2">3</span> Measurement Channels</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<table id="org98c14df" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org2f154cd" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Description of each measurement channel</caption> <caption class="t-above"><span class="table-number">Table 2:</span> Description of each measurement channel</caption>
<colgroup> <colgroup>
@ -434,10 +198,10 @@ The structure is excited using an <b>instrumented hammer</b> with impacts on
</div> </div>
</div> </div>
<div id="outline-container-orgee6f009" class="outline-2"> <div id="outline-container-org083916b" class="outline-2">
<h2 id="orgee6f009"><span class="section-number-2">4</span> Experiments</h2> <h2 id="org083916b"><span class="section-number-2">4</span> Experiments</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
<table id="orgd57c63a" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org1021f8b" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 3:</span> Description of the location of direction of the excitation for each measurement</caption> <caption class="t-above"><span class="table-number">Table 3:</span> Description of the location of direction of the excitation for each measurement</caption>
<colgroup> <colgroup>
@ -497,21 +261,21 @@ The structure is excited using an <b>instrumented hammer</b> with impacts on
</div> </div>
</div> </div>
<div id="outline-container-orgc91528e" class="outline-2"> <div id="outline-container-orga6855fa" class="outline-2">
<h2 id="orgc91528e"><span class="section-number-2">5</span> Data Analysis</h2> <h2 id="orga6855fa"><span class="section-number-2">5</span> Data Analysis</h2>
<div class="outline-text-2" id="text-5"> <div class="outline-text-2" id="text-5">
</div> </div>
<div id="outline-container-org64c9d55" class="outline-3"> <div id="outline-container-orgf4e2716" class="outline-3">
<h3 id="org64c9d55"><span class="section-number-3">5.1</span> Loading and pre-processing of the data</h3> <h3 id="orgf4e2716"><span class="section-number-3">5.1</span> Loading and pre-processing of the data</h3>
<div class="outline-text-3" id="text-5-1"> <div class="outline-text-3" id="text-5-1">
<p> <p>
The Geophone sensitivity is defined below: The Geophone sensitivity is defined below:
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">w0 = <span class="org-highlight-numbers-number">4</span>.<span class="org-highlight-numbers-number">5</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% [rad/s]</span> <pre class="src src-matlab">w0 = 4.5<span class="org-type">*</span>2<span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% [rad/s]</span>
ksi = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">38</span>; ksi = 0.38;
G0 = <span class="org-highlight-numbers-number">31</span>.<span class="org-highlight-numbers-number">3</span>; <span class="org-comment">% [V/(m/s)]</span> G0 = 31.3; <span class="org-comment">% [V/(m/s)]</span>
G = G0<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type">/</span>w0<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span>s<span class="org-type">/</span>w0<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span> <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>ksi<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>s<span class="org-type">/</span>w0<span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">+</span> <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% [V/(m/s)]</span> G = G0<span class="org-type">*</span>(s<span class="org-type">/</span>w0)<span class="org-type">^</span>2<span class="org-type">/</span>((s<span class="org-type">/</span>w0)<span class="org-type">^</span>2 <span class="org-type">+</span> 2<span class="org-type">*</span>ksi<span class="org-type">*</span>(s<span class="org-type">/</span>w0) <span class="org-type">+</span> 1); <span class="org-comment">% [V/(m/s)]</span>
</pre> </pre>
</div> </div>
@ -525,96 +289,96 @@ We then:
<li>scaled with the sensitivity of the Geophone</li> <li>scaled with the sensitivity of the Geophone</li>
</ul> </ul>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/freq_frf.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% freq_frf</span> <pre class="src src-matlab">load(<span class="org-string">'./raw_data/freq_frf.mat'</span>) <span class="org-comment">% freq_frf</span>
w = <span class="org-constant">j</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf; <span class="org-comment">% j.omega in [rad/s]</span> w = <span class="org-constant">j</span><span class="org-type">*</span>2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf; <span class="org-comment">% j.omega in [rad/s]</span>
scaling = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>freqresp<span class="org-rainbow-delimiters-depth-2">(</span>G, <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span>G0; scaling = squeeze(freqresp(G, 2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf))<span class="org-type">/</span>G0;
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/frf_marble_x.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% ReIm1</span> load(<span class="org-string">'./raw_data/frf_marble_x.mat'</span>) <span class="org-comment">% ReIm1</span>
frf_marble_x = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>ReIm1, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; frf_marble_x = zeros(size(ReIm1, 1), 3);
frf_marble_x<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>ReIm1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% marble_x</span> frf_marble_x(<span class="org-type">:</span>, 1) = <span class="org-type">-</span>ReIm1(<span class="org-type">:</span>, 2)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% marble_x</span>
frf_marble_x<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>ReIm1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% tilt_x</span> frf_marble_x(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>ReIm1(<span class="org-type">:</span>, 3)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% tilt_x</span>
frf_marble_x<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>ReIm1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% hexa_x</span> frf_marble_x(<span class="org-type">:</span>, 3) = <span class="org-type">-</span>ReIm1(<span class="org-type">:</span>, 4)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% hexa_x</span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/frf_hexa_x.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% ReIm2</span> load(<span class="org-string">'./raw_data/frf_hexa_x.mat'</span>) <span class="org-comment">% ReIm2</span>
frf_hexa_x = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>ReIm2, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; frf_hexa_x = zeros(size(ReIm2, 1), 3);
frf_hexa_x<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>ReIm2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% marble_x</span> frf_hexa_x(<span class="org-type">:</span>, 1) = <span class="org-type">-</span>ReIm2(<span class="org-type">:</span>, 2)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% marble_x</span>
frf_hexa_x<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>ReIm2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% tilt_x</span> frf_hexa_x(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>ReIm2(<span class="org-type">:</span>, 3)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% tilt_x</span>
frf_hexa_x<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>ReIm2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% hexa_x</span> frf_hexa_x(<span class="org-type">:</span>, 3) = <span class="org-type">-</span>ReIm2(<span class="org-type">:</span>, 4)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% hexa_x</span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/frf_marble_y.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% ReIm3</span> load(<span class="org-string">'./raw_data/frf_marble_y.mat'</span>) <span class="org-comment">% ReIm3</span>
frf_marble_y = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>ReIm3, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; frf_marble_y = zeros(size(ReIm3, 1), 3);
frf_marble_y<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>ReIm3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% marble_y</span> frf_marble_y(<span class="org-type">:</span>, 1) = <span class="org-type">-</span>ReIm3(<span class="org-type">:</span>, 2)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% marble_y</span>
frf_marble_y<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>ReIm3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% tilt_y</span> frf_marble_y(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>ReIm3(<span class="org-type">:</span>, 3)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% tilt_y</span>
frf_marble_y<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>ReIm3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% hexa_y</span> frf_marble_y(<span class="org-type">:</span>, 3) = <span class="org-type">-</span>ReIm3(<span class="org-type">:</span>, 4)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% hexa_y</span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/frf_hexa_y.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% ReIm4</span> load(<span class="org-string">'./raw_data/frf_hexa_y.mat'</span>) <span class="org-comment">% ReIm4</span>
frf_hexa_y = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>ReIm4, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; frf_hexa_y = zeros(size(ReIm4, 1), 3);
frf_hexa_y<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = ReIm4<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% marble_y</span> frf_hexa_y(<span class="org-type">:</span>, 1) = ReIm4(<span class="org-type">:</span>, 2)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% marble_y</span>
frf_hexa_y<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = ReIm4<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% tilt_y</span> frf_hexa_y(<span class="org-type">:</span>, 2) = ReIm4(<span class="org-type">:</span>, 3)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% tilt_y</span>
frf_hexa_y<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = ReIm4<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% hexa_y</span> frf_hexa_y(<span class="org-type">:</span>, 3) = ReIm4(<span class="org-type">:</span>, 4)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% hexa_y</span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/frf_marble_z.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% ReIm5</span> load(<span class="org-string">'./raw_data/frf_marble_z.mat'</span>) <span class="org-comment">% ReIm5</span>
frf_marble_z = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>ReIm5, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; frf_marble_z = zeros(size(ReIm5, 1), 3);
frf_marble_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = ReIm5<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% marble_z</span> frf_marble_z(<span class="org-type">:</span>, 1) = ReIm5(<span class="org-type">:</span>, 2)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% marble_z</span>
frf_marble_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = ReIm5<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% tilt_z</span> frf_marble_z(<span class="org-type">:</span>, 2) = ReIm5(<span class="org-type">:</span>, 3)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% tilt_z</span>
frf_marble_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = ReIm5<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% hexa_z</span> frf_marble_z(<span class="org-type">:</span>, 3) = ReIm5(<span class="org-type">:</span>, 4)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% hexa_z</span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/frf_hexa_z.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% ReIm6</span> load(<span class="org-string">'./raw_data/frf_hexa_z.mat'</span>) <span class="org-comment">% ReIm6</span>
frf_hexa_z = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>ReIm6, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; frf_hexa_z = zeros(size(ReIm6, 1), 3);
frf_hexa_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = ReIm6<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% marble_z</span> frf_hexa_z(<span class="org-type">:</span>, 1) = ReIm6(<span class="org-type">:</span>, 2)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% marble_z</span>
frf_hexa_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = ReIm6<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% tilt_z</span> frf_hexa_z(<span class="org-type">:</span>, 2) = ReIm6(<span class="org-type">:</span>, 3)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% tilt_z</span>
frf_hexa_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = ReIm6<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% hexa_z</span> frf_hexa_z(<span class="org-type">:</span>, 3) = ReIm6(<span class="org-type">:</span>, 4)<span class="org-type">./</span>w<span class="org-type">./</span>scaling; <span class="org-comment">% hexa_z</span>
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/coher_marble_x.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% coh1</span> <pre class="src src-matlab">load(<span class="org-string">'./raw_data/coher_marble_x.mat'</span>) <span class="org-comment">% coh1</span>
coh_marble_x = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>coh1, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; coh_marble_x = zeros(size(coh1, 1), 3);
coh_marble_x<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% marble_x</span> coh_marble_x(<span class="org-type">:</span>, 1) = coh1(<span class="org-type">:</span>, 2); <span class="org-comment">% marble_x</span>
coh_marble_x<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% tilt_x</span> coh_marble_x(<span class="org-type">:</span>, 2) = coh1(<span class="org-type">:</span>, 3); <span class="org-comment">% tilt_x</span>
coh_marble_x<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% hexa_x</span> coh_marble_x(<span class="org-type">:</span>, 3) = coh1(<span class="org-type">:</span>, 4); <span class="org-comment">% hexa_x</span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/coher_hexa_x.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% coh2</span> load(<span class="org-string">'./raw_data/coher_hexa_x.mat'</span>) <span class="org-comment">% coh2</span>
coh_hexa_x = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>coh2, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; coh_hexa_x = zeros(size(coh2, 1), 3);
coh_hexa_x<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% marble_x</span> coh_hexa_x(<span class="org-type">:</span>, 1) = coh2(<span class="org-type">:</span>, 2); <span class="org-comment">% marble_x</span>
coh_hexa_x<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% tilt_x</span> coh_hexa_x(<span class="org-type">:</span>, 2) = coh2(<span class="org-type">:</span>, 3); <span class="org-comment">% tilt_x</span>
coh_hexa_x<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% hexa_x</span> coh_hexa_x(<span class="org-type">:</span>, 3) = coh2(<span class="org-type">:</span>, 4); <span class="org-comment">% hexa_x</span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/coher_marble_y.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% coh3</span> load(<span class="org-string">'./raw_data/coher_marble_y.mat'</span>) <span class="org-comment">% coh3</span>
coh_marble_y = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>coh3, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; coh_marble_y = zeros(size(coh3, 1), 3);
coh_marble_y<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% marble_y</span> coh_marble_y(<span class="org-type">:</span>, 1) = coh3(<span class="org-type">:</span>, 2); <span class="org-comment">% marble_y</span>
coh_marble_y<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% tilt_y</span> coh_marble_y(<span class="org-type">:</span>, 2) = coh3(<span class="org-type">:</span>, 3); <span class="org-comment">% tilt_y</span>
coh_marble_y<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% hexa_y</span> coh_marble_y(<span class="org-type">:</span>, 3) = coh3(<span class="org-type">:</span>, 4); <span class="org-comment">% hexa_y</span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/coher_hexa_y.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% coh4</span> load(<span class="org-string">'./raw_data/coher_hexa_y.mat'</span>) <span class="org-comment">% coh4</span>
coh_hexa_y = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>coh4, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; coh_hexa_y = zeros(size(coh4, 1), 3);
coh_hexa_y<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh4<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% marble_y</span> coh_hexa_y(<span class="org-type">:</span>, 1) = coh4(<span class="org-type">:</span>, 2); <span class="org-comment">% marble_y</span>
coh_hexa_y<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh4<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% tilt_y</span> coh_hexa_y(<span class="org-type">:</span>, 2) = coh4(<span class="org-type">:</span>, 3); <span class="org-comment">% tilt_y</span>
coh_hexa_y<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh4<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% hexa_y</span> coh_hexa_y(<span class="org-type">:</span>, 3) = coh4(<span class="org-type">:</span>, 4); <span class="org-comment">% hexa_y</span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/coher_marble_z.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% coh5</span> load(<span class="org-string">'./raw_data/coher_marble_z.mat'</span>) <span class="org-comment">% coh5</span>
coh_marble_z = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>coh5, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; coh_marble_z = zeros(size(coh5, 1), 3);
coh_marble_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh5<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% marble_z</span> coh_marble_z(<span class="org-type">:</span>, 1) = coh5(<span class="org-type">:</span>, 2); <span class="org-comment">% marble_z</span>
coh_marble_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh5<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% tilt_z</span> coh_marble_z(<span class="org-type">:</span>, 2) = coh5(<span class="org-type">:</span>, 3); <span class="org-comment">% tilt_z</span>
coh_marble_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh5<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% hexa_z</span> coh_marble_z(<span class="org-type">:</span>, 3) = coh5(<span class="org-type">:</span>, 4); <span class="org-comment">% hexa_z</span>
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/coher_hexa_z.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-comment">% coh6</span> load(<span class="org-string">'./raw_data/coher_hexa_z.mat'</span>) <span class="org-comment">% coh6</span>
coh_hexa_z = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>coh6, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; coh_hexa_z = zeros(size(coh6, 1), 3);
coh_hexa_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh6<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% marble_z</span> coh_hexa_z(<span class="org-type">:</span>, 1) = coh6(<span class="org-type">:</span>, 2); <span class="org-comment">% marble_z</span>
coh_hexa_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh6<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% tilt_z</span> coh_hexa_z(<span class="org-type">:</span>, 2) = coh6(<span class="org-type">:</span>, 3); <span class="org-comment">% tilt_z</span>
coh_hexa_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = coh6<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% hexa_z</span> coh_hexa_z(<span class="org-type">:</span>, 3) = coh6(<span class="org-type">:</span>, 4); <span class="org-comment">% hexa_z</span>
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org528d8bd" class="outline-3"> <div id="outline-container-orged9d5af" class="outline-3">
<h3 id="org528d8bd"><span class="section-number-3">5.2</span> X-direction FRF</h3> <h3 id="orged9d5af"><span class="section-number-3">5.2</span> X-direction FRF</h3>
<div class="outline-text-3" id="text-5-2"> <div class="outline-text-3" id="text-5-2">
<div id="orgbe46711" class="figure"> <div id="orge7f979c" class="figure">
<p><img src="figs/marble_x_frf.png" alt="marble_x_frf.png" /> <p><img src="figs/marble_x_frf.png" alt="marble_x_frf.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Response to a force applied on the marble in the X direction</p> <p><span class="figure-number">Figure 1: </span>Response to a force applied on the marble in the X direction</p>
@ -622,7 +386,7 @@ coh_hexa_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-
<div id="org4005c39" class="figure"> <div id="orgaa49b69" class="figure">
<p><img src="figs/hexa_x_frf.png" alt="hexa_x_frf.png" /> <p><img src="figs/hexa_x_frf.png" alt="hexa_x_frf.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Response to a force applied on the hexa in the X direction</p> <p><span class="figure-number">Figure 2: </span>Response to a force applied on the hexa in the X direction</p>
@ -630,18 +394,18 @@ coh_hexa_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-
</div> </div>
</div> </div>
<div id="outline-container-orgb043f14" class="outline-3"> <div id="outline-container-orgc5bca15" class="outline-3">
<h3 id="orgb043f14"><span class="section-number-3">5.3</span> Y-direction FRF</h3> <h3 id="orgc5bca15"><span class="section-number-3">5.3</span> Y-direction FRF</h3>
<div class="outline-text-3" id="text-5-3"> <div class="outline-text-3" id="text-5-3">
<div id="org959d073" class="figure"> <div id="orgb8bc82d" class="figure">
<p><img src="figs/marble_y_frf.png" alt="marble_y_frf.png" /> <p><img src="figs/marble_y_frf.png" alt="marble_y_frf.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Response to a force applied on the marble in the Y direction</p> <p><span class="figure-number">Figure 3: </span>Response to a force applied on the marble in the Y direction</p>
</div> </div>
<div id="orge15a0ff" class="figure"> <div id="orgab0bae7" class="figure">
<p><img src="figs/hexa_y_frf.png" alt="hexa_y_frf.png" /> <p><img src="figs/hexa_y_frf.png" alt="hexa_y_frf.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Response to a force applied on the hexa in the Y direction</p> <p><span class="figure-number">Figure 4: </span>Response to a force applied on the hexa in the Y direction</p>
@ -649,56 +413,56 @@ coh_hexa_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-
</div> </div>
</div> </div>
<div id="outline-container-org63f36f4" class="outline-3"> <div id="outline-container-org281b6fd" class="outline-3">
<h3 id="org63f36f4"><span class="section-number-3">5.4</span> Z-direction FRF</h3> <h3 id="org281b6fd"><span class="section-number-3">5.4</span> Z-direction FRF</h3>
<div class="outline-text-3" id="text-5-4"> <div class="outline-text-3" id="text-5-4">
<div id="orgf2ca329" class="figure"> <div id="orgfeeae0c" class="figure">
<p><img src="figs/marble_z_frf.png" alt="marble_z_frf.png" /> <p><img src="figs/marble_z_frf.png" alt="marble_z_frf.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Response to a force applied on the marble in the Z direction</p> <p><span class="figure-number">Figure 5: </span>Response to a force applied on the marble in the Z direction</p>
</div> </div>
<div id="orgbb33b62" class="figure"> <div id="org1d0823f" class="figure">
<p><img src="figs/hexa_z_frf.png" alt="hexa_z_frf.png" /> <p><img src="figs/hexa_z_frf.png" alt="hexa_z_frf.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Response to a force applied on the hexa in the Z direction</p> <p><span class="figure-number">Figure 6: </span>Response to a force applied on the hexa in the Z direction</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org9fd4cff" class="outline-3"> <div id="outline-container-org79b392d" class="outline-3">
<h3 id="org9fd4cff"><span class="section-number-3">5.5</span> Save the processed data</h3> <h3 id="org79b392d"><span class="section-number-3">5.5</span> Save the processed data</h3>
<div class="outline-text-3" id="text-5-5"> <div class="outline-text-3" id="text-5-5">
<p> <p>
Finally, we save the processed data. Finally, we save the processed data.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/id31_microstation_2018_01_12_frf.mat'</span>, <span class="org-underline">...</span> <pre class="src src-matlab">save(<span class="org-string">'./data/id31_microstation_2018_01_12_frf.mat'</span>, ...
<span class="org-string">'freq_frf'</span>, <span class="org-underline">...</span> <span class="org-string">'freq_frf'</span>, ...
<span class="org-string">'frf_marble_x'</span>, <span class="org-underline">...</span> <span class="org-string">'frf_marble_x'</span>, ...
<span class="org-string">'frf_marble_y'</span>, <span class="org-underline">...</span> <span class="org-string">'frf_marble_y'</span>, ...
<span class="org-string">'frf_marble_z'</span>, <span class="org-underline">...</span> <span class="org-string">'frf_marble_z'</span>, ...
<span class="org-string">'frf_hexa_x'</span>, <span class="org-underline">...</span> <span class="org-string">'frf_hexa_x'</span>, ...
<span class="org-string">'frf_hexa_y'</span>, <span class="org-underline">...</span> <span class="org-string">'frf_hexa_y'</span>, ...
<span class="org-string">'frf_hexa_z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-string">'frf_hexa_z'</span>);
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/id31_microstation_2018_01_12_coh.mat'</span>, <span class="org-underline">...</span> save(<span class="org-string">'./data/id31_microstation_2018_01_12_coh.mat'</span>, ...
<span class="org-string">'freq_frf'</span>, <span class="org-underline">...</span> <span class="org-string">'freq_frf'</span>, ...
<span class="org-string">'coh_marble_x'</span>, <span class="org-underline">...</span> <span class="org-string">'coh_marble_x'</span>, ...
<span class="org-string">'coh_marble_y'</span>, <span class="org-underline">...</span> <span class="org-string">'coh_marble_y'</span>, ...
<span class="org-string">'coh_marble_z'</span>, <span class="org-underline">...</span> <span class="org-string">'coh_marble_z'</span>, ...
<span class="org-string">'coh_hexa_x'</span>, <span class="org-underline">...</span> <span class="org-string">'coh_hexa_x'</span>, ...
<span class="org-string">'coh_hexa_y'</span>, <span class="org-underline">...</span> <span class="org-string">'coh_hexa_y'</span>, ...
<span class="org-string">'coh_hexa_z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-string">'coh_hexa_z'</span>);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orge5ef1a0" class="outline-2"> <div id="outline-container-orgfbc6e27" class="outline-2">
<h2 id="orge5ef1a0"><span class="section-number-2">6</span> Results</h2> <h2 id="orgfbc6e27"><span class="section-number-2">6</span> Results</h2>
<div class="outline-text-2" id="text-6"> <div class="outline-text-2" id="text-6">
<div class="important"> <div class="important" id="orgbc7d1c6">
<ul class="org-ul"> <ul class="org-ul">
<li>Resonances at 42Hz, 70Hz and 125Hz have been identified</li> <li>Resonances at 42Hz, 70Hz and 125Hz have been identified</li>
<li>The coherence is much better than when using accelerometers</li> <li>The coherence is much better than when using accelerometers</li>
@ -710,8 +474,7 @@ save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-14 mar. 23:06</p> <p class="date">Created: 2020-11-12 jeu. 10:26</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>
</html> </html>

9
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@ -9,13 +9,8 @@
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371
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@ -3,249 +3,13 @@
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -258,21 +22,22 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orga941937">1. Experimental conditions</a></li> <li><a href="#org4a44203">1. Experimental conditions</a></li>
<li><a href="#org0a36397">2. Measurements procedure</a></li> <li><a href="#org91fa62d">2. Measurements procedure</a></li>
<li><a href="#org9c8604e">3. Measurement Channels</a></li> <li><a href="#org015e1bd">3. Measurement Channels</a></li>
<li><a href="#org3ee1fb7">4. Experiments</a></li> <li><a href="#org807ceb5">4. Experiments</a></li>
<li><a href="#orgaf6691c">5. Data Analysis</a> <li><a href="#org3f0d1ab">5. Data Analysis</a>
<ul> <ul>
<li><a href="#orge954440">5.1. Loading of the data</a></li> <li><a href="#org589082c">5.1. Loading of the data</a></li>
<li><a href="#org48f106f">5.2. test</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orga941937" class="outline-2"> <div id="outline-container-org4a44203" class="outline-2">
<h2 id="orga941937"><span class="section-number-2">1</span> Experimental conditions</h2> <h2 id="org4a44203"><span class="section-number-2">1</span> Experimental conditions</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<ul class="org-ul"> <ul class="org-ul">
<li>Measurement made in the experiment hutch</li> <li>Measurement made in the experiment hutch</li>
@ -321,18 +86,18 @@ for the JavaScript code in this tag.
</div> </div>
</div> </div>
<div id="outline-container-org0a36397" class="outline-2"> <div id="outline-container-org91fa62d" class="outline-2">
<h2 id="org0a36397"><span class="section-number-2">2</span> Measurements procedure</h2> <h2 id="org91fa62d"><span class="section-number-2">2</span> Measurements procedure</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
8 <b>Geophone</b> are used (see table <a href="#org84ab1ff">3</a>): 8 <b>Geophone</b> are used (see table <a href="#org0f49883">3</a>):
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>7 L-28LB geophones (table <a href="#org4eafe61">1</a>)</li> <li>7 L-28LB geophones (table <a href="#org42d983e">1</a>)</li>
<li>1 L-4C geophone (table <a href="#org1f04e75">2</a>)</li> <li>1 L-4C geophone (table <a href="#orge7d5d0f">2</a>)</li>
</ul> </ul>
<table id="org4eafe61" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org42d983e" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> L-28LB Geophone characteristics</caption> <caption class="t-above"><span class="table-number">Table 1:</span> L-28LB Geophone characteristics</caption>
<colgroup> <colgroup>
@ -358,7 +123,7 @@ for the JavaScript code in this tag.
</tbody> </tbody>
</table> </table>
<table id="org1f04e75" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="orge7d5d0f" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> L-4C Geophone characteristics</caption> <caption class="t-above"><span class="table-number">Table 2:</span> L-4C Geophone characteristics</caption>
<colgroup> <colgroup>
@ -385,7 +150,7 @@ for the JavaScript code in this tag.
</table> </table>
<p> <p>
The structure is excited using an <b>instrumented hammer</b> with impacts on (see table <a href="#orgd034fab">4</a>): The structure is excited using an <b>instrumented hammer</b> with impacts on (see table <a href="#orgb99d784">4</a>):
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Marble</li> <li>Marble</li>
@ -395,14 +160,14 @@ The structure is excited using an <b>instrumented hammer</b> with impacts on (se
</div> </div>
</div> </div>
<div id="outline-container-org9c8604e" class="outline-2"> <div id="outline-container-org015e1bd" class="outline-2">
<h2 id="org9c8604e"><span class="section-number-2">3</span> Measurement Channels</h2> <h2 id="org015e1bd"><span class="section-number-2">3</span> Measurement Channels</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
Les fichiers xxx<sub>raw</sub> sont sans traitement dans le domaine temporel (environ 10 impacts par fichier) Les fichiers xxx_raw sont sans traitement dans le domaine temporel (environ 10 impacts par fichier)
</p> </p>
<table id="org84ab1ff" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org0f49883" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 3:</span> Description of each measurement channel</caption> <caption class="t-above"><span class="table-number">Table 3:</span> Description of each measurement channel</caption>
<colgroup> <colgroup>
@ -491,10 +256,10 @@ Les fichiers xxx<sub>raw</sub> sont sans traitement dans le domaine temporel (en
</div> </div>
</div> </div>
<div id="outline-container-org3ee1fb7" class="outline-2"> <div id="outline-container-org807ceb5" class="outline-2">
<h2 id="org3ee1fb7"><span class="section-number-2">4</span> Experiments</h2> <h2 id="org807ceb5"><span class="section-number-2">4</span> Experiments</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
<table id="orgd034fab" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="orgb99d784" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 4:</span> Description of the location of direction of the excitation for each measurement</caption> <caption class="t-above"><span class="table-number">Table 4:</span> Description of the location of direction of the excitation for each measurement</caption>
<colgroup> <colgroup>
@ -572,39 +337,72 @@ Les fichiers xxx<sub>raw</sub> sont sans traitement dans le domaine temporel (en
</div> </div>
</div> </div>
<div id="outline-container-orgaf6691c" class="outline-2"> <div id="outline-container-org3f0d1ab" class="outline-2">
<h2 id="orgaf6691c"><span class="section-number-2">5</span> Data Analysis</h2> <h2 id="org3f0d1ab"><span class="section-number-2">5</span> Data Analysis</h2>
<div class="outline-text-2" id="text-5"> <div class="outline-text-2" id="text-5">
</div> </div>
<div id="outline-container-orge954440" class="outline-3"> <div id="outline-container-org589082c" class="outline-3">
<h3 id="orge954440"><span class="section-number-3">5.1</span> Loading of the data</h3> <h3 id="org589082c"><span class="section-number-3">5.1</span> Loading of the data</h3>
<div class="outline-text-3" id="text-5-1"> <div class="outline-text-3" id="text-5-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/freq_frf.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">load(<span class="org-string">'./data/freq_frf.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/frf_hexa_x.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/frf_hexa_x.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/frf_hexa_y.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/frf_hexa_y.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/frf_hexa_z.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/frf_hexa_z.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/frf_marble_x.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/frf_marble_x.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/frf_marble_y.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/frf_marble_y.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/frf_marble_z.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/frf_marble_z.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/frf_ty_x.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/frf_ty_x.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/frf_ty_y.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/frf_ty_y.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/frf_ty_z.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/frf_ty_z.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/phs_hexa_x.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/phs_hexa_x.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/phs_hexa_y.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/phs_hexa_y.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/phs_hexa_z.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/phs_hexa_z.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/phs_marble_x.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/phs_marble_x.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/phs_marble_y.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/phs_marble_y.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/phs_marble_z.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/phs_marble_z.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/phs_ty_x.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/phs_ty_x.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/phs_ty_y.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/phs_ty_y.mat'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./data/phs_ty_z.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'./data/phs_ty_z.mat'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-org48f106f" class="outline-3">
<h3 id="org48f106f"><span class="section-number-3">5.2</span> test</h3>
<div class="outline-text-3" id="text-5-2">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot(freq_frf, abs(ReIm7(<span class="org-type">:</span>, 5))<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble'</span>)
plot(freq_frf, abs(ReIm8(<span class="org-type">:</span>, 6))<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty'</span>)
<span class="org-comment">% plot(freq_frf, abs(ReIm5(:, 3))./(2*pi*freq_frf), 'DisplayName', 'Tilt')</span>
plot(freq_frf, abs(ReIm9(<span class="org-type">:</span>, 8))<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexapod'</span>)
hold off;
xlim([1, 100]);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
legend(<span class="org-string">'location'</span>, <span class="org-string">'northwest'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot(freq_frf, abs(ReIm5(<span class="org-type">:</span>, 1))<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble'</span>)
plot(freq_frf, abs(ReIm5(<span class="org-type">:</span>, 2))<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty'</span>)
plot(freq_frf, abs(ReIm5(<span class="org-type">:</span>, 3))<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Tilt'</span>)
plot(freq_frf, abs(ReIm5(<span class="org-type">:</span>, 4))<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexapod'</span>)
hold off;
xlim([1, 100]);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
legend(<span class="org-string">'location'</span>, <span class="org-string">'northwest'</span>);
</pre> </pre>
</div> </div>
</div> </div>
@ -613,8 +411,7 @@ load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-14 mar. 23:06</p> <p class="date">Created: 2020-11-12 jeu. 10:27</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>
</html> </html>

9
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@ -9,13 +9,8 @@
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ../index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/> #+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="../js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
#+HTML_MATHJAX: align: center tagside: right font: TeX #+HTML_MATHJAX: align: center tagside: right font: TeX

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#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ../index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/> #+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="../js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
#+HTML_MATHJAX: align: center tagside: right font: TeX #+HTML_MATHJAX: align: center tagside: right font: TeX

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#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ../index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/> #+HTML_HEAD: <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Effect on the control system of each stages on the vibration of the station</title> <title>Effect on the control system of each stages on the vibration of the station</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
<meta name="author" content="Dehaeze Thomas" /> <meta name="author" content="Dehaeze Thomas" />
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<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -28,46 +22,46 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org51d7a3e">1. Effect of all the control systems on the Sample vibrations</a> <li><a href="#org90c65f2">1. Effect of all the control systems on the Sample vibrations</a>
<ul> <ul>
<li><a href="#org053d9fe">1.1. Experimental Setup</a></li> <li><a href="#org440b68a">1.1. Experimental Setup</a></li>
<li><a href="#orgcb36bc1">1.2. Load data</a></li> <li><a href="#orgd930ba3">1.2. Load data</a></li>
<li><a href="#org5895a96">1.3. Analysis - Time Domain</a></li> <li><a href="#orgaf61ea2">1.3. Analysis - Time Domain</a></li>
<li><a href="#org390bba0">1.4. Analysis - Frequency Domain</a> <li><a href="#org3f46904">1.4. Analysis - Frequency Domain</a>
<ul> <ul>
<li><a href="#org3a4a488">1.4.1. Vibrations at the sample location</a></li> <li><a href="#org6cda42c">1.4.1. Vibrations at the sample location</a></li>
<li><a href="#org49d7279">1.4.2. Vibrations on the marble</a></li> <li><a href="#orga943462">1.4.2. Vibrations on the marble</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org9b2f5fd">1.5. Conclusion</a></li> <li><a href="#orgeca50d8">1.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org4eafed3">2. Effect of all the control systems on the Sample vibrations - One stage at a time</a> <li><a href="#org1592cd8">2. Effect of all the control systems on the Sample vibrations - One stage at a time</a>
<ul> <ul>
<li><a href="#org4addbe8">2.1. Experimental Setup</a></li> <li><a href="#orgf7f587e">2.1. Experimental Setup</a></li>
<li><a href="#orgb60aa2f">2.2. Load data</a></li> <li><a href="#org3554496">2.2. Load data</a></li>
<li><a href="#org68831ee">2.3. Voltage to Velocity</a></li> <li><a href="#org5b2dc21">2.3. Voltage to Velocity</a></li>
<li><a href="#orgbbb370a">2.4. Analysis - Time Domain</a></li> <li><a href="#orga044f95">2.4. Analysis - Time Domain</a></li>
<li><a href="#orgd436876">2.5. Analysis - Frequency Domain</a> <li><a href="#org2132360">2.5. Analysis - Frequency Domain</a>
<ul> <ul>
<li><a href="#org2e1f962">2.5.1. Vibrations at the sample location</a></li> <li><a href="#orgf096039">2.5.1. Vibrations at the sample location</a></li>
<li><a href="#org8f33a44">2.5.2. Vibrations on the marble</a></li> <li><a href="#org2457465">2.5.2. Vibrations on the marble</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org381e6c2">2.6. Conclusion</a></li> <li><a href="#org2a3582c">2.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgce5eef9">3. Effect of the Symetrie Driver</a> <li><a href="#org8e41411">3. Effect of the Symetrie Driver</a>
<ul> <ul>
<li><a href="#org6e62fbe">3.1. Experimental Setup</a></li> <li><a href="#org2c71144">3.1. Experimental Setup</a></li>
<li><a href="#orgd0c4704">3.2. Load data</a></li> <li><a href="#org86d2cac">3.2. Load data</a></li>
<li><a href="#org30686ba">3.3. Analysis - Time Domain</a></li> <li><a href="#org8866dd0">3.3. Analysis - Time Domain</a></li>
<li><a href="#orgd922ea4">3.4. Analysis - Frequency Domain</a> <li><a href="#org42b0b80">3.4. Analysis - Frequency Domain</a>
<ul> <ul>
<li><a href="#orgd49e7c3">3.4.1. Vibrations at the sample location</a></li> <li><a href="#org327f014">3.4.1. Vibrations at the sample location</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org031a084">3.5. Conclusion</a></li> <li><a href="#org19a7dad">3.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -78,29 +72,29 @@
This file is organized as follow: This file is organized as follow:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Section <a href="#org3b0d32c">1</a>: <li>Section <a href="#orgf43e1ad">1</a>:
<ul class="org-ul"> <ul class="org-ul">
<li>One geophone on the marble and one at the sample location</li> <li>One geophone on the marble and one at the sample location</li>
<li>Each stage is turned on one by one</li> <li>Each stage is turned on one by one</li>
</ul></li> </ul></li>
<li>Section <a href="#org757823f">2</a>: <li>Section <a href="#org2896ac0">2</a>:
<ul class="org-ul"> <ul class="org-ul">
<li>One geophone on the marble and one at the sample location</li> <li>One geophone on the marble and one at the sample location</li>
<li>Each stage is turned on one at a time</li> <li>Each stage is turned on one at a time</li>
</ul></li> </ul></li>
<li>Section <a href="#orgd9c378b">3</a>: <li>Section <a href="#org01c82bb">3</a>:
<ul class="org-ul"> <ul class="org-ul">
<li>We check if the Symetrie driver induces some vibrations when placed on the marble</li> <li>We check if the Symetrie driver induces some vibrations when placed on the marble</li>
</ul></li> </ul></li>
</ul> </ul>
<div id="outline-container-org51d7a3e" class="outline-2"> <div id="outline-container-org90c65f2" class="outline-2">
<h2 id="org51d7a3e"><span class="section-number-2">1</span> Effect of all the control systems on the Sample vibrations</h2> <h2 id="org90c65f2"><span class="section-number-2">1</span> Effect of all the control systems on the Sample vibrations</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<a id="org3b0d32c"></a> <a id="orgf43e1ad"></a>
</p> </p>
<div class="note"> <div class="note" id="org09dadc9">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/effect_control_all.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/effect_control_all.zip">here</a>.
</p> </p>
@ -108,8 +102,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/effect_cont
</div> </div>
</div> </div>
<div id="outline-container-org053d9fe" class="outline-3"> <div id="outline-container-org440b68a" class="outline-3">
<h3 id="org053d9fe"><span class="section-number-3">1.1</span> Experimental Setup</h3> <h3 id="org440b68a"><span class="section-number-3">1.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
We here measure the signals of two L22 geophones: We here measure the signals of two L22 geophones:
@ -137,7 +131,7 @@ First, all the control systems are turned ON, then, they are turned one by one.
Each measurement are done during 50s. Each measurement are done during 50s.
</p> </p>
<table id="org8234ce1" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="orgfda8785" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Summary of the measurements and the states of the control systems</caption> <caption class="t-above"><span class="table-number">Table 1:</span> Summary of the measurements and the states of the control systems</caption>
<colgroup> <colgroup>
@ -257,76 +251,76 @@ Each of the <code>mat</code> file contains one array <code>data</code> with 3 co
</div> </div>
</div> </div>
<div id="outline-container-orgcb36bc1" class="outline-3"> <div id="outline-container-orgd930ba3" class="outline-3">
<h3 id="orgcb36bc1"><span class="section-number-3">1.2</span> Load data</h3> <h3 id="orgd930ba3"><span class="section-number-3">1.2</span> Load data</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">d3 = load('mat/data_003.mat', 'data'); d3 = d3.data; <pre class="src src-matlab">d3 = load(<span class="org-string">'mat/data_003.mat'</span>, <span class="org-string">'data'</span>); d3 = d3.data;
d4 = load('mat/data_004.mat', 'data'); d4 = d4.data; d4 = load(<span class="org-string">'mat/data_004.mat'</span>, <span class="org-string">'data'</span>); d4 = d4.data;
d5 = load('mat/data_005.mat', 'data'); d5 = d5.data; d5 = load(<span class="org-string">'mat/data_005.mat'</span>, <span class="org-string">'data'</span>); d5 = d5.data;
d6 = load('mat/data_006.mat', 'data'); d6 = d6.data; d6 = load(<span class="org-string">'mat/data_006.mat'</span>, <span class="org-string">'data'</span>); d6 = d6.data;
d7 = load('mat/data_007.mat', 'data'); d7 = d7.data; d7 = load(<span class="org-string">'mat/data_007.mat'</span>, <span class="org-string">'data'</span>); d7 = d7.data;
d8 = load('mat/data_008.mat', 'data'); d8 = d8.data; d8 = load(<span class="org-string">'mat/data_008.mat'</span>, <span class="org-string">'data'</span>); d8 = d8.data;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org5895a96" class="outline-3"> <div id="outline-container-orgaf61ea2" class="outline-3">
<h3 id="org5895a96"><span class="section-number-3">1.3</span> Analysis - Time Domain</h3> <h3 id="orgaf61ea2"><span class="section-number-3">1.3</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-1-3"> <div class="outline-text-3" id="text-1-3">
<p> <p>
First, we can look at the time domain data and compare all the measurements: First, we can look at the time domain data and compare all the measurements:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>comparison for the geophone at the sample location (figure <a href="#org2c7f590">1</a>)</li> <li>comparison for the geophone at the sample location (figure <a href="#org2d0b601">1</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#org51a2672">2</a>)</li> <li>comparison for the geophone on the granite (figure <a href="#orgb35182d">2</a>)</li>
</ul> </ul>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">figure; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot(d3(:, 3), d3(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty'); plot(d3(<span class="org-type">:</span>, 3), d3(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz, SR, Ry, Ty'</span>);
plot(d4(:, 3), d4(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry'); plot(d4(<span class="org-type">:</span>, 3), d4(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz, SR, Ry'</span>);
plot(d5(:, 3), d5(:, 2), 'DisplayName', 'Hexa, Rz, SR'); plot(d5(<span class="org-type">:</span>, 3), d5(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz, SR'</span>);
plot(d6(:, 3), d6(:, 2), 'DisplayName', 'Hexa, Rz'); plot(d6(<span class="org-type">:</span>, 3), d6(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz'</span>);
plot(d7(:, 3), d7(:, 2), 'DisplayName', 'Hexa'); plot(d7(<span class="org-type">:</span>, 3), d7(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa'</span>);
plot(d8(:, 3), d8(:, 2), 'DisplayName', 'All OFF'); plot(d8(<span class="org-type">:</span>, 3), d8(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'All OFF'</span>);
hold off; hold off;
xlabel('Time [s]'); ylabel('Voltage [V]'); xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim([0, 50]); xlim([0, 50]);
legend('Location', 'bestoutside'); legend(<span class="org-string">'Location'</span>, <span class="org-string">'bestoutside'</span>);
</pre> </pre>
</div> </div>
<div id="org2c7f590" class="figure"> <div id="org2d0b601" class="figure">
<p><img src="figs/time_domain_sample.png" alt="time_domain_sample.png" /> <p><img src="figs/time_domain_sample.png" alt="time_domain_sample.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p> <p><span class="figure-number">Figure 1: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">figure; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot(d3(:, 3), d3(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty'); plot(d3(<span class="org-type">:</span>, 3), d3(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz, SR, Ry, Ty'</span>);
plot(d4(:, 3), d4(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry'); plot(d4(<span class="org-type">:</span>, 3), d4(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz, SR, Ry'</span>);
plot(d5(:, 3), d5(:, 1), 'DisplayName', 'Hexa, Rz, SR'); plot(d5(<span class="org-type">:</span>, 3), d5(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz, SR'</span>);
plot(d6(:, 3), d6(:, 1), 'DisplayName', 'Hexa, Rz'); plot(d6(<span class="org-type">:</span>, 3), d6(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz'</span>);
plot(d7(:, 3), d7(:, 1), 'DisplayName', 'Hexa'); plot(d7(<span class="org-type">:</span>, 3), d7(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa'</span>);
plot(d8(:, 3), d8(:, 1), 'DisplayName', 'All OFF'); plot(d8(<span class="org-type">:</span>, 3), d8(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'All OFF'</span>);
hold off; hold off;
xlabel('Time [s]'); ylabel('Voltage [V]'); xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim([0, 50]); xlim([0, 50]);
legend('Location', 'bestoutside'); legend(<span class="org-string">'Location'</span>, <span class="org-string">'bestoutside'</span>);
</pre> </pre>
</div> </div>
<div id="org51a2672" class="figure"> <div id="orgb35182d" class="figure">
<p><img src="figs/time_domain_marble.png" alt="time_domain_marble.png" /> <p><img src="figs/time_domain_marble.png" alt="time_domain_marble.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p> <p><span class="figure-number">Figure 2: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p>
@ -334,129 +328,127 @@ legend('Location', 'bestoutside');
</div> </div>
</div> </div>
<div id="outline-container-org390bba0" class="outline-3"> <div id="outline-container-org3f46904" class="outline-3">
<h3 id="org390bba0"><span class="section-number-3">1.4</span> Analysis - Frequency Domain</h3> <h3 id="org3f46904"><span class="section-number-3">1.4</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-1-4"> <div class="outline-text-3" id="text-1-4">
<div class="org-src-container">
<pre class="src src-matlab">dt = d3(2, 3) - d3(1, 3);
Fs = 1/dt;
win = hanning(ceil(10*Fs));
</pre>
</div> </div>
</div> <div id="outline-container-org6cda42c" class="outline-4">
<h4 id="org6cda42c"><span class="section-number-4">1.4.1</span> Vibrations at the sample location</h4>
<div id="outline-container-org3a4a488" class="outline-4">
<h4 id="org3a4a488"><span class="section-number-4">1.4.1</span> Vibrations at the sample location</h4>
<div class="outline-text-4" id="text-1-4-1"> <div class="outline-text-4" id="text-1-4-1">
<p> <p>
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location. First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">[px3, f] = pwelch(d3(:, 2), win, [], [], Fs); <pre class="src src-matlab">[px3, f] = pwelch(d3(<span class="org-type">:</span>, 2), win, [], [], Fs);
[px4, ~] = pwelch(d4(:, 2), win, [], [], Fs); [px4, <span class="org-type">~</span>] = pwelch(d4(<span class="org-type">:</span>, 2), win, [], [], Fs);
[px5, ~] = pwelch(d5(:, 2), win, [], [], Fs); [px5, <span class="org-type">~</span>] = pwelch(d5(<span class="org-type">:</span>, 2), win, [], [], Fs);
[px6, ~] = pwelch(d6(:, 2), win, [], [], Fs); [px6, <span class="org-type">~</span>] = pwelch(d6(<span class="org-type">:</span>, 2), win, [], [], Fs);
[px7, ~] = pwelch(d7(:, 2), win, [], [], Fs); [px7, <span class="org-type">~</span>] = pwelch(d7(<span class="org-type">:</span>, 2), win, [], [], Fs);
[px8, ~] = pwelch(d8(:, 2), win, [], [], Fs); [px8, <span class="org-type">~</span>] = pwelch(d8(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre> </pre>
</div> </div>
<p> <p>
And we compare all the signals (figures <a href="#org939f58a">3</a> and <a href="#orgf26e845">4</a>). And we compare all the signals (figures <a href="#orgfad1dca">3</a> and <a href="#orgbb85235">4</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">figure; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty'); plot(f, sqrt(px3), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz, SR, Ry, Ty'</span>);
plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry'); plot(f, sqrt(px4), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz, SR, Ry'</span>);
plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR'); plot(f, sqrt(px5), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz, SR'</span>);
plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz'); plot(f, sqrt(px6), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz'</span>);
plot(f, sqrt(px7), 'DisplayName', 'Hexa'); plot(f, sqrt(px7), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa'</span>);
plot(f, sqrt(px8), 'DisplayName', 'All OFF'); plot(f, sqrt(px8), <span class="org-string">'DisplayName'</span>, <span class="org-string">'All OFF'</span>);
hold off; hold off;
set(gca, 'xscale', 'log'); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
set(gca, 'yscale', 'log'); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$') xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$'</span>)
xlim([0.1, 500]); xlim([0.1, 500]);
legend('Location', 'southwest'); legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
</pre> </pre>
</div> </div>
<div id="org939f58a" class="figure"> <div id="orgfad1dca" class="figure">
<p><img src="figs/psd_sample_comp.png" alt="psd_sample_comp.png" /> <p><img src="figs/psd_sample_comp.png" alt="psd_sample_comp.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Amplitude Spectral Density of the signal coming from the top geophone</p> <p><span class="figure-number">Figure 3: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
</div> </div>
<div id="orgf26e845" class="figure"> <div id="orgbb85235" class="figure">
<p><img src="figs/psd_sample_comp_high_freq.png" alt="psd_sample_comp_high_freq.png" /> <p><img src="figs/psd_sample_comp_high_freq.png" alt="psd_sample_comp_high_freq.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p> <p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
</div> </div>
<div id="org3ad8776" class="figure">
<p><img src="figs/cas_sample_comp.png" alt="cas_sample_comp.png" />
</p>
</div>
</div> </div>
</div> </div>
<div id="outline-container-org49d7279" class="outline-4"> <div id="outline-container-orga943462" class="outline-4">
<h4 id="org49d7279"><span class="section-number-4">1.4.2</span> Vibrations on the marble</h4> <h4 id="orga943462"><span class="section-number-4">1.4.2</span> Vibrations on the marble</h4>
<div class="outline-text-4" id="text-1-4-2"> <div class="outline-text-4" id="text-1-4-2">
<p> <p>
Now we plot the same curves for the geophone located on the marble. Now we plot the same curves for the geophone located on the marble.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">[px3, f] = pwelch(d3(:, 1), win, [], [], Fs); <pre class="src src-matlab">[px3, f] = pwelch(d3(<span class="org-type">:</span>, 1), win, [], [], Fs);
[px4, ~] = pwelch(d4(:, 1), win, [], [], Fs); [px4, <span class="org-type">~</span>] = pwelch(d4(<span class="org-type">:</span>, 1), win, [], [], Fs);
[px5, ~] = pwelch(d5(:, 1), win, [], [], Fs); [px5, <span class="org-type">~</span>] = pwelch(d5(<span class="org-type">:</span>, 1), win, [], [], Fs);
[px6, ~] = pwelch(d6(:, 1), win, [], [], Fs); [px6, <span class="org-type">~</span>] = pwelch(d6(<span class="org-type">:</span>, 1), win, [], [], Fs);
[px7, ~] = pwelch(d7(:, 1), win, [], [], Fs); [px7, <span class="org-type">~</span>] = pwelch(d7(<span class="org-type">:</span>, 1), win, [], [], Fs);
[px8, ~] = pwelch(d8(:, 1), win, [], [], Fs); [px8, <span class="org-type">~</span>] = pwelch(d8(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre> </pre>
</div> </div>
<p> <p>
And we compare the Amplitude Spectral Densities (figures <a href="#org3fd93c6">5</a> and <a href="#org2185be4">6</a>) And we compare the Amplitude Spectral Densities (figures <a href="#orge409077">6</a> and <a href="#orgf19188f">7</a>)
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">figure; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty'); plot(f, sqrt(px3), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz, SR, Ry, Ty'</span>);
plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry'); plot(f, sqrt(px4), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz, SR, Ry'</span>);
plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR'); plot(f, sqrt(px5), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz, SR'</span>);
plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz'); plot(f, sqrt(px6), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa, Rz'</span>);
plot(f, sqrt(px7), 'DisplayName', 'Hexa'); plot(f, sqrt(px7), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa'</span>);
plot(f, sqrt(px8), 'DisplayName', 'All OFF'); plot(f, sqrt(px8), <span class="org-string">'DisplayName'</span>, <span class="org-string">'All OFF'</span>);
hold off; hold off;
set(gca, 'xscale', 'log'); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
set(gca, 'yscale', 'log'); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$') xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$'</span>)
xlim([0.1, 500]); xlim([0.1, 500]);
legend('Location', 'northeast'); legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
</pre> </pre>
</div> </div>
<div id="org3fd93c6" class="figure"> <div id="orge409077" class="figure">
<p><img src="figs/psd_marble_comp.png" alt="psd_marble_comp.png" /> <p><img src="figs/psd_marble_comp.png" alt="psd_marble_comp.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the signal coming from the top geophone</p> <p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
</div> </div>
<div id="org2185be4" class="figure"> <div id="orgf19188f" class="figure">
<p><img src="figs/psd_marble_comp_high_freq.png" alt="psd_marble_comp_high_freq.png" /> <p><img src="figs/psd_marble_comp_high_freq.png" alt="psd_marble_comp_high_freq.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p> <p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
</div> </div>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org9b2f5fd" class="outline-3"> <div id="outline-container-orgeca50d8" class="outline-3">
<h3 id="org9b2f5fd"><span class="section-number-3">1.5</span> Conclusion</h3> <h3 id="orgeca50d8"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5"> <div class="outline-text-3" id="text-1-5">
<div class="important"> <div class="important" id="org3e2d674">
<ul class="org-ul"> <ul class="org-ul">
<li>The control system of the Ty stage induces a lot of vibrations of the marble above 100Hz</li> <li>The control system of the Ty stage induces a lot of vibrations of the marble above 100Hz</li>
<li>The hexapod control system add vibrations of the sample only above 200Hz</li> <li>The hexapod control system add vibrations of the sample only above 200Hz</li>
@ -468,13 +460,13 @@ legend('Location', 'northeast');
</div> </div>
</div> </div>
<div id="outline-container-org4eafed3" class="outline-2"> <div id="outline-container-org1592cd8" class="outline-2">
<h2 id="org4eafed3"><span class="section-number-2">2</span> Effect of all the control systems on the Sample vibrations - One stage at a time</h2> <h2 id="org1592cd8"><span class="section-number-2">2</span> Effect of all the control systems on the Sample vibrations - One stage at a time</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org757823f"></a> <a id="org2896ac0"></a>
</p> </p>
<div class="note"> <div class="note" id="orgdf47cc5">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/effect_control_one.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/effect_control_one.zip">here</a>.
</p> </p>
@ -482,8 +474,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/effect_cont
</div> </div>
</div> </div>
<div id="outline-container-org4addbe8" class="outline-3"> <div id="outline-container-orgf7f587e" class="outline-3">
<h3 id="org4addbe8"><span class="section-number-3">2.1</span> Experimental Setup</h3> <h3 id="orgf7f587e"><span class="section-number-3">2.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
We here measure the signals of two geophones: We here measure the signals of two geophones:
@ -506,7 +498,7 @@ Each measurement are done during 100s.
</p> </p>
<p> <p>
The settings of the voltage amplifier are shown on figure <a href="#orgeb410b4">7</a>: The settings of the voltage amplifier are shown on figure <a href="#orgd8f9a31">8</a>:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>gain of 60dB</li> <li>gain of 60dB</li>
@ -518,7 +510,7 @@ The settings of the voltage amplifier are shown on figure <a href="#orgeb410b4">
A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier. A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
</p> </p>
<table id="orgb3e54be" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org2eb327f" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Summary of the measurements and the states of the control systems</caption> <caption class="t-above"><span class="table-number">Table 2:</span> Summary of the measurements and the states of the control systems</caption>
<colgroup> <colgroup>
@ -637,189 +629,189 @@ Each of the <code>mat</code> file contains one array <code>data</code> with 3 co
</table> </table>
<div id="orgeb410b4" class="figure"> <div id="orgd8f9a31" class="figure">
<p><img src="./img/IMG_20190507_101459.jpg" alt="IMG_20190507_101459.jpg" width="500px" /> <p><img src="./img/IMG_20190507_101459.jpg" alt="IMG_20190507_101459.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Voltage amplifier settings for the measurement</p> <p><span class="figure-number">Figure 8: </span>Voltage amplifier settings for the measurement</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgb60aa2f" class="outline-3"> <div id="outline-container-org3554496" class="outline-3">
<h3 id="orgb60aa2f"><span class="section-number-3">2.2</span> Load data</h3> <h3 id="org3554496"><span class="section-number-3">2.2</span> Load data</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">d_of = load('mat/data_013.mat', 'data'); d_of = d_of.data; <pre class="src src-matlab">d_of = load(<span class="org-string">'mat/data_013.mat'</span>, <span class="org-string">'data'</span>); d_of = d_of.data;
d_ty = load('mat/data_014.mat', 'data'); d_ty = d_ty.data; d_ty = load(<span class="org-string">'mat/data_014.mat'</span>, <span class="org-string">'data'</span>); d_ty = d_ty.data;
d_ry = load('mat/data_015.mat', 'data'); d_ry = d_ry.data; d_ry = load(<span class="org-string">'mat/data_015.mat'</span>, <span class="org-string">'data'</span>); d_ry = d_ry.data;
d_sr = load('mat/data_016.mat', 'data'); d_sr = d_sr.data; d_sr = load(<span class="org-string">'mat/data_016.mat'</span>, <span class="org-string">'data'</span>); d_sr = d_sr.data;
d_rz = load('mat/data_017.mat', 'data'); d_rz = d_rz.data; d_rz = load(<span class="org-string">'mat/data_017.mat'</span>, <span class="org-string">'data'</span>); d_rz = d_rz.data;
d_he = load('mat/data_018.mat', 'data'); d_he = d_he.data; d_he = load(<span class="org-string">'mat/data_018.mat'</span>, <span class="org-string">'data'</span>); d_he = d_he.data;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org68831ee" class="outline-3"> <div id="outline-container-org5b2dc21" class="outline-3">
<h3 id="org68831ee"><span class="section-number-3">2.3</span> Voltage to Velocity</h3> <h3 id="org5b2dc21"><span class="section-number-3">2.3</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/thesis/meas/srcindex.html">here</a>). We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/thesis/meas/srcindex.html">here</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">gain = 60; % [dB] <pre class="src src-matlab">gain = 60; <span class="org-comment">% [dB]</span>
d_of(:, 1) = voltageToVelocityL22(d_of(:, 1), d_of(:, 3), gain); d_of(<span class="org-type">:</span>, 1) = voltageToVelocityL22(d_of(<span class="org-type">:</span>, 1), d_of(<span class="org-type">:</span>, 3), gain);
d_ty(:, 1) = voltageToVelocityL22(d_ty(:, 1), d_ty(:, 3), gain); d_ty(<span class="org-type">:</span>, 1) = voltageToVelocityL22(d_ty(<span class="org-type">:</span>, 1), d_ty(<span class="org-type">:</span>, 3), gain);
d_ry(:, 1) = voltageToVelocityL22(d_ry(:, 1), d_ry(:, 3), gain); d_ry(<span class="org-type">:</span>, 1) = voltageToVelocityL22(d_ry(<span class="org-type">:</span>, 1), d_ry(<span class="org-type">:</span>, 3), gain);
d_sr(:, 1) = voltageToVelocityL22(d_sr(:, 1), d_sr(:, 3), gain); d_sr(<span class="org-type">:</span>, 1) = voltageToVelocityL22(d_sr(<span class="org-type">:</span>, 1), d_sr(<span class="org-type">:</span>, 3), gain);
d_rz(:, 1) = voltageToVelocityL22(d_rz(:, 1), d_rz(:, 3), gain); d_rz(<span class="org-type">:</span>, 1) = voltageToVelocityL22(d_rz(<span class="org-type">:</span>, 1), d_rz(<span class="org-type">:</span>, 3), gain);
d_he(:, 1) = voltageToVelocityL22(d_he(:, 1), d_he(:, 3), gain); d_he(<span class="org-type">:</span>, 1) = voltageToVelocityL22(d_he(<span class="org-type">:</span>, 1), d_he(<span class="org-type">:</span>, 3), gain);
d_of(:, 2) = voltageToVelocityL22(d_of(:, 2), d_of(:, 3), gain); d_of(<span class="org-type">:</span>, 2) = voltageToVelocityL22(d_of(<span class="org-type">:</span>, 2), d_of(<span class="org-type">:</span>, 3), gain);
d_ty(:, 2) = voltageToVelocityL22(d_ty(:, 2), d_ty(:, 3), gain); d_ty(<span class="org-type">:</span>, 2) = voltageToVelocityL22(d_ty(<span class="org-type">:</span>, 2), d_ty(<span class="org-type">:</span>, 3), gain);
d_ry(:, 2) = voltageToVelocityL22(d_ry(:, 2), d_ry(:, 3), gain); d_ry(<span class="org-type">:</span>, 2) = voltageToVelocityL22(d_ry(<span class="org-type">:</span>, 2), d_ry(<span class="org-type">:</span>, 3), gain);
d_sr(:, 2) = voltageToVelocityL22(d_sr(:, 2), d_sr(:, 3), gain); d_sr(<span class="org-type">:</span>, 2) = voltageToVelocityL22(d_sr(<span class="org-type">:</span>, 2), d_sr(<span class="org-type">:</span>, 3), gain);
d_rz(:, 2) = voltageToVelocityL22(d_rz(:, 2), d_rz(:, 3), gain); d_rz(<span class="org-type">:</span>, 2) = voltageToVelocityL22(d_rz(<span class="org-type">:</span>, 2), d_rz(<span class="org-type">:</span>, 3), gain);
d_he(:, 2) = voltageToVelocityL22(d_he(:, 2), d_he(:, 3), gain); d_he(<span class="org-type">:</span>, 2) = voltageToVelocityL22(d_he(<span class="org-type">:</span>, 2), d_he(<span class="org-type">:</span>, 3), gain);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgbbb370a" class="outline-3"> <div id="outline-container-orga044f95" class="outline-3">
<h3 id="orgbbb370a"><span class="section-number-3">2.4</span> Analysis - Time Domain</h3> <h3 id="orga044f95"><span class="section-number-3">2.4</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
First, we can look at the time domain data and compare all the measurements: First, we can look at the time domain data and compare all the measurements:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>comparison for the geophone at the sample location (figure <a href="#org03fb45e">8</a>)</li> <li>comparison for the geophone at the sample location (figure <a href="#orgcae4035">9</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#orgc177b3a">9</a>)</li> <li>comparison for the geophone on the granite (figure <a href="#orgece9ecc">10</a>)</li>
<li>relative displacement of the sample with respect to the marble (figure <a href="#orgc177b3a">9</a>)</li> <li>relative displacement of the sample with respect to the marble (figure <a href="#orgece9ecc">10</a>)</li>
</ul> </ul>
<div id="org03fb45e" class="figure"> <div id="orgcae4035" class="figure">
<p><img src="figs/time_domain_sample_lpf.png" alt="time_domain_sample_lpf.png" /> <p><img src="figs/time_domain_sample_lpf.png" alt="time_domain_sample_lpf.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p> <p><span class="figure-number">Figure 9: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
</div> </div>
<div id="orgc177b3a" class="figure"> <div id="orgece9ecc" class="figure">
<p><img src="figs/time_domain_marble_lpf.png" alt="time_domain_marble_lpf.png" /> <p><img src="figs/time_domain_marble_lpf.png" alt="time_domain_marble_lpf.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p> <p><span class="figure-number">Figure 10: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p>
</div> </div>
<div id="orgb57231f" class="figure"> <div id="org68dbb45" class="figure">
<p><img src="figs/time_domain_relative_disp.png" alt="time_domain_relative_disp.png" /> <p><img src="figs/time_domain_relative_disp.png" alt="time_domain_relative_disp.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Relative displacement of the sample with respect to the marble</p> <p><span class="figure-number">Figure 11: </span>Relative displacement of the sample with respect to the marble</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgd436876" class="outline-3"> <div id="outline-container-org2132360" class="outline-3">
<h3 id="orgd436876"><span class="section-number-3">2.5</span> Analysis - Frequency Domain</h3> <h3 id="org2132360"><span class="section-number-3">2.5</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = d_of(2, 3) - d_of(1, 3); <pre class="src src-matlab">dt = d_of(2, 3) <span class="org-type">-</span> d_of(1, 3);
Fs = 1/dt; Fs = 1<span class="org-type">/</span>dt;
win = hanning(ceil(10*Fs)); win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
</div> </div>
<div id="outline-container-org2e1f962" class="outline-4"> <div id="outline-container-orgf096039" class="outline-4">
<h4 id="org2e1f962"><span class="section-number-4">2.5.1</span> Vibrations at the sample location</h4> <h4 id="orgf096039"><span class="section-number-4">2.5.1</span> Vibrations at the sample location</h4>
<div class="outline-text-4" id="text-2-5-1"> <div class="outline-text-4" id="text-2-5-1">
<p> <p>
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location. First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">[px_of, f] = pwelch(d_of(:, 2), win, [], [], Fs); <pre class="src src-matlab">[px_of, f] = pwelch(d_of(<span class="org-type">:</span>, 2), win, [], [], Fs);
[px_ty, ~] = pwelch(d_ty(:, 2), win, [], [], Fs); [px_ty, <span class="org-type">~</span>] = pwelch(d_ty(<span class="org-type">:</span>, 2), win, [], [], Fs);
[px_ry, ~] = pwelch(d_ry(:, 2), win, [], [], Fs); [px_ry, <span class="org-type">~</span>] = pwelch(d_ry(<span class="org-type">:</span>, 2), win, [], [], Fs);
[px_sr, ~] = pwelch(d_sr(:, 2), win, [], [], Fs); [px_sr, <span class="org-type">~</span>] = pwelch(d_sr(<span class="org-type">:</span>, 2), win, [], [], Fs);
[px_rz, ~] = pwelch(d_rz(:, 2), win, [], [], Fs); [px_rz, <span class="org-type">~</span>] = pwelch(d_rz(<span class="org-type">:</span>, 2), win, [], [], Fs);
[px_he, ~] = pwelch(d_he(:, 2), win, [], [], Fs); [px_he, <span class="org-type">~</span>] = pwelch(d_he(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre> </pre>
</div> </div>
<p> <p>
And we compare all the signals (figures <a href="#orgb661144">11</a> and <a href="#orgd36a2b1">12</a>). And we compare all the signals (figures <a href="#orgc1c0a30">12</a> and <a href="#orga1e7d03">13</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">figure; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot(f, sqrt(px_of), 'DisplayName', 'All OFF'); plot(f, sqrt(px_of), <span class="org-string">'DisplayName'</span>, <span class="org-string">'All OFF'</span>);
plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON'); plot(f, sqrt(px_ty), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty ON'</span>);
plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON'); plot(f, sqrt(px_ry), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ry ON'</span>);
plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON'); plot(f, sqrt(px_sr), <span class="org-string">'DisplayName'</span>, <span class="org-string">'S-R ON'</span>);
plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON'); plot(f, sqrt(px_rz), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Rz ON'</span>);
plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON'); plot(f, sqrt(px_he), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Hexa ON'</span>);
hold off; hold off;
set(gca, 'xscale', 'log'); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
set(gca, 'yscale', 'log'); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$') xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
xlim([0.1, 500]); xlim([0.1, 500]);
legend('Location', 'southwest'); legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
</pre> </pre>
</div> </div>
<div id="orgb661144" class="figure"> <div id="orgc1c0a30" class="figure">
<p><img src="figs/psd_sample_comp_lpf.png" alt="psd_sample_comp_lpf.png" /> <p><img src="figs/psd_sample_comp_lpf.png" alt="psd_sample_comp_lpf.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Amplitude Spectral Density of the sample velocity</p> <p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the sample velocity</p>
</div> </div>
<div id="orgd36a2b1" class="figure"> <div id="orga1e7d03" class="figure">
<p><img src="figs/psd_sample_comp_high_freq_lpf.png" alt="psd_sample_comp_high_freq_lpf.png" /> <p><img src="figs/psd_sample_comp_high_freq_lpf.png" alt="psd_sample_comp_high_freq_lpf.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the sample velocity (zoom at high frequencies)</p> <p><span class="figure-number">Figure 13: </span>Amplitude Spectral Density of the sample velocity (zoom at high frequencies)</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org8f33a44" class="outline-4"> <div id="outline-container-org2457465" class="outline-4">
<h4 id="org8f33a44"><span class="section-number-4">2.5.2</span> Vibrations on the marble</h4> <h4 id="org2457465"><span class="section-number-4">2.5.2</span> Vibrations on the marble</h4>
<div class="outline-text-4" id="text-2-5-2"> <div class="outline-text-4" id="text-2-5-2">
<p> <p>
Now we plot the same curves for the geophone located on the marble. Now we plot the same curves for the geophone located on the marble.
And we compare the Amplitude Spectral Densities (figures <a href="#org57f110f">13</a> and <a href="#orgcbf8e87">14</a>) And we compare the Amplitude Spectral Densities (figures <a href="#org76a7420">14</a> and <a href="#org9dda36a">15</a>)
</p> </p>
<div id="org57f110f" class="figure"> <div id="org76a7420" class="figure">
<p><img src="figs/psd_marble_comp_lpf.png" alt="psd_marble_comp_lpf.png" /> <p><img src="figs/psd_marble_comp_lpf.png" alt="psd_marble_comp_lpf.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Amplitude Spectral Density of the marble velocity</p> <p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the marble velocity</p>
</div> </div>
<div id="orgcbf8e87" class="figure"> <div id="org9dda36a" class="figure">
<p><img src="figs/psd_marble_lpf_high_freq.png" alt="psd_marble_lpf_high_freq.png" /> <p><img src="figs/psd_marble_lpf_high_freq.png" alt="psd_marble_lpf_high_freq.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Amplitude Spectral Density of the marble velocity (zoom at high frequencies)</p> <p><span class="figure-number">Figure 15: </span>Amplitude Spectral Density of the marble velocity (zoom at high frequencies)</p>
</div> </div>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org381e6c2" class="outline-3"> <div id="outline-container-org2a3582c" class="outline-3">
<h3 id="org381e6c2"><span class="section-number-3">2.6</span> Conclusion</h3> <h3 id="org2a3582c"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-6">
<div class="important"> <div class="important" id="org0b59337">
<ul class="org-ul"> <ul class="org-ul">
<li>The Ty stage induces vibrations of the marble and at the sample location above 100Hz</li> <li>The Ty stage induces vibrations of the marble and at the sample location above 100Hz</li>
<li>The hexapod stage induces vibrations at the sample position above 220Hz</li> <li>The hexapod stage induces vibrations at the sample position above 220Hz</li>
@ -830,13 +822,13 @@ And we compare the Amplitude Spectral Densities (figures <a href="#org57f110f">1
</div> </div>
</div> </div>
<div id="outline-container-orgce5eef9" class="outline-2"> <div id="outline-container-org8e41411" class="outline-2">
<h2 id="orgce5eef9"><span class="section-number-2">3</span> Effect of the Symetrie Driver</h2> <h2 id="org8e41411"><span class="section-number-2">3</span> Effect of the Symetrie Driver</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
<a id="orgd9c378b"></a> <a id="org01c82bb"></a>
</p> </p>
<div class="note"> <div class="note" id="orgbddd3ee">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/effect_symetrie_driver.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/effect_symetrie_driver.zip">here</a>.
</p> </p>
@ -844,8 +836,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/effect_syme
</div> </div>
</div> </div>
<div id="outline-container-org6e62fbe" class="outline-3"> <div id="outline-container-org2c71144" class="outline-3">
<h3 id="org6e62fbe"><span class="section-number-3">3.1</span> Experimental Setup</h3> <h3 id="org2c71144"><span class="section-number-3">3.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
We here measure the signals of two geophones: We here measure the signals of two geophones:
@ -925,103 +917,103 @@ Each of the <code>mat</code> file contains one array <code>data</code> with 3 co
</div> </div>
</div> </div>
<div id="outline-container-orgd0c4704" class="outline-3"> <div id="outline-container-org86d2cac" class="outline-3">
<h3 id="orgd0c4704"><span class="section-number-3">3.2</span> Load data</h3> <h3 id="org86d2cac"><span class="section-number-3">3.2</span> Load data</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">d_18 = load('mat/data_018.mat', 'data'); d_18 = d_18.data; <pre class="src src-matlab">d_18 = load(<span class="org-string">'mat/data_018.mat'</span>, <span class="org-string">'data'</span>); d_18 = d_18.data;
d_19 = load('mat/data_019.mat', 'data'); d_19 = d_19.data; d_19 = load(<span class="org-string">'mat/data_019.mat'</span>, <span class="org-string">'data'</span>); d_19 = d_19.data;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org30686ba" class="outline-3"> <div id="outline-container-org8866dd0" class="outline-3">
<h3 id="org30686ba"><span class="section-number-3">3.3</span> Analysis - Time Domain</h3> <h3 id="org8866dd0"><span class="section-number-3">3.3</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">figure; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot(d_19(:, 3), d_19(:, 1), 'DisplayName', 'Driver - Ground'); plot(d_19(<span class="org-type">:</span>, 3), d_19(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Driver - Ground'</span>);
plot(d_18(:, 3), d_18(:, 1), 'DisplayName', 'Driver - Granite'); plot(d_18(<span class="org-type">:</span>, 3), d_18(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Driver - Granite'</span>);
hold off; hold off;
xlabel('Time [s]'); ylabel('Voltage [V]'); xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim([0, 50]); xlim([0, 50]);
legend('Location', 'bestoutside'); legend(<span class="org-string">'Location'</span>, <span class="org-string">'bestoutside'</span>);
</pre> </pre>
</div> </div>
<div id="orgd0329f8" class="figure"> <div id="org3b49fad" class="figure">
<p><img src="figs/time_domain_hexa_driver.png" alt="time_domain_hexa_driver.png" /> <p><img src="figs/time_domain_hexa_driver.png" alt="time_domain_hexa_driver.png" />
</p> </p>
<p><span class="figure-number">Figure 15: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p> <p><span class="figure-number">Figure 16: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgd922ea4" class="outline-3"> <div id="outline-container-org42b0b80" class="outline-3">
<h3 id="orgd922ea4"><span class="section-number-3">3.4</span> Analysis - Frequency Domain</h3> <h3 id="org42b0b80"><span class="section-number-3">3.4</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-3-4"> <div class="outline-text-3" id="text-3-4">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = d_18(2, 3) - d_18(1, 3); <pre class="src src-matlab">dt = d_18(2, 3) <span class="org-type">-</span> d_18(1, 3);
Fs = 1/dt; Fs = 1<span class="org-type">/</span>dt;
win = hanning(ceil(10*Fs)); win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
</div> </div>
<div id="outline-container-orgd49e7c3" class="outline-4"> <div id="outline-container-org327f014" class="outline-4">
<h4 id="orgd49e7c3"><span class="section-number-4">3.4.1</span> Vibrations at the sample location</h4> <h4 id="org327f014"><span class="section-number-4">3.4.1</span> Vibrations at the sample location</h4>
<div class="outline-text-4" id="text-3-4-1"> <div class="outline-text-4" id="text-3-4-1">
<p> <p>
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location. First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">[px_18, f] = pwelch(d_18(:, 1), win, [], [], Fs); <pre class="src src-matlab">[px_18, f] = pwelch(d_18(<span class="org-type">:</span>, 1), win, [], [], Fs);
[px_19, ~] = pwelch(d_19(:, 1), win, [], [], Fs); [px_19, <span class="org-type">~</span>] = pwelch(d_19(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">figure; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot(f, sqrt(px_19), 'DisplayName', 'Driver - Ground'); plot(f, sqrt(px_19), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Driver - Ground'</span>);
plot(f, sqrt(px_18), 'DisplayName', 'Driver - Granite'); plot(f, sqrt(px_18), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Driver - Granite'</span>);
hold off; hold off;
set(gca, 'xscale', 'log'); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
set(gca, 'yscale', 'log'); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$') xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$'</span>)
xlim([0.1, 500]); xlim([0.1, 500]);
legend('Location', 'southwest'); legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
</pre> </pre>
</div> </div>
<div id="org474aa6e" class="figure"> <div id="org6757aa8" class="figure">
<p><img src="figs/psd_hexa_driver.png" alt="psd_hexa_driver.png" /> <p><img src="figs/psd_hexa_driver.png" alt="psd_hexa_driver.png" />
</p> </p>
<p><span class="figure-number">Figure 16: </span>Amplitude Spectral Density of the signal coming from the top geophone</p> <p><span class="figure-number">Figure 17: </span>Amplitude Spectral Density of the signal coming from the top geophone</p>
</div> </div>
<div id="org01ebad8" class="figure"> <div id="orga4175a1" class="figure">
<p><img src="figs/psd_hexa_driver_high_freq.png" alt="psd_hexa_driver_high_freq.png" /> <p><img src="figs/psd_hexa_driver_high_freq.png" alt="psd_hexa_driver_high_freq.png" />
</p> </p>
<p><span class="figure-number">Figure 17: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p> <p><span class="figure-number">Figure 18: </span>Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)</p>
</div> </div>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org031a084" class="outline-3"> <div id="outline-container-org19a7dad" class="outline-3">
<h3 id="org031a084"><span class="section-number-3">3.5</span> Conclusion</h3> <h3 id="org19a7dad"><span class="section-number-3">3.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-5"> <div class="outline-text-3" id="text-3-5">
<div class="important"> <div class="important" id="org73be6df">
<p> <p>
Even tough the Hexapod&rsquo;s driver vibrates quite a lot, it does not generate significant vibrations of the granite when either placed on the granite or on the ground. Even tough the Hexapod&rsquo;s driver vibrates quite a lot, it does not generate significant vibrations of the granite when either placed on the granite or on the ground.
</p> </p>
@ -1033,7 +1025,7 @@ Even tough the Hexapod&rsquo;s driver vibrates quite a lot, it does not generate
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-04-27 lun. 10:18</p> <p class="date">Created: 2020-11-12 jeu. 10:27</p>
</div> </div>
</body> </body>
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9
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@ -9,13 +9,8 @@
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -258,23 +22,24 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orga44a9d5">1. Experimental Setup</a></li> <li><a href="#org2422081">1. Experimental Setup</a></li>
<li><a href="#orgb5a2f1a">2. Data Analysis</a> <li><a href="#org6220fc6">2. Data Analysis</a>
<ul> <ul>
<li><a href="#org239b200">2.1. Load data</a></li> <li><a href="#org122f0e9">2.1. Load data</a></li>
<li><a href="#org66889bf">2.2. Voltage to Velocity</a></li> <li><a href="#orgaea71b5">2.2. Voltage to Velocity</a></li>
<li><a href="#orgd049ddc">2.3. Time domain plots</a></li> <li><a href="#org485d23f">2.3. Time domain plots</a></li>
<li><a href="#orgfee57e5">2.4. Frequency Domain</a></li> <li><a href="#org38cf97f">2.4. Frequency Domain</a></li>
<li><a href="#org7d3ac71">2.5. Relative Motion</a></li> <li><a href="#orgbaa08aa">2.5. Relative Motion</a></li>
<li><a href="#org1464a72">2.6. Conclusion</a></li> <li><a href="#orgad3b42a">2.6. Save</a></li>
<li><a href="#org0a44924">2.7. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orga44a9d5" class="outline-2"> <div id="outline-container-org2422081" class="outline-2">
<h2 id="orga44a9d5"><span class="section-number-2">1</span> Experimental Setup</h2> <h2 id="org2422081"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<b>Setup</b>: <b>Setup</b>:
@ -383,11 +148,11 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table> </table>
<p> <p>
A movie showing the experiment is shown on figure <a href="#org1669ed1">1</a>. A movie showing the experiment is shown on figure <a href="#orgc1e7286">1</a>.
</p> </p>
<div id="org1669ed1" class="figure"> <div id="orgc1e7286" class="figure">
<p><img src="./img/VID_20190510_155655.gif" alt="VID_20190510_155655.gif" width="300px" /> <p><img src="./img/VID_20190510_155655.gif" alt="VID_20190510_155655.gif" width="300px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Movie of the experiment, rotation speed is 6rpm</p> <p><span class="figure-number">Figure 1: </span>Movie of the experiment, rotation speed is 6rpm</p>
@ -395,13 +160,13 @@ A movie showing the experiment is shown on figure <a href="#org1669ed1">1</a>.
</div> </div>
</div> </div>
<div id="outline-container-orgb5a2f1a" class="outline-2"> <div id="outline-container-org6220fc6" class="outline-2">
<h2 id="orgb5a2f1a"><span class="section-number-2">2</span> Data Analysis</h2> <h2 id="org6220fc6"><span class="section-number-2">2</span> Data Analysis</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org73b6124"></a> <a id="org8446070"></a>
</p> </p>
<div class="note"> <div class="note" id="orga7b7a45">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/spindle_slip_ring_vibrations.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/spindle_slip_ring_vibrations.zip">here</a>.
</p> </p>
@ -409,17 +174,17 @@ All the files (data and Matlab scripts) are accessible <a href="data/spindle_sli
</div> </div>
</div> </div>
<div id="outline-container-org239b200" class="outline-3"> <div id="outline-container-org122f0e9" class="outline-3">
<h3 id="org239b200"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="org122f0e9"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_024.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; of = of.data; <pre class="src src-matlab">of = load(<span class="org-string">'mat/data_024.mat'</span>, <span class="org-string">'data'</span>); of = of.data; <span class="org-comment">% OFF</span>
sr = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_025.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr = sr.data; sr = load(<span class="org-string">'mat/data_025.mat'</span>, <span class="org-string">'data'</span>); sr = sr.data; <span class="org-comment">% Slip Ring</span>
sp = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_026.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sp = sp.data; sp = load(<span class="org-string">'mat/data_026.mat'</span>, <span class="org-string">'data'</span>); sp = sp.data; <span class="org-comment">% Spindle</span>
</pre> </pre>
</div> </div>
<div class="warning"> <div class="warning" id="orgb2b819c">
<p> <p>
There is a sign error for the Geophone located on top of the Hexapod. There is a sign error for the Geophone located on top of the Hexapod.
The problem probably comes from the wiring in the Slip-Ring. The problem probably comes from the wiring in the Slip-Ring.
@ -428,54 +193,54 @@ The problem probably comes from the wiring in the Slip-Ring.
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">of(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>of(<span class="org-type">:</span>, 2);
sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>sr(<span class="org-type">:</span>, 2);
sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; sp(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>sp(<span class="org-type">:</span>, 2);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org66889bf" class="outline-3"> <div id="outline-container-orgaea71b5" class="outline-3">
<h3 id="org66889bf"><span class="section-number-3">2.2</span> Voltage to Velocity</h3> <h3 id="orgaea71b5"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="../src/index.html">here</a>). We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="../src/index.html">here</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">gain = <span class="org-highlight-numbers-number">60</span>; <span class="org-comment">% [dB]</span> <pre class="src src-matlab">gain = 60; <span class="org-comment">% [dB]</span>
of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; of(<span class="org-type">:</span>, 1) = voltageToVelocityL22(of(<span class="org-type">:</span>, 1), of(<span class="org-type">:</span>, 3), gain);
sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; sr(<span class="org-type">:</span>, 1) = voltageToVelocityL22(sr(<span class="org-type">:</span>, 1), sr(<span class="org-type">:</span>, 3), gain);
sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; sp(<span class="org-type">:</span>, 1) = voltageToVelocityL22(sp(<span class="org-type">:</span>, 1), sp(<span class="org-type">:</span>, 3), gain);
of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; of(<span class="org-type">:</span>, 2) = voltageToVelocityL22(of(<span class="org-type">:</span>, 2), of(<span class="org-type">:</span>, 3), gain);
sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; sr(<span class="org-type">:</span>, 2) = voltageToVelocityL22(sr(<span class="org-type">:</span>, 2), sr(<span class="org-type">:</span>, 3), gain);
sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; sp(<span class="org-type">:</span>, 2) = voltageToVelocityL22(sp(<span class="org-type">:</span>, 2), sp(<span class="org-type">:</span>, 3), gain);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgd049ddc" class="outline-3"> <div id="outline-container-org485d23f" class="outline-3">
<h3 id="orgd049ddc"><span class="section-number-3">2.3</span> Time domain plots</h3> <h3 id="org485d23f"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(sp(<span class="org-type">:</span>, 3), sp(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(sr(<span class="org-type">:</span>, 3), sr(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(of(<span class="org-type">:</span>, 3), of(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Velocity [m/s]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 100]);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
</pre> </pre>
</div> </div>
<div id="org4e9bed0" class="figure"> <div id="org4a00ffe" class="figure">
<p><img src="figs/slip_ring_spindle_marble_time.png" alt="slip_ring_spindle_marble_time.png" /> <p><img src="figs/slip_ring_spindle_marble_time.png" alt="slip_ring_spindle_marble_time.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Velocity as measured by the geophone located on the marble - Time domain</p> <p><span class="figure-number">Figure 2: </span>Velocity as measured by the geophone located on the marble - Time domain</p>
@ -484,25 +249,25 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle and Slip-Ring'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(sp(<span class="org-type">:</span>, 3), sp(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle and Slip-Ring'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Only Slip-Ring'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(sr(<span class="org-type">:</span>, 3), sr(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Only Slip-Ring'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(of(<span class="org-type">:</span>, 3), of(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Velocity [m/s]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 100]);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
</pre> </pre>
</div> </div>
<div id="org8be7963" class="figure"> <div id="orgcea5a30" class="figure">
<p><img src="figs/slip_ring_spindle_sample_time.png" alt="slip_ring_spindle_sample_time.png" /> <p><img src="figs/slip_ring_spindle_sample_time.png" alt="slip_ring_spindle_sample_time.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Velocity as measured by the geophone at the sample location - Time domain</p> <p><span class="figure-number">Figure 3: </span>Velocity as measured by the geophone at the sample location - Time domain</p>
</div> </div>
<div id="orgfc19876" class="figure"> <div id="org3c59dd5" class="figure">
<p><img src="figs/slip_ring_spindle_sample_zoom.png" alt="slip_ring_spindle_sample_zoom.png" /> <p><img src="figs/slip_ring_spindle_sample_zoom.png" alt="slip_ring_spindle_sample_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Velocity as measured by the geophone at the sample location - Time domain</p> <p><span class="figure-number">Figure 4: </span>Velocity as measured by the geophone at the sample location - Time domain</p>
@ -510,18 +275,18 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-orgfee57e5" class="outline-3"> <div id="outline-container-org38cf97f" class="outline-3">
<h3 id="orgfee57e5"><span class="section-number-3">2.4</span> Frequency Domain</h3> <h3 id="org38cf97f"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
We first compute some parameters that will be used for the PSD computation. We first compute some parameters that will be used for the PSD computation.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% [s]</span> <pre class="src src-matlab">dt = of(2, 3)<span class="org-type">-</span>of(1, 3); <span class="org-comment">% [s]</span>
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Window used</span> win = hanning(ceil(10<span class="org-type">*</span>Fs)); <span class="org-comment">% Window used</span>
</pre> </pre>
</div> </div>
@ -533,9 +298,9 @@ Then we compute the Power Spectral Density using <code>pwelch</code> function.
First for the geophone located on the marble First for the geophone located on the marble
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_m, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxof_m, f] = pwelch(of(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxsr_m, <span class="org-type">~</span>] = pwelch(sr(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxsp_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxsp_m, <span class="org-type">~</span>] = pwelch(sp(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre> </pre>
</div> </div>
@ -543,9 +308,9 @@ First for the geophone located on the marble
And for the geophone located at the sample position. And for the geophone located at the sample position.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxof_s, <span class="org-type">~</span>] = pwelch(of(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxsr_s, <span class="org-type">~</span>] = pwelch(sr(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxsp_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxsp_s, <span class="org-type">~</span>] = pwelch(sp(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre> </pre>
</div> </div>
@ -553,27 +318,27 @@ And for the geophone located at the sample position.
And we plot the ASD of the measured velocities: And we plot the ASD of the measured velocities:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>figure <a href="#org704b4b4">5</a> for the geophone located on the marble</li> <li>figure <a href="#orgf38cb1d">5</a> for the geophone located on the marble</li>
<li>figure <a href="#orga078b66">6</a> for the geophone at the sample position</li> <li>figure <a href="#orgbe7eafc">6</a> for the geophone at the sample position</li>
</ul> </ul>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxsp_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxsr_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxof_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([2, 500]);
</pre> </pre>
</div> </div>
<div id="org704b4b4" class="figure"> <div id="orgf38cb1d" class="figure">
<p><img src="figs/sr_sp_psd_marble_compare.png" alt="sr_sp_psd_marble_compare.png" /> <p><img src="figs/sr_sp_psd_marble_compare.png" alt="sr_sp_psd_marble_compare.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Comparison of the ASD of the measured velocities from the Geophone on the marble</p> <p><span class="figure-number">Figure 5: </span>Comparison of the ASD of the measured velocities from the Geophone on the marble</p>
@ -582,52 +347,52 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxsp_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxsr_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxof_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([2, 500]);
</pre> </pre>
</div> </div>
<div id="orga078b66" class="figure"> <div id="orgbe7eafc" class="figure">
<p><img src="figs/sr_sp_psd_sample_compare.png" alt="sr_sp_psd_sample_compare.png" /> <p><img src="figs/sr_sp_psd_sample_compare.png" alt="sr_sp_psd_sample_compare.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Comparison of the ASD of the measured velocities from the Geophone at the sample location</p> <p><span class="figure-number">Figure 6: </span>Comparison of the ASD of the measured velocities from the Geophone at the sample location</p>
</div> </div>
<p> <p>
We load the ground motion to compare with the measurements (Fig. <a href="#org71cc947">7</a>). We load the ground motion to compare with the measurements (Fig. <a href="#org71b3fba">7</a>).
We see that the motion is dominated by the ground motion below 20Hz. We see that the motion is dominated by the ground motion below 20Hz.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">gm = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'../ground-motion/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gv'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">gm = load(<span class="org-string">'../ground-motion/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gv'</span>);
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxsp_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxsr_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxof_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>gm.f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>gm.psd_gv<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(gm.f, sqrt(gm.psd_gv), <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ground Motion'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([2, 500]);
</pre> </pre>
</div> </div>
<div id="org71cc947" class="figure"> <div id="org71b3fba" class="figure">
<p><img src="figs/ty_comp_gm.png" alt="ty_comp_gm.png" /> <p><img src="figs/ty_comp_gm.png" alt="ty_comp_gm.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Comparison of the ground velocity with the measured velocity (<a href="./figs/ty_comp_gm.png">png</a>, <a href="./figs/ty_comp_gm.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 7: </span>Comparison of the ground velocity with the measured velocity (<a href="./figs/ty_comp_gm.png">png</a>, <a href="./figs/ty_comp_gm.pdf">pdf</a>)</p>
@ -636,16 +401,16 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="outline-container-org7d3ac71" class="outline-3"> <div id="outline-container-orgbaa08aa" class="outline-3">
<h3 id="org7d3ac71"><span class="section-number-3">2.5</span> Relative Motion</h3> <h3 id="orgbaa08aa"><span class="section-number-3">2.5</span> Relative Motion</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<p> <p>
The relative velocity between the sample and the marble is shown in Fig. <a href="#org21be4d0">8</a>. The relative velocity between the sample and the marble is shown in Fig. <a href="#orgb098e37">8</a>.
The velocity is integrated to have the relative displacement in Fig. <a href="#org2d58d24">9</a>. The velocity is integrated to have the relative displacement in Fig. <a href="#org3dac066">9</a>.
</p> </p>
<div id="org21be4d0" class="figure"> <div id="orgb098e37" class="figure">
<p><img src="figs/rz_relative_velocity.png" alt="rz_relative_velocity.png" /> <p><img src="figs/rz_relative_velocity.png" alt="rz_relative_velocity.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Relative velocity between the hexapod and the marble (<a href="./figs/rz_relative_velocity.png">png</a>, <a href="./figs/rz_relative_velocity.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 8: </span>Relative velocity between the hexapod and the marble (<a href="./figs/rz_relative_velocity.png">png</a>, <a href="./figs/rz_relative_velocity.pdf">pdf</a>)</p>
@ -655,7 +420,7 @@ The velocity is integrated to have the relative displacement in Fig. <a href="#o
Time domain: Integration to have the displacement Time domain: Integration to have the displacement
</p> </p>
<div id="org2d58d24" class="figure"> <div id="org3dac066" class="figure">
<p><img src="figs/rz_relative_motion.png" alt="rz_relative_motion.png" /> <p><img src="figs/rz_relative_motion.png" alt="rz_relative_motion.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Relative displacement between the Hexapod and the marble (<a href="./figs/rz_relative_motion.png">png</a>, <a href="./figs/rz_relative_motion.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 9: </span>Relative displacement between the Hexapod and the marble (<a href="./figs/rz_relative_motion.png">png</a>, <a href="./figs/rz_relative_motion.pdf">pdf</a>)</p>
@ -665,52 +430,52 @@ Time domain: Integration to have the displacement
We compute the PSD of the relative velocity between the sample and the marble. We compute the PSD of the relative velocity between the sample and the marble.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxof_r, f] = pwelch(of(<span class="org-type">:</span>, 2)<span class="org-type">-</span>of(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxsr_r, <span class="org-type">~</span>] = pwelch(sr(<span class="org-type">:</span>, 2)<span class="org-type">-</span>sr(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxsp_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxsp_r, <span class="org-type">~</span>] = pwelch(sp(<span class="org-type">:</span>, 2)<span class="org-type">-</span>sp(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre> </pre>
</div> </div>
<p> <p>
The Power Spectral Density of the Granite Velocity, Sample velocity and relative velocity are compare in Fig. <a href="#org0cfb4b3">10</a>. The Power Spectral Density of the Granite Velocity, Sample velocity and relative velocity are compare in Fig. <a href="#orga42fb07">10</a>.
</p> </p>
<div id="org0cfb4b3" class="figure"> <div id="orga42fb07" class="figure">
<p><img src="figs/rz_psd_sample_granite_relative_comp.png" alt="rz_psd_sample_granite_relative_comp.png" /> <p><img src="figs/rz_psd_sample_granite_relative_comp.png" alt="rz_psd_sample_granite_relative_comp.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Comparison of the PSD of the velocity of the Sample, Granite and relative velocity (<a href="./figs/rz_psd_sample_granite_relative_comp.png">png</a>, <a href="./figs/rz_psd_sample_granite_relative_comp.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 10: </span>Comparison of the PSD of the velocity of the Sample, Granite and relative velocity (<a href="./figs/rz_psd_sample_granite_relative_comp.png">png</a>, <a href="./figs/rz_psd_sample_granite_relative_comp.pdf">pdf</a>)</p>
</div> </div>
<p> <p>
Then, we display the PSD of the relative velocity for all three cases in Fig. <a href="#org9d08176">11</a>. Then, we display the PSD of the relative velocity for all three cases in Fig. <a href="#org1f1dfc7">11</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxsp_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxsr_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxof_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the relative velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the relative velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([2, 500]);
</pre> </pre>
</div> </div>
<div id="org9d08176" class="figure"> <div id="org1f1dfc7" class="figure">
<p><img src="figs/sr_sp_psd_relative_compare.png" alt="sr_sp_psd_relative_compare.png" /> <p><img src="figs/sr_sp_psd_relative_compare.png" alt="sr_sp_psd_relative_compare.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Comparison of the ASD of the relative velocity</p> <p><span class="figure-number">Figure 11: </span>Comparison of the ASD of the relative velocity</p>
</div> </div>
<p> <p>
The Cumulative Power Spectrum of the relative velocity is shown in Fig. <a href="#org76a9b23">12</a> and in Fig. <a href="#org61e2e4a">13</a> (integrated in reverse direction). The Cumulative Power Spectrum of the relative velocity is shown in Fig. <a href="#org11a9cb7">12</a> and in Fig. <a href="#orga256753">13</a> (integrated in reverse direction).
</p> </p>
<div id="org76a9b23" class="figure"> <div id="org11a9cb7" class="figure">
<p><img src="figs/dist_rz_cps.png" alt="dist_rz_cps.png" /> <p><img src="figs/dist_rz_cps.png" alt="dist_rz_cps.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Cumulative Power Spectrum of the relative velocity (<a href="./figs/dist_rz_cps.png">png</a>, <a href="./figs/dist_rz_cps.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 12: </span>Cumulative Power Spectrum of the relative velocity (<a href="./figs/dist_rz_cps.png">png</a>, <a href="./figs/dist_rz_cps.pdf">pdf</a>)</p>
@ -718,7 +483,7 @@ The Cumulative Power Spectrum of the relative velocity is shown in Fig. <a href=
<div id="org61e2e4a" class="figure"> <div id="orga256753" class="figure">
<p><img src="figs/dist_rz_cps_reverse.png" alt="dist_rz_cps_reverse.png" /> <p><img src="figs/dist_rz_cps_reverse.png" alt="dist_rz_cps_reverse.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Cumulative Power Spectrum of the relative velocity (integrated from high to low frequencies) (<a href="./figs/dist_rz_cps_reverse.png">png</a>, <a href="./figs/dist_rz_cps_reverse.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 13: </span>Cumulative Power Spectrum of the relative velocity (integrated from high to low frequencies) (<a href="./figs/dist_rz_cps_reverse.png">png</a>, <a href="./figs/dist_rz_cps_reverse.pdf">pdf</a>)</p>
@ -726,43 +491,48 @@ The Cumulative Power Spectrum of the relative velocity is shown in Fig. <a href=
<p> <p>
Finally, the Cumulative Amplitude Spectrum of the relative position between the hexapod and the marble is shown in Fig. <a href="#org454a2a7">14</a>. Finally, the Cumulative Amplitude Spectrum of the relative position between the hexapod and the marble is shown in Fig. <a href="#orgb16a9f7">14</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>flip<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">-</span>cumtrapz<span class="org-rainbow-delimiters-depth-4">(</span>flip<span class="org-rainbow-delimiters-depth-5">(</span>f<span class="org-rainbow-delimiters-depth-5">)</span>, flip<span class="org-rainbow-delimiters-depth-5">(</span>pxsp_r<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-6">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-6">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(flip(<span class="org-type">-</span>cumtrapz(flip(f), flip(pxsp_r<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f)<span class="org-type">.^</span>2)))), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>flip<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">-</span>cumtrapz<span class="org-rainbow-delimiters-depth-4">(</span>flip<span class="org-rainbow-delimiters-depth-5">(</span>f<span class="org-rainbow-delimiters-depth-5">)</span>, flip<span class="org-rainbow-delimiters-depth-5">(</span>pxsr_r<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-6">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-6">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(flip(<span class="org-type">-</span>cumtrapz(flip(f), flip(pxsr_r<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f)<span class="org-type">.^</span>2)))), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>flip<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">-</span>cumtrapz<span class="org-rainbow-delimiters-depth-4">(</span>flip<span class="org-rainbow-delimiters-depth-5">(</span>f<span class="org-rainbow-delimiters-depth-5">)</span>, flip<span class="org-rainbow-delimiters-depth-5">(</span>pxof_r<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-6">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-6">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(flip(<span class="org-type">-</span>cumtrapz(flip(f), flip(pxof_r<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f)<span class="org-type">.^</span>2)))), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'CAS of the relative displacement $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'CAS of the relative displacement $\left[\frac{m}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([2, 500]);
</pre> </pre>
</div> </div>
<div id="org454a2a7" class="figure"> <div id="orgb16a9f7" class="figure">
<p><img src="figs/dist_rz_cas.png" alt="dist_rz_cas.png" /> <p><img src="figs/dist_rz_cas.png" alt="dist_rz_cas.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Cumulative Amplitude Spectrum of the relative motion Hexapod/Granite (<a href="./figs/dist_rz_cas.png">png</a>, <a href="./figs/dist_rz_cas.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 14: </span>Cumulative Amplitude Spectrum of the relative motion Hexapod/Granite (<a href="./figs/dist_rz_cas.png">png</a>, <a href="./figs/dist_rz_cas.pdf">pdf</a>)</p>
</div> </div>
</div>
</div>
<div id="outline-container-orgad3b42a" class="outline-3">
<h3 id="orgad3b42a"><span class="section-number-3">2.6</span> Save</h3>
<div class="outline-text-3" id="text-2-6">
<p> <p>
The Power Spectral Density of the relative velocity is saved for further analysis. The Power Spectral Density of the relative velocity and of the hexapod velocity is saved for further analysis.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/pxsp_r.mat'</span>, <span class="org-string">'pxsp_r'</span>, <span class="org-string">'f'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">save(<span class="org-string">'mat/pxsp_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxsp_r'</span>, <span class="org-string">'pxsp_s'</span>);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org1464a72" class="outline-3"> <div id="outline-container-org0a44924" class="outline-3">
<h3 id="org1464a72"><span class="section-number-3">2.6</span> Conclusion</h3> <h3 id="org0a44924"><span class="section-number-3">2.7</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-7">
<div class="important"> <div class="important" id="orga7d722f">
<p> <p>
The relative motion below 20Hz is dominated by another effect than the rotation of the Spindle (probably ground motion). The relative motion below 20Hz is dominated by another effect than the rotation of the Spindle (probably ground motion).
</p> </p>
@ -777,7 +547,7 @@ The Spindle rotation induces relative motion of the hexapod with respect to the
</div> </div>
<div class="important"> <div class="important" id="orga4c2e01">
<p> <p>
There is a huge peak at 24Hz on the sample vibration but not on the granite vibration There is a huge peak at 24Hz on the sample vibration but not on the granite vibration
</p> </p>
@ -793,8 +563,7 @@ There is a huge peak at 24Hz on the sample vibration but not on the granite vibr
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-10-31 jeu. 16:19</p> <p class="date">Created: 2020-11-12 jeu. 10:27</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>
</html> </html>

9
disturbance-sr-rz/index.org
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@ -9,13 +9,8 @@
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564
disturbance-ty-sr/index.html
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@ -3,249 +3,13 @@
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -258,28 +22,28 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orge303e87">1. Measurement description</a></li> <li><a href="#org5be3e39">1. Measurement description</a></li>
<li><a href="#orgc23d6dc">2. Data Analysis</a> <li><a href="#orgedd4b9f">2. Data Analysis</a>
<ul> <ul>
<li><a href="#org629d4b4">2.1. Load data</a></li> <li><a href="#org5c43df8">2.1. Load data</a></li>
<li><a href="#org79a2c27">2.2. Voltage to Velocity</a></li> <li><a href="#org64ca923">2.2. Voltage to Velocity</a></li>
<li><a href="#org1bafa09">2.3. Time domain plots</a></li> <li><a href="#org28e12e9">2.3. Time domain plots</a></li>
<li><a href="#org05973bc">2.4. Frequency Domain</a></li> <li><a href="#org2072860">2.4. Frequency Domain</a></li>
<li><a href="#org57188a5">2.5. Ty motion and current</a> <li><a href="#org556cfcd">2.5. Ty motion and current</a>
<ul> <ul>
<li><a href="#org07bb77c">2.5.1. Data pre-processing</a></li> <li><a href="#orga6f989f">2.5.1. Data pre-processing</a></li>
<li><a href="#org8bcb0f7">2.5.2. Time domain data</a></li> <li><a href="#orgf4ca54c">2.5.2. Time domain data</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org005d22e">2.6. Conclusion</a></li> <li><a href="#org7e6aef2">2.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orge303e87" class="outline-2"> <div id="outline-container-org5be3e39" class="outline-2">
<h2 id="orge303e87"><span class="section-number-2">1</span> Measurement description</h2> <h2 id="org5be3e39"><span class="section-number-2">1</span> Measurement description</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<b>Setup</b>: <b>Setup</b>:
@ -384,13 +148,13 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
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<div id="outline-container-orgc23d6dc" class="outline-2"> <div id="outline-container-orgedd4b9f" class="outline-2">
<h2 id="orgc23d6dc"><span class="section-number-2">2</span> Data Analysis</h2> <h2 id="orgedd4b9f"><span class="section-number-2">2</span> Data Analysis</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org4563c51"></a> <a id="orgf5774c2"></a>
</p> </p>
<div class="note"> <div class="note" id="org87cd5df">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/disturbance_ty_sr.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/disturbance_ty_sr.zip">here</a>.
</p> </p>
@ -398,66 +162,66 @@ All the files (data and Matlab scripts) are accessible <a href="data/disturbance
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<div id="outline-container-org629d4b4" class="outline-3"> <div id="outline-container-org5c43df8" class="outline-3">
<h3 id="org629d4b4"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="org5c43df8"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">ty_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_050.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_of = ty_of.data; <pre class="src src-matlab">ty_of = load(<span class="org-string">'mat/data_050.mat'</span>, <span class="org-string">'data'</span>); ty_of = ty_of.data;
ty_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_051.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_on = ty_on.data; ty_on = load(<span class="org-string">'mat/data_051.mat'</span>, <span class="org-string">'data'</span>); ty_on = ty_on.data;
ty_1h = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_052.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_1h = ty_1h.data; ty_1h = load(<span class="org-string">'mat/data_052.mat'</span>, <span class="org-string">'data'</span>); ty_1h = ty_1h.data;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org79a2c27" class="outline-3"> <div id="outline-container-org64ca923" class="outline-3">
<h3 id="org79a2c27"><span class="section-number-3">2.2</span> Voltage to Velocity</h3> <h3 id="org64ca923"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/These/meas/src/index.html">here</a>). We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/These/meas/src/index.html">here</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">gain = <span class="org-highlight-numbers-number">40</span>; <span class="org-comment">% [dB]</span> <pre class="src src-matlab">gain = 40; <span class="org-comment">% [dB]</span>
ty_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; ty_of(<span class="org-type">:</span>, 1) = voltageToVelocityL22(ty_of(<span class="org-type">:</span>, 1), ty_of(<span class="org-type">:</span>, 3), gain);
ty_on<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; ty_on(<span class="org-type">:</span>, 1) = voltageToVelocityL22(ty_on(<span class="org-type">:</span>, 1), ty_on(<span class="org-type">:</span>, 3), gain);
ty_1h<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; ty_1h(<span class="org-type">:</span>, 1) = voltageToVelocityL22(ty_1h(<span class="org-type">:</span>, 1), ty_1h(<span class="org-type">:</span>, 3), gain);
ty_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; ty_of(<span class="org-type">:</span>, 2) = voltageToVelocityL22(ty_of(<span class="org-type">:</span>, 2), ty_of(<span class="org-type">:</span>, 3), gain);
ty_on<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; ty_on(<span class="org-type">:</span>, 2) = voltageToVelocityL22(ty_on(<span class="org-type">:</span>, 2), ty_on(<span class="org-type">:</span>, 3), gain);
ty_1h<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; ty_1h(<span class="org-type">:</span>, 2) = voltageToVelocityL22(ty_1h(<span class="org-type">:</span>, 2), ty_1h(<span class="org-type">:</span>, 3), gain);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org1bafa09" class="outline-3"> <div id="outline-container-org28e12e9" class="outline-3">
<h3 id="org1bafa09"><span class="section-number-3">2.3</span> Time domain plots</h3> <h3 id="org28e12e9"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
We plot the measured velocity of the marble (figure <a href="#org53f1c30">1</a>), sample (figure <a href="#org6938117">2</a>) and the relative velocity of the sample with respect to the marble (figure <a href="#orgfd8af3e">3</a>). We plot the measured velocity of the marble (figure <a href="#orgd7a043f">1</a>), sample (figure <a href="#orgd957b15">2</a>) and the relative velocity of the sample with respect to the marble (figure <a href="#org0571475">3</a>).
</p> </p>
<p> <p>
We also integrate the relative velocity to obtain the relative displacement (figure <a href="#org425e005">4</a>). We also integrate the relative velocity to obtain the relative displacement (figure <a href="#orgca7d76b">4</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Marble <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_1h(<span class="org-type">:</span>, 3), ty_1h(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - Ty 1Hz'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_on(<span class="org-type">:</span>, 3), ty_on(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - Ty ON'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_of(<span class="org-type">:</span>, 3), ty_of(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - Ty OFF'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Velocity [m/s]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 2]);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
</pre> </pre>
</div> </div>
<div id="org53f1c30" class="figure"> <div id="orgd7a043f" class="figure">
<p><img src="figs/ty_marble_time.png" alt="ty_marble_time.png" /> <p><img src="figs/ty_marble_time.png" alt="ty_marble_time.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Velocity of the marble in the vertical direction</p> <p><span class="figure-number">Figure 1: </span>Velocity of the marble in the vertical direction</p>
@ -466,18 +230,18 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Sample <span class="org-type">-</span> Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_1h(<span class="org-type">:</span>, 3), ty_1h(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Sample - Ty - 1Hz'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_on(<span class="org-type">:</span>, 3), ty_on(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Sample - Ty - ON'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_of(<span class="org-type">:</span>, 3), ty_of(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Sample - Ty - OFF'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Velocity [m/s]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 2]);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
</pre> </pre>
</div> </div>
<div id="org6938117" class="figure"> <div id="orgd957b15" class="figure">
<p><img src="figs/ty_sample_time.png" alt="ty_sample_time.png" /> <p><img src="figs/ty_sample_time.png" alt="ty_sample_time.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Velocity of the sample in the vertical direction</p> <p><span class="figure-number">Figure 2: </span>Velocity of the sample in the vertical direction</p>
@ -486,18 +250,18 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Relative Velocity <span class="org-type">-</span> Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_1h(<span class="org-type">:</span>, 3), ty_1h(<span class="org-type">:</span>, 2)<span class="org-type">-</span>ty_1h(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Relative Velocity - Ty - 1Hz'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative Velocity - Ty - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_on(<span class="org-type">:</span>, 3), ty_on(<span class="org-type">:</span>, 2)<span class="org-type">-</span>ty_on(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Relative Velocity - Ty - ON'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative Velocity - Ty - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_of(<span class="org-type">:</span>, 3), ty_of(<span class="org-type">:</span>, 2)<span class="org-type">-</span>ty_of(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Relative Velocity - Ty - OFF'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Velocity [m/s]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 2]);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
</pre> </pre>
</div> </div>
<div id="orgfd8af3e" class="figure"> <div id="org0571475" class="figure">
<p><img src="figs/ty_relative_time.png" alt="ty_relative_time.png" /> <p><img src="figs/ty_relative_time.png" alt="ty_relative_time.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Relative velocity of the sample with respect to the marble</p> <p><span class="figure-number">Figure 3: </span>Relative velocity of the sample with respect to the marble</p>
@ -506,18 +270,18 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, ty_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>ty_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, ty_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Relative Displacement<span class="org-type">-</span> Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_1h(<span class="org-type">:</span>, 3), lsim(1<span class="org-type">/</span>s, ty_1h(<span class="org-type">:</span>, 2)<span class="org-type">-</span>ty_1h(<span class="org-type">:</span>, 1), ty_1h(<span class="org-type">:</span>, 3)), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Relative Displacement- Ty - 1Hz'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, ty_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>ty_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, ty_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative Displacement- Ty - ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_on(<span class="org-type">:</span>, 3), lsim(1<span class="org-type">/</span>s, ty_on(<span class="org-type">:</span>, 2)<span class="org-type">-</span>ty_on(<span class="org-type">:</span>, 1), ty_on(<span class="org-type">:</span>, 3)), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Relative Displacement- Ty - ON'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, ty_of<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>ty_of<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, ty_of<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative Displacement- Ty - OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_of(<span class="org-type">:</span>, 3), lsim(1<span class="org-type">/</span>s, ty_of(<span class="org-type">:</span>, 2)<span class="org-type">-</span>ty_of(<span class="org-type">:</span>, 1), ty_of(<span class="org-type">:</span>, 3)), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Relative Displacement- Ty - OFF'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Displacement </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Displacement [m]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 2]);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
</pre> </pre>
</div> </div>
<div id="org425e005" class="figure"> <div id="orgca7d76b" class="figure">
<p><img src="figs/ty_relative_disp_time.png" alt="ty_relative_disp_time.png" /> <p><img src="figs/ty_relative_disp_time.png" alt="ty_relative_disp_time.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Relative Displacement of the sample with respect to the marble</p> <p><span class="figure-number">Figure 4: </span>Relative Displacement of the sample with respect to the marble</p>
@ -525,18 +289,18 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-org05973bc" class="outline-3"> <div id="outline-container-org2072860" class="outline-3">
<h3 id="org05973bc"><span class="section-number-3">2.4</span> Frequency Domain</h3> <h3 id="org2072860"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
We first compute some parameters that will be used for the PSD computation. We first compute some parameters that will be used for the PSD computation.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = ty_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>ty_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = ty_of(2, 3)<span class="org-type">-</span>ty_of(1, 3);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
@ -548,9 +312,9 @@ Then we compute the Power Spectral Density using <code>pwelch</code> function.
First for the geophone located on the marble First for the geophone located on the marble
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_m, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxof_m, f] = pwelch(ty_of(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxon_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxon_m, <span class="org-type">~</span>] = pwelch(ty_on(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px1h_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px1h_m, <span class="org-type">~</span>] = pwelch(ty_1h(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre> </pre>
</div> </div>
@ -558,9 +322,9 @@ First for the geophone located on the marble
And for the geophone located at the sample position. And for the geophone located at the sample position.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_s, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxof_s, f] = pwelch(ty_of(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxon_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxon_s, <span class="org-type">~</span>] = pwelch(ty_on(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px1h_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px1h_s, <span class="org-type">~</span>] = pwelch(ty_1h(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre> </pre>
</div> </div>
@ -568,9 +332,9 @@ And for the geophone located at the sample position.
Finally, for the relative velocity. Finally, for the relative velocity.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_r, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxof_r, f] = pwelch(ty_of(<span class="org-type">:</span>, 2)<span class="org-type">-</span>ty_of(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxon_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxon_r, <span class="org-type">~</span>] = pwelch(ty_on(<span class="org-type">:</span>, 2)<span class="org-type">-</span>ty_on(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px1h_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>ty_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px1h_r, <span class="org-type">~</span>] = pwelch(ty_1h(<span class="org-type">:</span>, 2)<span class="org-type">-</span>ty_1h(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre> </pre>
</div> </div>
@ -578,28 +342,28 @@ Finally, for the relative velocity.
And we plot the ASD of the measured velocities: And we plot the ASD of the measured velocities:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>figure <a href="#org00eb9e9">5</a> for the geophone located on the marble</li> <li>figure <a href="#org177c365">5</a> for the geophone located on the marble</li>
<li>figure <a href="#org192c441">6</a> for the geophone at the sample position</li> <li>figure <a href="#org7f50f38">6</a> for the geophone at the sample position</li>
<li>figure <a href="#org1b88cd2">7</a> for the relative velocity</li> <li>figure <a href="#org5c98070">7</a> for the relative velocity</li>
</ul> </ul>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px1h_m<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Marble <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px1h_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - Ty 1Hz'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxon_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxon_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - Ty ON'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxof_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - Ty OFF'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([1, 500]);
</pre> </pre>
</div> </div>
<div id="org00eb9e9" class="figure"> <div id="org177c365" class="figure">
<p><img src="figs/psd_marble_compare.png" alt="psd_marble_compare.png" /> <p><img src="figs/psd_marble_compare.png" alt="psd_marble_compare.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Comparison of the ASD of the measured velocities from the Geophone on the marble</p> <p><span class="figure-number">Figure 5: </span>Comparison of the ASD of the measured velocities from the Geophone on the marble</p>
@ -608,20 +372,20 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px1h_s<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Sample <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px1h_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Sample - Ty 1Hz'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxon_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxon_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Sample - Ty ON'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxof_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Sample - Ty OFF'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([1, 500]);
</pre> </pre>
</div> </div>
<div id="org192c441" class="figure"> <div id="org7f50f38" class="figure">
<p><img src="figs/psd_sample_compare.png" alt="psd_sample_compare.png" /> <p><img src="figs/psd_sample_compare.png" alt="psd_sample_compare.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Comparison of the ASD of the measured velocities from the Geophone at the sample location</p> <p><span class="figure-number">Figure 6: </span>Comparison of the ASD of the measured velocities from the Geophone at the sample location</p>
@ -630,20 +394,20 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px1h_r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', 'Relative <span class="org-type">-</span> Ty <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px1h_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Relative - Ty 1Hz'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxon_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative - Ty ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxon_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Relative - Ty ON'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Relative - Ty OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxof_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Relative - Ty OFF'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([1, 500]);
</pre> </pre>
</div> </div>
<div id="org1b88cd2" class="figure"> <div id="org5c98070" class="figure">
<p><img src="figs/psd_relative_compare.png" alt="psd_relative_compare.png" /> <p><img src="figs/psd_relative_compare.png" alt="psd_relative_compare.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Comparison of the ASD of the relative velocity</p> <p><span class="figure-number">Figure 7: </span>Comparison of the ASD of the relative velocity</p>
@ -651,41 +415,74 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-org57188a5" class="outline-3"> <div id="outline-container-org556cfcd" class="outline-3">
<h3 id="org57188a5"><span class="section-number-3">2.5</span> Ty motion and current</h3> <h3 id="org556cfcd"><span class="section-number-3">2.5</span> Ty motion and current</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<p> <p>
The position of the translation stage and current flowing in its actuator are measured using the elmo software and saved as an csv file. The position of the translation stage and current flowing in its actuator are measured using the elmo software and saved as an csv file.
</p> </p>
</div> </div>
<div id="outline-container-org07bb77c" class="outline-4"> <div id="outline-container-orga6f989f" class="outline-4">
<h4 id="org07bb77c"><span class="section-number-4">2.5.1</span> Data pre-processing</h4> <h4 id="orga6f989f"><span class="section-number-4">2.5.1</span> Data pre-processing</h4>
<div class="outline-text-4" id="text-2-5-1"> <div class="outline-text-4" id="text-2-5-1">
<p> <p>
Let's look at at the start of the csv file. Let&rsquo;s look at at the start of the csv file.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-bash">sed -n <span class="org-highlight-numbers-number">1,30p</span> mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv | nl -ba - <pre class="src src-bash">sed -n 1,30p mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv | nl -ba -
</pre> </pre>
</div> </div>
<pre class="example" id="org149992b">
1 Elmo txt chart ver 2.0
2
3 [File Properties]
4 Creation Time,2019-05-13 05:33:43
5 Last Updated,2019-05-13 05:33:43
6 Resolution,0.001
7 Sampling Time,5E-05
8 Recording Time,5.461
9
10 [Chart Properties]
11 No.,Name,X Linear,X No.
12 1,Chart #1,True,0
13 2,Chart #2,True,0
14
15 [Chart Data]
16 Display No.,X No.,Y No.,X Unit,Y Unit,Color,Style,Width
17 1,1,2,sec,N/A,ff0000ff,Solid,TwoPoint
18 2,1,3,sec,N/A,ff0000ff,Solid,TwoPoint
19 2,1,4,sec,N/A,ff007f00,Solid,TwoPoint
20
21 [Signal Names]
22 1,Time (sec)
23 2,Position [cnt]
24 3,Current Command [A]
25 4,Total Current Command [A]
26
27 [Signals Data Group 1]
28 1,2,3,4,
29 0,-141044,-0.537239575086517,-0.537239575086517,
30 0.001,-143127,-0.530803752974691,-0.530803752974691,
</pre>
<p> <p>
The real data starts at line 29. The real data starts at line 29.
We then load this <code>cvs</code> file starting at line 29. We then load this <code>cvs</code> file starting at line 29.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">tye_on = csvread<span class="org-rainbow-delimiters-depth-1">(</span>"mat<span class="org-type">/</span>Ty<span class="org-type">-</span>when<span class="org-type">-</span>Rz<span class="org-type">-</span><span class="org-highlight-numbers-number">1Hz</span>.csv", <span class="org-highlight-numbers-number">29</span>, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">tye_on = csvread(<span class="org-string">"mat/Ty-when-Rz-1Hz.csv"</span>, 29, 0);
tye_1h = csvread<span class="org-rainbow-delimiters-depth-1">(</span>"mat<span class="org-type">/</span>Ty<span class="org-type">-</span>when<span class="org-type">-</span>Rz<span class="org-type">-</span><span class="org-highlight-numbers-number">1Hz</span><span class="org-type">-</span>and<span class="org-type">-</span>Ty<span class="org-type">-</span><span class="org-highlight-numbers-number">1Hz</span>.csv", <span class="org-highlight-numbers-number">29</span>, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>; tye_1h = csvread(<span class="org-string">"mat/Ty-when-Rz-1Hz-and-Ty-1Hz.csv"</span>, 29, 0);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org8bcb0f7" class="outline-4"> <div id="outline-container-orgf4ca54c" class="outline-4">
<h4 id="org8bcb0f7"><span class="section-number-4">2.5.2</span> Time domain data</h4> <h4 id="orgf4ca54c"><span class="section-number-4">2.5.2</span> Time domain data</h4>
<div class="outline-text-4" id="text-2-5-2"> <div class="outline-text-4" id="text-2-5-2">
<p> <p>
We plot the position of the translation stage measured by the encoders. We plot the position of the translation stage measured by the encoders.
@ -696,27 +493,27 @@ There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm
</p> </p>
<p> <p>
The result is shown on figure <a href="#orgfeb408e">8</a>. The result is shown on figure <a href="#org10136ca">8</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; subplot(1, 2, 1);
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">(</span>tye_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-3">(</span>tye_on<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">200000</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(tye_on(<span class="org-type">:</span>, 1), (tye_on(<span class="org-type">:</span>, 2)<span class="org-type">-</span>mean(tye_on(<span class="org-type">:</span>, 2)))<span class="org-type">/</span>200000);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 5]);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Position </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Position [mm]'</span>);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span><span class="org-string">'Ty - ON'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">, 'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend({<span class="org-string">'Ty - ON'</span>}, <span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; subplot(1, 2, 2);
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">(</span>tye_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-3">(</span>tye_1h<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">200000</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(tye_1h(<span class="org-type">:</span>, 1), (tye_1h(<span class="org-type">:</span>, 2)<span class="org-type">-</span>mean(tye_1h(<span class="org-type">:</span>, 2)))<span class="org-type">/</span>200000);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 5]);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Position </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Position [mm]'</span>);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span>'Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-2">}</span>, 'Location', 'northeast'<span class="org-rainbow-delimiters-depth-1">)</span>; legend({<span class="org-string">'Ty - 1Hz'</span>}, <span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
</pre> </pre>
</div> </div>
<div id="orgfeb408e" class="figure"> <div id="org10136ca" class="figure">
<p><img src="figs/ty_position_time.png" alt="ty_position_time.png" /> <p><img src="figs/ty_position_time.png" alt="ty_position_time.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Y position of the translation stage measured by the encoders</p> <p><span class="figure-number">Figure 8: </span>Y position of the translation stage measured by the encoders</p>
@ -724,27 +521,27 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rain
<p> <p>
We also plot the current as function of the time on figure <a href="#orgbd294dc">9</a>. We also plot the current as function of the time on figure <a href="#org553205c">9</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; subplot(1, 2, 1);
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, tye_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-2">(</span>tye_on<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(tye_on(<span class="org-type">:</span>, 1), tye_on(<span class="org-type">:</span>, 3)<span class="org-type">-</span>mean(tye_on(<span class="org-type">:</span>, 3)));
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 5]);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Current </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">A</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Current [A]'</span>);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span><span class="org-string">'Ty - ON'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-string">, 'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend({<span class="org-string">'Ty - ON'</span>}, <span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; subplot(1, 2, 2);
plot<span class="org-rainbow-delimiters-depth-1">(</span>tye_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, tye_1h<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>mean<span class="org-rainbow-delimiters-depth-2">(</span>tye_1h<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(tye_1h(<span class="org-type">:</span>, 1), tye_1h(<span class="org-type">:</span>, 3)<span class="org-type">-</span>mean(tye_1h(<span class="org-type">:</span>, 3)));
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 5]);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Current </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">A</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Current [A]'</span>);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">{</span>'Ty <span class="org-type">-</span> <span class="org-highlight-numbers-number">1Hz</span>'<span class="org-rainbow-delimiters-depth-2">}</span>, 'Location', 'northeast'<span class="org-rainbow-delimiters-depth-1">)</span>; legend({<span class="org-string">'Ty - 1Hz'</span>}, <span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
</pre> </pre>
</div> </div>
<div id="orgbd294dc" class="figure"> <div id="org553205c" class="figure">
<p><img src="figs/ty_current_time.png" alt="ty_current_time.png" /> <p><img src="figs/ty_current_time.png" alt="ty_current_time.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Current going through the actuator of the translation stage</p> <p><span class="figure-number">Figure 9: </span>Current going through the actuator of the translation stage</p>
@ -753,10 +550,10 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rain
</div> </div>
</div> </div>
<div id="outline-container-org005d22e" class="outline-3"> <div id="outline-container-org7e6aef2" class="outline-3">
<h3 id="org005d22e"><span class="section-number-3">2.6</span> Conclusion</h3> <h3 id="org7e6aef2"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-6">
<div class="important"> <div class="important" id="org6da1178">
<ul class="org-ul"> <ul class="org-ul">
<li></li> <li></li>
</ul> </ul>
@ -768,8 +565,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rain
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-15 mer. 15:49</p> <p class="date">Created: 2020-11-12 jeu. 10:27</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -258,30 +22,30 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org810c300">1. Measurement description</a></li> <li><a href="#org2aaea5a">1. Measurement description</a></li>
<li><a href="#orge7c9591">2. Measurement Analysis</a> <li><a href="#orgb83e4a0">2. Measurement Analysis</a>
<ul> <ul>
<li><a href="#orgec8ecca">2.1. Load data</a></li> <li><a href="#orga4b0f90">2.1. Load data</a></li>
<li><a href="#orgcd50803">2.2. Voltage to Velocity</a></li> <li><a href="#org08f7d3b">2.2. Voltage to Velocity</a></li>
<li><a href="#org1c8a0dc">2.3. Time domain plots</a></li> <li><a href="#orga7eb7f7">2.3. Time domain plots</a></li>
<li><a href="#org0d692f4">2.4. Frequency Domain</a></li> <li><a href="#org7915079">2.4. Frequency Domain</a></li>
<li><a href="#orgd741d6b">2.5. Relative Motion</a></li> <li><a href="#org7197f2e">2.5. Relative Motion</a></li>
<li><a href="#org3ded48e">2.6. Save</a></li> <li><a href="#orgdef72b0">2.6. Save</a></li>
<li><a href="#org4fbe75b">2.7. Position of the translation stage and Current</a> <li><a href="#org6e3ca4c">2.7. Position of the translation stage and Current</a>
<ul> <ul>
<li><a href="#orge07cd8f">2.7.1. Data pre-processing</a></li> <li><a href="#org363d3eb">2.7.1. Data pre-processing</a></li>
<li><a href="#org851b639">2.7.2. Time domain data</a></li> <li><a href="#org7b14198">2.7.2. Time domain data</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org011cbae">2.8. Conclusion</a></li> <li><a href="#orge66d0f8">2.8. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org810c300" class="outline-2"> <div id="outline-container-org2aaea5a" class="outline-2">
<h2 id="org810c300"><span class="section-number-2">1</span> Measurement description</h2> <h2 id="org2aaea5a"><span class="section-number-2">1</span> Measurement description</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<b>Setup</b>: <b>Setup</b>:
@ -311,7 +75,7 @@ The scans are done with the ELMO software.
</p> </p>
<p> <p>
The North of the Geophones corresponds to the +Y direction and the East of the Geophones to the +X direction (see figure <a href="#orgc5e9621">1</a>). The North of the Geophones corresponds to the +Y direction and the East of the Geophones to the +X direction (see figure <a href="#org0e95dcd">1</a>).
</p> </p>
<p> <p>
@ -395,7 +159,7 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table> </table>
<div id="orgc5e9621" class="figure"> <div id="org0e95dcd" class="figure">
<p><img src="./img/IMG_20190513_163032.jpg" alt="IMG_20190513_163032.jpg" width="500px" /> <p><img src="./img/IMG_20190513_163032.jpg" alt="IMG_20190513_163032.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Picture of the experimental setup</p> <p><span class="figure-number">Figure 1: </span>Picture of the experimental setup</p>
@ -408,13 +172,13 @@ The setup used for the measurement is described <a href="file:///home/thomas/Clo
</div> </div>
</div> </div>
<div id="outline-container-orge7c9591" class="outline-2"> <div id="outline-container-orgb83e4a0" class="outline-2">
<h2 id="orge7c9591"><span class="section-number-2">2</span> Measurement Analysis</h2> <h2 id="orgb83e4a0"><span class="section-number-2">2</span> Measurement Analysis</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org8955a2d"></a> <a id="orgacbdcf3"></a>
</p> </p>
<div class="note"> <div class="note" id="org3969b90">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/disturbance_ty.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/disturbance_ty.zip">here</a>.
</p> </p>
@ -422,18 +186,18 @@ All the files (data and Matlab scripts) are accessible <a href="data/disturbance
</div> </div>
</div> </div>
<div id="outline-container-orgec8ecca" class="outline-3"> <div id="outline-container-orga4b0f90" class="outline-3">
<h3 id="orgec8ecca"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="orga4b0f90"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">z_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_040.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; z_ty = z_ty.data; <pre class="src src-matlab">z_ty = load(<span class="org-string">'mat/data_040.mat'</span>, <span class="org-string">'data'</span>); z_ty = z_ty.data;
z_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_051.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; z_of = z_of.data; z_of = load(<span class="org-string">'mat/data_051.mat'</span>, <span class="org-string">'data'</span>); z_of = z_of.data;
e_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_041.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; e_ty = e_ty.data; e_ty = load(<span class="org-string">'mat/data_041.mat'</span>, <span class="org-string">'data'</span>); e_ty = e_ty.data;
e_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_042.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; e_of = e_of.data; e_of = load(<span class="org-string">'mat/data_042.mat'</span>, <span class="org-string">'data'</span>); e_of = e_of.data;
</pre> </pre>
</div> </div>
<div class="warning"> <div class="warning" id="orgd72d7d3">
<p> <p>
There is probably a sign error for the Geophone located on top of the Hexapod (only for the z direction). There is probably a sign error for the Geophone located on top of the Hexapod (only for the z direction).
The problem probably comes from the wiring in the Slip-Ring. The problem probably comes from the wiring in the Slip-Ring.
@ -442,70 +206,70 @@ The problem probably comes from the wiring in the Slip-Ring.
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">z_ty(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>z_ty(<span class="org-type">:</span>, 2);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgcd50803" class="outline-3"> <div id="outline-container-org08f7d3b" class="outline-3">
<h3 id="orgcd50803"><span class="section-number-3">2.2</span> Voltage to Velocity</h3> <h3 id="org08f7d3b"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/thesis/meas/srcindex.html">here</a>). We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="file:///home/thomas/Cloud/thesis/meas/srcindex.html">here</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">gain = <span class="org-highlight-numbers-number">40</span>; <span class="org-comment">% [dB]</span> <pre class="src src-matlab">gain = 40; <span class="org-comment">% [dB]</span>
z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; z_ty(<span class="org-type">:</span>, 1) = voltageToVelocityL22(z_ty(<span class="org-type">:</span>, 1), z_ty(<span class="org-type">:</span>, 3), gain);
z_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; z_of(<span class="org-type">:</span>, 1) = voltageToVelocityL22(z_of(<span class="org-type">:</span>, 1), z_of(<span class="org-type">:</span>, 3), gain);
e_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; e_ty(<span class="org-type">:</span>, 1) = voltageToVelocityL22(e_ty(<span class="org-type">:</span>, 1), e_ty(<span class="org-type">:</span>, 3), gain);
e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; e_of(<span class="org-type">:</span>, 1) = voltageToVelocityL22(e_of(<span class="org-type">:</span>, 1), e_of(<span class="org-type">:</span>, 3), gain);
z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; z_ty(<span class="org-type">:</span>, 2) = voltageToVelocityL22(z_ty(<span class="org-type">:</span>, 2), z_ty(<span class="org-type">:</span>, 3), gain);
z_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; z_of(<span class="org-type">:</span>, 2) = voltageToVelocityL22(z_of(<span class="org-type">:</span>, 2), z_of(<span class="org-type">:</span>, 3), gain);
e_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; e_ty(<span class="org-type">:</span>, 2) = voltageToVelocityL22(e_ty(<span class="org-type">:</span>, 2), e_ty(<span class="org-type">:</span>, 3), gain);
e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>; e_of(<span class="org-type">:</span>, 2) = voltageToVelocityL22(e_of(<span class="org-type">:</span>, 2), e_of(<span class="org-type">:</span>, 3), gain);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org1c8a0dc" class="outline-3"> <div id="outline-container-orga7eb7f7" class="outline-3">
<h3 id="org1c8a0dc"><span class="section-number-3">2.3</span> Time domain plots</h3> <h3 id="orga7eb7f7"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
We plot the measured velocity of the marble and sample in the vertical direction (figure <a href="#org60b7c99">2</a>) and in the X direction (figure <a href="#orgc2eb360">3</a>). We plot the measured velocity of the marble and sample in the vertical direction (figure <a href="#org2bf33b7">2</a>) and in the X direction (figure <a href="#orgfdb2237">3</a>).
</p> </p>
<p> <p>
We also integrate the relative velocity to obtain the relative displacement (figure <a href="#orgdcb90f2">4</a> in the X direction and figure <a href="#orgd1edd4b">5</a> in the Z direction). We also integrate the relative velocity to obtain the relative displacement (figure <a href="#orgdf208c5">4</a> in the X direction and figure <a href="#org29f0aa7">5</a> in the Z direction).
</p> </p>
<div id="org60b7c99" class="figure"> <div id="org2bf33b7" class="figure">
<p><img src="figs/ty_z_time.png" alt="ty_z_time.png" /> <p><img src="figs/ty_z_time.png" alt="ty_z_time.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Z velocity of the sample and marble when scanning with the translation stage</p> <p><span class="figure-number">Figure 2: </span>Z velocity of the sample and marble when scanning with the translation stage</p>
</div> </div>
<div id="orgc2eb360" class="figure"> <div id="orgfdb2237" class="figure">
<p><img src="figs/ty_e_time.png" alt="ty_e_time.png" /> <p><img src="figs/ty_e_time.png" alt="ty_e_time.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Velocity of the sample and marble in the east direction when scanning with the translation stage</p> <p><span class="figure-number">Figure 3: </span>Velocity of the sample and marble in the east direction when scanning with the translation stage</p>
</div> </div>
<div id="orgdcb90f2" class="figure"> <div id="orgdf208c5" class="figure">
<p><img src="figs/x_relative_disp.png" alt="x_relative_disp.png" /> <p><img src="figs/x_relative_disp.png" alt="x_relative_disp.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>X relative displacement of the sample with respect to the marble</p> <p><span class="figure-number">Figure 4: </span>X relative displacement of the sample with respect to the marble</p>
</div> </div>
<div id="orgd1edd4b" class="figure"> <div id="org29f0aa7" class="figure">
<p><img src="figs/z_relative_disp.png" alt="z_relative_disp.png" /> <p><img src="figs/z_relative_disp.png" alt="z_relative_disp.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Z relative disp of the sample with respect to the marble</p> <p><span class="figure-number">Figure 5: </span>Z relative disp of the sample with respect to the marble</p>
@ -513,14 +277,14 @@ We also integrate the relative velocity to obtain the relative displacement (fig
</div> </div>
</div> </div>
<div id="outline-container-org0d692f4" class="outline-3"> <div id="outline-container-org7915079" class="outline-3">
<h3 id="org0d692f4"><span class="section-number-3">2.4</span> Frequency Domain</h3> <h3 id="org7915079"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
We load measured ground motion at ID31 to compare with the velocities measured. We load measured ground motion at ID31 to compare with the velocities measured.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">gm = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'../ground-motion/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gm'</span>, <span class="org-string">'psd_gv'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">gm = load(<span class="org-string">'../ground-motion/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gm'</span>, <span class="org-string">'psd_gv'</span>);
</pre> </pre>
</div> </div>
@ -528,11 +292,11 @@ We load measured ground motion at ID31 to compare with the velocities measured.
We first compute some parameters that will be used for the PSD computation. We first compute some parameters that will be used for the PSD computation.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>z_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = z_ty(2, 3)<span class="org-type">-</span>z_ty(1, 3);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
@ -544,10 +308,10 @@ Then we compute the Power Spectral Density using <code>pwelch</code> function.
First for the geophone located on the marble First for the geophone located on the marble
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxz_ty_m, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxz_ty_m, f] = pwelch(z_ty(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxz_of_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxz_of_m, <span class="org-type">~</span>] = pwelch(z_of(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_ty_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxe_ty_m, <span class="org-type">~</span>] = pwelch(e_ty(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_of_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxe_of_m, <span class="org-type">~</span>] = pwelch(e_of(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
</pre> </pre>
</div> </div>
@ -555,10 +319,10 @@ First for the geophone located on the marble
And for the geophone located at the sample position. And for the geophone located at the sample position.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxz_ty_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxz_ty_s, <span class="org-type">~</span>] = pwelch(z_ty(<span class="org-type">:</span>, 2), win, [], gm.f, Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxz_of_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxz_of_s, <span class="org-type">~</span>] = pwelch(z_of(<span class="org-type">:</span>, 2), win, [], gm.f, Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_ty_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxe_ty_s, <span class="org-type">~</span>] = pwelch(e_ty(<span class="org-type">:</span>, 2), win, [], gm.f, Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_of_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxe_of_s, <span class="org-type">~</span>] = pwelch(e_of(<span class="org-type">:</span>, 2), win, [], gm.f, Fs);
</pre> </pre>
</div> </div>
@ -566,13 +330,13 @@ And for the geophone located at the sample position.
And we plot the ASD of the measured velocities: And we plot the ASD of the measured velocities:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>figure <a href="#org888ff45">6</a> compares the marble velocity in the east direction when scanning and when Ty is OFF</li> <li>figure <a href="#orgca2c421">6</a> compares the marble velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#orgde2e042">7</a> compares the sample velocity in the east direction when scanning and when Ty is OFF</li> <li>figure <a href="#org0dcea9c">7</a> compares the sample velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#orga58a3f5">8</a> shows the marble and sample velocities in the Z direction when scanning with the translation stage</li> <li>figure <a href="#orgd07432f">8</a> shows the marble and sample velocities in the Z direction when scanning with the translation stage</li>
</ul> </ul>
<div id="org888ff45" class="figure"> <div id="orgca2c421" class="figure">
<p><img src="figs/asd_east_marble.png" alt="asd_east_marble.png" /> <p><img src="figs/asd_east_marble.png" alt="asd_east_marble.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Amplitude spectral density of the measured velocities corresponding to the geophone in the east direction located on the marble when the translation stage is OFF and when it is scanning at 1Hz</p> <p><span class="figure-number">Figure 6: </span>Amplitude spectral density of the measured velocities corresponding to the geophone in the east direction located on the marble when the translation stage is OFF and when it is scanning at 1Hz</p>
@ -580,7 +344,7 @@ And we plot the ASD of the measured velocities:
<div id="orgde2e042" class="figure"> <div id="org0dcea9c" class="figure">
<p><img src="figs/asd_east_sample.png" alt="asd_east_sample.png" /> <p><img src="figs/asd_east_sample.png" alt="asd_east_sample.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Amplitude spectral density of the measured velocities corresponding to the geophone in the east direction located at the sample location when the translation stage is OFF and when it is scanning at 1Hz</p> <p><span class="figure-number">Figure 7: </span>Amplitude spectral density of the measured velocities corresponding to the geophone in the east direction located at the sample location when the translation stage is OFF and when it is scanning at 1Hz</p>
@ -588,14 +352,14 @@ And we plot the ASD of the measured velocities:
<div id="orga58a3f5" class="figure"> <div id="orgd07432f" class="figure">
<p><img src="figs/asd_z_direction.png" alt="asd_z_direction.png" /> <p><img src="figs/asd_z_direction.png" alt="asd_z_direction.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz</p> <p><span class="figure-number">Figure 8: </span>Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz</p>
</div> </div>
<div id="org1dd835a" class="figure"> <div id="org7ccf215" class="figure">
<p><img src="figs/asd_z_direction.png" alt="asd_z_direction.png" /> <p><img src="figs/asd_z_direction.png" alt="asd_z_direction.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz</p> <p><span class="figure-number">Figure 9: </span>Amplitude spectral density of the measure velocity corresponding to the geophone in the vertical direction located on the granite and at the sample location when the translation stage is scanning at 1Hz</p>
@ -603,39 +367,53 @@ And we plot the ASD of the measured velocities:
</div> </div>
</div> </div>
<div id="outline-container-orgd741d6b" class="outline-3"> <div id="outline-container-org7197f2e" class="outline-3">
<h3 id="orgd741d6b"><span class="section-number-3">2.5</span> Relative Motion</h3> <h3 id="org7197f2e"><span class="section-number-3">2.5</span> Relative Motion</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<p> <p>
And finally for the relative velocity between the sample and the marble. And finally for the relative velocity between the sample and the marble.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxz_ty_r, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>z_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxz_ty_r, f] = pwelch(z_ty(<span class="org-type">:</span>, 2)<span class="org-type">-</span>z_ty(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxz_of_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>z_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxz_of_r, <span class="org-type">~</span>] = pwelch(z_of(<span class="org-type">:</span>, 2)<span class="org-type">-</span>z_of(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_ty_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>e_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxe_ty_r, <span class="org-type">~</span>] = pwelch(e_ty(<span class="org-type">:</span>, 2)<span class="org-type">-</span>e_ty(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxe_of_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>e_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxe_of_r, <span class="org-type">~</span>] = pwelch(e_of(<span class="org-type">:</span>, 2)<span class="org-type">-</span>e_of(<span class="org-type">:</span>, 1), win, [], gm.f, Fs);
</pre> </pre>
</div> </div>
<p> <p>
Fig. <a href="#org7d4814e">11</a> shows the relative velocity of the sample with respect to the granite in the X direction when the translation stage is OFF and when it is scanning at 1Hz Fig. <a href="#org4172285">11</a> shows the relative velocity of the sample with respect to the granite in the X direction when the translation stage is OFF and when it is scanning at 1Hz
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxz_of_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty OFF - Relative - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxz_of_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty OFF - Relative - Z'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxz_ty_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Relative <span class="org-type">-</span> Z<span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxz_of_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty 1Hz - Relative - Z'</span>);
plot(f, sqrt(pxz_of_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty 1Hz - Relative - Z'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0.1, 500]);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot(f, sqrt(pxz_of_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty OFF - Relative - Z'</span>);
plot(f, sqrt(pxz_ty_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty 1Hz - Relative - Z'</span>);
hold off;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span>);
xlim([0.1, 500]);
</pre> </pre>
</div> </div>
<div id="org61c3a2e" class="figure"> <div id="org0a0b6dc" class="figure">
<p><img src="figs/asd_z_relative.png" alt="asd_z_relative.png" /> <p><img src="figs/asd_z_relative.png" alt="asd_z_relative.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Amplitude spectral density of the measured relative velocity in the X direction</p> <p><span class="figure-number">Figure 10: </span>Amplitude spectral density of the measured relative velocity in the X direction</p>
@ -644,19 +422,19 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_of_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty OFF - Relative - E'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxe_of_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty OFF - Relative - E'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxe_ty_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Relative <span class="org-type">-</span> E<span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxe_ty_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty 1Hz - Relative - E'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0.1, 500]);
</pre> </pre>
</div> </div>
<div id="org7d4814e" class="figure"> <div id="org4172285" class="figure">
<p><img src="figs/asd_e_relative.png" alt="asd_e_relative.png" /> <p><img src="figs/asd_e_relative.png" alt="asd_e_relative.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Amplitude spectral density of the measured relative velocity in the X direction</p> <p><span class="figure-number">Figure 11: </span>Amplitude spectral density of the measured relative velocity in the X direction</p>
@ -664,108 +442,141 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-org3ded48e" class="outline-3"> <div id="outline-container-orgdef72b0" class="outline-3">
<h3 id="org3ded48e"><span class="section-number-3">2.6</span> Save</h3> <h3 id="orgdef72b0"><span class="section-number-3">2.6</span> Save</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-6">
<p> <p>
The Power Spectral Density of the relative velocity is saved for further analysis. The Power Spectral Density of the relative velocity is saved for further analysis.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/pxz_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxz_ty_r'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">save(<span class="org-string">'mat/pxz_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxz_ty_r'</span>, <span class="org-string">'pxz_ty_s'</span>);
save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/pxe_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxe_ty_r'</span><span class="org-rainbow-delimiters-depth-1">)</span>; save(<span class="org-string">'mat/pxe_ty_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxe_ty_r'</span>, <span class="org-string">'pxe_ty_s'</span>);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org4fbe75b" class="outline-3"> <div id="outline-container-org6e3ca4c" class="outline-3">
<h3 id="org4fbe75b"><span class="section-number-3">2.7</span> Position of the translation stage and Current</h3> <h3 id="org6e3ca4c"><span class="section-number-3">2.7</span> Position of the translation stage and Current</h3>
<div class="outline-text-3" id="text-2-7"> <div class="outline-text-3" id="text-2-7">
<p> <p>
The position of the translation and current flowing in its actuator are measured using the elmo software and saved as an csv file. The position of the translation and current flowing in its actuator are measured using the elmo software and saved as an csv file.
</p> </p>
</div> </div>
<div id="outline-container-orge07cd8f" class="outline-4"> <div id="outline-container-org363d3eb" class="outline-4">
<h4 id="orge07cd8f"><span class="section-number-4">2.7.1</span> Data pre-processing</h4> <h4 id="org363d3eb"><span class="section-number-4">2.7.1</span> Data pre-processing</h4>
<div class="outline-text-4" id="text-2-7-1"> <div class="outline-text-4" id="text-2-7-1">
<p> <p>
Let's look at at the start of the csv file. Let&rsquo;s look at at the start of the csv file.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-bash">sed -n <span class="org-highlight-numbers-number">1,30p</span> mat/sin_elmo.csv | nl -ba - <pre class="src src-bash">sed -n 1,30p mat/sin_elmo.csv | nl -ba -
</pre> </pre>
</div> </div>
<pre class="example" id="org7539d3f">
1 Elmo txt chart ver 2.0
2
3 [File Properties]
4 Creation Time,2019-05-13 05:11:45
5 Last Updated,2019-05-13 05:11:45
6 Resolution,0.001
7 Sampling Time,5E-05
8 Recording Time,5.461
9
10 [Chart Properties]
11 No.,Name,X Linear,X No.
12 1,Chart #1,True,0
13 2,Chart #2,True,0
14
15 [Chart Data]
16 Display No.,X No.,Y No.,X Unit,Y Unit,Color,Style,Width
17 1,1,2,sec,N/A,ff0000ff,Solid,TwoPoint
18 2,1,3,sec,N/A,ff0000ff,Solid,TwoPoint
19 2,1,4,sec,N/A,ff007f00,Solid,TwoPoint
20
21 [Signal Names]
22 1,Time (sec)
23 2,Position [cnt]
24 3,Current Command [A]
25 4,Total Current Command [A]
26
27 [Signals Data Group 1]
28 1,2,3,4,
29 0,1110769,-0.320872406596209,-0.320872406596209,
30 0.001,1108743,-0.319658428261391,-0.319658428261391,
</pre>
<p> <p>
The real data starts at line 29. The real data starts at line 29.
We then load this <code>cvs</code> file starting at line 29. We then load this <code>cvs</code> file starting at line 29.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">data = csvread<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">"mat/sin_elmo.csv"</span>, <span class="org-highlight-numbers-number">29</span>, <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">data = csvread(<span class="org-string">"mat/sin_elmo.csv"</span>, 29, 0);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org851b639" class="outline-4"> <div id="outline-container-org7b14198" class="outline-4">
<h4 id="org851b639"><span class="section-number-4">2.7.2</span> Time domain data</h4> <h4 id="org7b14198"><span class="section-number-4">2.7.2</span> Time domain data</h4>
<div class="outline-text-4" id="text-2-7-2"> <div class="outline-text-4" id="text-2-7-2">
<p> <p>
We plot the position of the translation stage measured by the encoders. We plot the position of the translation stage measured by the encoders.
There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm. There is 200000 encoder count for each mm, we then divide by 200000 to obtain mm.
The result is shown on figure <a href="#orgf3ec62f">12</a>. The result is shown on figure <a href="#org5fc3c58">12</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">200000</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(data(<span class="org-type">:</span>, 1), data(<span class="org-type">:</span>, 2)<span class="org-type">/</span>200000);
hold off; hold off;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 5]);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Position </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Position [mm]'</span>);
</pre> </pre>
</div> </div>
<div id="orgf3ec62f" class="figure"> <div id="org5fc3c58" class="figure">
<p><img src="figs/ty_position_time.png" alt="ty_position_time.png" /> <p><img src="figs/ty_position_time.png" alt="ty_position_time.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Y position of the translation stage measured by the encoders</p> <p><span class="figure-number">Figure 12: </span>Y position of the translation stage measured by the encoders</p>
</div> </div>
<div id="org501c879" class="figure"> <div id="org8a1581f" class="figure">
<p><img src="figs/ty_position_time_zoom.png" alt="ty_position_time_zoom.png" /> <p><img src="figs/ty_position_time_zoom.png" alt="ty_position_time_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Y position of the translation stage measured by the encoders - Zoom</p> <p><span class="figure-number">Figure 13: </span>Y position of the translation stage measured by the encoders - Zoom</p>
</div> </div>
<p> <p>
We also plot the current as function of the time on figure <a href="#orge486741">14</a>. We also plot the current as function of the time on figure <a href="#org43368d0">14</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(data(<span class="org-type">:</span>, 1), data(<span class="org-type">:</span>, 3));
hold off; hold off;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">5</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">10</span>, <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 5]); ylim([<span class="org-type">-</span>10, 10]);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Current </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">A</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Current [A]'</span>);
</pre> </pre>
</div> </div>
<div id="orge486741" class="figure"> <div id="org43368d0" class="figure">
<p><img src="figs/current_time.png" alt="current_time.png" /> <p><img src="figs/current_time.png" alt="current_time.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Current going through the actuator of the translation stage</p> <p><span class="figure-number">Figure 14: </span>Current going through the actuator of the translation stage</p>
</div> </div>
<div id="org8b9bcbe" class="figure"> <div id="org6a48bae" class="figure">
<p><img src="figs/current_time_zoom.png" alt="current_time_zoom.png" /> <p><img src="figs/current_time_zoom.png" alt="current_time_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 15: </span>Current going through the actuator of the translation stage - Zoom</p> <p><span class="figure-number">Figure 15: </span>Current going through the actuator of the translation stage - Zoom</p>
@ -774,10 +585,10 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-org011cbae" class="outline-3"> <div id="outline-container-orge66d0f8" class="outline-3">
<h3 id="org011cbae"><span class="section-number-3">2.8</span> Conclusion</h3> <h3 id="orge66d0f8"><span class="section-number-3">2.8</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-8"> <div class="outline-text-3" id="text-2-8">
<div class="important"> <div class="important" id="org637452e">
<ul class="org-ul"> <ul class="org-ul">
<li>The acquisition is done using the Speedgoat as well as using ELMO. The two acquisition are <b>not</b> synchronize</li> <li>The acquisition is done using the Speedgoat as well as using ELMO. The two acquisition are <b>not</b> synchronize</li>
<li>The value of the translation stage encoder can also be read with the speedgoat, this could permit to synchronize the measurements</li> <li>The value of the translation stage encoder can also be read with the speedgoat, this could permit to synchronize the measurements</li>
@ -790,8 +601,7 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-10-31 jeu. 18:00</p> <p class="date">Created: 2020-11-12 jeu. 10:27</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>
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9
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -258,26 +22,26 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org2ead7e9">1. Experimental Setup</a></li> <li><a href="#org4cf6966">1. Experimental Setup</a></li>
<li><a href="#org8e5682f">2. Data Analysis</a> <li><a href="#org9e2bd9f">2. Data Analysis</a>
<ul> <ul>
<li><a href="#org71d31f6">2.1. Load data</a></li> <li><a href="#org3b8531a">2.1. Load data</a></li>
<li><a href="#org36715e9">2.2. Time domain plots</a></li> <li><a href="#orgf20b247">2.2. Time domain plots</a></li>
<li><a href="#org32ab030">2.3. Compute the power spectral densities</a></li> <li><a href="#org581339a">2.3. Compute the power spectral densities</a></li>
<li><a href="#orgb8b258a">2.4. Compute the transfer function from floor motion to ground motion</a></li> <li><a href="#orgdfd290d">2.4. Compute the transfer function from floor motion to ground motion</a></li>
<li><a href="#org806c2da">2.5. Conclusion</a></li> <li><a href="#org184f531">2.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org2ead7e9" class="outline-2"> <div id="outline-container-org4cf6966" class="outline-2">
<h2 id="org2ead7e9"><span class="section-number-2">1</span> Experimental Setup</h2> <h2 id="org4cf6966"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<b>Setup</b>: <b>Setup</b>:
One geophone is located on the marble, the other one on the floor (see figure <a href="#org04c2f7b">1</a>). One geophone is located on the marble, the other one on the floor (see figure <a href="#org509b52d">1</a>).
</p> </p>
@ -382,14 +146,14 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table> </table>
<div id="org04c2f7b" class="figure"> <div id="org509b52d" class="figure">
<p><img src="./img/IMG_20190513_161729.jpg" alt="IMG_20190513_161729.jpg" width="500px" /> <p><img src="./img/IMG_20190513_161729.jpg" alt="IMG_20190513_161729.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Picture of the experimental setup</p> <p><span class="figure-number">Figure 1: </span>Picture of the experimental setup</p>
</div> </div>
<div id="orge39c59f" class="figure"> <div id="orgcc7cff8" class="figure">
<p><img src="./img/IMG_20190513_161718.jpg" alt="IMG_20190513_161718.jpg" width="500px" /> <p><img src="./img/IMG_20190513_161718.jpg" alt="IMG_20190513_161718.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Picture of the experimental setup</p> <p><span class="figure-number">Figure 2: </span>Picture of the experimental setup</p>
@ -397,14 +161,13 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</div> </div>
</div> </div>
<div id="outline-container-org8e5682f" class="outline-2"> <div id="outline-container-org9e2bd9f" class="outline-2">
<h2 id="org8e5682f"><span class="section-number-2">2</span> Data Analysis</h2> <h2 id="org9e2bd9f"><span class="section-number-2">2</span> Data Analysis</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org4b537af"></a> <a id="org216b8bb"></a>
</p> </p>
<div class="note" id="org5f7cf2d">
<div class="note">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/marble_dynamics.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/marble_dynamics.zip">here</a>.
</p> </p>
@ -412,54 +175,54 @@ All the files (data and Matlab scripts) are accessible <a href="data/marble_dyna
</div> </div>
</div> </div>
<div id="outline-container-org71d31f6" class="outline-3"> <div id="outline-container-org3b8531a" class="outline-3">
<h3 id="org71d31f6"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="org3b8531a"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">m_z = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_037.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_z = m_z.data; <pre class="src src-matlab">m_z = load(<span class="org-string">'mat/data_037.mat'</span>, <span class="org-string">'data'</span>); m_z = m_z.data;
m_n = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_038.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_n = m_n.data; m_n = load(<span class="org-string">'mat/data_038.mat'</span>, <span class="org-string">'data'</span>); m_n = m_n.data;
m_e = load<span class="org-rainbow-delimiters-depth-1">(</span>'mat<span class="org-type">/</span>data_039.mat', <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_e = m_e.data; m_e = load(<span class="org-string">'mat/data_039.mat'</span>, <span class="org-string">'data'</span>); m_e = m_e.data;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org36715e9" class="outline-3"> <div id="outline-container-orgf20b247" class="outline-3">
<h3 id="org36715e9"><span class="section-number-3">2.2</span> Time domain plots</h3> <h3 id="orgf20b247"><span class="section-number-3">2.2</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; subplot(1, 3, 1);
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(m_z(<span class="org-type">:</span>, 3), m_z(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - Z'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Floor - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(m_z(<span class="org-type">:</span>, 3), m_z(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Floor - Z'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">2</span> <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 100]); ylim([<span class="org-type">-</span>2 2]);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; subplot(1, 3, 2);
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - N'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(m_n(<span class="org-type">:</span>, 3), m_n(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - N'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Floor - N'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(m_n(<span class="org-type">:</span>, 3), m_n(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Floor - N'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">2</span> <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 100]); ylim([<span class="org-type">-</span>2 2]);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; subplot(1, 3, 3);
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - E'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(m_e(<span class="org-type">:</span>, 3), m_e(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - E'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Floor - E'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(m_e(<span class="org-type">:</span>, 3), m_e(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Floor - E'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">2</span> <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 100]); ylim([<span class="org-type">-</span>2 2]);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
</pre> </pre>
</div> </div>
<div id="org10ef412" class="figure"> <div id="org79e8540" class="figure">
<p><img src="figs/marble_floor_motion_time.png" alt="marble_floor_motion_time.png" /> <p><img src="figs/marble_floor_motion_time.png" alt="marble_floor_motion_time.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Floor and ground motion</p> <p><span class="figure-number">Figure 3: </span>Floor and ground motion</p>
@ -467,18 +230,18 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-org32ab030" class="outline-3"> <div id="outline-container-org581339a" class="outline-3">
<h3 id="org32ab030"><span class="section-number-3">2.3</span> Compute the power spectral densities</h3> <h3 id="org581339a"><span class="section-number-3">2.3</span> Compute the power spectral densities</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
We first compute some parameters that will be used for the PSD computation. We first compute some parameters that will be used for the PSD computation.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = m_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>m_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = m_z(2, 3)<span class="org-type">-</span>m_z(1, 3);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
@ -486,38 +249,38 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
Then we compute the Power Spectral Density using <code>pwelch</code> function. Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px_fz, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[px_fz, f] = pwelch(m_z(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px_gz, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px_gz, <span class="org-type">~</span>] = pwelch(m_z(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px_fn, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px_fn, <span class="org-type">~</span>] = pwelch(m_n(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px_gn, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px_gn, <span class="org-type">~</span>] = pwelch(m_n(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px_fe, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px_fe, <span class="org-type">~</span>] = pwelch(m_e(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px_ge, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px_ge, <span class="org-type">~</span>] = pwelch(m_e(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre> </pre>
</div> </div>
<p> <p>
The results are shown on figure <a href="#org0484222">4</a> for the Z direction, figure <a href="#org691dab7">5</a> for the north direction, and figure <a href="#org0047fc8">6</a> for the east direction. The results are shown on figure <a href="#orga9e6519">4</a> for the Z direction, figure <a href="#orgdb1e6aa">5</a> for the north direction, and figure <a href="#orgc40ceda">6</a> for the east direction.
</p> </p>
<div id="org0484222" class="figure"> <div id="orga9e6519" class="figure">
<p><img src="figs/floor_marble_psd_z.png" alt="floor_marble_psd_z.png" /> <p><img src="figs/floor_marble_psd_z.png" alt="floor_marble_psd_z.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - Z direction</p> <p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - Z direction</p>
</div> </div>
<div id="org691dab7" class="figure"> <div id="orgdb1e6aa" class="figure">
<p><img src="figs/floor_marble_psd_n.png" alt="floor_marble_psd_n.png" /> <p><img src="figs/floor_marble_psd_n.png" alt="floor_marble_psd_n.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - N direction</p> <p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - N direction</p>
</div> </div>
<div id="org0047fc8" class="figure"> <div id="orgc40ceda" class="figure">
<p><img src="figs/floor_marble_psd_e.png" alt="floor_marble_psd_e.png" /> <p><img src="figs/floor_marble_psd_e.png" alt="floor_marble_psd_e.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - E direction</p> <p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - E direction</p>
@ -525,25 +288,25 @@ The results are shown on figure <a href="#org0484222">4</a> for the Z direction,
</div> </div>
</div> </div>
<div id="outline-container-orgb8b258a" class="outline-3"> <div id="outline-container-orgdfd290d" class="outline-3">
<h3 id="orgb8b258a"><span class="section-number-3">2.4</span> Compute the transfer function from floor motion to ground motion</h3> <h3 id="orgdfd290d"><span class="section-number-3">2.4</span> Compute the transfer function from floor motion to ground motion</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
We now compute the transfer function from the floor motion to the granite motion. We now compute the transfer function from the floor motion to the granite motion.
</p> </p>
<p> <p>
The result is shown on figure <a href="#orgac80e8a">7</a>. The result is shown on figure <a href="#orgc536396">7</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>TZ, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">-</span>m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[TZ, f] = tfestimate(m_z(<span class="org-type">:</span>, 1), <span class="org-type">-</span>m_z(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>TN, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">-</span>m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [TN, <span class="org-type">~</span>] = tfestimate(m_n(<span class="org-type">:</span>, 1), <span class="org-type">-</span>m_n(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>TE, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">-</span>m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [TE, <span class="org-type">~</span>] = tfestimate(m_e(<span class="org-type">:</span>, 1), <span class="org-type">-</span>m_e(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre> </pre>
</div> </div>
<div id="orgac80e8a" class="figure"> <div id="orgc536396" class="figure">
<p><img src="figs/tf_granite.png" alt="tf_granite.png" /> <p><img src="figs/tf_granite.png" alt="tf_granite.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Transfer function from floor motion to granite motion</p> <p><span class="figure-number">Figure 7: </span>Transfer function from floor motion to granite motion</p>
@ -551,10 +314,10 @@ The result is shown on figure <a href="#orgac80e8a">7</a>.
</div> </div>
</div> </div>
<div id="outline-container-org806c2da" class="outline-3"> <div id="outline-container-org184f531" class="outline-3">
<h3 id="org806c2da"><span class="section-number-3">2.5</span> Conclusion</h3> <h3 id="org184f531"><span class="section-number-3">2.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<div class="important"> <div class="important" id="org1429884">
<ul class="org-ul"> <ul class="org-ul">
<li>We see resonance of the granite at 33Hz in the horizontal directions</li> <li>We see resonance of the granite at 33Hz in the horizontal directions</li>
<li>We see two resonances for the z direction: at 60Hz and 75Hz</li> <li>We see two resonances for the z direction: at 60Hz and 75Hz</li>
@ -567,8 +330,7 @@ The result is shown on figure <a href="#orgac80e8a">7</a>.
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-14 mar. 11:25</p> <p class="date">Created: 2020-11-12 jeu. 10:28</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
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9
dynamical-meas-granite/index.org
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equipment/index.html
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<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org1c9b83c">1. Geophone</a></li> <li><a href="#org70e1d6f">1. Geophone</a></li>
<li><a href="#orgad1cff7">2. Speedgoat</a></li> <li><a href="#org66f7217">2. Speedgoat</a></li>
<li><a href="#org9898f44">3. Voltage amplifier</a></li> <li><a href="#org63a67fa">3. Voltage amplifier</a></li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org1c9b83c" class="outline-2"> <div id="outline-container-org70e1d6f" class="outline-2">
<h2 id="org1c9b83c"><span class="section-number-2">1</span> Geophone</h2> <h2 id="org70e1d6f"><span class="section-number-2">1</span> Geophone</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
L22 L22
@ -274,8 +38,8 @@ L22
</div> </div>
</div> </div>
<div id="outline-container-orgad1cff7" class="outline-2"> <div id="outline-container-org66f7217" class="outline-2">
<h2 id="orgad1cff7"><span class="section-number-2">2</span> Speedgoat</h2> <h2 id="org66f7217"><span class="section-number-2">2</span> Speedgoat</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<ul class="org-ul"> <ul class="org-ul">
<li>ADC: 16bits</li> <li>ADC: 16bits</li>
@ -284,11 +48,11 @@ L22
</div> </div>
</div> </div>
<div id="outline-container-org9898f44" class="outline-2"> <div id="outline-container-org63a67fa" class="outline-2">
<h2 id="org9898f44"><span class="section-number-2">3</span> Voltage amplifier</h2> <h2 id="org63a67fa"><span class="section-number-2">3</span> Voltage amplifier</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<div id="org7270884" class="figure"> <div id="org6ee2878" class="figure">
<p><img src="./img/DLPVA_W_R2.jpg" alt="DLPVA_W_R2.jpg" /> <p><img src="./img/DLPVA_W_R2.jpg" alt="DLPVA_W_R2.jpg" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Picture of the voltage amplifier DLPVA</p> <p><span class="figure-number">Figure 1: </span>Picture of the voltage amplifier DLPVA</p>
@ -320,8 +84,7 @@ The exact model is DLPVA-100-B-D
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-15 mer. 08:42</p> <p class="date">Created: 2020-11-12 jeu. 10:28</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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9
equipment/index.org
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@ -9,13 +9,8 @@
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<title>Ground Motion Measurements</title> <title>Ground Motion Measurements</title>
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<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -284,21 +30,21 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org5f3a483">1. Experimental Setup</a></li> <li><a href="#org98d0be2">1. Experimental Setup</a></li>
<li><a href="#orgb6a54b7">2. Measurement Analysis</a> <li><a href="#org7e6d21c">2. Measurement Analysis</a>
<ul> <ul>
<li><a href="#org4ded9a6">2.1. Load data</a></li> <li><a href="#orgb4815e7">2.1. Load data</a></li>
<li><a href="#orgddfc81a">2.2. Time domain plots of the measured voltage</a></li> <li><a href="#org76505c6">2.2. Time domain plots of the measured voltage</a></li>
<li><a href="#orgf447e5f">2.3. Computation of the ASD of the measured voltage</a></li> <li><a href="#orge77c65d">2.3. Computation of the ASD of the measured voltage</a></li>
<li><a href="#org7130c8f">2.4. Scaling to take into account the sensibility of the geophone and the voltage amplifier</a></li> <li><a href="#org7f9c12d">2.4. Scaling to take into account the sensibility of the geophone and the voltage amplifier</a></li>
<li><a href="#org456f387">2.5. Time domain plots of the ground motion</a></li> <li><a href="#org7f5940d">2.5. Time domain plots of the ground motion</a></li>
<li><a href="#org76df958">2.6. Computation of the ASD of the velocity and displacement</a></li> <li><a href="#org02ba5d0">2.6. Computation of the ASD of the velocity and displacement</a></li>
<li><a href="#org63b1f9a">2.7. Save</a></li> <li><a href="#org1e033f3">2.7. Save</a></li>
<li><a href="#orgabb922e">2.8. Comparison with other measurements of ground motion</a> <li><a href="#org8d373fd">2.8. Comparison with other measurements of ground motion</a>
<ul> <ul>
<li><a href="#org499997c">2.8.1. Load the measurement data</a></li> <li><a href="#orgad95d8a">2.8.1. Load the measurement data</a></li>
<li><a href="#org3b715d1">2.8.2. Compute PSD of the measurements</a></li> <li><a href="#orgd5a5c4f">2.8.2. Compute PSD of the measurements</a></li>
<li><a href="#org59b7d0c">2.8.3. Compare PSD of Cern, ID09 and ID31</a></li> <li><a href="#org4688ea2">2.8.3. Compare PSD of Cern, ID09 and ID31</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -307,8 +53,8 @@ for the JavaScript code in this tag.
</div> </div>
</div> </div>
<div id="outline-container-org5f3a483" class="outline-2"> <div id="outline-container-org98d0be2" class="outline-2">
<h2 id="org5f3a483"><span class="section-number-2">1</span> Experimental Setup</h2> <h2 id="org98d0be2"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
The goal here is to compare the ground motion at the location of the micro-station (ID31 beamline at ESRF) with other measurements of the ground motion. The goal here is to compare the ground motion at the location of the micro-station (ID31 beamline at ESRF) with other measurements of the ground motion.
@ -330,11 +76,11 @@ Then the signal is amplified by a Voltage Amplifier with the following settings:
</ul> </ul>
<p> <p>
On figure <a href="#org138fc2c">1</a> is an overview of multiple measurements made at famous location. On figure <a href="#orgb7f8464">1</a> is an overview of multiple measurements made at famous location.
</p> </p>
<div id="org138fc2c" class="figure"> <div id="orgb7f8464" class="figure">
<p><img src="./img/ground_motion_measurements.png" alt="ground_motion_measurements.png" width="800px" /> <p><img src="./img/ground_motion_measurements.png" alt="ground_motion_measurements.png" width="800px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Power spectral density of ground vibration in the vertical direction at multiple locations (<a href="https://vibration.desy.de/">source</a>)</p> <p><span class="figure-number">Figure 1: </span>Power spectral density of ground vibration in the vertical direction at multiple locations (<a href="https://vibration.desy.de/">source</a>)</p>
@ -342,13 +88,13 @@ On figure <a href="#org138fc2c">1</a> is an overview of multiple measurements ma
</div> </div>
</div> </div>
<div id="outline-container-orgb6a54b7" class="outline-2"> <div id="outline-container-org7e6d21c" class="outline-2">
<h2 id="orgb6a54b7"><span class="section-number-2">2</span> Measurement Analysis</h2> <h2 id="org7e6d21c"><span class="section-number-2">2</span> Measurement Analysis</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org50bb0e4"></a> <a id="orgcc23e80"></a>
</p> </p>
<div class="note"> <div class="note" id="org6e1fb83">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/ground_meas_id31.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/ground_meas_id31.zip">here</a>.
</p> </p>
@ -356,8 +102,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/ground_meas
</div> </div>
</div> </div>
<div id="outline-container-org4ded9a6" class="outline-3"> <div id="outline-container-orgb4815e7" class="outline-3">
<h3 id="org4ded9a6"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="orgb4815e7"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">data = load(<span class="org-string">'mat/data_028.mat'</span>, <span class="org-string">'data'</span>); data = data.data; <pre class="src src-matlab">data = load(<span class="org-string">'mat/data_028.mat'</span>, <span class="org-string">'data'</span>); data = data.data;
@ -366,8 +112,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/ground_meas
</div> </div>
</div> </div>
<div id="outline-container-orgddfc81a" class="outline-3"> <div id="outline-container-org76505c6" class="outline-3">
<h3 id="orgddfc81a"><span class="section-number-3">2.2</span> Time domain plots of the measured voltage</h3> <h3 id="org76505c6"><span class="section-number-3">2.2</span> Time domain plots of the measured voltage</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
@ -380,7 +126,7 @@ xlim([0, 100]);
</div> </div>
<div id="org62b557f" class="figure"> <div id="org32fab28" class="figure">
<p><img src="figs/ground_motion_id31_time.png" alt="ground_motion_id31_time.png" /> <p><img src="figs/ground_motion_id31_time.png" alt="ground_motion_id31_time.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Measurement of the ground motion - Time domain</p> <p><span class="figure-number">Figure 2: </span>Measurement of the ground motion - Time domain</p>
@ -388,8 +134,8 @@ xlim([0, 100]);
</div> </div>
</div> </div>
<div id="outline-container-orgf447e5f" class="outline-3"> <div id="outline-container-orge77c65d" class="outline-3">
<h3 id="orgf447e5f"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3> <h3 id="orge77c65d"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = data(2, 3) <span class="org-type">-</span> data(1, 3); <pre class="src src-matlab">dt = data(2, 3) <span class="org-type">-</span> data(1, 3);
@ -417,7 +163,7 @@ xlim([0.1, 500]);
</div> </div>
<div id="org3ff16a1" class="figure"> <div id="org46dd80c" class="figure">
<p><img src="figs/ground_motion_id31_asd_volt.png" alt="ground_motion_id31_asd_volt.png" /> <p><img src="figs/ground_motion_id31_asd_volt.png" alt="ground_motion_id31_asd_volt.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Amplitude Spectral Density of the measured Voltage</p> <p><span class="figure-number">Figure 3: </span>Amplitude Spectral Density of the measured Voltage</p>
@ -425,11 +171,11 @@ xlim([0.1, 500]);
</div> </div>
</div> </div>
<div id="outline-container-org7130c8f" class="outline-3"> <div id="outline-container-org7f9c12d" class="outline-3">
<h3 id="org7130c8f"><span class="section-number-3">2.4</span> Scaling to take into account the sensibility of the geophone and the voltage amplifier</h3> <h3 id="org7f9c12d"><span class="section-number-3">2.4</span> Scaling to take into account the sensibility of the geophone and the voltage amplifier</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
The Geophone used are L22. Their sensibility is shown on figure <a href="#org3a2258d">4</a>. The Geophone used are L22. Their sensibility is shown on figure <a href="#org8006b4c">4</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -454,7 +200,7 @@ xlim([0.1, 100]);
</div> </div>
<div id="org3a2258d" class="figure"> <div id="org8006b4c" class="figure">
<p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" /> <p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Sensibility of the Geophone</p> <p><span class="figure-number">Figure 4: </span>Sensibility of the Geophone</p>
@ -491,8 +237,8 @@ Finally, we obtain the PSD of the ground motion in \(m^2/Hz\) by dividing by the
</div> </div>
</div> </div>
<div id="outline-container-org456f387" class="outline-3"> <div id="outline-container-org7f5940d" class="outline-3">
<h3 id="org456f387"><span class="section-number-3">2.5</span> Time domain plots of the ground motion</h3> <h3 id="org7f5940d"><span class="section-number-3">2.5</span> Time domain plots of the ground motion</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<p> <p>
We can inverse the dynamics of the geophone to convert the measured voltage into the estimated ground motion. We can inverse the dynamics of the geophone to convert the measured voltage into the estimated ground motion.
@ -506,14 +252,14 @@ est_dis = lsim(1<span class="org-type">/</span>(1<span class="org-type">+</span>
</div> </div>
<div id="org85b0910" class="figure"> <div id="org3674cd1" class="figure">
<p><img src="figs/time_domain_velocity.png" alt="time_domain_velocity.png" /> <p><img src="figs/time_domain_velocity.png" alt="time_domain_velocity.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Time domain velocity (<a href="./figs/time_domain_velocity.png">png</a>, <a href="./figs/time_domain_velocity.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 5: </span>Time domain velocity (<a href="./figs/time_domain_velocity.png">png</a>, <a href="./figs/time_domain_velocity.pdf">pdf</a>)</p>
</div> </div>
<div id="org5dd32fd" class="figure"> <div id="org39fbab6" class="figure">
<p><img src="figs/time_domain_displacement.png" alt="time_domain_displacement.png" /> <p><img src="figs/time_domain_displacement.png" alt="time_domain_displacement.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Time domain absolute displacement (<a href="./figs/time_domain_displacement.png">png</a>, <a href="./figs/time_domain_displacement.pdf">pdf</a>)</p> <p><span class="figure-number">Figure 6: </span>Time domain absolute displacement (<a href="./figs/time_domain_displacement.png">png</a>, <a href="./figs/time_domain_displacement.pdf">pdf</a>)</p>
@ -521,11 +267,11 @@ est_dis = lsim(1<span class="org-type">/</span>(1<span class="org-type">+</span>
</div> </div>
</div> </div>
<div id="outline-container-org76df958" class="outline-3"> <div id="outline-container-org02ba5d0" class="outline-3">
<h3 id="org76df958"><span class="section-number-3">2.6</span> Computation of the ASD of the velocity and displacement</h3> <h3 id="org02ba5d0"><span class="section-number-3">2.6</span> Computation of the ASD of the velocity and displacement</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-6">
<p> <p>
The ASD of the measured velocity is shown on figure <a href="#org5031b4e">7</a>. The ASD of the measured velocity is shown on figure <a href="#orgddc47d6">7</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -541,14 +287,14 @@ xlim([0.1, 500]);
</div> </div>
<div id="org5031b4e" class="figure"> <div id="orgddc47d6" class="figure">
<p><img src="figs/ground_motion_id31_asd_velocity.png" alt="ground_motion_id31_asd_velocity.png" /> <p><img src="figs/ground_motion_id31_asd_velocity.png" alt="ground_motion_id31_asd_velocity.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the Velocity</p> <p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the Velocity</p>
</div> </div>
<p> <p>
We also plot the ASD in displacement (figure <a href="#org593f7fc">8</a>); We also plot the ASD in displacement (figure <a href="#org9eb24d7">8</a>);
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
@ -562,15 +308,15 @@ xlim([0.1, 500]);
</div> </div>
<div id="org593f7fc" class="figure"> <div id="org9eb24d7" class="figure">
<p><img src="figs/ground_motion_id31_asd_displacement.png" alt="ground_motion_id31_asd_displacement.png" /> <p><img src="figs/ground_motion_id31_asd_displacement.png" alt="ground_motion_id31_asd_displacement.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Amplitude Spectral Density of the Displacement</p> <p><span class="figure-number">Figure 8: </span>Amplitude Spectral Density of the Displacement</p>
</div> </div>
<p> <p>
And we also plot the PSD of the displacement in \(\frac{{\mu u}^2}{Hz}\) as it is a usual unit used (figure <a href="#orgfab6718">9</a>). And we also plot the PSD of the displacement in \(\frac{{\mu u}^2}{Hz}\) as it is a usual unit used (figure <a href="#org5008310">9</a>).
One can then compare this curve with the figure <a href="#org138fc2c">1</a>. One can then compare this curve with the figure <a href="#orgb7f8464">1</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -586,7 +332,7 @@ xlim([0.1, 500]); ylim([1e<span class="org-type">-</span>13, 1e3]);
</div> </div>
<div id="orgfab6718" class="figure"> <div id="org5008310" class="figure">
<p><img src="figs/ground_motion_id31_psd_displacement.png" alt="ground_motion_id31_psd_displacement.png" /> <p><img src="figs/ground_motion_id31_psd_displacement.png" alt="ground_motion_id31_psd_displacement.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Power Spectral Density of the measured displacement</p> <p><span class="figure-number">Figure 9: </span>Power Spectral Density of the measured displacement</p>
@ -594,8 +340,8 @@ xlim([0.1, 500]); ylim([1e<span class="org-type">-</span>13, 1e3]);
</div> </div>
</div> </div>
<div id="outline-container-org63b1f9a" class="outline-3"> <div id="outline-container-org1e033f3" class="outline-3">
<h3 id="org63b1f9a"><span class="section-number-3">2.7</span> Save</h3> <h3 id="org1e033f3"><span class="section-number-3">2.7</span> Save</h3>
<div class="outline-text-3" id="text-2-7"> <div class="outline-text-3" id="text-2-7">
<p> <p>
We save the PSD of the ground motion for further analysis. We save the PSD of the ground motion for further analysis.
@ -607,16 +353,16 @@ We save the PSD of the ground motion for further analysis.
</div> </div>
</div> </div>
<div id="outline-container-orgabb922e" class="outline-3"> <div id="outline-container-org8d373fd" class="outline-3">
<h3 id="orgabb922e"><span class="section-number-3">2.8</span> Comparison with other measurements of ground motion</h3> <h3 id="org8d373fd"><span class="section-number-3">2.8</span> Comparison with other measurements of ground motion</h3>
<div class="outline-text-3" id="text-2-8"> <div class="outline-text-3" id="text-2-8">
<p> <p>
Now we will compare with other measurements. Now we will compare with other measurements.
</p> </p>
</div> </div>
<div id="outline-container-org499997c" class="outline-4"> <div id="outline-container-orgad95d8a" class="outline-4">
<h4 id="org499997c"><span class="section-number-4">2.8.1</span> Load the measurement data</h4> <h4 id="orgad95d8a"><span class="section-number-4">2.8.1</span> Load the measurement data</h4>
<div class="outline-text-4" id="text-2-8-1"> <div class="outline-text-4" id="text-2-8-1">
<p> <p>
First we load the measurement data. First we load the measurement data.
@ -630,8 +376,8 @@ cern = load(<span class="org-string">'./mat/ground_motion_dist.mat'</span>);
</div> </div>
</div> </div>
<div id="outline-container-org3b715d1" class="outline-4"> <div id="outline-container-orgd5a5c4f" class="outline-4">
<h4 id="org3b715d1"><span class="section-number-4">2.8.2</span> Compute PSD of the measurements</h4> <h4 id="orgd5a5c4f"><span class="section-number-4">2.8.2</span> Compute PSD of the measurements</h4>
<div class="outline-text-4" id="text-2-8-2"> <div class="outline-text-4" id="text-2-8-2">
<p> <p>
We compute the Power Spectral Densities of the measurements. We compute the Power Spectral Densities of the measurements.
@ -652,11 +398,11 @@ win_cern = hanning(ceil(10<span class="org-type">*</span>Fs_cern));
</div> </div>
</div> </div>
<div id="outline-container-org59b7d0c" class="outline-4"> <div id="outline-container-org4688ea2" class="outline-4">
<h4 id="org59b7d0c"><span class="section-number-4">2.8.3</span> Compare PSD of Cern, ID09 and ID31</h4> <h4 id="org4688ea2"><span class="section-number-4">2.8.3</span> Compare PSD of Cern, ID09 and ID31</h4>
<div class="outline-text-4" id="text-2-8-3"> <div class="outline-text-4" id="text-2-8-3">
<p> <p>
And we compare all the measurements (figure <a href="#orgfc63def">10</a>). And we compare all the measurements (figure <a href="#orgbef99fa">10</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -674,7 +420,7 @@ xlim([0.1, 500]);
</div> </div>
<div id="orgfc63def" class="figure"> <div id="orgbef99fa" class="figure">
<p><img src="figs/ground_motion_compare.png" alt="ground_motion_compare.png" /> <p><img src="figs/ground_motion_compare.png" alt="ground_motion_compare.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Comparison of the PSD of the ground motion measured at different location</p> <p><span class="figure-number">Figure 10: </span>Comparison of the PSD of the ground motion measured at different location</p>
@ -686,7 +432,7 @@ xlim([0.1, 500]);
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-01-28 mar. 15:01</p> <p class="date">Created: 2020-11-12 jeu. 10:28</p>
</div> </div>
</body> </body>
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<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgc7e4a9f">1. Experimental Setup</a></li> <li><a href="#orgb47b0b2">1. Experimental Setup</a></li>
<li><a href="#org6abc0c5">2. Signal Processing</a> <li><a href="#org0b1e99e">2. Signal Processing</a>
<ul> <ul>
<li><a href="#orgda0769c">2.1. Load data</a></li> <li><a href="#org35507da">2.1. Load data</a></li>
<li><a href="#orgf362871">2.2. Time Domain Data</a></li> <li><a href="#org69bec1f">2.2. Time Domain Data</a></li>
<li><a href="#org3a306be">2.3. Computation of the ASD of the measured voltage</a></li> <li><a href="#orgf0a72da">2.3. Computation of the ASD of the measured voltage</a></li>
<li><a href="#org0a45f4a">2.4. Scaling to take into account the sensibility of the geophone and the voltage amplifier</a></li> <li><a href="#org7acabeb">2.4. Scaling to take into account the sensibility of the geophone and the voltage amplifier</a></li>
<li><a href="#org63db1c4">2.5. Computation of the ASD of the velocity</a></li> <li><a href="#org4b3b8a7">2.5. Computation of the ASD of the velocity</a></li>
<li><a href="#org6df28e4">2.6. Transfer function between the two geophones</a></li> <li><a href="#orgaaca76b">2.6. Transfer function between the two geophones</a></li>
<li><a href="#org2a1c732">2.7. Estimation of the sensor noise</a></li> <li><a href="#org5c32c39">2.7. Estimation of the sensor noise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orga1d7838">3. Compare axis</a> <li><a href="#org52fed77">3. Compare axis</a>
<ul> <ul>
<li><a href="#org1153270">3.1. Load data</a></li> <li><a href="#org7f52c4b">3.1. Load data</a></li>
<li><a href="#orgd3a0160">3.2. Compare PSD</a></li> <li><a href="#orgb105293">3.2. Compare PSD</a></li>
<li><a href="#orgcd6137b">3.3. Compare TF</a></li> <li><a href="#orgbce3b98">3.3. Compare TF</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org693291d">4. Appendix</a> <li><a href="#orgd32606c">4. Appendix</a>
<ul> <ul>
<li><a href="#org58d8ebb">4.1. Computation of coherence from PSD and CSD</a></li> <li><a href="#orge652a09">4.1. Computation of coherence from PSD and CSD</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orgc7e4a9f" class="outline-2"> <div id="outline-container-orgb47b0b2" class="outline-2">
<h2 id="orgc7e4a9f"><span class="section-number-2">1</span> Experimental Setup</h2> <h2 id="orgb47b0b2"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
Two L22 geophones are used. Two L22 geophones are used.
@ -327,14 +77,14 @@ The voltage amplifiers includes:
</ul> </ul>
<div id="orga476294" class="figure"> <div id="orgfc98f42" class="figure">
<p><img src="./img/setup.jpg" alt="setup.jpg" width="500px" /> <p><img src="./img/setup.jpg" alt="setup.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Setup</p> <p><span class="figure-number">Figure 1: </span>Setup</p>
</div> </div>
<div id="org2fb54a0" class="figure"> <div id="org01be4e4" class="figure">
<p><img src="./img/geophones.jpg" alt="geophones.jpg" width="500px" /> <p><img src="./img/geophones.jpg" alt="geophones.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Geophones</p> <p><span class="figure-number">Figure 2: </span>Geophones</p>
@ -342,13 +92,13 @@ The voltage amplifiers includes:
</div> </div>
</div> </div>
<div id="outline-container-org6abc0c5" class="outline-2"> <div id="outline-container-org0b1e99e" class="outline-2">
<h2 id="org6abc0c5"><span class="section-number-2">2</span> Signal Processing</h2> <h2 id="org0b1e99e"><span class="section-number-2">2</span> Signal Processing</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="orged15cd2"></a> <a id="org28ac54a"></a>
</p> </p>
<div class="note"> <div class="note" id="orgdb9b9cc">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/huddle_test_signal_processing.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/huddle_test_signal_processing.zip">here</a>.
</p> </p>
@ -356,38 +106,38 @@ All the files (data and Matlab scripts) are accessible <a href="data/huddle_test
</div> </div>
</div> </div>
<div id="outline-container-orgda0769c" class="outline-3"> <div id="outline-container-org35507da" class="outline-3">
<h3 id="orgda0769c"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="org35507da"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">load(<span class="org-string">'mat/data_001.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x1'</span>, <span class="org-string">'x2'</span>);
dt = t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; dt = t(2) <span class="org-type">-</span> t(1);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgf362871" class="outline-3"> <div id="outline-container-org69bec1f" class="outline-3">
<h3 id="orgf362871"><span class="section-number-3">2.2</span> Time Domain Data</h3> <h3 id="org69bec1f"><span class="section-number-3">2.2</span> Time Domain Data</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>t, x1<span class="org-rainbow-delimiters-depth-1">)</span>; plot(t, x1);
plot<span class="org-rainbow-delimiters-depth-1">(</span>t, x2<span class="org-rainbow-delimiters-depth-1">)</span>; plot(t, x2);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>);
ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span>, t<span class="org-rainbow-delimiters-depth-3">(</span>end<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([t(1), t(end)]);
</pre> </pre>
</div> </div>
<div id="orgb109da2" class="figure"> <div id="orgc871843" class="figure">
<p><img src="figs/data_time_domain.png" alt="data_time_domain.png" /> <p><img src="figs/data_time_domain.png" alt="data_time_domain.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Time domain Data</p> <p><span class="figure-number">Figure 3: </span>Time domain Data</p>
@ -397,17 +147,17 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>t, x1<span class="org-rainbow-delimiters-depth-1">)</span>; plot(t, x1);
plot<span class="org-rainbow-delimiters-depth-1">(</span>t, x2<span class="org-rainbow-delimiters-depth-1">)</span>; plot(t, x2);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>);
ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0 1]);
</pre> </pre>
</div> </div>
<div id="org09931c1" class="figure"> <div id="org30ca9f2" class="figure">
<p><img src="figs/data_time_domain_zoom.png" alt="data_time_domain_zoom.png" /> <p><img src="figs/data_time_domain_zoom.png" alt="data_time_domain_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Time domain Data - Zoom</p> <p><span class="figure-number">Figure 4: </span>Time domain Data - Zoom</p>
@ -415,16 +165,16 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-org3a306be" class="outline-3"> <div id="outline-container-orgf0a72da" class="outline-3">
<h3 id="org3a306be"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3> <h3 id="orgf0a72da"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
We first define the parameters for the frequency domain analysis. We first define the parameters for the frequency domain analysis.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> <pre class="src src-matlab">Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
@ -432,30 +182,30 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
Then we compute the Power Spectral Density using <code>pwelch</code> function. Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx1, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>x1, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxx1, f] = pwelch(x1, win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxx2, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>x2, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxx2, <span class="org-type">~</span>] = pwelch(x2, win, [], [], Fs);
</pre> </pre>
</div> </div>
<p> <p>
And we plot the result on figure <a href="#org7cf943c">5</a>. And we plot the result on figure <a href="#orgf270ed7">5</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx1<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxx1));
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx2<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxx2));
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$'</span>)
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0.1, 500]);
</pre> </pre>
</div> </div>
<div id="org7cf943c" class="figure"> <div id="orgf270ed7" class="figure">
<p><img src="figs/asd_voltage.png" alt="asd_voltage.png" /> <p><img src="figs/asd_voltage.png" alt="asd_voltage.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured voltage</p> <p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured voltage</p>
@ -463,23 +213,23 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-org0a45f4a" class="outline-3"> <div id="outline-container-org7acabeb" class="outline-3">
<h3 id="org0a45f4a"><span class="section-number-3">2.4</span> Scaling to take into account the sensibility of the geophone and the voltage amplifier</h3> <h3 id="org7acabeb"><span class="section-number-3">2.4</span> Scaling to take into account the sensibility of the geophone and the voltage amplifier</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
The Geophone used are L22. Their sensibility is shown on figure <a href="#org045b636">6</a>. The Geophone used are L22. Their sensibility is shown on figure <a href="#orgc586e06">6</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">S0 = <span class="org-highlight-numbers-number">88</span>; <span class="org-comment">% Sensitivity [V/(m/s)]</span> <pre class="src src-matlab">S0 = 88; <span class="org-comment">% Sensitivity [V/(m/s)]</span>
f0 = <span class="org-highlight-numbers-number">2</span>; <span class="org-comment">% Cut-off frequnecy [Hz]</span> f0 = 2; <span class="org-comment">% Cut-off frequnecy [Hz]</span>
S = S0<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>f0<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>f0<span class="org-rainbow-delimiters-depth-1">)</span>; S = S0<span class="org-type">*</span>(s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>f0)<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>f0);
</pre> </pre>
</div> </div>
<div id="org045b636" class="figure"> <div id="orgc586e06" class="figure">
<p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" /> <p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Sensibility of the Geophone</p> <p><span class="figure-number">Figure 6: </span>Sensibility of the Geophone</p>
@ -491,9 +241,9 @@ We also take into account the gain of the electronics which is here set to be \(
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">G0_db = <span class="org-highlight-numbers-number">60</span>; <span class="org-comment">% [dB]</span> <pre class="src src-matlab">G0_db = 60; <span class="org-comment">% [dB]</span>
G0 = <span class="org-highlight-numbers-number">10</span><span class="org-type">^</span><span class="org-rainbow-delimiters-depth-1">(</span>G0_db<span class="org-type">/</span><span class="org-highlight-numbers-number">20</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% [abs]</span> G0 = 10<span class="org-type">^</span>(G0_db<span class="org-type">/</span>20); <span class="org-comment">% [abs]</span>
</pre> </pre>
</div> </div>
@ -503,57 +253,57 @@ We further divide the result by the sensibility of the Geophone to obtain the AS
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">scaling = <span class="org-highlight-numbers-number">1</span><span class="org-type">./</span>squeeze<span class="org-rainbow-delimiters-depth-1">(</span>abs<span class="org-rainbow-delimiters-depth-2">(</span>freqresp<span class="org-rainbow-delimiters-depth-3">(</span>G0<span class="org-type">*</span>S, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">scaling = 1<span class="org-type">./</span>squeeze(abs(freqresp(G0<span class="org-type">*</span>S, f, <span class="org-string">'Hz'</span>)));
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org63db1c4" class="outline-3"> <div id="outline-container-org4b3b8a7" class="outline-3">
<h3 id="org63db1c4"><span class="section-number-3">2.5</span> Computation of the ASD of the velocity</h3> <h3 id="org4b3b8a7"><span class="section-number-3">2.5</span> Computation of the ASD of the velocity</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<p> <p>
The ASD of the measured velocity is shown on figure <a href="#org1aa0246">7</a>. The ASD of the measured velocity is shown on figure <a href="#orgdacf8d0">7</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx1<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxx1)<span class="org-type">.*</span>scaling);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx2<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxx2)<span class="org-type">.*</span>scaling);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0.1, 500]);
</pre> </pre>
</div> </div>
<div id="org1aa0246" class="figure"> <div id="orgdacf8d0" class="figure">
<p><img src="figs/psd_velocity.png" alt="psd_velocity.png" /> <p><img src="figs/psd_velocity.png" alt="psd_velocity.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the Velocity</p> <p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the Velocity</p>
</div> </div>
<p> <p>
We also plot the ASD in displacement (figure <a href="#org2fbcc25">8</a>); We also plot the ASD in displacement (figure <a href="#org47aa587">8</a>);
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-rainbow-delimiters-depth-2">(</span>sqrt<span class="org-rainbow-delimiters-depth-3">(</span>pxx1<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, (sqrt(pxx1)<span class="org-type">.*</span>scaling)<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f));
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-rainbow-delimiters-depth-2">(</span>sqrt<span class="org-rainbow-delimiters-depth-3">(</span>pxx2<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, (sqrt(pxx2)<span class="org-type">.*</span>scaling)<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f));
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the displacement $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$'</span>)
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0.1, 500]);
</pre> </pre>
</div> </div>
<div id="org2fbcc25" class="figure"> <div id="org47aa587" class="figure">
<p><img src="figs/asd_displacement.png" alt="asd_displacement.png" /> <p><img src="figs/asd_displacement.png" alt="asd_displacement.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Amplitude Spectral Density of the Displacement</p> <p><span class="figure-number">Figure 8: </span>Amplitude Spectral Density of the Displacement</p>
@ -561,37 +311,37 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-org6df28e4" class="outline-3"> <div id="outline-container-orgaaca76b" class="outline-3">
<h3 id="org6df28e4"><span class="section-number-3">2.6</span> Transfer function between the two geophones</h3> <h3 id="orgaaca76b"><span class="section-number-3">2.6</span> Transfer function between the two geophones</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-6">
<p> <p>
We here compute the transfer function from one geophone to the other. We here compute the transfer function from one geophone to the other.
The result is shown on figure <a href="#org008cd50">9</a>. The result is shown on figure <a href="#org313c704">9</a>.
</p> </p>
<p> <p>
We also compute the coherence between the two signals (figure <a href="#org47fd0f6">10</a>). We also compute the coherence between the two signals (figure <a href="#orgbed81d4">10</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>T12, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>x1, x2, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[T12, <span class="org-type">~</span>] = tfestimate(x1, x2, win, [], [], Fs);
</pre> </pre>
</div> </div>
<div id="org008cd50" class="figure"> <div id="org313c704" class="figure">
<p><img src="figs/tf_geophones.png" alt="tf_geophones.png" /> <p><img src="figs/tf_geophones.png" alt="tf_geophones.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Estimated transfer function between the two geophones</p> <p><span class="figure-number">Figure 9: </span>Estimated transfer function between the two geophones</p>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>coh12, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>x1, x2, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[coh12, <span class="org-type">~</span>] = mscohere(x1, x2, win, [], [], Fs);
</pre> </pre>
</div> </div>
<div id="org47fd0f6" class="figure"> <div id="orgbed81d4" class="figure">
<p><img src="figs/coh_geophones.png" alt="coh_geophones.png" /> <p><img src="figs/coh_geophones.png" alt="coh_geophones.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Cohererence between the signals of the two geophones</p> <p><span class="figure-number">Figure 10: </span>Cohererence between the signals of the two geophones</p>
@ -599,11 +349,11 @@ We also compute the coherence between the two signals (figure <a href="#org47fd0
</div> </div>
</div> </div>
<div id="outline-container-org2a1c732" class="outline-3"> <div id="outline-container-org5c32c39" class="outline-3">
<h3 id="org2a1c732"><span class="section-number-3">2.7</span> Estimation of the sensor noise</h3> <h3 id="org5c32c39"><span class="section-number-3">2.7</span> Estimation of the sensor noise</h3>
<div class="outline-text-3" id="text-2-7"> <div class="outline-text-3" id="text-2-7">
<p> <p>
The technique to estimate the sensor noise is taken from <a class='org-ref-reference' href="#barzilai98_techn_measur_noise_sensor_presen">barzilai98_techn_measur_noise_sensor_presen</a>. The technique to estimate the sensor noise is taken from (<a href="#citeproc_bib_item_1">Barzilai, VanZandt, and Kenny 1998</a>).
</p> </p>
<p> <p>
@ -630,11 +380,11 @@ where:
</ul> </ul>
<p> <p>
The <code>mscohere</code> function is compared with this formula on Appendix (section <a href="#orgd79f363">4.1</a>), it is shown that it is identical. The <code>mscohere</code> function is compared with this formula on Appendix (section <a href="#org06003b1">4.1</a>), it is shown that it is identical.
</p> </p>
<p> <p>
Figure <a href="#org7d058c1">11</a> illustrate a block diagram model of the system used to determine the sensor noise of the geophone. Figure <a href="#orgae83a33">11</a> illustrate a block diagram model of the system used to determine the sensor noise of the geophone.
</p> </p>
<p> <p>
@ -646,7 +396,7 @@ Each sensor has noise \(N\) and \(M\).
</p> </p>
<div id="org7d058c1" class="figure"> <div id="orgae83a33" class="figure">
<p><img src="figs/huddle-test.png" alt="huddle-test.png" /> <p><img src="figs/huddle-test.png" alt="huddle-test.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Huddle test block diagram</p> <p><span class="figure-number">Figure 11: </span>Huddle test block diagram</p>
@ -661,7 +411,7 @@ We also assume that \(S_1 = S_2 = 1\).
We then obtain: We then obtain:
</p> </p>
\begin{equation} \begin{equation}
\label{org68c59ea} \label{orgbacdde9}
\gamma_{XY}^2(\omega) = \frac{1}{1 + 2 \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right) + \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right)^2} \gamma_{XY}^2(\omega) = \frac{1}{1 + 2 \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right) + \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right)^2}
\end{equation} \end{equation}
@ -669,67 +419,67 @@ We then obtain:
Since the input signal \(U\) and the instrumental noise \(N\) are incoherent: Since the input signal \(U\) and the instrumental noise \(N\) are incoherent:
</p> </p>
\begin{equation} \begin{equation}
\label{org6525ac9} \label{org21035bd}
|G_X(\omega)| = |G_N(\omega)| + |G_U(\omega)| |G_X(\omega)| = |G_N(\omega)| + |G_U(\omega)|
\end{equation} \end{equation}
<p> <p>
From equations \eqref{org68c59ea} and \eqref{org6525ac9}, we finally obtain From equations \eqref{orgbacdde9} and \eqref{org21035bd}, we finally obtain
</p> </p>
<div class="important"> <div class="important" id="org594bc6f">
\begin{equation} \begin{equation}
\label{orgcac9782} \label{orga8ac5d9}
|G_N(\omega)| = |G_X(\omega)| \left( 1 - \sqrt{\gamma_{XY}^2(\omega)} \right) |G_N(\omega)| = |G_X(\omega)| \left( 1 - \sqrt{\gamma_{XY}^2(\omega)} \right)
\end{equation} \end{equation}
</div> </div>
<p> <p>
The instrumental noise is computed below. The result in V<sup>2</sup>/Hz is shown on figure <a href="#org0f85822">12</a>. The instrumental noise is computed below. The result in V^2/Hz is shown on figure <a href="#org7943278">12</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">pxxN = pxx1<span class="org-type">.*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">-</span> coh12<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">pxxN = pxx1<span class="org-type">.*</span>(1 <span class="org-type">-</span> coh12);
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, pxx1, <span class="org-string">'-'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, pxx1, <span class="org-string">'-'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, pxx2, <span class="org-string">'-'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, pxx2, <span class="org-string">'-'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, pxxN, <span class="org-string">'k--'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, pxxN, <span class="org-string">'k--'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>PSD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">}{</span>Hz<span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'PSD of the measured Voltage $\left[\frac{V^2}{Hz}\right]$'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0.1, 500]);
</pre> </pre>
</div> </div>
<div id="org0f85822" class="figure"> <div id="org7943278" class="figure">
<p><img src="figs/intrumental_noise_V.png" alt="intrumental_noise_V.png" /> <p><img src="figs/intrumental_noise_V.png" alt="intrumental_noise_V.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Instrumental Noise and Measurement in \(V^2/Hz\)</p> <p><span class="figure-number">Figure 12: </span>Instrumental Noise and Measurement in \(V^2/Hz\)</p>
</div> </div>
<p> <p>
This is then further converted into velocity and compared with the ground velocity measurement. (figure <a href="#org81c8985">13</a>) This is then further converted into velocity and compared with the ground velocity measurement. (figure <a href="#org8ecfd08">13</a>)
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx1<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">.*</span>scaling, <span class="org-string">'-'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxx1)<span class="org-type">.*</span>scaling, <span class="org-string">'-'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx2<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">.*</span>scaling, <span class="org-string">'-'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxx2)<span class="org-type">.*</span>scaling, <span class="org-string">'-'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxxN<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">.*</span>scaling, <span class="org-string">'k--'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxxN)<span class="org-type">.*</span>scaling, <span class="org-string">'k--'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the Velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0.1, 500]);
</pre> </pre>
</div> </div>
<div id="org81c8985" class="figure"> <div id="org8ecfd08" class="figure">
<p><img src="figs/intrumental_noise_velocity.png" alt="intrumental_noise_velocity.png" /> <p><img src="figs/intrumental_noise_velocity.png" alt="intrumental_noise_velocity.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Instrumental Noise and Measurement in \(m/s/\sqrt{Hz}\)</p> <p><span class="figure-number">Figure 13: </span>Instrumental Noise and Measurement in \(m/s/\sqrt{Hz}\)</p>
@ -738,14 +488,14 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-orga1d7838" class="outline-2"> <div id="outline-container-org52fed77" class="outline-2">
<h2 id="orga1d7838"><span class="section-number-2">3</span> Compare axis</h2> <h2 id="org52fed77"><span class="section-number-2">3</span> Compare axis</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
<a id="org73446c8"></a> <a id="org4f6c263"></a>
</p> </p>
<div class="note"> <div class="note" id="org7d50518">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/huddle_test_compare_axis.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/huddle_test_compare_axis.zip">here</a>.
</p> </p>
@ -753,44 +503,44 @@ All the files (data and Matlab scripts) are accessible <a href="data/huddle_test
</div> </div>
</div> </div>
<div id="outline-container-org1153270" class="outline-3"> <div id="outline-container-org7f52c4b" class="outline-3">
<h3 id="org1153270"><span class="section-number-3">3.1</span> Load data</h3> <h3 id="org7f52c4b"><span class="section-number-3">3.1</span> Load data</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
We first load the data for the three axis. We first load the data for the three axis.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">z = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">z = load(<span class="org-string">'mat/data_001.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x1'</span>, <span class="org-string">'x2'</span>);
east = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_002.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>; east = load(<span class="org-string">'mat/data_002.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x1'</span>, <span class="org-string">'x2'</span>);
north = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_003.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>; north = load(<span class="org-string">'mat/data_003.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x1'</span>, <span class="org-string">'x2'</span>);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgd3a0160" class="outline-3"> <div id="outline-container-orgb105293" class="outline-3">
<h3 id="orgd3a0160"><span class="section-number-3">3.2</span> Compare PSD</h3> <h3 id="orgb105293"><span class="section-number-3">3.2</span> Compare PSD</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
The PSD for each axis of the two geophones are computed. The PSD for each axis of the two geophones are computed.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pz1, fz<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z.x1, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span>length<span class="org-rainbow-delimiters-depth-4">(</span>z.x1<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-2">(</span>z.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>z.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pz1, fz] = pwelch(z.x1, hanning(ceil(length(z.x1)<span class="org-type">/</span>100)), [], [], 1<span class="org-type">/</span>(z.t(2)<span class="org-type">-</span>z.t(1)));
<span class="org-rainbow-delimiters-depth-1">[</span>pz2, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>z.x2, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span>length<span class="org-rainbow-delimiters-depth-4">(</span>z.x2<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-2">(</span>z.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>z.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; [pz2, <span class="org-type">~</span>] = pwelch(z.x2, hanning(ceil(length(z.x2)<span class="org-type">/</span>100)), [], [], 1<span class="org-type">/</span>(z.t(2)<span class="org-type">-</span>z.t(1)));
<span class="org-rainbow-delimiters-depth-1">[</span>pe1, fe<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>east.x1, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span>length<span class="org-rainbow-delimiters-depth-4">(</span>east.x1<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-2">(</span>east.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>east.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; [pe1, fe] = pwelch(east.x1, hanning(ceil(length(east.x1)<span class="org-type">/</span>100)), [], [], 1<span class="org-type">/</span>(east.t(2)<span class="org-type">-</span>east.t(1)));
<span class="org-rainbow-delimiters-depth-1">[</span>pe2, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>east.x2, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span>length<span class="org-rainbow-delimiters-depth-4">(</span>east.x2<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-2">(</span>east.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>east.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; [pe2, <span class="org-type">~</span>] = pwelch(east.x2, hanning(ceil(length(east.x2)<span class="org-type">/</span>100)), [], [], 1<span class="org-type">/</span>(east.t(2)<span class="org-type">-</span>east.t(1)));
<span class="org-rainbow-delimiters-depth-1">[</span>pn1, fn<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>north.x1, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span>length<span class="org-rainbow-delimiters-depth-4">(</span>north.x1<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-2">(</span>north.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>north.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; [pn1, fn] = pwelch(north.x1, hanning(ceil(length(north.x1)<span class="org-type">/</span>100)), [], [], 1<span class="org-type">/</span>(north.t(2)<span class="org-type">-</span>north.t(1)));
<span class="org-rainbow-delimiters-depth-1">[</span>pn2, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>north.x2, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span>length<span class="org-rainbow-delimiters-depth-4">(</span>north.x2<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-2">(</span>north.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>north.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; [pn2, <span class="org-type">~</span>] = pwelch(north.x2, hanning(ceil(length(north.x2)<span class="org-type">/</span>100)), [], [], 1<span class="org-type">/</span>(north.t(2)<span class="org-type">-</span>north.t(1)));
</pre> </pre>
</div> </div>
<p> <p>
We compare them. The result is shown on figure <a href="#org16d65ef">14</a>. We compare them. The result is shown on figure <a href="#orgf6d7705">14</a>.
</p> </p>
<div id="org16d65ef" class="figure"> <div id="orgf6d7705" class="figure">
<p><img src="figs/compare_axis_psd.png" alt="compare_axis_psd.png" /> <p><img src="figs/compare_axis_psd.png" alt="compare_axis_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Compare the measure PSD of the two geophones for the three axis</p> <p><span class="figure-number">Figure 14: </span>Compare the measure PSD of the two geophones for the three axis</p>
@ -798,23 +548,23 @@ We compare them. The result is shown on figure <a href="#org16d65ef">14</a>.
</div> </div>
</div> </div>
<div id="outline-container-orgcd6137b" class="outline-3"> <div id="outline-container-orgbce3b98" class="outline-3">
<h3 id="orgcd6137b"><span class="section-number-3">3.3</span> Compare TF</h3> <h3 id="orgbce3b98"><span class="section-number-3">3.3</span> Compare TF</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<p> <p>
The transfer functions from one geophone to the other are also computed for each axis. The transfer functions from one geophone to the other are also computed for each axis.
The result is shown on figure <a href="#orgdcda32f">15</a>. The result is shown on figure <a href="#org1936d29">15</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>Tz, fz<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>z.x1, z.x2, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span>length<span class="org-rainbow-delimiters-depth-4">(</span>z.x1<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-2">(</span>z.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>z.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[Tz, fz] = tfestimate(z.x1, z.x2, hanning(ceil(length(z.x1)<span class="org-type">/</span>100)), [], [], 1<span class="org-type">/</span>(z.t(2)<span class="org-type">-</span>z.t(1)));
<span class="org-rainbow-delimiters-depth-1">[</span>Te, fe<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>east.x1, east.x2, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span>length<span class="org-rainbow-delimiters-depth-4">(</span>east.x1<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-2">(</span>east.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>east.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; [Te, fe] = tfestimate(east.x1, east.x2, hanning(ceil(length(east.x1)<span class="org-type">/</span>100)), [], [], 1<span class="org-type">/</span>(east.t(2)<span class="org-type">-</span>east.t(1)));
<span class="org-rainbow-delimiters-depth-1">[</span>Tn, fn<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>north.x1, north.x2, hanning<span class="org-rainbow-delimiters-depth-2">(</span>ceil<span class="org-rainbow-delimiters-depth-3">(</span>length<span class="org-rainbow-delimiters-depth-4">(</span>north.x1<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-2">(</span>north.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">-</span>north.t<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; [Tn, fn] = tfestimate(north.x1, north.x2, hanning(ceil(length(north.x1)<span class="org-type">/</span>100)), [], [], 1<span class="org-type">/</span>(north.t(2)<span class="org-type">-</span>north.t(1)));
</pre> </pre>
</div> </div>
<div id="orgdcda32f" class="figure"> <div id="org1936d29" class="figure">
<p><img src="figs/compare_tf_axis.png" alt="compare_tf_axis.png" /> <p><img src="figs/compare_tf_axis.png" alt="compare_tf_axis.png" />
</p> </p>
<p><span class="figure-number">Figure 15: </span>Compare the transfer function from one geophone to the other for the 3 axis</p> <p><span class="figure-number">Figure 15: </span>Compare the transfer function from one geophone to the other for the 3 axis</p>
@ -823,46 +573,46 @@ The result is shown on figure <a href="#orgdcda32f">15</a>.
</div> </div>
</div> </div>
<div id="outline-container-org693291d" class="outline-2"> <div id="outline-container-orgd32606c" class="outline-2">
<h2 id="org693291d"><span class="section-number-2">4</span> Appendix</h2> <h2 id="orgd32606c"><span class="section-number-2">4</span> Appendix</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
</div> </div>
<div id="outline-container-org58d8ebb" class="outline-3"> <div id="outline-container-orge652a09" class="outline-3">
<h3 id="org58d8ebb"><span class="section-number-3">4.1</span> Computation of coherence from PSD and CSD</h3> <h3 id="orge652a09"><span class="section-number-3">4.1</span> Computation of coherence from PSD and CSD</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-4-1">
<p> <p>
<a id="orgd79f363"></a> <a id="org06003b1"></a>
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">load(<span class="org-string">'mat/data_001.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x1'</span>, <span class="org-string">'x2'</span>);
dt = t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; dt = t(2) <span class="org-type">-</span> t(1);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; Fs = 1<span class="org-type">/</span>dt;
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span>length<span class="org-rainbow-delimiters-depth-3">(</span>x1<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(length(x1)<span class="org-type">/</span>100));
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">pxy = cpsd<span class="org-rainbow-delimiters-depth-1">(</span>x1, x2, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">pxy = cpsd(x1, x2, win, [], [], Fs);
pxx = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>x1, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; pxx = pwelch(x1, win, [], [], Fs);
pyy = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>x2, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; pyy = pwelch(x2, win, [], [], Fs);
coh = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>x1, x2, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; coh = mscohere(x1, x2, win, [], [], Fs);
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>pxy<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">./</span>abs<span class="org-rainbow-delimiters-depth-2">(</span>pxx<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>abs<span class="org-rainbow-delimiters-depth-2">(</span>pyy<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'-'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, abs(pxy)<span class="org-type">.^</span>2<span class="org-type">./</span>abs(pxx)<span class="org-type">./</span>abs(pyy), <span class="org-string">'-'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, coh, <span class="org-string">'--'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, coh, <span class="org-string">'--'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Coherence'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Frequency'</span>); ylabel(<span class="org-string">'Coherence'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([1, 500]);
</pre> </pre>
</div> </div>
<div id="orgc65c7db" class="figure"> <div id="org3ae3bcc" class="figure">
<p><img src="figs/comp_coherence_formula.png" alt="comp_coherence_formula.png" /> <p><img src="figs/comp_coherence_formula.png" alt="comp_coherence_formula.png" />
</p> </p>
<p><span class="figure-number">Figure 16: </span>Comparison of <code>mscohere</code> and manual computation</p> <p><span class="figure-number">Figure 16: </span>Comparison of <code>mscohere</code> and manual computation</p>
@ -873,15 +623,16 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
<p> <p>
<h1 class='org-ref-bib-h1'>Bibliography</h1>
<ul class='org-ref-bib'><li><a id="barzilai98_techn_measur_noise_sensor_presen">[barzilai98_techn_measur_noise_sensor_presen]</a> <a name="barzilai98_techn_measur_noise_sensor_presen"></a>Aaron Barzilai, Tom VanZandt & Tom Kenny, Technique for Measurement of the Noise of a Sensor in the Presence of Large Background Signals, <i>Review of Scientific Instruments</i>, <b>69(7)</b>, 2767-2772 (1998). <a href="https://doi.org/10.1063/1.1149013">link</a>. <a href="http://dx.doi.org/10.1063/1.1149013">doi</a>.</li>
</ul>
</p> </p>
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><h2 class='citeproc-org-bib-h2'>Bibliography</h2>
<div class="csl-bib-body">
<div class="csl-entry"><a name="citeproc_bib_item_1"></a>Barzilai, Aaron, Tom VanZandt, and Tom Kenny. 1998. “Technique for Measurement of the Noise of a Sensor in the Presence of Large Background Signals.” <i>Review of Scientific Instruments</i> 69 (7):2767–72. <a href="https://doi.org/10.1063/1.1149013">https://doi.org/10.1063/1.1149013</a>.</div>
</div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-15 mer. 10:08</p> <p class="date">Created: 2020-11-12 jeu. 10:28</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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</div><div id="content">
<h1 class="title">Measurement of the ID31 Micro-Station</h1> <h1 class="title">Measurement of the ID31 Micro-Station</h1>
<div id="table-of-contents"> <div id="table-of-contents">
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org33281aa">1. Measurements of the dynamics of the station</a></li> <li><a href="#org47542da">1. Measurements of the dynamics of the station</a></li>
<li><a href="#org004aa83">2. Measurements of perturbations</a></li> <li><a href="#org5e85e2f">2. Measurements of perturbations</a></li>
<li><a href="#org254dfd2">3. Measurement Noise</a></li> <li><a href="#org5e348c8">3. Measurement Noise</a></li>
<li><a href="#org403ddcd">4. Modal Analysis</a></li> <li><a href="#org3f01b31">4. Modal Analysis</a></li>
<li><a href="#org2ec2737">5. Other</a></li> <li><a href="#orgfec2c5c">5. Other</a></li>
</ul> </ul>
</div> </div>
</div> </div>
@ -35,8 +34,8 @@
This web-page gathers all the measurements done on the ID31 Micro Station. This web-page gathers all the measurements done on the ID31 Micro Station.
</p> </p>
<div id="outline-container-org33281aa" class="outline-2"> <div id="outline-container-org47542da" class="outline-2">
<h2 id="org33281aa"><span class="section-number-2">1</span> Measurements of the dynamics of the station</h2> <h2 id="org47542da"><span class="section-number-2">1</span> Measurements of the dynamics of the station</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<ul class="org-ul"> <ul class="org-ul">
<li><a href="dynamical-meas-granite/index.html">Dynamics from floor motion to marble motion</a></li> <li><a href="dynamical-meas-granite/index.html">Dynamics from floor motion to marble motion</a></li>
@ -47,8 +46,8 @@ This web-page gathers all the measurements done on the ID31 Micro Station.
</div> </div>
</div> </div>
<div id="outline-container-org004aa83" class="outline-2"> <div id="outline-container-org5e85e2f" class="outline-2">
<h2 id="org004aa83"><span class="section-number-2">2</span> Measurements of perturbations</h2> <h2 id="org5e85e2f"><span class="section-number-2">2</span> Measurements of perturbations</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
Vibrations during scans: Vibrations during scans:
@ -84,8 +83,8 @@ Control loop influence:
</div> </div>
</div> </div>
<div id="outline-container-org254dfd2" class="outline-2"> <div id="outline-container-org5e348c8" class="outline-2">
<h2 id="org254dfd2"><span class="section-number-2">3</span> Measurement Noise</h2> <h2 id="org5e348c8"><span class="section-number-2">3</span> Measurement Noise</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
Noise coming from the Slip-Ring: Noise coming from the Slip-Ring:
@ -97,8 +96,8 @@ Noise coming from the Slip-Ring:
</div> </div>
</div> </div>
<div id="outline-container-org403ddcd" class="outline-2"> <div id="outline-container-org3f01b31" class="outline-2">
<h2 id="org403ddcd"><span class="section-number-2">4</span> Modal Analysis</h2> <h2 id="org3f01b31"><span class="section-number-2">4</span> Modal Analysis</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
<ul class="org-ul"> <ul class="org-ul">
<li><a href="modal-analysis/index.html">Modal Analysis</a></li> <li><a href="modal-analysis/index.html">Modal Analysis</a></li>
@ -106,8 +105,8 @@ Noise coming from the Slip-Ring:
</div> </div>
</div> </div>
<div id="outline-container-org2ec2737" class="outline-2"> <div id="outline-container-orgfec2c5c" class="outline-2">
<h2 id="org2ec2737"><span class="section-number-2">5</span> Other</h2> <h2 id="orgfec2c5c"><span class="section-number-2">5</span> Other</h2>
<div class="outline-text-2" id="text-5"> <div class="outline-text-2" id="text-5">
<ul class="org-ul"> <ul class="org-ul">
<li><a href="huddle-test-geophones/index.html">Huddle Test - Geophones</a></li> <li><a href="huddle-test-geophones/index.html">Huddle Test - Geophones</a></li>
@ -122,7 +121,7 @@ Noise coming from the Slip-Ring:
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p> <p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2020-11-03 mar. 14:33</p> <p class="date">Created: 2020-11-12 jeu. 10:30</p>
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This web-page gathers all the measurements done on the ID31 Micro Station. This web-page gathers all the measurements done on the ID31 Micro Station.

612
instrumentation/index.html
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<h1 class="title">Measurements on the instrumentation</h1> <h1 class="title">Measurements on the instrumentation</h1>
<div id="table-of-contents"> <div id="table-of-contents">
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org9b0dd42">1. Measure of the noise of the Voltage Amplifier</a> <li><a href="#org0b9c6e7">1. Measure of the noise of the Voltage Amplifier</a>
<ul> <ul>
<li><a href="#org494f3b2">1.1. Measurement Description</a></li> <li><a href="#orgce5ef47">1.1. Measurement Description</a></li>
<li><a href="#orgf9402f3">1.2. Load data</a></li> <li><a href="#org4658c5c">1.2. Load data</a></li>
<li><a href="#orgd0212e2">1.3. Time Domain</a></li> <li><a href="#org5de2d60">1.3. Time Domain</a></li>
<li><a href="#org18fa6ce">1.4. Frequency Domain</a></li> <li><a href="#org5fc539a">1.4. Frequency Domain</a></li>
<li><a href="#org36eaef7">1.5. Conclusion</a></li> <li><a href="#orgbc39043">1.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org15e4c95">2. Measure of the influence of the AC/DC option on the voltage amplifiers</a> <li><a href="#org182f3d2">2. Measure of the influence of the AC/DC option on the voltage amplifiers</a>
<ul> <ul>
<li><a href="#org313898e">2.1. Measurement Description</a></li> <li><a href="#orgc5cfc61">2.1. Measurement Description</a></li>
<li><a href="#org86b59a1">2.2. Load data</a></li> <li><a href="#org0c0a3f2">2.2. Load data</a></li>
<li><a href="#org22f801c">2.3. Time Domain</a></li> <li><a href="#orgb381461">2.3. Time Domain</a></li>
<li><a href="#orgbd72638">2.4. Frequency Domain</a></li> <li><a href="#org831a8d7">2.4. Frequency Domain</a></li>
<li><a href="#org2647596">2.5. Conclusion</a></li> <li><a href="#org0f7903d">2.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org9623ca1">3. Transfer function of the Low Pass Filter</a> <li><a href="#orge486804">3. Transfer function of the Low Pass Filter</a>
<ul> <ul>
<li><a href="#org921fe36">3.1. First LPF with a Cut-off frequency of 160Hz</a> <li><a href="#org400e34d">3.1. First LPF with a Cut-off frequency of 160Hz</a>
<ul> <ul>
<li><a href="#org122c7a6">3.1.1. Measurement Description</a></li> <li><a href="#org8e6b3f9">3.1.1. Measurement Description</a></li>
<li><a href="#orgba94437">3.1.2. Load data</a></li> <li><a href="#org3c2d014">3.1.2. Load data</a></li>
<li><a href="#org087582c">3.1.3. Transfer function of the LPF</a></li> <li><a href="#orgddafe0a">3.1.3. Transfer function of the LPF</a></li>
<li><a href="#orgf2dc541">3.1.4. Conclusion</a></li> <li><a href="#org7a0daf9">3.1.4. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgd6132bd">3.2. Second LPF with a Cut-off frequency of 1000Hz</a> <li><a href="#org5504322">3.2. Second LPF with a Cut-off frequency of 1000Hz</a>
<ul> <ul>
<li><a href="#org76b4e0d">3.2.1. Measurement description</a></li> <li><a href="#orge51e102">3.2.1. Measurement description</a></li>
<li><a href="#org2941697">3.2.2. Load data</a></li> <li><a href="#org609fd78">3.2.2. Load data</a></li>
<li><a href="#org45462d2">3.2.3. Transfer function of the LPF</a></li> <li><a href="#orgad7e872">3.2.3. Transfer function of the LPF</a></li>
<li><a href="#org438a172">3.2.4. Conclusion</a></li> <li><a href="#org73a58fb">3.2.4. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -318,20 +72,22 @@ for the JavaScript code in this tag.
</div> </div>
</div> </div>
<div id="outline-container-org9b0dd42" class="outline-2"> <div id="outline-container-org0b9c6e7" class="outline-2">
<h2 id="org9b0dd42"><span class="section-number-2">1</span> Measure of the noise of the Voltage Amplifier</h2> <h2 id="org0b9c6e7"><span class="section-number-2">1</span> Measure of the noise of the Voltage Amplifier</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<a id="orgbd691e3"></a> <a id="org6a52764"></a>
</p>
<div class="note" id="orge2ed99a">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/meas_volt_amp.zip">here</a>.
</p> </p>
<p> </div>
The data and matlab files are accessible <a href="data/meas_volt_amp.zip">here</a>.
</p>
</div> </div>
<div id="outline-container-org494f3b2" class="outline-3"> <div id="outline-container-orgce5ef47" class="outline-3">
<h3 id="org494f3b2"><span class="section-number-3">1.1</span> Measurement Description</h3> <h3 id="orgce5ef47"><span class="section-number-3">1.1</span> Measurement Description</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
<b>Goal</b>: <b>Goal</b>:
@ -362,28 +118,28 @@ The data and matlab files are accessible <a href="data/meas_volt_amp.zip">here</
</div> </div>
</div> </div>
<div id="outline-container-orgf9402f3" class="outline-3"> <div id="outline-container-org4658c5c" class="outline-3">
<h3 id="orgf9402f3"><span class="section-number-3">1.2</span> Load data</h3> <h3 id="org4658c5c"><span class="section-number-3">1.2</span> Load data</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">amp_off = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_003.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_off = amp_off.data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">amp_off = load(<span class="org-string">'mat/data_003.mat'</span>, <span class="org-string">'data'</span>); amp_off = amp_off.data(<span class="org-type">:</span>, [1,3]);
amp_20d = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_004.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_20d = amp_20d.data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_20d = load(<span class="org-string">'mat/data_004.mat'</span>, <span class="org-string">'data'</span>); amp_20d = amp_20d.data(<span class="org-type">:</span>, [1,3]);
amp_40d = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_005.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_40d = amp_40d.data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_40d = load(<span class="org-string">'mat/data_005.mat'</span>, <span class="org-string">'data'</span>); amp_40d = amp_40d.data(<span class="org-type">:</span>, [1,3]);
amp_60d = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_006.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_60d = amp_60d.data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>,<span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; amp_60d = load(<span class="org-string">'mat/data_006.mat'</span>, <span class="org-string">'data'</span>); amp_60d = amp_60d.data(<span class="org-type">:</span>, [1,3]);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgd0212e2" class="outline-3"> <div id="outline-container-org5de2d60" class="outline-3">
<h3 id="orgd0212e2"><span class="section-number-3">1.3</span> Time Domain</h3> <h3 id="org5de2d60"><span class="section-number-3">1.3</span> Time Domain</h3>
<div class="outline-text-3" id="text-1-3"> <div class="outline-text-3" id="text-1-3">
<p> <p>
The time domain signals are shown on figure <a href="#org98f097d">1</a>. The time domain signals are shown on figure <a href="#org2fccd36">1</a>.
</p> </p>
<div id="org98f097d" class="figure"> <div id="org2fccd36" class="figure">
<p><img src="figs/ampli_noise_time.png" alt="ampli_noise_time.png" /> <p><img src="figs/ampli_noise_time.png" alt="ampli_noise_time.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Output of the amplifier</p> <p><span class="figure-number">Figure 1: </span>Output of the amplifier</p>
@ -391,18 +147,18 @@ The time domain signals are shown on figure <a href="#org98f097d">1</a>.
</div> </div>
</div> </div>
<div id="outline-container-org18fa6ce" class="outline-3"> <div id="outline-container-org5fc539a" class="outline-3">
<h3 id="org18fa6ce"><span class="section-number-3">1.4</span> Frequency Domain</h3> <h3 id="org5fc539a"><span class="section-number-3">1.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-1-4"> <div class="outline-text-3" id="text-1-4">
<p> <p>
We first compute some parameters that will be used for the PSD computation. We first compute some parameters that will be used for the PSD computation.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = amp_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>amp_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = amp_off(2, 2)<span class="org-type">-</span>amp_off(1, 2);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
@ -410,10 +166,10 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
Then we compute the Power Spectral Density using <code>pwelch</code> function. Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxoff, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>amp_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxoff, f] = pwelch(amp_off(<span class="org-type">:</span>,1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px20d, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>amp_20d<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px20d, <span class="org-type">~</span>] = pwelch(amp_20d(<span class="org-type">:</span>,1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px40d, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>amp_40d<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px40d, <span class="org-type">~</span>] = pwelch(amp_40d(<span class="org-type">:</span>,1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px60d, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>amp_60d<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>,<span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px60d, <span class="org-type">~</span>] = pwelch(amp_60d(<span class="org-type">:</span>,1), win, [], [], Fs);
</pre> </pre>
</div> </div>
@ -421,16 +177,16 @@ Then we compute the Power Spectral Density using <code>pwelch</code> function.
We compute the theoretical ADC noise. We compute the theoretical ADC noise.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">q = <span class="org-highlight-numbers-number">20</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">^</span><span class="org-highlight-numbers-number">16</span>; <span class="org-comment">% quantization</span> <pre class="src src-matlab">q = 20<span class="org-type">/</span>2<span class="org-type">^</span>16; <span class="org-comment">% quantization</span>
Sq = q<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-highlight-numbers-number">12</span><span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span>; <span class="org-comment">% PSD of the ADC noise</span> Sq = q<span class="org-type">^</span>2<span class="org-type">/</span>12<span class="org-type">/</span>1000; <span class="org-comment">% PSD of the ADC noise</span>
</pre> </pre>
</div> </div>
<p> <p>
Finally, the ASD is shown on figure <a href="#orga4734ea">2</a>. Finally, the ASD is shown on figure <a href="#org46e6591">2</a>.
</p> </p>
<div id="orga4734ea" class="figure"> <div id="org46e6591" class="figure">
<p><img src="figs/ampli_noise_psd.png" alt="ampli_noise_psd.png" /> <p><img src="figs/ampli_noise_psd.png" alt="ampli_noise_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Amplitude Spectral Density of the measured voltage at the output of the voltage amplifier</p> <p><span class="figure-number">Figure 2: </span>Amplitude Spectral Density of the measured voltage at the output of the voltage amplifier</p>
@ -438,10 +194,10 @@ Finally, the ASD is shown on figure <a href="#orga4734ea">2</a>.
</div> </div>
</div> </div>
<div id="outline-container-org36eaef7" class="outline-3"> <div id="outline-container-orgbc39043" class="outline-3">
<h3 id="org36eaef7"><span class="section-number-3">1.5</span> Conclusion</h3> <h3 id="orgbc39043"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5"> <div class="outline-text-3" id="text-1-5">
<div class="important"> <div class="important" id="orgb8e9939">
<p> <p>
<b>Questions</b>: <b>Questions</b>:
</p> </p>
@ -458,20 +214,22 @@ Noise induced by the voltage amplifiers seems not to be a limiting factor as we
</div> </div>
</div> </div>
<div id="outline-container-org15e4c95" class="outline-2"> <div id="outline-container-org182f3d2" class="outline-2">
<h2 id="org15e4c95"><span class="section-number-2">2</span> Measure of the influence of the AC/DC option on the voltage amplifiers</h2> <h2 id="org182f3d2"><span class="section-number-2">2</span> Measure of the influence of the AC/DC option on the voltage amplifiers</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org1e85a61"></a> <a id="org4bf4c36"></a>
</p>
<div class="note" id="org66d7fee">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/meas_noise_ac_dc.zip">here</a>.
</p> </p>
<p> </div>
The data and matlab files are accessible <a href="data/meas_noise_ac_dc.zip">here</a>.
</p>
</div> </div>
<div id="outline-container-org313898e" class="outline-3"> <div id="outline-container-orgc5cfc61" class="outline-3">
<h3 id="org313898e"><span class="section-number-3">2.1</span> Measurement Description</h3> <h3 id="orgc5cfc61"><span class="section-number-3">2.1</span> Measurement Description</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
<b>Goal</b>: <b>Goal</b>:
@ -485,7 +243,7 @@ The data and matlab files are accessible <a href="data/meas_noise_ac_dc.zip">her
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>One geophone is located on the marble.</li> <li>One geophone is located on the marble.</li>
<li>It's signal goes to two voltage amplifiers with a gain of 60dB.</li> <li>It&rsquo;s signal goes to two voltage amplifiers with a gain of 60dB.</li>
<li>One voltage amplifier is on the AC option, the other is on the DC option.</li> <li>One voltage amplifier is on the AC option, the other is on the DC option.</li>
</ul> </ul>
@ -561,7 +319,7 @@ Second measurement (<code>mat/data_015.mat</code> file):
</table> </table>
<div id="org6faa1f8" class="figure"> <div id="org52bc26f" class="figure">
<p><img src="./img/IMG_20190503_170936.jpg" alt="IMG_20190503_170936.jpg" width="500px" /> <p><img src="./img/IMG_20190503_170936.jpg" alt="IMG_20190503_170936.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Picture of the two voltages amplifiers</p> <p><span class="figure-number">Figure 3: </span>Picture of the two voltages amplifiers</p>
@ -569,28 +327,28 @@ Second measurement (<code>mat/data_015.mat</code> file):
</div> </div>
</div> </div>
<div id="outline-container-org86b59a1" class="outline-3"> <div id="outline-container-org0c0a3f2" class="outline-3">
<h3 id="org86b59a1"><span class="section-number-3">2.2</span> Load data</h3> <h3 id="org0c0a3f2"><span class="section-number-3">2.2</span> Load data</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">meas14 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_014.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; meas14 = meas14.data; <pre class="src src-matlab">meas14 = load(<span class="org-string">'mat/data_014.mat'</span>, <span class="org-string">'data'</span>); meas14 = meas14.data;
meas15 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_015.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; meas15 = meas15.data; meas15 = load(<span class="org-string">'mat/data_015.mat'</span>, <span class="org-string">'data'</span>); meas15 = meas15.data;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org22f801c" class="outline-3"> <div id="outline-container-orgb381461" class="outline-3">
<h3 id="org22f801c"><span class="section-number-3">2.3</span> Time Domain</h3> <h3 id="orgb381461"><span class="section-number-3">2.3</span> Time Domain</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
The signals are shown on figure <a href="#org4a464f5">4</a>. The signals are shown on figure <a href="#org26ff108">4</a>.
</p> </p>
<div id="org4a464f5" class="figure"> <div id="org26ff108" class="figure">
<p><img src="figs/ac_dc_option_time.png" alt="ac_dc_option_time.png" /> <p><img src="figs/ac_dc_option_time.png" alt="ac_dc_option_time.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Comparison of the signals going through the Voltage amplifiers</p> <p><span class="figure-number">Figure 4: </span>Comparison of the signals going through the Voltage amplifiers</p>
@ -598,18 +356,18 @@ The signals are shown on figure <a href="#org4a464f5">4</a>.
</div> </div>
</div> </div>
<div id="outline-container-orgbd72638" class="outline-3"> <div id="outline-container-org831a8d7" class="outline-3">
<h3 id="orgbd72638"><span class="section-number-3">2.4</span> Frequency Domain</h3> <h3 id="org831a8d7"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
We first compute some parameters that will be used for the PSD computation. We first compute some parameters that will be used for the PSD computation.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = meas14<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>meas14<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = meas14(2, 3)<span class="org-type">-</span>meas14(1, 3);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
@ -617,19 +375,19 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
Then we compute the Power Spectral Density using <code>pwelch</code> function. Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxamp1ac, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas14<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxamp1ac, f] = pwelch(meas14(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxamp2dc, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas14<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxamp2dc, <span class="org-type">~</span>] = pwelch(meas14(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxamp1dc, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas15<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxamp1dc, <span class="org-type">~</span>] = pwelch(meas15(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxamp2ac, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>meas15<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxamp2ac, <span class="org-type">~</span>] = pwelch(meas15(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre> </pre>
</div> </div>
<p> <p>
The ASD of the signals are compare on figure <a href="#org73d3360">5</a>. The ASD of the signals are compare on figure <a href="#org252ca9f">5</a>.
</p> </p>
<div id="org73d3360" class="figure"> <div id="org252ca9f" class="figure">
<p><img src="figs/ac_dc_option_asd.png" alt="ac_dc_option_asd.png" /> <p><img src="figs/ac_dc_option_asd.png" alt="ac_dc_option_asd.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured signals</p> <p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured signals</p>
@ -637,10 +395,10 @@ The ASD of the signals are compare on figure <a href="#org73d3360">5</a>.
</div> </div>
</div> </div>
<div id="outline-container-org2647596" class="outline-3"> <div id="outline-container-org0f7903d" class="outline-3">
<h3 id="org2647596"><span class="section-number-3">2.5</span> Conclusion</h3> <h3 id="org0f7903d"><span class="section-number-3">2.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<div class="important"> <div class="important" id="orga7652b6">
<ul class="org-ul"> <ul class="org-ul">
<li>The voltage amplifiers include some very sharp high pass filters at 1.5Hz (maybe 4th order)</li> <li>The voltage amplifiers include some very sharp high pass filters at 1.5Hz (maybe 4th order)</li>
<li>There is a DC offset on the time domain signal because the DC-offset knob was not set to zero</li> <li>There is a DC offset on the time domain signal because the DC-offset knob was not set to zero</li>
@ -651,24 +409,23 @@ The ASD of the signals are compare on figure <a href="#org73d3360">5</a>.
</div> </div>
</div> </div>
<div id="outline-container-org9623ca1" class="outline-2"> <div id="outline-container-orge486804" class="outline-2">
<h2 id="org9623ca1"><span class="section-number-2">3</span> Transfer function of the Low Pass Filter</h2> <h2 id="orge486804"><span class="section-number-2">3</span> Transfer function of the Low Pass Filter</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
<a id="org5eb1733"></a> <a id="orgae11ccf"></a>
</p> </p>
<p> <p>
The computation files for this section are accessible <a href="data/low_pass_filter_measurements.zip">here</a>. The computation files for this section are accessible <a href="data/low_pass_filter_measurements.zip">here</a>.
</p> </p>
</div> </div>
<div id="outline-container-org921fe36" class="outline-3"> <div id="outline-container-org400e34d" class="outline-3">
<h3 id="org921fe36"><span class="section-number-3">3.1</span> First LPF with a Cut-off frequency of 160Hz</h3> <h3 id="org400e34d"><span class="section-number-3">3.1</span> First LPF with a Cut-off frequency of 160Hz</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
</div> </div>
<div id="outline-container-org122c7a6" class="outline-4"> <div id="outline-container-org8e6b3f9" class="outline-4">
<h4 id="org122c7a6"><span class="section-number-4">3.1.1</span> Measurement Description</h4> <h4 id="org8e6b3f9"><span class="section-number-4">3.1.1</span> Measurement Description</h4>
<div class="outline-text-4" id="text-3-1-1"> <div class="outline-text-4" id="text-3-1-1">
<p> <p>
<b>Goal</b>: <b>Goal</b>:
@ -689,7 +446,7 @@ Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-latex" id="org336f6c8"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>} <pre class="src src-latex" id="orgebabef7"><span class="org-font-latex-sedate"><span class="org-keyword">\begin</span></span>{<span class="org-function-name">tikzpicture</span>}
<span class="org-font-latex-sedate">\draw</span> (0,2) <span class="org-font-latex-sedate">\draw</span> (0,2)
to [R=<span class="org-font-latex-sedate"><span class="org-font-latex-math">\(R\)</span></span>] ++(2,0) node[circ] to [R=<span class="org-font-latex-sedate"><span class="org-font-latex-math">\(R\)</span></span>] ++(2,0) node[circ]
to ++(2,0) to ++(2,0)
@ -703,7 +460,7 @@ Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\).
</div> </div>
<div id="orgda67620" class="figure"> <div id="org19a615d" class="figure">
<p><img src="figs/lpf.png" alt="lpf.png" /> <p><img src="figs/lpf.png" alt="lpf.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Schematic of the Low Pass Filter used</p> <p><span class="figure-number">Figure 6: </span>Schematic of the Low Pass Filter used</p>
@ -756,7 +513,7 @@ Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\).
</table> </table>
<div id="org5022f0b" class="figure"> <div id="org91c0742" class="figure">
<p><img src="./img/IMG_20190507_102756.jpg" alt="IMG_20190507_102756.jpg" width="500px" /> <p><img src="./img/IMG_20190507_102756.jpg" alt="IMG_20190507_102756.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Picture of the low pass filter used</p> <p><span class="figure-number">Figure 7: </span>Picture of the low pass filter used</p>
@ -764,86 +521,86 @@ Which makes a cut-off frequency of \(f_c = \frac{1}{RC} = 1000 rad/s = 160Hz\).
</div> </div>
</div> </div>
<div id="outline-container-orgba94437" class="outline-4"> <div id="outline-container-org3c2d014" class="outline-4">
<h4 id="orgba94437"><span class="section-number-4">3.1.2</span> Load data</h4> <h4 id="org3c2d014"><span class="section-number-4">3.1.2</span> Load data</h4>
<div class="outline-text-4" id="text-3-1-2"> <div class="outline-text-4" id="text-3-1-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">data = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_018.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; data = data.data; <pre class="src src-matlab">data = load(<span class="org-string">'mat/data_018.mat'</span>, <span class="org-string">'data'</span>); data = data.data;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org087582c" class="outline-4"> <div id="outline-container-orgddafe0a" class="outline-4">
<h4 id="org087582c"><span class="section-number-4">3.1.3</span> Transfer function of the LPF</h4> <h4 id="orgddafe0a"><span class="section-number-4">3.1.3</span> Transfer function of the LPF</h4>
<div class="outline-text-4" id="text-3-1-3"> <div class="outline-text-4" id="text-3-1-3">
<p> <p>
We compute the transfer function from the signal without the LPF to the signal measured with the LPF. We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = data(2, 3)<span class="org-type">-</span>data(1, 3);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>Glpf, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[Glpf, f] = tfestimate(data(<span class="org-type">:</span>, 2), data(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre> </pre>
</div> </div>
<p> <p>
We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of \(1000rad/s\). We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of \(1000rad/s\).
We obtain the result on figure <a href="#orgeb8ea3c">8</a>. We obtain the result on figure <a href="#orgb174301">8</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Gth = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-1">)</span> <pre class="src src-matlab">Gth = 1<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>1000)
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; ax1 = subplot(2, 1, 1);
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>Glpf<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, abs(Glpf));
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>Gth, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, abs(squeeze(freqresp(Gth, f, <span class="org-string">'Hz'</span>))));
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,<span class="org-rainbow-delimiters-depth-2">[]</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,[]);
ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Magnitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel(<span class="org-string">'Magnitude'</span>);
ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; ax2 = subplot(2, 1, 2);
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>Glpf<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, mod(180<span class="org-type">+</span>180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase(Glpf), 360)<span class="org-type">-</span>180);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>unwrap<span class="org-rainbow-delimiters-depth-2">(</span>angle<span class="org-rainbow-delimiters-depth-3">(</span>squeeze<span class="org-rainbow-delimiters-depth-4">(</span>freqresp<span class="org-rainbow-delimiters-depth-5">(</span>Gth, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, 180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>unwrap(angle(squeeze(freqresp(Gth, f, <span class="org-string">'Hz'</span>)))));
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim([<span class="org-type">-</span>180, 180]);
yticks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; yticks([<span class="org-type">-</span>180, <span class="org-type">-</span>90, 0, 90, 180]);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Phase'</span>);
linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</span><span class="org-rainbow-delimiters-depth-1">)</span>; linkaxes([ax1,ax2],<span class="org-string">'x'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([1, 500]);
</pre> </pre>
</div> </div>
<div id="orgeb8ea3c" class="figure"> <div id="orgb174301" class="figure">
<p><img src="figs/Glpf_bode.png" alt="Glpf_bode.png" /> <p><img src="figs/Glpf_bode.png" alt="Glpf_bode.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Bode Diagram of the measured Low Pass filter and the theoritical one</p> <p><span class="figure-number">Figure 8: </span>Bode Diagram of the measured Low Pass filter and the theoritical one</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgf2dc541" class="outline-4"> <div id="outline-container-org7a0daf9" class="outline-4">
<h4 id="orgf2dc541"><span class="section-number-4">3.1.4</span> Conclusion</h4> <h4 id="org7a0daf9"><span class="section-number-4">3.1.4</span> Conclusion</h4>
<div class="outline-text-4" id="text-3-1-4"> <div class="outline-text-4" id="text-3-1-4">
<div class="important"> <div class="important" id="org84503a8">
<p> <p>
As we want to measure things up to \(500Hz\), we chose to change the value of the capacitor to obtain a cut-off frequency of \(1kHz\). As we want to measure things up to \(500Hz\), we chose to change the value of the capacitor to obtain a cut-off frequency of \(1kHz\).
</p> </p>
@ -853,12 +610,12 @@ As we want to measure things up to \(500Hz\), we chose to change the value of th
</div> </div>
</div> </div>
<div id="outline-container-orgd6132bd" class="outline-3"> <div id="outline-container-org5504322" class="outline-3">
<h3 id="orgd6132bd"><span class="section-number-3">3.2</span> Second LPF with a Cut-off frequency of 1000Hz</h3> <h3 id="org5504322"><span class="section-number-3">3.2</span> Second LPF with a Cut-off frequency of 1000Hz</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
</div> </div>
<div id="outline-container-org76b4e0d" class="outline-4"> <div id="outline-container-orge51e102" class="outline-4">
<h4 id="org76b4e0d"><span class="section-number-4">3.2.1</span> Measurement description</h4> <h4 id="orge51e102"><span class="section-number-4">3.2.1</span> Measurement description</h4>
<div class="outline-text-4" id="text-3-2-1"> <div class="outline-text-4" id="text-3-2-1">
<p> <p>
This time, the value are This time, the value are
@ -873,86 +630,86 @@ Which makes a low pass filter with a cut-off frequency of \(f_c = 1060Hz\).
</div> </div>
</div> </div>
<div id="outline-container-org2941697" class="outline-4"> <div id="outline-container-org609fd78" class="outline-4">
<h4 id="org2941697"><span class="section-number-4">3.2.2</span> Load data</h4> <h4 id="org609fd78"><span class="section-number-4">3.2.2</span> Load data</h4>
<div class="outline-text-4" id="text-3-2-2"> <div class="outline-text-4" id="text-3-2-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">data = load<span class="org-rainbow-delimiters-depth-1">(</span>'mat<span class="org-type">/</span>data_019.mat', <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; data = data.data; <pre class="src src-matlab">data = load(<span class="org-string">'mat/data_019.mat'</span>, <span class="org-string">'data'</span>); data = data.data;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org45462d2" class="outline-4"> <div id="outline-container-orgad7e872" class="outline-4">
<h4 id="org45462d2"><span class="section-number-4">3.2.3</span> Transfer function of the LPF</h4> <h4 id="orgad7e872"><span class="section-number-4">3.2.3</span> Transfer function of the LPF</h4>
<div class="outline-text-4" id="text-3-2-3"> <div class="outline-text-4" id="text-3-2-3">
<p> <p>
We compute the transfer function from the signal without the LPF to the signal measured with the LPF. We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = data(2, 3)<span class="org-type">-</span>data(1, 3);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>Glpf, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[Glpf, f] = tfestimate(data(<span class="org-type">:</span>, 2), data(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre> </pre>
</div> </div>
<p> <p>
We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of \(1060Hz\). We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of \(1060Hz\).
We obtain the result on figure <a href="#org19f2e2d">9</a>. We obtain the result on figure <a href="#org9707219">9</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">Gth = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">1060</span><span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">Gth = 1<span class="org-type">/</span>(1<span class="org-type">+</span>s<span class="org-type">/</span>1060<span class="org-type">/</span>2<span class="org-type">/</span><span class="org-constant">pi</span>);
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; ax1 = subplot(2, 1, 1);
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>Glpf<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, abs(Glpf));
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>squeeze<span class="org-rainbow-delimiters-depth-3">(</span>freqresp<span class="org-rainbow-delimiters-depth-4">(</span>Gth, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, abs(squeeze(freqresp(Gth, f, <span class="org-string">'Hz'</span>))));
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,<span class="org-rainbow-delimiters-depth-2">[]</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,[]);
ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Magnitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel(<span class="org-string">'Magnitude'</span>);
ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; ax2 = subplot(2, 1, 2);
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>Glpf<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, mod(180<span class="org-type">+</span>180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase(Glpf), 360)<span class="org-type">-</span>180);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>unwrap<span class="org-rainbow-delimiters-depth-2">(</span>angle<span class="org-rainbow-delimiters-depth-3">(</span>squeeze<span class="org-rainbow-delimiters-depth-4">(</span>freqresp<span class="org-rainbow-delimiters-depth-5">(</span>Gth, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, 180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>unwrap(angle(squeeze(freqresp(Gth, f, <span class="org-string">'Hz'</span>)))));
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim([<span class="org-type">-</span>180, 180]);
yticks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; yticks([<span class="org-type">-</span>180, <span class="org-type">-</span>90, 0, 90, 180]);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Phase'</span>);
linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</span><span class="org-rainbow-delimiters-depth-1">)</span>; linkaxes([ax1,ax2],<span class="org-string">'x'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([1, 500]);
</pre> </pre>
</div> </div>
<div id="org19f2e2d" class="figure"> <div id="org9707219" class="figure">
<p><img src="figs/Glpf_bode_bis.png" alt="Glpf_bode_bis.png" /> <p><img src="figs/Glpf_bode_bis.png" alt="Glpf_bode_bis.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Bode Diagram of the measured Low Pass filter and the theoritical one</p> <p><span class="figure-number">Figure 9: </span>Bode Diagram of the measured Low Pass filter and the theoritical one</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org438a172" class="outline-4"> <div id="outline-container-org73a58fb" class="outline-4">
<h4 id="org438a172"><span class="section-number-4">3.2.4</span> Conclusion</h4> <h4 id="org73a58fb"><span class="section-number-4">3.2.4</span> Conclusion</h4>
<div class="outline-text-4" id="text-3-2-4"> <div class="outline-text-4" id="text-3-2-4">
<div class="important"> <div class="important" id="org1fede99">
<p> <p>
The added LPF has the expected behavior. The added LPF has the expected behavior.
</p> </p>
@ -964,9 +721,8 @@ The added LPF has the expected behavior.
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-10 ven. 10:07</p> <p class="date">Created: 2020-11-12 jeu. 10:28</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>
</html> </html>

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@ -3,18 +3,13 @@
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2020-11-03 mar. 09:32 --> <!-- 2020-11-12 jeu. 10:28 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Compliance Measurement of the Micro Station</title> <title>Compliance Measurement of the Micro Station</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
<meta name="author" content="Dehaeze Thomas" /> <meta name="author" content="Dehaeze Thomas" />
<link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
<link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/> <script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
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<script>MathJax = { <script>MathJax = {
tex: { tex: {
tags: 'ams', tags: 'ams',
@ -35,32 +30,32 @@
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgaec7e8e">1. Setup</a> <li><a href="#org6d3ca7a">1. Setup</a>
<ul> <ul>
<li><a href="#org43be1a2">1.1. Position of inertial sensors on top of the micro-hexapod</a></li> <li><a href="#org9d1f825">1.1. Position of inertial sensors on top of the micro-hexapod</a></li>
<li><a href="#org095d116">1.2. Hammer blow position/orientation</a></li> <li><a href="#orgee54e47">1.2. Hammer blow position/orientation</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org7140136">2. Results</a> <li><a href="#orgda5861d">2. Results</a>
<ul> <ul>
<li><a href="#org6082142">2.1. Load Data</a></li> <li><a href="#org981bf00">2.1. Load Data</a></li>
<li><a href="#orgd4012ad">2.2. Compute Transfer Functions</a></li> <li><a href="#org890d2d0">2.2. Compute Transfer Functions</a></li>
<li><a href="#org7af3187">2.3. Diagonal Dynamics</a></li> <li><a href="#org05266f7">2.3. Diagonal Dynamics</a></li>
<li><a href="#org23b9749">2.4. Equivalent Stiffness and Mass Estimation</a></li> <li><a href="#orgef95ff7">2.4. Equivalent Stiffness and Mass Estimation</a></li>
<li><a href="#org208dda9">2.5. Compare with Model</a></li> <li><a href="#org68cfbfb">2.5. Compare with Model</a></li>
<li><a href="#org94eb6da">2.6. Coupling Dynamics</a></li> <li><a href="#org0bfb71d">2.6. Coupling Dynamics</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orgaec7e8e" class="outline-2"> <div id="outline-container-org6d3ca7a" class="outline-2">
<h2 id="orgaec7e8e"><span class="section-number-2">1</span> Setup</h2> <h2 id="org6d3ca7a"><span class="section-number-2">1</span> Setup</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
</div> </div>
<div id="outline-container-org43be1a2" class="outline-3"> <div id="outline-container-org9d1f825" class="outline-3">
<h3 id="org43be1a2"><span class="section-number-3">1.1</span> Position of inertial sensors on top of the micro-hexapod</h3> <h3 id="org9d1f825"><span class="section-number-3">1.1</span> Position of inertial sensors on top of the micro-hexapod</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
Orientation is relative to the frame determined by the X-ray Orientation is relative to the frame determined by the X-ray
@ -329,8 +324,8 @@ From the acceleration measurement of the 4 accelerometers, we can compute the tr
</div> </div>
</div> </div>
<div id="outline-container-org095d116" class="outline-3"> <div id="outline-container-orgee54e47" class="outline-3">
<h3 id="org095d116"><span class="section-number-3">1.2</span> Hammer blow position/orientation</h3> <h3 id="orgee54e47"><span class="section-number-3">1.2</span> Hammer blow position/orientation</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
@ -474,12 +469,12 @@ From hammer blows to pure forces / torques:
</div> </div>
</div> </div>
<div id="outline-container-org7140136" class="outline-2"> <div id="outline-container-orgda5861d" class="outline-2">
<h2 id="org7140136"><span class="section-number-2">2</span> Results</h2> <h2 id="orgda5861d"><span class="section-number-2">2</span> Results</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
</div> </div>
<div id="outline-container-org6082142" class="outline-3"> <div id="outline-container-org981bf00" class="outline-3">
<h3 id="org6082142"><span class="section-number-3">2.1</span> Load Data</h3> <h3 id="org981bf00"><span class="section-number-3">2.1</span> Load Data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">m1 = load(<span class="org-string">'data/Measurement1.mat'</span>); <pre class="src src-matlab">m1 = load(<span class="org-string">'data/Measurement1.mat'</span>);
@ -497,8 +492,8 @@ m10 = load(<span class="org-string">'data/Measurement10.mat'</span>);
</div> </div>
</div> </div>
<div id="outline-container-orgd4012ad" class="outline-3"> <div id="outline-container-org890d2d0" class="outline-3">
<h3 id="orgd4012ad"><span class="section-number-3">2.2</span> Compute Transfer Functions</h3> <h3 id="org890d2d0"><span class="section-number-3">2.2</span> Compute Transfer Functions</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">freqs = m3.FFT1_H1_1_13_X_Val; <pre class="src src-matlab">freqs = m3.FFT1_H1_1_13_X_Val;
@ -589,8 +584,8 @@ G<span class="org-type">(6,6,:) </span>= 1<span class="org-type">/</span>A<span
</div> </div>
</div> </div>
<div id="outline-container-org7af3187" class="outline-3"> <div id="outline-container-org05266f7" class="outline-3">
<h3 id="org7af3187"><span class="section-number-3">2.3</span> Diagonal Dynamics</h3> <h3 id="org05266f7"><span class="section-number-3">2.3</span> Diagonal Dynamics</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
@ -622,7 +617,7 @@ xlim([30, 300]);
</div> </div>
<div id="orgf9adbb6" class="figure"> <div id="org3b79c32" class="figure">
<p><img src="figs/compliance_diagonal_translations.png" alt="compliance_diagonal_translations.png" /> <p><img src="figs/compliance_diagonal_translations.png" alt="compliance_diagonal_translations.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Dynamics from Forces to Translations</p> <p><span class="figure-number">Figure 1: </span>Dynamics from Forces to Translations</p>
@ -658,7 +653,7 @@ xlim([30, 300]);
</div> </div>
<div id="org1468ca5" class="figure"> <div id="orgd6380a4" class="figure">
<p><img src="figs/compliance_diagonal_rotations.png" alt="compliance_diagonal_rotations.png" /> <p><img src="figs/compliance_diagonal_rotations.png" alt="compliance_diagonal_rotations.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Dynamics from Torques to Rotations</p> <p><span class="figure-number">Figure 2: </span>Dynamics from Torques to Rotations</p>
@ -666,8 +661,8 @@ xlim([30, 300]);
</div> </div>
</div> </div>
<div id="outline-container-org23b9749" class="outline-3"> <div id="outline-container-orgef95ff7" class="outline-3">
<h3 id="org23b9749"><span class="section-number-3">2.4</span> Equivalent Stiffness and Mass Estimation</h3> <h3 id="orgef95ff7"><span class="section-number-3">2.4</span> Equivalent Stiffness and Mass Estimation</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">K = [1e7, 1e7, 2e8, 5e7, 3e7, 2e7]; <pre class="src src-matlab">K = [1e7, 1e7, 2e8, 5e7, 3e7, 2e7];
@ -733,8 +728,8 @@ Here is the inertia / stiffness to the granite that can represent the micro-stat
</div> </div>
</div> </div>
<div id="outline-container-org208dda9" class="outline-3"> <div id="outline-container-org68cfbfb" class="outline-3">
<h3 id="org208dda9"><span class="section-number-3">2.5</span> Compare with Model</h3> <h3 id="org68cfbfb"><span class="section-number-3">2.5</span> Compare with Model</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'./mat/model.mat'</span>, <span class="org-string">'Gm'</span>); <pre class="src src-matlab">load(<span class="org-string">'./mat/model.mat'</span>, <span class="org-string">'Gm'</span>);
@ -779,7 +774,7 @@ xlim([30, 300]);
</div> </div>
<div id="orgbdba037" class="figure"> <div id="org17d53d6" class="figure">
<p><img src="figs/compliance_diagonal_translations_comp_model.png" alt="compliance_diagonal_translations_comp_model.png" /> <p><img src="figs/compliance_diagonal_translations_comp_model.png" alt="compliance_diagonal_translations_comp_model.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Dynamics from Forces to Translations</p> <p><span class="figure-number">Figure 3: </span>Dynamics from Forces to Translations</p>
@ -823,7 +818,7 @@ xlim([30, 300]);
</div> </div>
<div id="org3c85450" class="figure"> <div id="org5de58b2" class="figure">
<p><img src="figs/compliance_diagonal_rotations_comp_model.png" alt="compliance_diagonal_rotations_comp_model.png" /> <p><img src="figs/compliance_diagonal_rotations_comp_model.png" alt="compliance_diagonal_rotations_comp_model.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Dynamics from Torques to Rotations</p> <p><span class="figure-number">Figure 4: </span>Dynamics from Torques to Rotations</p>
@ -887,8 +882,8 @@ xlim([30, 300]);
</div> </div>
</div> </div>
<div id="outline-container-org94eb6da" class="outline-3"> <div id="outline-container-org0bfb71d" class="outline-3">
<h3 id="org94eb6da"><span class="section-number-3">2.6</span> Coupling Dynamics</h3> <h3 id="org0bfb71d"><span class="section-number-3">2.6</span> Coupling Dynamics</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-6">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
@ -965,7 +960,7 @@ xlim([30, 300]);
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-11-03 mar. 09:32</p> <p class="date">Created: 2020-11-12 jeu. 10:28</p>
</div> </div>
</body> </body>
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9
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@ -9,13 +9,8 @@
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@ -3,275 +3,25 @@
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@ -280,24 +30,24 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org8cc195e">1. Importation of measured FRF curves</a></li> <li><a href="#orgf7cf1c8">1. Importation of measured FRF curves</a></li>
<li><a href="#orge008f26">2. From accelerometer DOFs to solid body DOFs - Mathematics</a></li> <li><a href="#orgc506a92">2. From accelerometer DOFs to solid body DOFs - Mathematics</a></li>
<li><a href="#org542a5f3">3. What reference frame to choose?</a></li> <li><a href="#org681033c">3. What reference frame to choose?</a></li>
<li><a href="#org8595ef7">4. FRF expressed in a common frame</a> <li><a href="#org964462f">4. FRF expressed in a common frame</a>
<ul> <ul>
<li><a href="#org23c660e">4.1. From accelerometer DOFs to solid body DOFs - Matlab Implementation</a></li> <li><a href="#orga50f5f9">4.1. From accelerometer DOFs to solid body DOFs - Matlab Implementation</a></li>
<li><a href="#orge7f0885">4.2. Analysis of some FRF in the global coordinates</a></li> <li><a href="#org3164705">4.2. Analysis of some FRF in the global coordinates</a></li>
<li><a href="#orgee41f84">4.3. Comparison of the relative motion of solid bodies</a></li> <li><a href="#org2faadba">4.3. Comparison of the relative motion of solid bodies</a></li>
<li><a href="#org2a5f7b7">4.4. Verify that we find the original FRF from the FRF in the global coordinates</a></li> <li><a href="#orgefe4113">4.4. Verify that we find the original FRF from the FRF in the global coordinates</a></li>
<li><a href="#org9323f41">4.5. Saving of the FRF expressed in the global coordinates</a></li> <li><a href="#orgc0f4ff6">4.5. Saving of the FRF expressed in the global coordinates</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org9a552f4">5. FRF expressed in a frame centered at the CoM of each solid body</a> <li><a href="#org6014915">5. FRF expressed in a frame centered at the CoM of each solid body</a>
<ul> <ul>
<li><a href="#org5580afc">5.1. Center of Mass of each solid body</a></li> <li><a href="#orgc5b91ab">5.1. Center of Mass of each solid body</a></li>
<li><a href="#org1128440">5.2. From accelerometer DOFs to solid body DOFs - Expressed at the CoM</a></li> <li><a href="#org9ea4330">5.2. From accelerometer DOFs to solid body DOFs - Expressed at the CoM</a></li>
<li><a href="#org0efe1de">5.3. Analysis of some FRF</a></li> <li><a href="#orga333d35">5.3. Analysis of some FRF</a></li>
<li><a href="#org1c6f529">5.4. Save the FRF</a></li> <li><a href="#org52ce77b">5.4. Save the FRF</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -333,15 +83,15 @@ Thus, we are only interested in \(6 \times 6 = 36\) degrees of freedom.
We here process the FRF matrix to go from the 69 measured DOFs to the wanted 36 DOFs. We here process the FRF matrix to go from the 69 measured DOFs to the wanted 36 DOFs.
</p> </p>
<div class="note"> <div class="note" id="orgdcd560d">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/frf_processing.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/frf_processing.zip">here</a>.
</p> </p>
</div> </div>
<div id="outline-container-org8cc195e" class="outline-2"> <div id="outline-container-orgf7cf1c8" class="outline-2">
<h2 id="org8cc195e"><span class="section-number-2">1</span> Importation of measured FRF curves</h2> <h2 id="orgf7cf1c8"><span class="section-number-2">1</span> Importation of measured FRF curves</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
We load the measured FRF and Coherence matrices. We load the measured FRF and Coherence matrices.
@ -349,18 +99,18 @@ We also load the geometric parameters of the station: solid bodies considered an
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/frf_coh_matrices.mat', 'FRFs', 'COHs', 'freqs'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">load(<span class="org-string">'mat/frf_coh_matrices.mat'</span>, <span class="org-string">'FRFs'</span>, <span class="org-string">'COHs'</span>, <span class="org-string">'freqs'</span>);
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/geometry.mat', 'solids', 'solid_names', 'acc_pos'</span><span class="org-rainbow-delimiters-depth-1">)</span>; load(<span class="org-string">'mat/geometry.mat'</span>, <span class="org-string">'solids'</span>, <span class="org-string">'solid_names'</span>, <span class="org-string">'acc_pos'</span>);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orge008f26" class="outline-2"> <div id="outline-container-orgc506a92" class="outline-2">
<h2 id="orge008f26"><span class="section-number-2">2</span> From accelerometer DOFs to solid body DOFs - Mathematics</h2> <h2 id="orgc506a92"><span class="section-number-2">2</span> From accelerometer DOFs to solid body DOFs - Mathematics</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
Let's consider the schematic shown on figure <a href="#org79eabe9">1</a> where we are measuring the motion of a (supposed) solid body at 4 distinct points in x-y-z. Let&rsquo;s consider the schematic shown on figure <a href="#orgabbad6c">1</a> where we are measuring the motion of a (supposed) solid body at 4 distinct points in x-y-z.
</p> </p>
<p> <p>
@ -368,7 +118,7 @@ The goal here is to link these \(4 \times 3 = 12\) measurements to the 6 DOFs of
</p> </p>
<div id="org79eabe9" class="figure"> <div id="orgabbad6c" class="figure">
<p><img src="figs/local_to_global_coordinates.png" alt="local_to_global_coordinates.png" /> <p><img src="figs/local_to_global_coordinates.png" alt="local_to_global_coordinates.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Schematic of the measured motions of a solid body</p> <p><span class="figure-number">Figure 1: </span>Schematic of the measured motions of a solid body</p>
@ -379,7 +129,7 @@ We consider the motion of the rigid body defined by its displacement \(\delta p\
</p> </p>
<p> <p>
From the figure <a href="#org79eabe9">1</a>, we can write: From the figure <a href="#orgabbad6c">1</a>, we can write:
</p> </p>
\begin{align*} \begin{align*}
\delta p_1 &= \delta p + \delta\Omega p_1\\ \delta p_1 &= \delta p + \delta\Omega p_1\\
@ -438,7 +188,7 @@ and then we obtain the velocity and rotation of the solid in the wanted frame \(
\end{bmatrix} \label{eq:determine_global_disp} \end{bmatrix} \label{eq:determine_global_disp}
\end{equation} \end{equation}
<div class="important"> <div class="important" id="orgf0f0c51">
<p> <p>
Using equation \eqref{eq:determine_global_disp}, we can determine the motion of the solid body expressed in a chosen frame \(\{O\}\) using the accelerometers attached to it. Using equation \eqref{eq:determine_global_disp}, we can determine the motion of the solid body expressed in a chosen frame \(\{O\}\) using the accelerometers attached to it.
The inversion is equivalent to resolving a mean square problem. The inversion is equivalent to resolving a mean square problem.
@ -448,8 +198,8 @@ The inversion is equivalent to resolving a mean square problem.
</div> </div>
</div> </div>
<div id="outline-container-org542a5f3" class="outline-2"> <div id="outline-container-org681033c" class="outline-2">
<h2 id="org542a5f3"><span class="section-number-2">3</span> What reference frame to choose?</h2> <h2 id="org681033c"><span class="section-number-2">3</span> What reference frame to choose?</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
The question we wish here to answer is how to choose the reference frame \(\{O\}\) in which the DOFs of the solid bodies are defined. The question we wish here to answer is how to choose the reference frame \(\{O\}\) in which the DOFs of the solid bodies are defined.
@ -464,7 +214,7 @@ The possibles choices are:
<li><b>Base located at the joint position</b>: this is where we want to see the motion and estimate stiffness</li> <li><b>Base located at the joint position</b>: this is where we want to see the motion and estimate stiffness</li>
</ul> </ul>
<table id="orgc4f6c97" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org1b39281" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Advantages and disadvantages for the choice of reference frame</caption> <caption class="t-above"><span class="table-number">Table 1:</span> Advantages and disadvantages for the choice of reference frame</caption>
<colgroup> <colgroup>
@ -517,12 +267,12 @@ In the next sections, we will express the FRF matrix in the different frames.
</div> </div>
</div> </div>
<div id="outline-container-org8595ef7" class="outline-2"> <div id="outline-container-org964462f" class="outline-2">
<h2 id="org8595ef7"><span class="section-number-2">4</span> FRF expressed in a common frame</h2> <h2 id="org964462f"><span class="section-number-2">4</span> FRF expressed in a common frame</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
</div> </div>
<div id="outline-container-org23c660e" class="outline-3"> <div id="outline-container-orga50f5f9" class="outline-3">
<h3 id="org23c660e"><span class="section-number-3">4.1</span> From accelerometer DOFs to solid body DOFs - Matlab Implementation</h3> <h3 id="orga50f5f9"><span class="section-number-3">4.1</span> From accelerometer DOFs to solid body DOFs - Matlab Implementation</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-4-1">
<p> <p>
First, we initialize a new FRF matrix <code>FRFs_O</code> which is an \(n \times p \times q\) with: First, we initialize a new FRF matrix <code>FRFs_O</code> which is an \(n \times p \times q\) with:
@ -533,7 +283,7 @@ First, we initialize a new FRF matrix <code>FRFs_O</code> which is an \(n \times
<li>\(q\) is the number of frequency points \(\omega_i\)</li> <li>\(q\) is the number of frequency points \(\omega_i\)</li>
</ul> </ul>
<div class="important"> <div class="important" id="org6359915">
<p> <p>
For each frequency point \(\omega_i\), the FRF matrix <code>FRFs_O</code> is a \(n\times p\) matrix: For each frequency point \(\omega_i\), the FRF matrix <code>FRFs_O</code> is a \(n\times p\) matrix:
</p> </p>
@ -561,23 +311,23 @@ Then, as we know the positions of the accelerometers on each solid body, and we
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">FRFs_O = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>solid_names<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">801</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">FRFs_O = zeros(length(solid_names)<span class="org-type">*</span>6, 3, 801);
<span class="org-keyword">for</span> <span class="org-variable-name">solid_i</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">solid_names</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span> <span class="org-keyword">for</span> <span class="org-variable-name">solid_i</span> = <span class="org-constant">1:length(solid_names)</span>
solids_i = solids.<span class="org-rainbow-delimiters-depth-1">(</span>solid_names<span class="org-rainbow-delimiters-depth-2">{</span>solid_i<span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>; solids_i = solids.(solid_names{solid_i});
A = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span>length<span class="org-rainbow-delimiters-depth-2">(</span>solids_i<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>; A = zeros(3<span class="org-type">*</span>length(solids_i), 6);
<span class="org-keyword">for</span> <span class="org-variable-name">i</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">solids_i</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span> <span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(solids_i)</span>
acc_i = solids_i<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span>; acc_i = solids_i(<span class="org-constant">i</span>);
A<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = eye<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; A(3<span class="org-type">*</span>(<span class="org-constant">i</span><span class="org-type">-</span>1)<span class="org-type">+</span>1<span class="org-type">:</span>3<span class="org-type">*</span><span class="org-constant">i</span>, 1<span class="org-type">:</span>3) = eye(3);
A<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">4</span><span class="org-type">:</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">[</span> <span class="org-highlight-numbers-number">0</span> acc_pos<span class="org-rainbow-delimiters-depth-2">(</span>acc_i, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>acc_pos<span class="org-rainbow-delimiters-depth-2">(</span>acc_i, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span> ; A(3<span class="org-type">*</span>(<span class="org-constant">i</span><span class="org-type">-</span>1)<span class="org-type">+</span>1<span class="org-type">:</span>3<span class="org-type">*</span><span class="org-constant">i</span>, 4<span class="org-type">:</span>6) = [ 0 acc_pos(acc_i, 3) <span class="org-type">-</span>acc_pos(acc_i, 2) ;
<span class="org-type">-</span>acc_pos<span class="org-rainbow-delimiters-depth-2">(</span>acc_i, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> acc_pos<span class="org-rainbow-delimiters-depth-2">(</span>acc_i, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span> ; <span class="org-type">-</span>acc_pos(acc_i, 3) 0 acc_pos(acc_i, 1) ;
acc_pos<span class="org-rainbow-delimiters-depth-2">(</span>acc_i, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>acc_pos<span class="org-rainbow-delimiters-depth-2">(</span>acc_i, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">]</span>; acc_pos(acc_i, 2) <span class="org-type">-</span>acc_pos(acc_i, 1) 0];
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
<span class="org-keyword">for</span> <span class="org-variable-name">exc_dir</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">3</span></span> <span class="org-keyword">for</span> <span class="org-variable-name">exc_dir</span> = <span class="org-constant">1:3</span>
FRFs_O<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span>solid_i<span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">6</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>solid_i<span class="org-type">*</span><span class="org-highlight-numbers-number">6</span>, exc_dir, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = A<span class="org-type">\</span>squeeze<span class="org-rainbow-delimiters-depth-1">(</span>FRFs<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">(</span>solids_i<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">3</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>solids_i<span class="org-rainbow-delimiters-depth-3">(</span>end<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">3</span>, exc_dir, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; FRFs_O((solid_i<span class="org-type">-</span>1)<span class="org-type">*</span>6<span class="org-type">+</span>1<span class="org-type">:</span>solid_i<span class="org-type">*</span>6, exc_dir, <span class="org-type">:</span>) = A<span class="org-type">\</span>squeeze(FRFs((solids_i(1)<span class="org-type">-</span>1)<span class="org-type">*</span>3<span class="org-type">+</span>1<span class="org-type">:</span>solids_i(end)<span class="org-type">*</span>3, exc_dir, <span class="org-type">:</span>));
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
</pre> </pre>
@ -585,26 +335,26 @@ Then, as we know the positions of the accelerometers on each solid body, and we
</div> </div>
</div> </div>
<div id="outline-container-orge7f0885" class="outline-3"> <div id="outline-container-org3164705" class="outline-3">
<h3 id="orge7f0885"><span class="section-number-3">4.2</span> Analysis of some FRF in the global coordinates</h3> <h3 id="org3164705"><span class="section-number-3">4.2</span> Analysis of some FRF in the global coordinates</h3>
<div class="outline-text-3" id="text-4-2"> <div class="outline-text-3" id="text-4-2">
<p> <p>
First, we can compare the motions of the 6 solid bodies in one direction (figure <a href="#org84991a7">2</a>) First, we can compare the motions of the 6 solid bodies in one direction (figure <a href="#orgcfb02aa">2</a>)
</p> </p>
<p> <p>
We can also compare all the DOFs of one solid body (figure <a href="#org2f3da04">3</a>). We can also compare all the DOFs of one solid body (figure <a href="#orga3b7df3">3</a>).
</p> </p>
<div id="org84991a7" class="figure"> <div id="orgcfb02aa" class="figure">
<p><img src="figs/frf_all_bodies_one_direction.png" alt="frf_all_bodies_one_direction.png" /> <p><img src="figs/frf_all_bodies_one_direction.png" alt="frf_all_bodies_one_direction.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>FRFs of all the 6 solid bodies in one direction</p> <p><span class="figure-number">Figure 2: </span>FRFs of all the 6 solid bodies in one direction</p>
</div> </div>
<div id="org2f3da04" class="figure"> <div id="orga3b7df3" class="figure">
<p><img src="figs/frf_one_body_all_directions.png" alt="frf_one_body_all_directions.png" /> <p><img src="figs/frf_one_body_all_directions.png" alt="frf_one_body_all_directions.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>FRFs of one solid body in all its DOFs</p> <p><span class="figure-number">Figure 3: </span>FRFs of one solid body in all its DOFs</p>
@ -612,8 +362,8 @@ We can also compare all the DOFs of one solid body (figure <a href="#org2f3da04"
</div> </div>
</div> </div>
<div id="outline-container-orgee41f84" class="outline-3"> <div id="outline-container-org2faadba" class="outline-3">
<h3 id="orgee41f84"><span class="section-number-3">4.3</span> Comparison of the relative motion of solid bodies</h3> <h3 id="org2faadba"><span class="section-number-3">4.3</span> Comparison of the relative motion of solid bodies</h3>
<div class="outline-text-3" id="text-4-3"> <div class="outline-text-3" id="text-4-3">
<p> <p>
Now that the motion of all the solid bodies are expressed in the same frame, we should be able to <b>compare them</b>. Now that the motion of all the solid bodies are expressed in the same frame, we should be able to <b>compare them</b>.
@ -622,7 +372,7 @@ This could help reduce the order of the model and simplify the extraction of the
</p> </p>
<p> <p>
We decide to plot the "normalized relative motion" between solid bodies \(i\) and \(j\): We decide to plot the &ldquo;normalized relative motion&rdquo; between solid bodies \(i\) and \(j\):
\[ 0 < \Delta_{ij, x} = \frac{\left| |D_{i,x}| - |D_{j,x}| \right|}{|D_{i,x}| + |D_{j,x}|} < 1 \] \[ 0 < \Delta_{ij, x} = \frac{\left| |D_{i,x}| - |D_{j,x}| \right|}{|D_{i,x}| + |D_{j,x}|} < 1 \]
</p> </p>
@ -631,17 +381,17 @@ Then, if \(\Delta_{ij,x} \ll 1\) in the frequency band of interest, we have that
</p> </p>
<p> <p>
This normalized relative motion is shown on figure <a href="#org0a58ea1">4</a> for all the directions and for all the adjacent pair of solid bodies. This normalized relative motion is shown on figure <a href="#org37e640c">4</a> for all the directions and for all the adjacent pair of solid bodies.
</p> </p>
<div id="org0a58ea1" class="figure"> <div id="org37e640c" class="figure">
<p><img src="figs/relative_motion_comparison.png" alt="relative_motion_comparison.png" /> <p><img src="figs/relative_motion_comparison.png" alt="relative_motion_comparison.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Relative motion between each stage</p> <p><span class="figure-number">Figure 4: </span>Relative motion between each stage</p>
</div> </div>
<div class="warning"> <div class="warning" id="org2160a28">
<p> <p>
Can we really compare the motion of two solid bodies from Frequency Response Functions that clearly depends on the excitation point and direction? Can we really compare the motion of two solid bodies from Frequency Response Functions that clearly depends on the excitation point and direction?
The relative motion of two solid bodies may be negligible when exciting the structure at on point and but at another point. The relative motion of two solid bodies may be negligible when exciting the structure at on point and but at another point.
@ -651,8 +401,8 @@ The relative motion of two solid bodies may be negligible when exciting the stru
</div> </div>
</div> </div>
<div id="outline-container-org2a5f7b7" class="outline-3"> <div id="outline-container-orgefe4113" class="outline-3">
<h3 id="org2a5f7b7"><span class="section-number-3">4.4</span> Verify that we find the original FRF from the FRF in the global coordinates</h3> <h3 id="orgefe4113"><span class="section-number-3">4.4</span> Verify that we find the original FRF from the FRF in the global coordinates</h3>
<div class="outline-text-3" id="text-4-4"> <div class="outline-text-3" id="text-4-4">
<p> <p>
We have computed the Frequency Response Functions Matrix <code>FRFs_O</code> representing the response of the 6 solid bodies in their 6 DOFs with respect to the frame \(\{O\}\). We have computed the Frequency Response Functions Matrix <code>FRFs_O</code> representing the response of the 6 solid bodies in their 6 DOFs with respect to the frame \(\{O\}\).
@ -689,22 +439,22 @@ Thus, we can obtain the FRF matrix <code>FRFs_A</code> that gives the responses
It is implemented in matlab as follow: It is implemented in matlab as follow:
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">FRFs_A = zeros<span class="org-rainbow-delimiters-depth-1">(</span>size<span class="org-rainbow-delimiters-depth-2">(</span>FRFs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">FRFs_A = zeros(size(FRFs));
<span class="org-comment">% For each excitation direction</span> <span class="org-comment">% For each excitation direction</span>
<span class="org-keyword">for</span> <span class="org-variable-name">exc_dir</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">3</span></span> <span class="org-keyword">for</span> <span class="org-variable-name">exc_dir</span> = <span class="org-constant">1:3</span>
<span class="org-comment">% For each solid</span> <span class="org-comment">% For each solid</span>
<span class="org-keyword">for</span> <span class="org-variable-name">solid_i</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">solid_names</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span> <span class="org-keyword">for</span> <span class="org-variable-name">solid_i</span> = <span class="org-constant">1:length(solid_names)</span>
v0 = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>FRFs_O<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">(</span>solid_i<span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">6</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">(</span>solid_i<span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">6</span><span class="org-type">+</span><span class="org-highlight-numbers-number">3</span>, exc_dir, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; v0 = squeeze(FRFs_O((solid_i<span class="org-type">-</span>1)<span class="org-type">*</span>6<span class="org-type">+</span>1<span class="org-type">:</span>(solid_i<span class="org-type">-</span>1)<span class="org-type">*</span>6<span class="org-type">+</span>3, exc_dir, <span class="org-type">:</span>));
W0 = squeeze<span class="org-rainbow-delimiters-depth-1">(</span>FRFs_O<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">(</span>solid_i<span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">6</span><span class="org-type">+</span><span class="org-highlight-numbers-number">4</span><span class="org-type">:</span><span class="org-rainbow-delimiters-depth-3">(</span>solid_i<span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">6</span><span class="org-type">+</span><span class="org-highlight-numbers-number">6</span>, exc_dir, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; W0 = squeeze(FRFs_O((solid_i<span class="org-type">-</span>1)<span class="org-type">*</span>6<span class="org-type">+</span>4<span class="org-type">:</span>(solid_i<span class="org-type">-</span>1)<span class="org-type">*</span>6<span class="org-type">+</span>6, exc_dir, <span class="org-type">:</span>));
<span class="org-comment">% For each accelerometer attached to the current solid</span> <span class="org-comment">% For each accelerometer attached to the current solid</span>
<span class="org-keyword">for</span> <span class="org-variable-name">acc_i</span> = <span class="org-constant">solids.</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">solid_names</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-2">{</span></span><span class="org-constant">solid_i</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-2">}</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span> <span class="org-keyword">for</span> <span class="org-variable-name">acc_i</span> = <span class="org-constant">solids.(solid_names{solid_i})</span>
<span class="org-comment">% We get the position of the accelerometer expressed in frame O</span> <span class="org-comment">% We get the position of the accelerometer expressed in frame O</span>
pos = acc_pos<span class="org-rainbow-delimiters-depth-1">(</span>acc_i, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span>'; pos = acc_pos(acc_i, <span class="org-type">:</span>)<span class="org-type">.'</span>;
posX = <span class="org-rainbow-delimiters-depth-1">[</span><span class="org-highlight-numbers-number">0</span> pos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>pos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>; <span class="org-type">-</span>pos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> pos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span> ; pos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>pos<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">]</span>; posX = [0 pos(3) <span class="org-type">-</span>pos(2); <span class="org-type">-</span>pos(3) 0 pos(1) ; pos(2) <span class="org-type">-</span>pos(1) 0];
FRFs_A<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>acc_i<span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>acc_i<span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">+</span><span class="org-highlight-numbers-number">3</span>, exc_dir, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = v0 <span class="org-type">+</span> posX<span class="org-type">*</span>W0; FRFs_A(3<span class="org-type">*</span>(acc_i<span class="org-type">-</span>1)<span class="org-type">+</span>1<span class="org-type">:</span>3<span class="org-type">*</span>(acc_i<span class="org-type">-</span>1)<span class="org-type">+</span>3, exc_dir, <span class="org-type">:</span>) = v0 <span class="org-type">+</span> posX<span class="org-type">*</span>W0;
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
@ -712,35 +462,35 @@ It is implemented in matlab as follow:
</div> </div>
<p> <p>
We then compare the original FRF measured for each accelerometer <code>FRFs</code> with the "recovered" FRF <code>FRFs_A</code> from the global FRF matrix in the common frame. We then compare the original FRF measured for each accelerometer <code>FRFs</code> with the &ldquo;recovered&rdquo; FRF <code>FRFs_A</code> from the global FRF matrix in the common frame.
</p> </p>
<p> <p>
The FRF for the 4 accelerometers on the Hexapod are compared on figure <a href="#org899c01d">5</a>. The FRF for the 4 accelerometers on the Hexapod are compared on figure <a href="#orgbfa953f">5</a>.
All the FRF are matching very well in all the frequency range displayed. All the FRF are matching very well in all the frequency range displayed.
</p> </p>
<p> <p>
The FRF for accelerometers located on the translation stage are compared on figure <a href="#org0b7d156">6</a>. The FRF for accelerometers located on the translation stage are compared on figure <a href="#orgeae40b9">6</a>.
The FRF are matching well until 100Hz. The FRF are matching well until 100Hz.
</p> </p>
<div id="org899c01d" class="figure"> <div id="orgbfa953f" class="figure">
<p><img src="figs/recovered_frf_comparison_hexa.png" alt="recovered_frf_comparison_hexa.png" /> <p><img src="figs/recovered_frf_comparison_hexa.png" alt="recovered_frf_comparison_hexa.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Comparison of the original FRF with the recovered ones - Hexapod</p> <p><span class="figure-number">Figure 5: </span>Comparison of the original FRF with the recovered ones - Hexapod</p>
</div> </div>
<div id="org0b7d156" class="figure"> <div id="orgeae40b9" class="figure">
<p><img src="figs/recovered_frf_comparison_ty.png" alt="recovered_frf_comparison_ty.png" /> <p><img src="figs/recovered_frf_comparison_ty.png" alt="recovered_frf_comparison_ty.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Comparison of the original FRF with the recovered ones - Ty</p> <p><span class="figure-number">Figure 6: </span>Comparison of the original FRF with the recovered ones - Ty</p>
</div> </div>
<div class="important"> <div class="important" id="org8db91c3">
<p> <p>
The reduction of the number of degrees of freedom from 69 (23 accelerometers with each 3DOF) to 36 (6 solid bodies with 6 DOF) seems to work well. The reduction of the number of degrees of freedom from 69 (23 accelerometers with each 3DOF) to 36 (6 solid bodies with 6 DOF) seems to work well.
</p> </p>
@ -754,23 +504,23 @@ This valid the fact that a multi-body model can be used to represent the dynamic
</div> </div>
</div> </div>
<div id="outline-container-org9323f41" class="outline-3"> <div id="outline-container-orgc0f4ff6" class="outline-3">
<h3 id="org9323f41"><span class="section-number-3">4.5</span> Saving of the FRF expressed in the global coordinates</h3> <h3 id="orgc0f4ff6"><span class="section-number-3">4.5</span> Saving of the FRF expressed in the global coordinates</h3>
<div class="outline-text-3" id="text-4-5"> <div class="outline-text-3" id="text-4-5">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/frf_o.mat', 'FRFs_O'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">save(<span class="org-string">'mat/frf_o.mat'</span>, <span class="org-string">'FRFs_O'</span>);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org9a552f4" class="outline-2"> <div id="outline-container-org6014915" class="outline-2">
<h2 id="org9a552f4"><span class="section-number-2">5</span> FRF expressed in a frame centered at the CoM of each solid body</h2> <h2 id="org6014915"><span class="section-number-2">5</span> FRF expressed in a frame centered at the CoM of each solid body</h2>
<div class="outline-text-2" id="text-5"> <div class="outline-text-2" id="text-5">
</div> </div>
<div id="outline-container-org5580afc" class="outline-3"> <div id="outline-container-orgc5b91ab" class="outline-3">
<h3 id="org5580afc"><span class="section-number-3">5.1</span> Center of Mass of each solid body</h3> <h3 id="orgc5b91ab"><span class="section-number-3">5.1</span> Center of Mass of each solid body</h3>
<div class="outline-text-3" id="text-5-1"> <div class="outline-text-3" id="text-5-1">
<p> <p>
From solidworks, we can export the position of the center of mass of each solid body considered. From solidworks, we can export the position of the center of mass of each solid body considered.
@ -782,12 +532,12 @@ We then process the exported file.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-bash">sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/1_granite_bot.txt | sed <span class="org-highlight-numbers-number">3q</span> | sed <span class="org-string">'s/^\s*\t*[XYZ] = \([-0-9.]*\)\r/\1/'</span> &gt; mat/model_solidworks_com.txt <pre class="src src-bash">sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/1_granite_bot.txt | sed 3q | sed <span class="org-string">'s/^\s*\t*[XYZ] = \([-0-9.]*\)\r/\1/'</span> &gt; mat/model_solidworks_com.txt
sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/2_granite_top.txt | sed <span class="org-highlight-numbers-number">3q</span> | sed <span class="org-string">'s/^\s*\t*[XYZ] = \([-0-9.]*\)\r/\1/'</span> &gt;&gt; mat/model_solidworks_com.txt sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/2_granite_top.txt | sed 3q | sed <span class="org-string">'s/^\s*\t*[XYZ] = \([-0-9.]*\)\r/\1/'</span> &gt;&gt; mat/model_solidworks_com.txt
sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/3_ty.txt | sed <span class="org-highlight-numbers-number">3q</span> | sed <span class="org-string">'s/^\s*\t*[XYZ] = \([-0-9.]*\)\r/\1/'</span> &gt;&gt; mat/model_solidworks_com.txt sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/3_ty.txt | sed 3q | sed <span class="org-string">'s/^\s*\t*[XYZ] = \([-0-9.]*\)\r/\1/'</span> &gt;&gt; mat/model_solidworks_com.txt
sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/4_ry.txt | sed <span class="org-highlight-numbers-number">3q</span> | sed <span class="org-string">'s/^\s*\t*[XYZ] = \([-0-9.]*\)\r/\1/'</span> &gt;&gt; mat/model_solidworks_com.txt sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/4_ry.txt | sed 3q | sed <span class="org-string">'s/^\s*\t*[XYZ] = \([-0-9.]*\)\r/\1/'</span> &gt;&gt; mat/model_solidworks_com.txt
sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/5_rz.txt | sed <span class="org-highlight-numbers-number">3q</span> | sed <span class="org-string">'s/^\s*\t*[XYZ] = \([-0-9.]*\)\r/\1/'</span> &gt;&gt; mat/model_solidworks_com.txt sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/5_rz.txt | sed 3q | sed <span class="org-string">'s/^\s*\t*[XYZ] = \([-0-9.]*\)\r/\1/'</span> &gt;&gt; mat/model_solidworks_com.txt
sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/6_hexa.txt | sed <span class="org-highlight-numbers-number">3q</span> | sed <span class="org-string">'s/^\s*\t*[XYZ] = \([-0-9.]*\)\r/\1/'</span> &gt;&gt; mat/model_solidworks_com.txt sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/6_hexa.txt | sed 3q | sed <span class="org-string">'s/^\s*\t*[XYZ] = \([-0-9.]*\)\r/\1/'</span> &gt;&gt; mat/model_solidworks_com.txt
</pre> </pre>
</div> </div>
@ -795,12 +545,12 @@ sed -e <span class="org-string">'1,/^Center of mass/ d'</span> mat/6_hexa.txt
And we import the Center of mass on Matlab. And we import the Center of mass on Matlab.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">model_com = table2array<span class="org-rainbow-delimiters-depth-1">(</span>readtable<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-string">'mat/model_solidworks_com.txt', 'ReadVariableNames'</span>, false<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">model_com = table2array(readtable(<span class="org-string">'mat/model_solidworks_com.txt'</span>, <span class="org-string">'ReadVariableNames'</span>, <span class="org-constant">false</span>));
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">model_com = reshape<span class="org-rainbow-delimiters-depth-1">(</span>model_com , <span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">model_com = reshape(model_com , [3, 6]);
</pre> </pre>
</div> </div>
@ -868,8 +618,8 @@ And we import the Center of mass on Matlab.
</div> </div>
</div> </div>
<div id="outline-container-org1128440" class="outline-3"> <div id="outline-container-org9ea4330" class="outline-3">
<h3 id="org1128440"><span class="section-number-3">5.2</span> From accelerometer DOFs to solid body DOFs - Expressed at the CoM</h3> <h3 id="org9ea4330"><span class="section-number-3">5.2</span> From accelerometer DOFs to solid body DOFs - Expressed at the CoM</h3>
<div class="outline-text-3" id="text-5-2"> <div class="outline-text-3" id="text-5-2">
<p> <p>
First, we initialize a new FRF matrix <code>FRFs_CoM</code> which is an \(n \times p \times q\) with: First, we initialize a new FRF matrix <code>FRFs_CoM</code> which is an \(n \times p \times q\) with:
@ -880,7 +630,7 @@ First, we initialize a new FRF matrix <code>FRFs_CoM</code> which is an \(n \tim
<li>\(q\) is the number of frequency points \(\omega_i\)</li> <li>\(q\) is the number of frequency points \(\omega_i\)</li>
</ul> </ul>
<div class="important"> <div class="important" id="org273c410">
<p> <p>
For each frequency point \(\omega_i\), the FRF matrix <code>FRFs_CoM</code> is a \(n\times p\) matrix: For each frequency point \(\omega_i\), the FRF matrix <code>FRFs_CoM</code> is a \(n\times p\) matrix:
</p> </p>
@ -904,7 +654,7 @@ where 1, 2, &#x2026;, 6 corresponds to the 6 solid bodies.
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">FRFs_CoM = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>solid_names<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">6</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">801</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">FRFs_CoM = zeros(length(solid_names)<span class="org-type">*</span>6, 3, 801);
</pre> </pre>
</div> </div>
@ -912,23 +662,23 @@ where 1, 2, &#x2026;, 6 corresponds to the 6 solid bodies.
Then, as we know the positions of the accelerometers on each solid body, and we have the response of those accelerometers, we can use the equations derived in the previous section to determine the response of each solid body expressed in the frame \(\{O\}\). Then, as we know the positions of the accelerometers on each solid body, and we have the response of those accelerometers, we can use the equations derived in the previous section to determine the response of each solid body expressed in the frame \(\{O\}\).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-keyword">for</span> <span class="org-variable-name">solid_i</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">solid_names</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span> <pre class="src src-matlab"><span class="org-keyword">for</span> <span class="org-variable-name">solid_i</span> = <span class="org-constant">1:length(solid_names)</span>
solids_i = solids.<span class="org-rainbow-delimiters-depth-1">(</span>solid_names<span class="org-rainbow-delimiters-depth-2">{</span>solid_i<span class="org-rainbow-delimiters-depth-2">}</span><span class="org-rainbow-delimiters-depth-1">)</span>; solids_i = solids.(solid_names{solid_i});
A = zeros<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span>length<span class="org-rainbow-delimiters-depth-2">(</span>solids_i<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span>; A = zeros(3<span class="org-type">*</span>length(solids_i), 6);
<span class="org-keyword">for</span> <span class="org-variable-name">i</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:length</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">solids_i</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span> <span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:length(solids_i)</span>
acc_i = solids_i<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span>; acc_i = solids_i(<span class="org-constant">i</span>);
acc_pos_com = acc_pos<span class="org-rainbow-delimiters-depth-1">(</span>acc_i, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span>' <span class="org-type">-</span> model_com<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, solid_i<span class="org-rainbow-delimiters-depth-1">)</span>; acc_pos_com = acc_pos(acc_i, <span class="org-type">:</span>)<span class="org-type">.'</span> <span class="org-type">-</span> model_com(<span class="org-type">:</span>, solid_i);
A<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> = eye<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; A(3<span class="org-type">*</span>(<span class="org-constant">i</span><span class="org-type">-</span>1)<span class="org-type">+</span>1<span class="org-type">:</span>3<span class="org-type">*</span><span class="org-constant">i</span>, 1<span class="org-type">:</span>3) = eye(3);
A<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-constant">i</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span><span class="org-highlight-numbers-number">3</span><span class="org-type">*</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">4</span><span class="org-type">:</span><span class="org-highlight-numbers-number">6</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-rainbow-delimiters-depth-1">[</span> <span class="org-highlight-numbers-number">0</span> acc_pos_com<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>acc_pos_com<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span> ; A(3<span class="org-type">*</span>(<span class="org-constant">i</span><span class="org-type">-</span>1)<span class="org-type">+</span>1<span class="org-type">:</span>3<span class="org-type">*</span><span class="org-constant">i</span>, 4<span class="org-type">:</span>6) = [ 0 acc_pos_com(3) <span class="org-type">-</span>acc_pos_com(2) ;
<span class="org-type">-</span>acc_pos_com<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span> acc_pos_com<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span> ; <span class="org-type">-</span>acc_pos_com(3) 0 acc_pos_com(1) ;
acc_pos_com<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span>acc_pos_com<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-highlight-numbers-number">0</span><span class="org-rainbow-delimiters-depth-1">]</span>; acc_pos_com<span class="org-type">(2) -acc_pos_com(1) 0];</span>
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
<span class="org-keyword">for</span> <span class="org-variable-name">exc_dir</span> = <span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:</span><span class="org-constant"><span class="org-highlight-numbers-number">3</span></span> <span class="org-keyword">for</span> <span class="org-variable-name">exc_dir</span> = <span class="org-constant">1:3</span>
FRFs_CoM<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span>solid_i<span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">6</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>solid_i<span class="org-type">*</span><span class="org-highlight-numbers-number">6</span>, exc_dir, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-1">)</span> = A<span class="org-type">\</span>squeeze<span class="org-rainbow-delimiters-depth-1">(</span>FRFs<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">(</span>solids_i<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">3</span><span class="org-type">+</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>solids_i<span class="org-rainbow-delimiters-depth-3">(</span>end<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span><span class="org-highlight-numbers-number">3</span>, exc_dir, <span class="org-type">:</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; FRFs_CoM((solid_i<span class="org-type">-</span>1)<span class="org-type">*</span>6<span class="org-type">+</span>1<span class="org-type">:</span>solid_i<span class="org-type">*</span>6, exc_dir, <span class="org-type">:</span>) = A<span class="org-type">\</span>squeeze(FRFs((solids_i(1)<span class="org-type">-</span>1)<span class="org-type">*</span>3<span class="org-type">+</span>1<span class="org-type">:</span>solids_i(end)<span class="org-type">*</span>3, exc_dir, <span class="org-type">:</span>));
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
</pre> </pre>
@ -936,18 +686,18 @@ Then, as we know the positions of the accelerometers on each solid body, and we
</div> </div>
</div> </div>
<div id="outline-container-org0efe1de" class="outline-3"> <div id="outline-container-orga333d35" class="outline-3">
<h3 id="org0efe1de"><span class="section-number-3">5.3</span> Analysis of some FRF</h3> <h3 id="orga333d35"><span class="section-number-3">5.3</span> Analysis of some FRF</h3>
<div class="outline-text-3" id="text-5-3"> <div class="outline-text-3" id="text-5-3">
<div id="org5d7089d" class="figure"> <div id="org5b77e73" class="figure">
<p><img src="figs/frf_com_all_bodies_one_direction.png" alt="frf_com_all_bodies_one_direction.png" /> <p><img src="figs/frf_com_all_bodies_one_direction.png" alt="frf_com_all_bodies_one_direction.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>FRFs of all the 6 solid bodies in one direction</p> <p><span class="figure-number">Figure 7: </span>FRFs of all the 6 solid bodies in one direction</p>
</div> </div>
<div id="orgb9eb188" class="figure"> <div id="org9db1fa9" class="figure">
<p><img src="figs/frf_com_one_body_all_directions.png" alt="frf_com_one_body_all_directions.png" /> <p><img src="figs/frf_com_one_body_all_directions.png" alt="frf_com_one_body_all_directions.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>FRFs of one solid body in all its DOFs (expressed with a frame centered with its center of mass)</p> <p><span class="figure-number">Figure 8: </span>FRFs of one solid body in all its DOFs (expressed with a frame centered with its center of mass)</p>
@ -955,21 +705,24 @@ Then, as we know the positions of the accelerometers on each solid body, and we
</div> </div>
</div> </div>
<div id="outline-container-org1c6f529" class="outline-3"> <div id="outline-container-org52ce77b" class="outline-3">
<h3 id="org1c6f529"><span class="section-number-3">5.4</span> Save the FRF</h3> <h3 id="org52ce77b"><span class="section-number-3">5.4</span> Save the FRF</h3>
<div class="outline-text-3" id="text-5-4"> <div class="outline-text-3" id="text-5-4">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/frf_com.mat', 'FRFs_CoM'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">save(<span class="org-string">'mat/frf_com.mat'</span>, <span class="org-string">'FRFs_CoM'</span>);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
</div> </div>
<p>
<a href="ref.bib">ref.bib</a>
</p>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-07-10 mer. 15:36</p> <p class="date">Created: 2020-11-12 jeu. 10:29</p>
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<a accesskey="H" href="../index.html"> HOME </a> <a accesskey="H" href="../index.html"> HOME </a>
</div><div id="content"> </div><div id="content">
<h1 class="title">Modal Analysis of the ID31 Micro-Station</h1> <h1 class="title">Modal Analysis of the ID31 Micro-Station</h1>
<p> <p>
The goal is to experimentally extract a <b>Spatial Model</b> (mass, damping, stiffness) of the structure (shown on figure <a href="#orgb25ffa7">1</a>) in order to tune the Multi-Body model. The goal is to experimentally extract a <b>Spatial Model</b> (mass, damping, stiffness) of the structure (shown on figure <a href="#org9f88298">1</a>) in order to tune the Multi-Body model.
</p> </p>
<div id="orgb25ffa7" class="figure"> <div id="org9f88298" class="figure">
<p><img src="img/nass_picture.png" alt="nass_picture.png" width="500px" /> <p><img src="img/nass_picture.png" alt="nass_picture.png" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Picture of the ID31 Micro-Station. (1) Granite (2) Translation Stage (3) Tilt Stage (4) Hexapod (5) Dummy Mass</p> <p><span class="figure-number">Figure 1: </span>Picture of the ID31 Micro-Station. (1) Granite (2) Translation Stage (3) Tilt Stage (4) Hexapod (5) Dummy Mass</p>
</div> </div>
<p> <p>
The procedure is represented on figure <a href="#orgabc49bf">2</a> where we go from left to right. The procedure is represented on figure <a href="#org9011d1b">2</a> where we go from left to right.
</p> </p>
<div id="orgabc49bf" class="figure"> <div id="org9011d1b" class="figure">
<p><img src="img/vibration_analysis_procedure.png" alt="vibration_analysis_procedure.png" width="400px" /> <p><img src="img/vibration_analysis_procedure.png" alt="vibration_analysis_procedure.png" width="400px" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Vibration Analysis Procedure</p> <p><span class="figure-number">Figure 2: </span>Vibration Analysis Procedure</p>
@ -316,7 +65,7 @@ Theses matrices will be used to tune the Simscape (multi-body) model.
The modes we want to identify are those in the frequency range between 0Hz and 150Hz. The modes we want to identify are those in the frequency range between 0Hz and 150Hz.
</p> </p>
<table id="org41b882b" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org4211aff" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Terminology for further analysis</caption> <caption class="t-above"><span class="table-number">Table 1:</span> Terminology for further analysis</caption>
<colgroup> <colgroup>
@ -366,7 +115,7 @@ The modes we want to identify are those in the frequency range between 0Hz and 1
</tbody> </tbody>
</table> </table>
<table id="org4089d51" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="orgc9968b6" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Terminology for further analysis</caption> <caption class="t-above"><span class="table-number">Table 2:</span> Terminology for further analysis</caption>
<colgroup> <colgroup>
@ -413,7 +162,7 @@ The modes we want to identify are those in the frequency range between 0Hz and 1
<tr> <tr>
<td class="org-center">\(a_r\)</td> <td class="org-center">\(a_r\)</td>
<td class="org-left">"Modal A" for mode \(r\)</td> <td class="org-left">&ldquo;Modal A&rdquo; for mode \(r\)</td>
</tr> </tr>
</tbody> </tbody>
</table> </table>
@ -429,7 +178,7 @@ The modal analysis of the ID31 Micro-station thus consists of several parts:
</ul> </ul>
<div id="org532fb43" class="figure"> <div id="org3b7e193" class="figure">
<p><img src="figs/modal_test_procedure_vertical.png" alt="modal_test_procedure_vertical.png" width="600px" /> <p><img src="figs/modal_test_procedure_vertical.png" alt="modal_test_procedure_vertical.png" width="600px" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Modal Anslysis Procedure</p> <p><span class="figure-number">Figure 3: </span>Modal Anslysis Procedure</p>
@ -437,8 +186,7 @@ The modal analysis of the ID31 Micro-station thus consists of several parts:
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-07-19 ven. 09:33</p> <p class="date">Created: 2020-11-12 jeu. 10:29</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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9
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<a accesskey="h" href="./index.html"> UP </a> <a accesskey="h" href="../index.html"> UP </a>
| |
<a accesskey="H" href="../index.html"> HOME </a> <a accesskey="H" href="../index.html"> HOME </a>
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@ -280,20 +30,20 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org93dde66">1. Type of Model</a></li> <li><a href="#org2a87d8f">1. Type of Model</a></li>
<li><a href="#orgfd7d140">2. <span class="todo TODO">TODO</span> Extract Physical Matrices</a></li> <li><a href="#orgdb0ed87">2. Extract Physical Matrices</a></li>
<li><a href="#orgdaaea25">3. Some notes about constraining the number of degrees of freedom</a></li> <li><a href="#orgcc897f4">3. Some notes about constraining the number of degrees of freedom</a></li>
</ul> </ul>
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<div id="outline-container-org93dde66" class="outline-2"> <div id="outline-container-org2a87d8f" class="outline-2">
<h2 id="org93dde66"><span class="section-number-2">1</span> Type of Model</h2> <h2 id="org2a87d8f"><span class="section-number-2">1</span> Type of Model</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
The model that we want to obtain is a <b>multi-body model</b>. The model that we want to obtain is a <b>multi-body model</b>.
It is composed of several <b>solid bodies connected with springs and dampers</b>. It is composed of several <b>solid bodies connected with springs and dampers</b>.
The solid bodies are represented with different colors on figure <a href="#org4703119">1</a>. The solid bodies are represented with different colors on figure <a href="#orga016307">1</a>.
</p> </p>
<p> <p>
@ -308,7 +58,7 @@ In the simscape model, the solid bodies are:
</ul> </ul>
<div id="org4703119" class="figure"> <div id="orga016307" class="figure">
<p><img src="img/nass_solidworks.png" alt="nass_solidworks.png" width="800px" /> <p><img src="img/nass_solidworks.png" alt="nass_solidworks.png" width="800px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>CAD view of the ID31 Micro-Station</p> <p><span class="figure-number">Figure 1: </span>CAD view of the ID31 Micro-Station</p>
@ -325,15 +75,15 @@ The modal identification done here will thus permit us to determine <b>which DOF
</div> </div>
</div> </div>
<div id="outline-container-orgfd7d140" class="outline-2"> <div id="outline-container-orgdb0ed87" class="outline-2">
<h2 id="orgfd7d140"><span class="section-number-2">2</span> <span class="todo TODO">TODO</span> Extract Physical Matrices</h2> <h2 id="orgdb0ed87"><span class="section-number-2">2</span> Extract Physical Matrices</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a class='org-ref-reference' href="#wang11_extrac_real_modes_physic_matric">wang11_extrac_real_modes_physic_matric</a> (<a href="#citeproc_bib_item_2">Wang, Zhang, and Tee 2011</a>)
</p> </p>
<p> <p>
Let's recall that: Let&rsquo;s recall that:
\[ \Lambda = \begin{bmatrix} \[ \Lambda = \begin{bmatrix}
s_1 & & 0 \\ s_1 & & 0 \\
& \ddots & \\ & \ddots & \\
@ -361,14 +111,14 @@ Let's recall that:
a = modal_a_M; a = modal_a_M;
lambda = eigen_val_M; lambda = eigen_val_M;
M = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-1">(</span>real<span class="org-rainbow-delimiters-depth-2">(</span>psi<span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-3">(</span>a<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span>lambda<span class="org-type">*</span>psi'<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; M = 0.5<span class="org-type">*</span>inv(real(psi<span class="org-type">*</span>inv(a)<span class="org-type">*</span>lambda<span class="org-type">*</span>psi<span class="org-type">'</span>));
C = <span class="org-type">-</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>M<span class="org-type">*</span>real<span class="org-rainbow-delimiters-depth-1">(</span>psi<span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>a<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span>lambda<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-2">(</span>a<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">*</span>psi'<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">*</span>M; C = <span class="org-type">-</span>2<span class="org-type">*</span>M<span class="org-type">*</span>real(psi<span class="org-type">*</span>inv(a)<span class="org-type">*</span>lambda<span class="org-type">^</span>2<span class="org-type">*</span>inv(a)<span class="org-type">*</span>psi<span class="org-type">'</span>)<span class="org-type">*</span>M;
K = <span class="org-type">-</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">5</span><span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-1">(</span>real<span class="org-rainbow-delimiters-depth-2">(</span>psi<span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-3">(</span>lambda<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span>inv<span class="org-rainbow-delimiters-depth-3">(</span>a<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">*</span>psi'<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; K = <span class="org-type">-</span>0.5<span class="org-type">*</span>inv(real(psi<span class="org-type">*</span>inv(lambda)<span class="org-type">*</span>inv(a)<span class="org-type">*</span>psi<span class="org-type">'</span>));
</pre> </pre>
</div> </div>
<p> <p>
From <a class='org-ref-reference' href="#ewins00_modal">ewins00_modal</a> From (<a href="#citeproc_bib_item_1">Ewins 2000</a>)
</p> </p>
\begin{align} \begin{align}
@ -378,8 +128,8 @@ From <a class='org-ref-reference' href="#ewins00_modal">ewins00_modal</a>
</div> </div>
</div> </div>
<div id="outline-container-orgdaaea25" class="outline-2"> <div id="outline-container-orgcc897f4" class="outline-2">
<h2 id="orgdaaea25"><span class="section-number-2">3</span> Some notes about constraining the number of degrees of freedom</h2> <h2 id="orgcc897f4"><span class="section-number-2">3</span> Some notes about constraining the number of degrees of freedom</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
We want to have the two eigen matrices. We want to have the two eigen matrices.
@ -492,16 +242,17 @@ Is it meaningful to compare mode shapes as they give no information about the am
</div> </div>
<p> <p>
<h1 class='org-ref-bib-h1'>Bibliography</h1>
<ul class='org-ref-bib'><li><a id="wang11_extrac_real_modes_physic_matric">[wang11_extrac_real_modes_physic_matric]</a> <a name="wang11_extrac_real_modes_physic_matric"></a>Tong Wang, Lingmi Zhang & Kong Fah Tee, Extraction of Real Modes and Physical Matrices From Modal Testing, <i>Earthquake Engineering and Engineering Vibration</i>, <b>10(2)</b>, 219-227 (2011). <a href="https://doi.org/10.1007/s11803-011-0060-6">link</a>. <a href="http://dx.doi.org/10.1007/s11803-011-0060-6">doi</a>.</li>
<li><a id="ewins00_modal">[ewins00_modal]</a> <a name="ewins00_modal"></a>Ewins, Modal testing: theory, practice and application, Wiley-Blackwell (2000).</li>
</ul>
</p> </p>
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><h2 class='citeproc-org-bib-h2'>Bibliography</h2>
<div class="csl-bib-body">
<div class="csl-entry"><a name="citeproc_bib_item_1"></a>Ewins, DJ. 2000. <i>Modal Testing: Theory, Practice and Application</i>. <i>Research Studies Pre, 2nd Ed., ISBN-13</i>. Baldock, Hertfordshire, England Philadelphia, PA: Wiley-Blackwell.</div>
<div class="csl-entry"><a name="citeproc_bib_item_2"></a>Wang, Tong, Lingmi Zhang, and Kong Fah Tee. 2011. “Extraction of Real Modes and Physical Matrices from Modal Testing.” <i>Earthquake Engineering and Engineering Vibration</i> 10 (2):219–27. <a href="https://doi.org/10.1007/s11803-011-0060-6">https://doi.org/10.1007/s11803-011-0060-6</a>.</div>
</div>
</div> </div>
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<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-10-08 mar. 10:48</p> <p class="date">Created: 2020-11-12 jeu. 10:29</p>
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@ -280,27 +30,27 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgbdb27eb">1. Experimental Setup</a> <li><a href="#orgd82eecc">1. Experimental Setup</a>
<ul> <ul>
<li><a href="#org8dbd49b">1.1. From Marble to Ty - <code>mat/meas_010.mat</code></a></li> <li><a href="#org82ae208">1.1. From Marble to Ty - <code>mat/meas_010.mat</code></a></li>
<li><a href="#orgf538b5e">1.2. From Marble to Ry - <code>mat/meas_011.mat</code></a></li> <li><a href="#org7b369e5">1.2. From Marble to Ry - <code>mat/meas_011.mat</code></a></li>
<li><a href="#orga48e2bc">1.3. From Ty to Ry - <code>mat/meas_012.mat</code></a></li> <li><a href="#org325c5f6">1.3. From Ty to Ry - <code>mat/meas_012.mat</code></a></li>
</ul> </ul>
</li> </li>
<li><a href="#org3ea309e">2. Measurement Analysis</a> <li><a href="#orgba49cdc">2. Measurement Analysis</a>
<ul> <ul>
<li><a href="#org1638277">2.1. Load data</a></li> <li><a href="#org8d52fe2">2.1. Load data</a></li>
<li><a href="#org0d3cc48">2.2. Analysis - Time Domain</a></li> <li><a href="#org9111ac4">2.2. Analysis - Time Domain</a></li>
<li><a href="#org65a5a79">2.3. Analysis - Frequency Domain</a></li> <li><a href="#orged11956">2.3. Analysis - Frequency Domain</a></li>
<li><a href="#orgbbc525b">2.4. Conclusion</a></li> <li><a href="#org5e2da99">2.4. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orgbdb27eb" class="outline-2"> <div id="outline-container-orgd82eecc" class="outline-2">
<h2 id="orgbdb27eb"><span class="section-number-2">1</span> Experimental Setup</h2> <h2 id="orgd82eecc"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
For all the measurements in this section: For all the measurements in this section:
@ -311,11 +61,11 @@ For all the measurements in this section:
</ul> </ul>
</div> </div>
<div id="outline-container-org8dbd49b" class="outline-3"> <div id="outline-container-org82ae208" class="outline-3">
<h3 id="org8dbd49b"><span class="section-number-3">1.1</span> From Marble to Ty - <code>mat/meas_010.mat</code></h3> <h3 id="org82ae208"><span class="section-number-3">1.1</span> From Marble to Ty - <code>mat/meas_010.mat</code></h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
One geophone is on the marble, one is on the Ty stage (see figures <a href="#orgee9d1f3">1</a>, <a href="#org0acaa0d">2</a> and <a href="#orgec4ad6b">3</a>). One geophone is on the marble, one is on the Ty stage (see figures <a href="#org0874a9a">1</a>, <a href="#orgc939aca">2</a> and <a href="#orgdb6f84a">3</a>).
</p> </p>
<p> <p>
@ -354,21 +104,21 @@ The <code>data</code> array contains the following columns:
</table> </table>
<div id="orgee9d1f3" class="figure"> <div id="org0874a9a" class="figure">
<p><img src="./img/IMG_20190430_155330.jpg" alt="IMG_20190430_155330.jpg" width="500px" /> <p><img src="./img/IMG_20190430_155330.jpg" alt="IMG_20190430_155330.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Setup with one geophone on the marble and one on top of the translation stage</p> <p><span class="figure-number">Figure 1: </span>Setup with one geophone on the marble and one on top of the translation stage</p>
</div> </div>
<div id="org0acaa0d" class="figure"> <div id="orgc939aca" class="figure">
<p><img src="./img/IMG_20190430_155335.jpg" alt="IMG_20190430_155335.jpg" width="500px" /> <p><img src="./img/IMG_20190430_155335.jpg" alt="IMG_20190430_155335.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Setup with one geophone on the marble and one on top of the translation stage - Close up view</p> <p><span class="figure-number">Figure 2: </span>Setup with one geophone on the marble and one on top of the translation stage - Close up view</p>
</div> </div>
<div id="orgec4ad6b" class="figure"> <div id="orgdb6f84a" class="figure">
<p><img src="./img/IMG_20190430_155342.jpg" alt="IMG_20190430_155342.jpg" width="500px" /> <p><img src="./img/IMG_20190430_155342.jpg" alt="IMG_20190430_155342.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Setup with one geophone on the marble and one on top of the translation stage - Top view</p> <p><span class="figure-number">Figure 3: </span>Setup with one geophone on the marble and one on top of the translation stage - Top view</p>
@ -376,11 +126,11 @@ The <code>data</code> array contains the following columns:
</div> </div>
</div> </div>
<div id="outline-container-orgf538b5e" class="outline-3"> <div id="outline-container-org7b369e5" class="outline-3">
<h3 id="orgf538b5e"><span class="section-number-3">1.2</span> From Marble to Ry - <code>mat/meas_011.mat</code></h3> <h3 id="org7b369e5"><span class="section-number-3">1.2</span> From Marble to Ry - <code>mat/meas_011.mat</code></h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<p> <p>
One geophone is on the marble, one is on the Ry stage (see figure <a href="#orgd643390">4</a>) One geophone is on the marble, one is on the Ry stage (see figure <a href="#org56e9797">4</a>)
</p> </p>
<p> <p>
@ -419,7 +169,7 @@ The <code>data</code> array contains the following columns:
</table> </table>
<div id="orgd643390" class="figure"> <div id="org56e9797" class="figure">
<p><img src="./img/IMG_20190430_163919.jpg" alt="IMG_20190430_163919.jpg" width="500px" /> <p><img src="./img/IMG_20190430_163919.jpg" alt="IMG_20190430_163919.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Setup with one geophone on the marble and one on top of the Tilt Stage</p> <p><span class="figure-number">Figure 4: </span>Setup with one geophone on the marble and one on top of the Tilt Stage</p>
@ -427,11 +177,11 @@ The <code>data</code> array contains the following columns:
</div> </div>
</div> </div>
<div id="outline-container-orga48e2bc" class="outline-3"> <div id="outline-container-org325c5f6" class="outline-3">
<h3 id="orga48e2bc"><span class="section-number-3">1.3</span> From Ty to Ry - <code>mat/meas_012.mat</code></h3> <h3 id="org325c5f6"><span class="section-number-3">1.3</span> From Ty to Ry - <code>mat/meas_012.mat</code></h3>
<div class="outline-text-3" id="text-1-3"> <div class="outline-text-3" id="text-1-3">
<p> <p>
One geophone is on the Ty stage, one is on the Ry stage (see figures <a href="#org4038125">5</a>, <a href="#orge841934">6</a> and <a href="#org7715257">7</a>) One geophone is on the Ty stage, one is on the Ry stage (see figures <a href="#org2645aca">5</a>, <a href="#org9559008">6</a> and <a href="#org697a065">7</a>)
One geophone on the Ty stage, one geophone on the Ry stage. One geophone on the Ty stage, one geophone on the Ry stage.
</p> </p>
@ -471,21 +221,21 @@ The <code>data</code> array contains the following columns:
</table> </table>
<div id="org4038125" class="figure"> <div id="org2645aca" class="figure">
<p><img src="./img/IMG_20190430_170405.jpg" alt="IMG_20190430_170405.jpg" width="500px" /> <p><img src="./img/IMG_20190430_170405.jpg" alt="IMG_20190430_170405.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage</p> <p><span class="figure-number">Figure 5: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage</p>
</div> </div>
<div id="orge841934" class="figure"> <div id="org9559008" class="figure">
<p><img src="./img/IMG_20190430_170418.jpg" alt="IMG_20190430_170418.jpg" width="500px" /> <p><img src="./img/IMG_20190430_170418.jpg" alt="IMG_20190430_170418.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Top view</p> <p><span class="figure-number">Figure 6: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Top view</p>
</div> </div>
<div id="org7715257" class="figure"> <div id="org697a065" class="figure">
<p><img src="./img/IMG_20190430_170425.jpg" alt="IMG_20190430_170425.jpg" width="500px" /> <p><img src="./img/IMG_20190430_170425.jpg" alt="IMG_20190430_170425.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Close up view</p> <p><span class="figure-number">Figure 7: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Close up view</p>
@ -494,13 +244,13 @@ The <code>data</code> array contains the following columns:
</div> </div>
</div> </div>
<div id="outline-container-org3ea309e" class="outline-2"> <div id="outline-container-orgba49cdc" class="outline-2">
<h2 id="org3ea309e"><span class="section-number-2">2</span> Measurement Analysis</h2> <h2 id="orgba49cdc"><span class="section-number-2">2</span> Measurement Analysis</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org88007a9"></a> <a id="org94fbe52"></a>
</p> </p>
<div class="note"> <div class="note" id="orgb7f13bf">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/tf_stages_geophone.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/tf_stages_geophone.zip">here</a>.
</p> </p>
@ -508,23 +258,23 @@ All the files (data and Matlab scripts) are accessible <a href="data/tf_stages_g
</div> </div>
</div> </div>
<div id="outline-container-org1638277" class="outline-3"> <div id="outline-container-org8d52fe2" class="outline-3">
<h3 id="org1638277"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="org8d52fe2"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">m_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_010.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_ty = m_ty.data; <pre class="src src-matlab">m_ty = load(<span class="org-string">'mat/data_010.mat'</span>, <span class="org-string">'data'</span>); m_ty = m_ty.data;
m_ry = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_011.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_ry = m_ry.data; m_ry = load(<span class="org-string">'mat/data_011.mat'</span>, <span class="org-string">'data'</span>); m_ry = m_ry.data;
ty_ry = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_012.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_ry = ty_ry.data; ty_ry = load(<span class="org-string">'mat/data_012.mat'</span>, <span class="org-string">'data'</span>); ty_ry = ty_ry.data;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org0d3cc48" class="outline-3"> <div id="outline-container-org9111ac4" class="outline-3">
<h3 id="org0d3cc48"><span class="section-number-3">2.2</span> Analysis - Time Domain</h3> <h3 id="org9111ac4"><span class="section-number-3">2.2</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
First, we can look at the time domain data. First, we can look at the time domain data.
@ -533,17 +283,17 @@ First, we can look at the time domain data.
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(m_ty(<span class="org-type">:</span>, 3), m_ty(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(m_ty(<span class="org-type">:</span>, 3), m_ty(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 500]);
</pre> </pre>
</div> </div>
<div id="org6d8a0eb" class="figure"> <div id="org0d4f84e" class="figure">
<p><img src="figs/time_domain_m_ty.png" alt="time_domain_m_ty.png" /> <p><img src="figs/time_domain_m_ty.png" alt="time_domain_m_ty.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Time domain - Marble and translation stage</p> <p><span class="figure-number">Figure 8: </span>Time domain - Marble and translation stage</p>
@ -553,17 +303,17 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(m_ry(<span class="org-type">:</span>, 3), m_ry(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(m_ry(<span class="org-type">:</span>, 3), m_ry(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 500]);
</pre> </pre>
</div> </div>
<div id="org8700a74" class="figure"> <div id="org98e315d" class="figure">
<p><img src="figs/time_domain_m_ry.png" alt="time_domain_m_ry.png" /> <p><img src="figs/time_domain_m_ry.png" alt="time_domain_m_ry.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Time domain - Marble and tilt stage</p> <p><span class="figure-number">Figure 9: </span>Time domain - Marble and tilt stage</p>
@ -572,17 +322,17 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_ry(<span class="org-type">:</span>, 3), ty_ry(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(ty_ry(<span class="org-type">:</span>, 3), ty_ry(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ry'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0, 500]);
</pre> </pre>
</div> </div>
<div id="orgcb2e12d" class="figure"> <div id="orgabbf859" class="figure">
<p><img src="figs/time_domain_ty_ry.png" alt="time_domain_ty_ry.png" /> <p><img src="figs/time_domain_ty_ry.png" alt="time_domain_ty_ry.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Time domain - Translation stage and tilt stage</p> <p><span class="figure-number">Figure 10: </span>Time domain - Translation stage and tilt stage</p>
@ -590,58 +340,58 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-org65a5a79" class="outline-3"> <div id="outline-container-orged11956" class="outline-3">
<h3 id="org65a5a79"><span class="section-number-3">2.3</span> Analysis - Frequency Domain</h3> <h3 id="orged11956"><span class="section-number-3">2.3</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = m_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> m_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = m_ty(2, 3) <span class="org-type">-</span> m_ty(1, 3);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; Fs = 1<span class="org-type">/</span>dt;
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(1<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
<p> <p>
First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure <a href="#orgc25589d">11</a>). We also plot their coherence (figure <a href="#org6b84c12">12</a>). First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure <a href="#orgca1b639">11</a>). We also plot their coherence (figure <a href="#org8a7c191">12</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>T_m_ty, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[T_m_ty, f] = tfestimate(m_ty(<span class="org-type">:</span>, 1), m_ty(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>T_m_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [T_m_ry, <span class="org-type">~</span>] = tfestimate(m_ry(<span class="org-type">:</span>, 1), m_ry(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>T_ty_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [T_ty_ry, <span class="org-type">~</span>] = tfestimate(ty_ry(<span class="org-type">:</span>, 1), ty_ry(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; ax1 = subplot(2, 1, 1);
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T_m_ty<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, abs(T_m_ty), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - Ty'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T_m_ry<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, abs(T_m_ry), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Marble - Ry'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T_ty_ry<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty - Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, abs(T_ty_ry), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ty - Ry'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,<span class="org-rainbow-delimiters-depth-2">[]</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XTickLabel'</span>,[]);
ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Magnitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel(<span class="org-string">'Magnitude'</span>);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northwest'</span>);
ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>; ax2 = subplot(2, 1, 2);
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T_m_ty<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, mod(180<span class="org-type">+</span>180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase(T_m_ty), 360)<span class="org-type">-</span>180);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T_m_ry<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, mod(180<span class="org-type">+</span>180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase(T_m_ry), 360)<span class="org-type">-</span>180);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T_ty_ry<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, mod(180<span class="org-type">+</span>180<span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase(T_ty_ry), 360)<span class="org-type">-</span>180);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim([<span class="org-type">-</span>180, 180]);
yticks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; yticks([<span class="org-type">-</span>180, <span class="org-type">-</span>90, 0, 90, 180]);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'Phase'</span>);
linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</span><span class="org-rainbow-delimiters-depth-1">)</span>; linkaxes([ax1,ax2],<span class="org-string">'x'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">10</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([10, 500]);
</pre> </pre>
</div> </div>
<div id="orgc25589d" class="figure"> <div id="orgca1b639" class="figure">
<p><img src="figs/compare_tf_geophones.png" alt="compare_tf_geophones.png" /> <p><img src="figs/compare_tf_geophones.png" alt="compare_tf_geophones.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Transfer function from the first geophone to the second geophone for the three experiments</p> <p><span class="figure-number">Figure 11: </span>Transfer function from the first geophone to the second geophone for the three experiments</p>
@ -649,14 +399,14 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>coh_m_ty, f<span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[coh_m_ty, f] = mscohere(m_ty(<span class="org-type">:</span>, 1), m_ty(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>coh_m_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [coh_m_ry, <span class="org-type">~</span>] = mscohere(m_ry(<span class="org-type">:</span>, 1), m_ry(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>coh_ty_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, ty_ry<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [coh_ty_ry, <span class="org-type">~</span>] = mscohere(ty_ry(<span class="org-type">:</span>, 1), ty_ry(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre> </pre>
</div> </div>
<div id="org6b84c12" class="figure"> <div id="org8a7c191" class="figure">
<p><img src="figs/coherence_two_geophones.png" alt="coherence_two_geophones.png" /> <p><img src="figs/coherence_two_geophones.png" alt="coherence_two_geophones.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Coherence between the two geophones for the three experiments</p> <p><span class="figure-number">Figure 12: </span>Coherence between the two geophones for the three experiments</p>
@ -664,10 +414,10 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-orgbbc525b" class="outline-3"> <div id="outline-container-org5e2da99" class="outline-3">
<h3 id="orgbbc525b"><span class="section-number-3">2.4</span> Conclusion</h3> <h3 id="org5e2da99"><span class="section-number-3">2.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<div class="important"> <div class="important" id="org0f3c17a">
<p> <p>
These measurements are not relevant. These measurements are not relevant.
</p> </p>
@ -679,8 +429,7 @@ These measurements are not relevant.
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-15 mer. 17:22</p> <p class="date">Created: 2020-11-12 jeu. 10:29</p>
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<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#orgc988f31">1. Effect of the rotation of the Slip-Ring - Noise</a> <li><a href="#orga0c7470">1. Effect of the rotation of the Slip-Ring - Noise</a>
<ul> <ul>
<li><a href="#org9c881d4">1.1. Measurement Description</a></li> <li><a href="#org5394d04">1.1. Measurement Description</a></li>
<li><a href="#org9671811">1.2. Load data</a></li> <li><a href="#org015bd45">1.2. Load data</a></li>
<li><a href="#orgf569f1a">1.3. Analysis</a></li> <li><a href="#org880c3cd">1.3. Analysis</a></li>
<li><a href="#orgf938632">1.4. Conclusion</a></li> <li><a href="#orgd0a405c">1.4. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org038eeb5">2. Measure of the noise induced by the Slip-Ring using voltage amplifiers - Noise</a> <li><a href="#orge484f16">2. Measure of the noise induced by the Slip-Ring using voltage amplifiers - Noise</a>
<ul> <ul>
<li><a href="#orgfecfa5c">2.1. Measurement Description</a></li> <li><a href="#orgcffd362">2.1. Measurement Description</a></li>
<li><a href="#org93676c7">2.2. Load data</a></li> <li><a href="#orgb04e3fc">2.2. Load data</a></li>
<li><a href="#org5c0f846">2.3. Time Domain</a></li> <li><a href="#orgeb6990e">2.3. Time Domain</a></li>
<li><a href="#org3cf58bf">2.4. Frequency Domain</a></li> <li><a href="#org9809223">2.4. Frequency Domain</a></li>
<li><a href="#orgfb3a7be">2.5. Conclusion</a></li> <li><a href="#org6edde18">2.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgf6e4281">3. Measure of the noise induced by the Slip-Ring rotation - LPF added</a> <li><a href="#org34a88cd">3. Measure of the noise induced by the Slip-Ring rotation - LPF added</a>
<ul> <ul>
<li><a href="#org7da9e34">3.1. Measurement description</a></li> <li><a href="#org9842ef1">3.1. Measurement description</a></li>
<li><a href="#org62f4c0b">3.2. Load data</a></li> <li><a href="#org301dd52">3.2. Load data</a></li>
<li><a href="#orgebd2a5c">3.3. Time Domain</a></li> <li><a href="#orgd6c3972">3.3. Time Domain</a></li>
<li><a href="#org3866b73">3.4. Frequency Domain - Direct Signal</a></li> <li><a href="#org6579314">3.4. Frequency Domain - Direct Signal</a></li>
<li><a href="#org9c9986f">3.5. Frequency Domain - Slip-Ring Signal</a></li> <li><a href="#orgf591b45">3.5. Frequency Domain - Slip-Ring Signal</a></li>
<li><a href="#org9d90d36">3.6. Conclusion</a></li> <li><a href="#org599231a">3.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<p> <p>
We determine if the slip-ring add some noise to the signal when it is turning: We determine if the slip-ring add some noise to the signal when it is turning:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>Section <a href="#orgb74a552">1</a>: <li>Section <a href="#org05554d3">1</a>:
<ul class="org-ul"> <ul class="org-ul">
<li>Noise is generated by the Speedgoat DAC and goes trough the slip-ring two times</li> <li>Noise is generated by the Speedgoat DAC and goes trough the slip-ring two times</li>
<li>We measure the signal when it is OFF, ON but not turning and ON and turning</li> <li>We measure the signal when it is OFF, ON but not turning and ON and turning</li>
<li>However, the measurement is limited by the ADC noise</li> <li>However, the measurement is limited by the ADC noise</li>
</ul></li> </ul></li>
<li>Section <a href="#org73e12a6">2</a>: <li>Section <a href="#org28c6f1d">2</a>:
<ul class="org-ul"> <ul class="org-ul">
<li>Voltage amplifiers are added, and the same measurements are done</li> <li>Voltage amplifiers are added, and the same measurements are done</li>
<li>However, the voltage amplifiers are saturating because of high frequency noise</li> <li>However, the voltage amplifiers are saturating because of high frequency noise</li>
</ul></li> </ul></li>
<li>Section <a href="#org6764371">3</a>: <li>Section <a href="#org6fb7c81">3</a>:
<ul class="org-ul"> <ul class="org-ul">
<li>Low pass filter are added at the input of the voltage amplifier and the same measurement is done</li> <li>Low pass filter are added at the input of the voltage amplifier and the same measurement is done</li>
</ul></li> </ul></li>
</ul> </ul>
<div id="outline-container-orgc988f31" class="outline-2"> <div id="outline-container-orga0c7470" class="outline-2">
<h2 id="orgc988f31"><span class="section-number-2">1</span> Effect of the rotation of the Slip-Ring - Noise</h2> <h2 id="orga0c7470"><span class="section-number-2">1</span> Effect of the rotation of the Slip-Ring - Noise</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<a id="orgb74a552"></a> <a id="org05554d3"></a>
</p> </p>
<div class="note"> <div class="note" id="org3e3398d">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/meas_effect_sr.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/meas_effect_sr.zip">here</a>.
</p> </p>
@ -346,8 +95,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/meas_effect
</div> </div>
</div> </div>
<div id="outline-container-org9c881d4" class="outline-3"> <div id="outline-container-org5394d04" class="outline-3">
<h3 id="org9c881d4"><span class="section-number-3">1.1</span> Measurement Description</h3> <h3 id="org5394d04"><span class="section-number-3">1.1</span> Measurement Description</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
<b>Setup</b>: <b>Setup</b>:
@ -436,83 +185,83 @@ For each measurement, the measured signals are:
</div> </div>
</div> </div>
<div id="outline-container-org9671811" class="outline-3"> <div id="outline-container-org015bd45" class="outline-3">
<h3 id="org9671811"><span class="section-number-3">1.2</span> Load data</h3> <h3 id="org015bd45"><span class="section-number-3">1.2</span> Load data</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">sr_off = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">sr_off = load(<span class="org-string">'mat/data_001.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x1'</span>, <span class="org-string">'x2'</span>);
sr_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_002.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_on = load(<span class="org-string">'mat/data_002.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'x1'</span>, <span class="org-string">'x2'</span>);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgf569f1a" class="outline-3"> <div id="outline-container-org880c3cd" class="outline-3">
<h3 id="orgf569f1a"><span class="section-number-3">1.3</span> Analysis</h3> <h3 id="org880c3cd"><span class="section-number-3">1.3</span> Analysis</h3>
<div class="outline-text-3" id="text-1-3"> <div class="outline-text-3" id="text-1-3">
<p> <p>
Let's first look at the signal produced by the DAC (figure <a href="#org9d6d3d5">1</a>). Let&rsquo;s first look at the signal produced by the DAC (figure <a href="#orgc840333">1</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr_on.t, sr_on.x1<span class="org-rainbow-delimiters-depth-1">)</span>; plot(sr_on.t, sr_on.x1);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0 10]);
</pre> </pre>
</div> </div>
<div id="org9d6d3d5" class="figure"> <div id="orgc840333" class="figure">
<p><img src="figs/random_signal.png" alt="random_signal.png" /> <p><img src="figs/random_signal.png" alt="random_signal.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Random signal produced by the DAC</p> <p><span class="figure-number">Figure 1: </span>Random signal produced by the DAC</p>
</div> </div>
<p> <p>
We now look at the difference between the signal directly measured by the ADC and the signal that goes through the slip-ring (figure <a href="#orgfb12ded">2</a>). We now look at the difference between the signal directly measured by the ADC and the signal that goes through the slip-ring (figure <a href="#org600f7bf">2</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr_on.t, sr_on.x1 <span class="org-type">-</span> sr_on.x2, <span class="org-string">'DisplayName', '</span>Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> $<span class="org-type">\</span>omega = <span class="org-highlight-numbers-number">1rpm$</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(sr_on.t, sr_on.x1 <span class="org-type">-</span> sr_on.x2, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - $\omega = 1rpm$'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr_off.t, sr_off.x1 <span class="org-type">-</span> sr_off.x2,<span class="org-string">'DisplayName', 'Slip-Ring off'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(sr_off.t, sr_off.x1 <span class="org-type">-</span> sr_off.x2,<span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring off'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Voltage [V]'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span> <span class="org-highlight-numbers-number">10</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0 10]);
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
</pre> </pre>
</div> </div>
<div id="orgfb12ded" class="figure"> <div id="org600f7bf" class="figure">
<p><img src="figs/slipring_comp_signals.png" alt="slipring_comp_signals.png" /> <p><img src="figs/slipring_comp_signals.png" alt="slipring_comp_signals.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Alteration of the signal when the slip-ring is turning</p> <p><span class="figure-number">Figure 2: </span>Alteration of the signal when the slip-ring is turning</p>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = sr_on.t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> sr_on.t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = sr_on.t(2) <span class="org-type">-</span> sr_on.t(1);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(1<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx_on, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_on.x1 <span class="org-type">-</span> sr_on.x2, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxx_on, f] = pwelch(sr_on.x1 <span class="org-type">-</span> sr_on.x2, win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxx_off, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_off.x1 <span class="org-type">-</span> sr_off.x2, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxx_off, <span class="org-type">~</span>] = pwelch(sr_off.x1 <span class="org-type">-</span> sr_off.x2, win, [], [], Fs);
</pre> </pre>
</div> </div>
<div id="orgacfda5a" class="figure"> <div id="org1b06395" class="figure">
<p><img src="figs/psd_noise.png" alt="psd_noise.png" /> <p><img src="figs/psd_noise.png" alt="psd_noise.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>ASD of the measured noise</p> <p><span class="figure-number">Figure 3: </span>ASD of the measured noise</p>
@ -520,13 +269,13 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
</div> </div>
</div> </div>
<div id="outline-container-orgf938632" class="outline-3"> <div id="outline-container-orgd0a405c" class="outline-3">
<h3 id="orgf938632"><span class="section-number-3">1.4</span> Conclusion</h3> <h3 id="orgd0a405c"><span class="section-number-3">1.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-4"> <div class="outline-text-3" id="text-1-4">
<div class="note"> <div class="note" id="org71fbb94">
<ul class="org-ul"> <ul class="org-ul">
<li>The measurement is mostly limited by the resolution of the Speedgoat DAC (16bits over \(\pm 10 V\))</li> <li>The measurement is mostly limited by the resolution of the Speedgoat DAC (16bits over \(\pm 10 V\))</li>
<li>In section <a href="#org73e12a6">2</a>, the same measurement is done but voltage amplifiers are added to amplify the noise</li> <li>In section <a href="#org28c6f1d">2</a>, the same measurement is done but voltage amplifiers are added to amplify the noise</li>
</ul> </ul>
</div> </div>
@ -534,13 +283,13 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
</div> </div>
</div> </div>
<div id="outline-container-org038eeb5" class="outline-2"> <div id="outline-container-orge484f16" class="outline-2">
<h2 id="org038eeb5"><span class="section-number-2">2</span> Measure of the noise induced by the Slip-Ring using voltage amplifiers - Noise</h2> <h2 id="orge484f16"><span class="section-number-2">2</span> Measure of the noise induced by the Slip-Ring using voltage amplifiers - Noise</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="org73e12a6"></a> <a id="org28c6f1d"></a>
</p> </p>
<div class="note"> <div class="note" id="orgb572c7d">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/meas_slip_ring.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/meas_slip_ring.zip">here</a>.
</p> </p>
@ -548,8 +297,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/meas_slip_r
</div> </div>
</div> </div>
<div id="outline-container-orgfecfa5c" class="outline-3"> <div id="outline-container-orgcffd362" class="outline-3">
<h3 id="orgfecfa5c"><span class="section-number-3">2.1</span> Measurement Description</h3> <h3 id="orgcffd362"><span class="section-number-3">2.1</span> Measurement Description</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
<b>Goal</b>: <b>Goal</b>:
@ -657,14 +406,14 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table> </table>
<div id="org1e3b32c" class="figure"> <div id="org0f30e7e" class="figure">
<p><img src="./img/VID_20190503_160831.gif" alt="VID_20190503_160831.gif" /> <p><img src="./img/VID_20190503_160831.gif" alt="VID_20190503_160831.gif" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Slip-Ring rotating at 6rpm</p> <p><span class="figure-number">Figure 4: </span>Slip-Ring rotating at 6rpm</p>
</div> </div>
<div id="org3cea729" class="figure"> <div id="orgc30f130" class="figure">
<p><img src="./img/VID_20190503_161401.gif" alt="VID_20190503_161401.gif" /> <p><img src="./img/VID_20190503_161401.gif" alt="VID_20190503_161401.gif" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Slip-Ring rotating at 60rpm</p> <p><span class="figure-number">Figure 5: </span>Slip-Ring rotating at 60rpm</p>
@ -672,31 +421,31 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</div> </div>
</div> </div>
<div id="outline-container-org93676c7" class="outline-3"> <div id="outline-container-orgb04e3fc" class="outline-3">
<h3 id="org93676c7"><span class="section-number-3">2.2</span> Load data</h3> <h3 id="orgb04e3fc"><span class="section-number-3">2.2</span> Load data</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">sr_off = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_008.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_off = sr_off.data; <pre class="src src-matlab">sr_off = load(<span class="org-string">'mat/data_008.mat'</span>, <span class="org-string">'data'</span>); sr_off = sr_off.data;
sr_on = load<span class="org-rainbow-delimiters-depth-1">(</span>'mat<span class="org-type">/</span>data_009.mat', <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_on = sr_on.data; sr_on = load(<span class="org-string">'mat/data_009.mat'</span>, <span class="org-string">'data'</span>); sr_on = sr_on.data;
sr_6r = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_010.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_6r = sr_6r.data; sr_6r = load(<span class="org-string">'mat/data_010.mat'</span>, <span class="org-string">'data'</span>); sr_6r = sr_6r.data;
sr_60r = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_011.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_60r = sr_60r.data; sr_60r = load(<span class="org-string">'mat/data_011.mat'</span>, <span class="org-string">'data'</span>); sr_60r = sr_60r.data;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org5c0f846" class="outline-3"> <div id="outline-container-orgeb6990e" class="outline-3">
<h3 id="org5c0f846"><span class="section-number-3">2.3</span> Time Domain</h3> <h3 id="orgeb6990e"><span class="section-number-3">2.3</span> Time Domain</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
We plot the time domain data for the direct measurement (figure <a href="#orgb38ee7b">6</a>) and for the signal going through the slip-ring (figure <a href="#orgb1b1fc7">7</a>); We plot the time domain data for the direct measurement (figure <a href="#orgab51d08">6</a>) and for the signal going through the slip-ring (figure <a href="#org660c7b1">7</a>);
</p> </p>
<div id="orgb38ee7b" class="figure"> <div id="orgab51d08" class="figure">
<p><img src="figs/sr_direct_time.png" alt="sr_direct_time.png" /> <p><img src="figs/sr_direct_time.png" alt="sr_direct_time.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Direct measurement</p> <p><span class="figure-number">Figure 6: </span>Direct measurement</p>
@ -704,7 +453,7 @@ We plot the time domain data for the direct measurement (figure <a href="#orgb38
<div id="orgb1b1fc7" class="figure"> <div id="org660c7b1" class="figure">
<p><img src="figs/sr_slipring_time.png" alt="sr_slipring_time.png" /> <p><img src="figs/sr_slipring_time.png" alt="sr_slipring_time.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Measurement of the signal going through the Slip-Ring</p> <p><span class="figure-number">Figure 7: </span>Measurement of the signal going through the Slip-Ring</p>
@ -712,18 +461,18 @@ We plot the time domain data for the direct measurement (figure <a href="#orgb38
</div> </div>
</div> </div>
<div id="outline-container-org3cf58bf" class="outline-3"> <div id="outline-container-org9809223" class="outline-3">
<h3 id="org3cf58bf"><span class="section-number-3">2.4</span> Frequency Domain</h3> <h3 id="org9809223"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
We first compute some parameters that will be used for the PSD computation. We first compute some parameters that will be used for the PSD computation.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = sr_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>sr_off<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = sr_off(2, 3)<span class="org-type">-</span>sr_off(1, 3);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
@ -731,43 +480,43 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
Then we compute the Power Spectral Density using <code>pwelch</code> function. Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxdir, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxdir, f] = pwelch(sr_off(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxoff, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_off<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxoff, <span class="org-type">~</span>] = pwelch(sr_off(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>pxon, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxon, <span class="org-type">~</span>] = pwelch(sr_on(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px6r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_6r<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px6r, <span class="org-type">~</span>] = pwelch(sr_6r(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px60r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_60r<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px60r, <span class="org-type">~</span>] = pwelch(sr_60r(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre> </pre>
</div> </div>
<p> <p>
And we plot the ASD of the measured signals (figure <a href="#org15417d9">8</a>); And we plot the ASD of the measured signals (figure <a href="#org3bc5568">8</a>);
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxoff<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxoff), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxon<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxon), <span class="org-string">'DisplayName'</span>, <span class="org-string">'ON'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px6r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', '<span class="org-highlight-numbers-number">6rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px6r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px60r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', '<span class="org-highlight-numbers-number">60rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px60r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'60rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxdir<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k-', 'DisplayName', 'Direct'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(pxdir), <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Direct'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0.1, 500]);
</pre> </pre>
</div> </div>
<div id="org15417d9" class="figure"> <div id="org3bc5568" class="figure">
<p><img src="figs/sr_psd_compare.png" alt="sr_psd_compare.png" /> <p><img src="figs/sr_psd_compare.png" alt="sr_psd_compare.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Comparison of the ASD of the measured signals when the slip-ring is ON, OFF and turning</p> <p><span class="figure-number">Figure 8: </span>Comparison of the ASD of the measured signals when the slip-ring is ON, OFF and turning</p>
</div> </div>
<div class="note"> <div class="note" id="org4b4a5f5">
<p> <p>
<b>Questions:</b> <b>Questions:</b>
</p> </p>
@ -780,10 +529,10 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-orgfb3a7be" class="outline-3"> <div id="outline-container-org6edde18" class="outline-3">
<h3 id="orgfb3a7be"><span class="section-number-3">2.5</span> Conclusion</h3> <h3 id="org6edde18"><span class="section-number-3">2.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<div class="important"> <div class="important" id="org401fc3c">
<ul class="org-ul"> <ul class="org-ul">
<li>The measurements are re-done using an additional low pass filter at the input of the voltage amplifier</li> <li>The measurements are re-done using an additional low pass filter at the input of the voltage amplifier</li>
</ul> </ul>
@ -792,13 +541,13 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgf6e4281" class="outline-2"> <div id="outline-container-org34a88cd" class="outline-2">
<h2 id="orgf6e4281"><span class="section-number-2">3</span> Measure of the noise induced by the Slip-Ring rotation - LPF added</h2> <h2 id="org34a88cd"><span class="section-number-2">3</span> Measure of the noise induced by the Slip-Ring rotation - LPF added</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
<a id="org6764371"></a> <a id="org6fb7c81"></a>
</p> </p>
<div class="note"> <div class="note" id="orgffe6059">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/meas_slip_ring_lpf.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/meas_slip_ring_lpf.zip">here</a>.
</p> </p>
@ -806,8 +555,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/meas_slip_r
</div> </div>
</div> </div>
<div id="outline-container-org7da9e34" class="outline-3"> <div id="outline-container-org9842ef1" class="outline-3">
<h3 id="org7da9e34"><span class="section-number-3">3.1</span> Measurement description</h3> <h3 id="org9842ef1"><span class="section-number-3">3.1</span> Measurement description</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
<b>Setup</b>: <b>Setup</b>:
@ -906,50 +655,50 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</div> </div>
</div> </div>
<div id="outline-container-org62f4c0b" class="outline-3"> <div id="outline-container-org301dd52" class="outline-3">
<h3 id="org62f4c0b"><span class="section-number-3">3.2</span> Load data</h3> <h3 id="org301dd52"><span class="section-number-3">3.2</span> Load data</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">sr_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_030.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_of = sr_of.data; <pre class="src src-matlab">sr_of = load(<span class="org-string">'mat/data_030.mat'</span>, <span class="org-string">'data'</span>); sr_of = sr_of.data;
sr_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_031.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_on = sr_on.data; sr_on = load(<span class="org-string">'mat/data_031.mat'</span>, <span class="org-string">'data'</span>); sr_on = sr_on.data;
sr_6r = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_032.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_6r = sr_6r.data; sr_6r = load(<span class="org-string">'mat/data_032.mat'</span>, <span class="org-string">'data'</span>); sr_6r = sr_6r.data;
sr_60 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_033.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr_60 = sr_60.data; sr_60 = load(<span class="org-string">'mat/data_033.mat'</span>, <span class="org-string">'data'</span>); sr_60 = sr_60.data;
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgebd2a5c" class="outline-3"> <div id="outline-container-orgd6c3972" class="outline-3">
<h3 id="orgebd2a5c"><span class="section-number-3">3.3</span> Time Domain</h3> <h3 id="orgd6c3972"><span class="section-number-3">3.3</span> Time Domain</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<p> <p>
We plot the time domain data for the direct measurement (figure <a href="#org5cb534e">9</a>) and for the signal going through the slip-ring (figure <a href="#org2958b47">11</a>); We plot the time domain data for the direct measurement (figure <a href="#org994e2d6">9</a>) and for the signal going through the slip-ring (figure <a href="#org87edab9">11</a>);
</p> </p>
<div id="org5cb534e" class="figure"> <div id="org994e2d6" class="figure">
<p><img src="figs/sr_direct_1khz_time.png" alt="sr_direct_1khz_time.png" /> <p><img src="figs/sr_direct_1khz_time.png" alt="sr_direct_1khz_time.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Direct measurement</p> <p><span class="figure-number">Figure 9: </span>Direct measurement</p>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">2e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">2e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">xlim([0, 0.2]); ylim([<span class="org-type">-</span>2e<span class="org-type">-</span>3, 2e<span class="org-type">-</span>3]);
</pre> </pre>
</div> </div>
<div id="orgc1ab96f" class="figure"> <div id="orgaf6700b" class="figure">
<p><img src="figs/sr_direct_1khz_time_zoom.png" alt="sr_direct_1khz_time_zoom.png" /> <p><img src="figs/sr_direct_1khz_time_zoom.png" alt="sr_direct_1khz_time_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Direct measurement - Zoom</p> <p><span class="figure-number">Figure 10: </span>Direct measurement - Zoom</p>
</div> </div>
<div id="org2958b47" class="figure"> <div id="org87edab9" class="figure">
<p><img src="figs/sr_slipring_1khz_time.png" alt="sr_slipring_1khz_time.png" /> <p><img src="figs/sr_slipring_1khz_time.png" alt="sr_slipring_1khz_time.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Measurement of the signal going through the Slip-Ring</p> <p><span class="figure-number">Figure 11: </span>Measurement of the signal going through the Slip-Ring</p>
@ -957,18 +706,18 @@ We plot the time domain data for the direct measurement (figure <a href="#org5cb
</div> </div>
</div> </div>
<div id="outline-container-org3866b73" class="outline-3"> <div id="outline-container-org6579314" class="outline-3">
<h3 id="org3866b73"><span class="section-number-3">3.4</span> Frequency Domain - Direct Signal</h3> <h3 id="org6579314"><span class="section-number-3">3.4</span> Frequency Domain - Direct Signal</h3>
<div class="outline-text-3" id="text-3-4"> <div class="outline-text-3" id="text-3-4">
<p> <p>
We first compute some parameters that will be used for the PSD computation. We first compute some parameters that will be used for the PSD computation.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = sr_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>sr_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = sr_of(2, 3)<span class="org-type">-</span>sr_of(1, 3);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(10<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
@ -976,31 +725,31 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
Then we compute the Power Spectral Density using <code>pwelch</code> function. Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px_d_of, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[px_d_of, f] = pwelch(sr_of(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px_d_on, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px_d_on, <span class="org-type">~</span>] = pwelch(sr_on(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px_d_6r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_6r<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px_d_6r, <span class="org-type">~</span>] = pwelch(sr_6r(<span class="org-type">:</span>, 1), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px_d_60, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_60<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px_d_60, <span class="org-type">~</span>] = pwelch(sr_60(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_d_of<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px_d_of), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_d_on<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px_d_on), <span class="org-string">'DisplayName'</span>, <span class="org-string">'ON'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_d_6r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', '<span class="org-highlight-numbers-number">6rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px_d_6r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_d_60<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', '<span class="org-highlight-numbers-number">60rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px_d_60), <span class="org-string">'DisplayName'</span>, <span class="org-string">'60rpm'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">5000</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0.1, 5000]);
</pre> </pre>
</div> </div>
<div id="org861f9e3" class="figure"> <div id="org5a81a77" class="figure">
<p><img src="figs/sr_psd_1khz_direct.png" alt="sr_psd_1khz_direct.png" /> <p><img src="figs/sr_psd_1khz_direct.png" alt="sr_psd_1khz_direct.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the signal going directly to the ADC</p> <p><span class="figure-number">Figure 12: </span>Amplitude Spectral Density of the signal going directly to the ADC</p>
@ -1008,36 +757,36 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-org9c9986f" class="outline-3"> <div id="outline-container-orgf591b45" class="outline-3">
<h3 id="org9c9986f"><span class="section-number-3">3.5</span> Frequency Domain - Slip-Ring Signal</h3> <h3 id="orgf591b45"><span class="section-number-3">3.5</span> Frequency Domain - Slip-Ring Signal</h3>
<div class="outline-text-3" id="text-3-5"> <div class="outline-text-3" id="text-3-5">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px_sr_of, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[px_sr_of, f] = pwelch(sr_of(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px_sr_on, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_on<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px_sr_on, <span class="org-type">~</span>] = pwelch(sr_on(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px_sr_6r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_6r<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px_sr_6r, <span class="org-type">~</span>] = pwelch(sr_6r(<span class="org-type">:</span>, 2), win, [], [], Fs);
<span class="org-rainbow-delimiters-depth-1">[</span>px_sr_60, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr_60<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [px_sr_60, <span class="org-type">~</span>] = pwelch(sr_60(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_sr_of<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px_sr_of), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_sr_on<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'ON'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px_sr_on), <span class="org-string">'DisplayName'</span>, <span class="org-string">'ON'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_sr_6r<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', '<span class="org-highlight-numbers-number">6rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px_sr_6r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'6rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_sr_60<span class="org-rainbow-delimiters-depth-2">)</span>, 'DisplayName', '<span class="org-highlight-numbers-number">60rpm</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px_sr_60), <span class="org-string">'DisplayName'</span>, <span class="org-string">'60rpm'</span>);
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>px_d_of<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'-k', 'DisplayName', 'Direct'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(px_d_of), <span class="org-string">'-k'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Direct'</span>);
hold off; hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span> xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$'</span>)
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>; legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">5000</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlim([0.1, 5000]);
</pre> </pre>
</div> </div>
<div id="org29ed3a7" class="figure"> <div id="orgab20b33" class="figure">
<p><img src="figs/sr_psd_1khz_slipring.png" alt="sr_psd_1khz_slipring.png" /> <p><img src="figs/sr_psd_1khz_slipring.png" alt="sr_psd_1khz_slipring.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Amplitude Spectral Density of the signal going through the slip-ring</p> <p><span class="figure-number">Figure 13: </span>Amplitude Spectral Density of the signal going through the slip-ring</p>
@ -1045,10 +794,10 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-org9d90d36" class="outline-3"> <div id="outline-container-org599231a" class="outline-3">
<h3 id="org9d90d36"><span class="section-number-3">3.6</span> Conclusion</h3> <h3 id="org599231a"><span class="section-number-3">3.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-3-6"> <div class="outline-text-3" id="text-3-6">
<div class="important"> <div class="important" id="org965e629">
<ul class="org-ul"> <ul class="org-ul">
<li>We observe peaks at 12Hz and its harmonics for the signal going through the slip-ring when it is turning at 60rpm.</li> <li>We observe peaks at 12Hz and its harmonics for the signal going through the slip-ring when it is turning at 60rpm.</li>
<li>Apart from that, the noise of the signal is the same when the slip-ring is off/on and turning</li> <li>Apart from that, the noise of the signal is the same when the slip-ring is off/on and turning</li>
@ -1063,8 +812,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-16 jeu. 13:34</p> <p class="date">Created: 2020-11-12 jeu. 10:29</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>
</html> </html>

9
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@ -9,13 +9,8 @@
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273
speedgoat-measurement/index.html
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@ -3,249 +3,13 @@
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -258,15 +22,15 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org3cefbc8">1. Get data from the target computer</a></li> <li><a href="#org47ff289">1. Get data from the target computer</a></li>
<li><a href="#orgb9e8597">2. Commands with the target object</a></li> <li><a href="#orgc235aed">2. Commands with the target object</a></li>
<li><a href="#org59c6ccd">3. FTP access to the target computer</a></li> <li><a href="#org3891b86">3. FTP access to the target computer</a></li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org3cefbc8" class="outline-2"> <div id="outline-container-org47ff289" class="outline-2">
<h2 id="org3cefbc8"><span class="section-number-2">1</span> Get data from the target computer</h2> <h2 id="org47ff289"><span class="section-number-2">1</span> Get data from the target computer</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
We first copy the <code>dat</code> file from the target computer to the host computer: We first copy the <code>dat</code> file from the target computer to the host computer:
@ -274,9 +38,9 @@ We first copy the <code>dat</code> file from the target computer to the host com
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">tg=slrt; <pre class="src src-matlab">tg=slrt;
f=SimulinkRealTime.openFTP<span class="org-rainbow-delimiters-depth-1">(</span>tg<span class="org-rainbow-delimiters-depth-1">)</span>; f=SimulinkRealTime.openFTP(tg);
mget<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-string">'DATA_001.dat', 'local_folder'</span><span class="org-rainbow-delimiters-depth-1">)</span>; mget(f, <span class="org-string">'DATA_001.dat'</span>, <span class="org-string">'local_folder'</span>);
close<span class="org-rainbow-delimiters-depth-1">(</span>f<span class="org-rainbow-delimiters-depth-1">)</span>; close(f);
</pre> </pre>
</div> </div>
@ -285,14 +49,14 @@ We then import the <code>dat</code> file to the workspace:
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">matlab_data = SimulinkRealTime.utils.getFileScopeData<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'DATA_001.dat'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">matlab_data = SimulinkRealTime.utils.getFileScopeData(<span class="org-string">'DATA_001.dat'</span>);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgb9e8597" class="outline-2"> <div id="outline-container-orgc235aed" class="outline-2">
<h2 id="orgb9e8597"><span class="section-number-2">2</span> Commands with the target object</h2> <h2 id="orgc235aed"><span class="section-number-2">2</span> Commands with the target object</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a href="https://fr.mathworks.com/help/xpc/api/simulinkrealtime.target.html">https://fr.mathworks.com/help/xpc/api/simulinkrealtime.target.html</a> <a href="https://fr.mathworks.com/help/xpc/api/simulinkrealtime.target.html">https://fr.mathworks.com/help/xpc/api/simulinkrealtime.target.html</a>
@ -511,8 +275,8 @@ We then import the <code>dat</code> file to the workspace:
</div> </div>
</div> </div>
<div id="outline-container-org59c6ccd" class="outline-2"> <div id="outline-container-org3891b86" class="outline-2">
<h2 id="org59c6ccd"><span class="section-number-2">3</span> FTP access to the target computer</h2> <h2 id="org3891b86"><span class="section-number-2">3</span> FTP access to the target computer</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
<a href="https://fr.mathworks.com/help/xpc/api/simulinkrealtime.openftp.html?s_tid=doc_ta">https://fr.mathworks.com/help/xpc/api/simulinkrealtime.openftp.html?s_tid=doc_ta</a> <a href="https://fr.mathworks.com/help/xpc/api/simulinkrealtime.openftp.html?s_tid=doc_ta">https://fr.mathworks.com/help/xpc/api/simulinkrealtime.openftp.html?s_tid=doc_ta</a>
@ -523,7 +287,7 @@ First run the following commands to have the <code>FTP</code> Object:
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">tg=slrt; <pre class="src src-matlab">tg=slrt;
f=SimulinkRealTime.openFTP<span class="org-rainbow-delimiters-depth-1">(</span>tg<span class="org-rainbow-delimiters-depth-1">)</span>; f=SimulinkRealTime.openFTP(tg);
</pre> </pre>
</div> </div>
@ -545,8 +309,7 @@ Then, the <code>f</code> object can be used to access the filesystem on the targ
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-10-08 mar. 10:44</p> <p class="date">Created: 2020-11-12 jeu. 10:30</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>
</html> </html>

9
speedgoat-measurement/index.org
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@ -9,13 +9,8 @@
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ../index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
:END: :END:
* Get data from the target computer * Get data from the target computer

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9
static-spindle/index.org
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@ -9,13 +9,8 @@
#+HTML_LINK_HOME: ../index.html #+HTML_LINK_HOME: ../index.html
#+HTML_LINK_UP: ../index.html #+HTML_LINK_UP: ../index.html
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/> #+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
#+HTML_MATHJAX: align: center tagside: right font: TeX #+HTML_MATHJAX: align: center tagside: right font: TeX

476
static-to-dynamic/index.html
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@ -3,271 +3,21 @@
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<!-- 2019-05-14 mar. 09:52 --> <!-- 2020-11-12 jeu. 10:30 -->
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<title>Static Measurements</title> <title>Static Measurements</title>
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<meta name="author" content="Dehaeze Thomas" /> <meta name="author" content="Dehaeze Thomas" />
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<body> <body>
<div id="org-div-home-and-up"> <div id="org-div-home-and-up">
@ -280,29 +30,75 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org9dbeefe">1. Ty Stage</a> <li><a href="#org4838532">1. Measurement description</a></li>
<li><a href="#org4641bb7">2. Static measurement of the translation stage</a>
<ul> <ul>
<li><a href="#org98becb2">1.1. Notes</a></li> <li><a href="#org9b77eea">2.1. Notes</a></li>
<li><a href="#orgbab4f4e">1.2. Data Pre-processing</a></li> <li><a href="#org47e3834">2.2. Data Pre-processing</a></li>
<li><a href="#orgbb084a6">1.3. Matlab - Data Import</a></li> <li><a href="#orgca79724">2.3. Matlab - Data Import</a></li>
<li><a href="#orgb7b2129">1.4. Data - Plot</a></li> <li><a href="#orga9b2e7b">2.4. Data - Plot</a></li>
<li><a href="#org01e23ef">1.5. Translate to time domain</a></li> <li><a href="#org0f2fcc8">2.5. Translate to time domain</a></li>
<li><a href="#org13bc3d4">1.6. Compute the PSD</a></li> <li><a href="#org01b8405">2.6. Compute the PSD</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgc7af6bd">2. <span class="todo TODO">TODO</span> Spindle</a></li> <li><a href="#org43f6210">3. Static Measurement of the spindle</a></li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org9dbeefe" class="outline-2"> <div id="outline-container-org4838532" class="outline-2">
<h2 id="org9dbeefe"><span class="section-number-2">1</span> Ty Stage</h2> <h2 id="org4838532"><span class="section-number-2">1</span> Measurement description</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
<a id="org0ab6482"></a> <b>Setup</b>:
Each stage is statically moved of all its stroke on after the other.
A metrology element is located at the sample position and its motion is measured in translations and rotations.
For each small displacement, the stage is stopped and the motion of the sample is recorded and averaged.
</p> </p>
<div class="note"> <p>
The report by H-P van der Kleij on the static measurement of the ID31 station is available <a href="data/ID31_report_static_meas.pdf">here</a>.
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><b>Date</b></td>
<td class="org-left">2019-01-09</td>
</tr>
<tr>
<td class="org-left"><b>Sensors</b></td>
<td class="org-left">Interferometer</td>
</tr>
<tr>
<td class="org-left"><b>Location</b></td>
<td class="org-left">Experimental Hutch</td>
</tr>
</tbody>
</table>
<p>
<b>Goal</b>:
The goal here is to analyze the static measurement on the station (guiding error of each stage) and convert them to dynamic disturbances that can be use in the model of the micro-station.
</p>
</div>
</div>
<div id="outline-container-org4641bb7" class="outline-2">
<h2 id="org4641bb7"><span class="section-number-2">2</span> Static measurement of the translation stage</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org46aa1d0"></a>
</p>
<div class="note" id="orge3ac46c">
<p> <p>
All the files (data and Matlab scripts) are accessible <a href="data/static_ty.zip">here</a>. All the files (data and Matlab scripts) are accessible <a href="data/static_ty.zip">here</a>.
</p> </p>
@ -310,9 +106,9 @@ All the files (data and Matlab scripts) are accessible <a href="data/static_ty.z
</div> </div>
</div> </div>
<div id="outline-container-org98becb2" class="outline-3"> <div id="outline-container-org9b77eea" class="outline-3">
<h3 id="org98becb2"><span class="section-number-3">1.1</span> Notes</h3> <h3 id="org9b77eea"><span class="section-number-3">2.1</span> Notes</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-2-1">
<ul class="org-ul"> <ul class="org-ul">
<li><b>5530</b>: Straightness Plot: Yz</li> <li><b>5530</b>: Straightness Plot: Yz</li>
<li><b>Filename</b>: <code>r:\home\PDMU\PEL\Measurement_library\ID31\ID31_u_station\TY\12_12_2018\linear deviation _tyz_401_points.txt</code></li> <li><b>Filename</b>: <code>r:\home\PDMU\PEL\Measurement_library\ID31\ID31_u_station\TY\12_12_2018\linear deviation _tyz_401_points.txt</code></li>
@ -393,7 +189,7 @@ All the files (data and Matlab scripts) are accessible <a href="data/static_ty.z
</table> </table>
<p> <p>
In a very schematic way, the measurement is explained on figure <a href="#orgb91392e">1</a>. In a very schematic way, the measurement is explained on figure <a href="#org6d44784">1</a>.
The positioning error \(d\) is measure as a function of \(x\). The positioning error \(d\) is measure as a function of \(x\).
Because the measurement is done in a static way, the dynamics of the station (represented by the mass-spring-damper system on the schematic) does not play a role in the measure. Because the measurement is done in a static way, the dynamics of the station (represented by the mass-spring-damper system on the schematic) does not play a role in the measure.
</p> </p>
@ -403,19 +199,19 @@ The obtained data corresponds to the guiding errors.
</p> </p>
<div id="orgb91392e" class="figure"> <div id="org6d44784" class="figure">
<p><img src="./figs/guiding_errors.png" alt="guiding_errors.png" /> <p><img src="./figs/guiding_error.png" alt="guiding_error.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Schematic of the measurement</p> <p><span class="figure-number">Figure 1: </span>Schematic of the measurement</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgbab4f4e" class="outline-3"> <div id="outline-container-org47e3834" class="outline-3">
<h3 id="orgbab4f4e"><span class="section-number-3">1.2</span> Data Pre-processing</h3> <h3 id="org47e3834"><span class="section-number-3">2.2</span> Data Pre-processing</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-shell">sed <span class="org-string">'s/\t/ /g;s/\,/./g'</span> <span class="org-string">"mat/linear_deviation_tyz_401_points.txt"</span> &gt; data/data_tyz.txt <pre class="src src-shell">sed <span class="org-string">'s/\t/ /g;s/\,/./g'</span> <span class="org-string">"mat/linear_deviation_tyz_401_points.txt"</span> &gt; mat/data_tyz.txt
</pre> </pre>
</div> </div>
@ -512,39 +308,39 @@ The obtained data corresponds to the guiding errors.
</div> </div>
</div> </div>
<div id="outline-container-orgbb084a6" class="outline-3"> <div id="outline-container-orgca79724" class="outline-3">
<h3 id="orgbb084a6"><span class="section-number-3">1.3</span> Matlab - Data Import</h3> <h3 id="orgca79724"><span class="section-number-3">2.3</span> Matlab - Data Import</h3>
<div class="outline-text-3" id="text-1-3"> <div class="outline-text-3" id="text-2-3">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">filename = <span class="org-string">'mat/data_tyz.txt'</span>; <pre class="src src-matlab">filename = <span class="org-string">'mat/data_tyz.txt'</span>;
fileID = fopen<span class="org-rainbow-delimiters-depth-1">(</span>filename<span class="org-rainbow-delimiters-depth-1">)</span>; fileID = fopen(filename);
data = cell2mat<span class="org-rainbow-delimiters-depth-1">(</span>textscan<span class="org-rainbow-delimiters-depth-2">(</span>fileID,'<span class="org-comment">%f %f %f </span>%f', 'collectoutput', <span class="org-highlight-numbers-number">1</span>,'headerlines',<span class="org-highlight-numbers-number">1</span>)); data = cell2mat(textscan(fileID,<span class="org-string">'%f %f %f %f'</span>, <span class="org-string">'collectoutput'</span>, 1,<span class="org-string">'headerlines'</span>,1));
fclose<span class="org-rainbow-delimiters-depth-3">(</span>fileID<span class="org-rainbow-delimiters-depth-3">)</span>; fclose(fileID);
</pre> </pre>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgb7b2129" class="outline-3"> <div id="outline-container-orga9b2e7b" class="outline-3">
<h3 id="orgb7b2129"><span class="section-number-3">1.4</span> Data - Plot</h3> <h3 id="orga9b2e7b"><span class="section-number-3">2.4</span> Data - Plot</h3>
<div class="outline-text-3" id="text-1-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
First, we plot the straightness error as a function of the position (figure <a href="#orge60d823">2</a>). First, we plot the straightness error as a function of the position (figure <a href="#orgcf088c0">2</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
<span class="org-keyword">for</span> <span class="org-variable-name">i</span>=<span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:data</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">end, </span><span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span> <span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span>=<span class="org-constant">1:data(end, 1)</span>
plot<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span>data<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span> <span class="org-type">==</span> <span class="org-constant">i</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span>data<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span> <span class="org-type">==</span> <span class="org-constant">i</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'-k'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(data(data(<span class="org-type">:</span>, 1) <span class="org-type">==</span> <span class="org-constant">i</span>, 3), data(data(<span class="org-type">:</span>, 1) <span class="org-type">==</span> <span class="org-constant">i</span>, 4), <span class="org-string">'-k'</span>);
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Target Value </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Error Value <span class="org-rainbow-delimiters-depth-2">[</span>$<span class="org-type">\</span>mu m$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Target Value [mm]'</span>); ylabel(<span class="org-string">'Error Value [$\mu m$]'</span>);
</pre> </pre>
</div> </div>
<div id="orge60d823" class="figure"> <div id="orgcf088c0" class="figure">
<p><img src="figs/raw_data_tyz.png" alt="raw_data_tyz.png" /> <p><img src="figs/raw_data_tyz.png" alt="raw_data_tyz.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Time domain Data</p> <p><span class="figure-number">Figure 2: </span>Time domain Data</p>
@ -552,12 +348,12 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
<p> <p>
Then, we compute mean value of each position, and we remove this mean value from the data. Then, we compute mean value of each position, and we remove this mean value from the data.
The results are shown on figure <a href="#org6b6ea44">3</a>. The results are shown on figure <a href="#orgff37b5d">3</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">mean_pos = zeros<span class="org-rainbow-delimiters-depth-1">(</span>sum<span class="org-rainbow-delimiters-depth-2">(</span>data<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">==</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">mean_pos = zeros(sum(data(<span class="org-type">:</span>, 1)<span class="org-type">==</span>1), 1);
<span class="org-keyword">for</span> <span class="org-variable-name">i</span>=<span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:sum</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">data</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-2">(</span></span><span class="org-constant">:, </span><span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-constant">==</span><span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span> <span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span>=<span class="org-constant">1:sum(data(:, 1)==1)</span>
mean_pos<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span> = mean<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span>data<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">==</span><span class="org-constant">i</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; mean_pos(<span class="org-constant">i</span>) = mean(data(data(<span class="org-type">:</span>, 2)<span class="org-type">==</span><span class="org-constant">i</span>, 4));
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
</pre> </pre>
</div> </div>
@ -565,17 +361,17 @@ The results are shown on figure <a href="#org6b6ea44">3</a>.
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
<span class="org-keyword">for</span> <span class="org-variable-name">i</span>=<span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:data</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">end, </span><span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span> <span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span>=<span class="org-constant">1:data(end, 1)</span>
filt = data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">==</span> <span class="org-constant">i</span>; filt = data(<span class="org-type">:</span>, 1) <span class="org-type">==</span> <span class="org-constant">i</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span>filt, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span>filt, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span> mean_pos, <span class="org-string">'-k'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(data(filt, 3), data(filt, 4) <span class="org-type">-</span> mean_pos, <span class="org-string">'-k'</span>);
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Target Value </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">mm</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>Error Value <span class="org-rainbow-delimiters-depth-2">[</span>$<span class="org-type">\</span>mu m$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Target Value [mm]'</span>); ylabel(<span class="org-string">'Error Value [$\mu m$]'</span>);
</pre> </pre>
</div> </div>
<div id="org6b6ea44" class="figure"> <div id="orgff37b5d" class="figure">
<p><img src="figs/processed_data_tyz.png" alt="processed_data_tyz.png" /> <p><img src="figs/processed_data_tyz.png" alt="processed_data_tyz.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>caption</p> <p><span class="figure-number">Figure 3: </span>caption</p>
@ -583,33 +379,33 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-org01e23ef" class="outline-3"> <div id="outline-container-org0f2fcc8" class="outline-3">
<h3 id="org01e23ef"><span class="section-number-3">1.5</span> Translate to time domain</h3> <h3 id="org0f2fcc8"><span class="section-number-3">2.5</span> Translate to time domain</h3>
<div class="outline-text-3" id="text-1-5"> <div class="outline-text-3" id="text-2-5">
<p> <p>
We here make the assumptions that, during a scan with the translation stage, the Z motion of the translation stage will follow the guiding error measured. We here make the assumptions that, during a scan with the translation stage, the Z motion of the translation stage will follow the guiding error measured.
</p> </p>
<p> <p>
We then create a time vector \(t\) from 0 to 1 second that corresponds to a typical scan, and we plot the guiding error as a function of the time on figure <a href="#orgb3c2727">4</a>. We then create a time vector \(t\) from 0 to 1 second that corresponds to a typical scan, and we plot the guiding error as a function of the time on figure <a href="#org70b707b">4</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">t = linspace<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">1</span>, length<span class="org-rainbow-delimiters-depth-2">(</span>data<span class="org-rainbow-delimiters-depth-3">(</span>data<span class="org-rainbow-delimiters-depth-4">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">==</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">t = linspace(0, 1, length(data(data(<span class="org-type">:</span>, 1)<span class="org-type">==</span>1, 4)));
</pre> </pre>
</div> </div>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>t, data<span class="org-rainbow-delimiters-depth-2">(</span>data<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-3">)</span> <span class="org-type">==</span> <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">-</span> mean_pos, <span class="org-string">'-k'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(t, data(data(<span class="org-type">:</span>, 1) <span class="org-type">==</span> 1, 4) <span class="org-type">-</span> mean_pos, <span class="org-string">'-k'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Error Value </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">um</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Error Value [um]'</span>);
</pre> </pre>
</div> </div>
<div id="orgb3c2727" class="figure"> <div id="org70b707b" class="figure">
<p><img src="figs/time_domain_tyz.png" alt="time_domain_tyz.png" /> <p><img src="figs/time_domain_tyz.png" alt="time_domain_tyz.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>caption</p> <p><span class="figure-number">Figure 4: </span>caption</p>
@ -617,18 +413,18 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-org13bc3d4" class="outline-3"> <div id="outline-container-org01b8405" class="outline-3">
<h3 id="org13bc3d4"><span class="section-number-3">1.6</span> Compute the PSD</h3> <h3 id="org01b8405"><span class="section-number-3">2.6</span> Compute the PSD</h3>
<div class="outline-text-3" id="text-1-6"> <div class="outline-text-3" id="text-2-6">
<p> <p>
We first compute some parameters that will be used for the PSD computation. We first compute some parameters that will be used for the PSD computation.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = t(2)<span class="org-type">-</span>t(1);
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span> Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; win = hanning(ceil(1<span class="org-type">*</span>Fs));
</pre> </pre>
</div> </div>
@ -636,7 +432,7 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
We remove the mean position from the data. We remove the mean position from the data.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">x = data<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">==</span> <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> mean_pos; <pre class="src src-matlab">x = data(data(<span class="org-type">:</span>, 1) <span class="org-type">==</span> 1, 4) <span class="org-type">-</span> mean_pos;
</pre> </pre>
</div> </div>
@ -645,17 +441,17 @@ And finally, we compute the power spectral density of the displacement obtained
</p> </p>
<p> <p>
The result is shown on figure <a href="#org7446cbb">5</a>. The result is shown on figure <a href="#orgdac0fa8">5</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>x, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">[pxx, f] = pwelch(x, win, [], [], Fs);
pxx_t = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span class="org-rainbow-delimiters-depth-2">(</span>pxx<span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span>end, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; pxx_t = zeros(length(pxx), data(end, 1));
<span class="org-keyword">for</span> <span class="org-variable-name">i</span>=<span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant">:data</span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-constant">end, </span><span class="org-constant"><span class="org-highlight-numbers-number">1</span></span><span class="org-constant"><span class="org-rainbow-delimiters-depth-1">)</span></span> <span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span>=<span class="org-constant">1:data(end, 1)</span>
x = data<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span> <span class="org-type">==</span> <span class="org-constant">i</span>, <span class="org-highlight-numbers-number">4</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> mean_pos; x = data(data(<span class="org-type">:</span>, 1) <span class="org-type">==</span> <span class="org-constant">i</span>, 4) <span class="org-type">-</span> mean_pos;
<span class="org-rainbow-delimiters-depth-1">[</span>pxx, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>x, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; [pxx, f] = pwelch(x, win, [], [], Fs);
pxx_t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-constant">i</span><span class="org-rainbow-delimiters-depth-1">)</span> = pxx; pxx_t(<span class="org-type">:</span>, <span class="org-constant">i</span>) = pxx;
<span class="org-keyword">end</span> <span class="org-keyword">end</span>
</pre> </pre>
</div> </div>
@ -663,16 +459,16 @@ pxx_t = zeros<span class="org-rainbow-delimiters-depth-1">(</span>length<span cl
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
hold on; hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>mean<span class="org-rainbow-delimiters-depth-3">(</span>pxx_t, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k-'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot(f, sqrt(mean(pxx_t, 2)), <span class="org-string">'k-'</span>);
hold off; hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">(</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">)</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; xlabel(<span class="org-string">'Frequency (Hz)'</span>);
ylabel<span class="org-rainbow-delimiters-depth-1">(</span>'Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>; ylabel(<span class="org-string">'Amplitude Spectral Density $\left[\frac{m}{\sqrt{Hz}}\right]$'</span>);
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'XScale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'XScale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'YScale'</span>, <span class="org-string">'log'</span>);
</pre> </pre>
</div> </div>
<div id="org7446cbb" class="figure"> <div id="orgdac0fa8" class="figure">
<p><img src="figs/psd_tyz.png" alt="psd_tyz.png" /> <p><img src="figs/psd_tyz.png" alt="psd_tyz.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>PSD of the Z motion when scanning with Ty at 1Hz</p> <p><span class="figure-number">Figure 5: </span>PSD of the Z motion when scanning with Ty at 1Hz</p>
@ -681,14 +477,24 @@ ylabel<span class="org-rainbow-delimiters-depth-1">(</span>'Amplitude Spectral D
</div> </div>
</div> </div>
<div id="outline-container-orgc7af6bd" class="outline-2"> <div id="outline-container-org43f6210" class="outline-2">
<h2 id="orgc7af6bd"><span class="section-number-2">2</span> <span class="todo TODO">TODO</span> Spindle</h2> <h2 id="org43f6210"><span class="section-number-2">3</span> Static Measurement of the spindle</h2>
<div class="outline-text-2" id="text-3">
<p>
<a id="orga1d620b"></a>
</p>
<div class="note" id="org889557b">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/spindle_static.zip">here</a>.
</p>
</div>
</div>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-14 mar. 09:52</p> <p class="date">Created: 2020-11-12 jeu. 10:30</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>
</html> </html>

9
static-to-dynamic/index.org
View File

@ -9,13 +9,8 @@
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