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Update Ty scans analysis

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Thomas Dehaeze 2019-05-15 16:36:05 +02:00
parent df4d100ddf
commit 1117428eaa
9 changed files with 256 additions and 120 deletions
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@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<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>
<!-- 2019-05-15 mer. 14:37 --> <!-- 2019-05-15 mer. 16:35 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Vibrations induced by the translation stage motion</title> <title>Vibrations induced by the translation stage motion</title>
@ -258,29 +258,29 @@ 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="#orgf453937">1. Measurement description</a></li> <li><a href="#org15ec826">1. Measurement description</a></li>
<li><a href="#org0d0d44a">2. Measurement Analysis</a> <li><a href="#orgb847946">2. Measurement Analysis</a>
<ul> <ul>
<li><a href="#org8623e83">2.1. Load data</a></li> <li><a href="#org7fc6c17">2.1. Load data</a></li>
<li><a href="#org29ed1af">2.2. Voltage to Velocity</a></li> <li><a href="#orga70e282">2.2. Voltage to Velocity</a></li>
<li><a href="#orgc0653a4">2.3. Time domain plots</a></li> <li><a href="#org4e85d3b">2.3. Time domain plots</a></li>
<li><a href="#orgaa04452">2.4. Frequency Domain analysis</a></li> <li><a href="#org121abe7">2.4. Frequency Domain analysis</a></li>
<li><a href="#org0579205">2.5. Transfer function from marble motion in the East direction to sample motion in the East direction</a></li> <li><a href="#org9bb2e68">2.5. Transfer function from marble motion in the East direction to sample motion in the East direction</a></li>
<li><a href="#org540379b">2.6. Position of the translation stage and Current</a> <li><a href="#org3557c4c">2.6. Position of the translation stage and Current</a>
<ul> <ul>
<li><a href="#orgf590ed7">2.6.1. Data pre-processing</a></li> <li><a href="#orgda3ab01">2.6.1. Data pre-processing</a></li>
<li><a href="#org0f186e6">2.6.2. Time domain data</a></li> <li><a href="#orgc12f6b8">2.6.2. Time domain data</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org4f5f98f">2.7. Conclusion</a></li> <li><a href="#orgd2aa958">2.7. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-orgf453937" class="outline-2"> <div id="outline-container-org15ec826" class="outline-2">
<h2 id="orgf453937"><span class="section-number-2">1</span> Measurement description</h2> <h2 id="org15ec826"><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>:
@ -310,7 +310,7 @@ 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="#org8f10353">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="#org045a67d">1</a>).
</p> </p>
<p> <p>
@ -394,7 +394,7 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table> </table>
<div id="org8f10353" class="figure"> <div id="org045a67d" 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>
@ -402,11 +402,11 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</div> </div>
</div> </div>
<div id="outline-container-org0d0d44a" class="outline-2"> <div id="outline-container-orgb847946" class="outline-2">
<h2 id="org0d0d44a"><span class="section-number-2">2</span> Measurement Analysis</h2> <h2 id="orgb847946"><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="org65b415b"></a> <a id="orgb039411"></a>
</p> </p>
<div class="note"> <div class="note">
<p> <p>
@ -416,8 +416,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/disturbance
</div> </div>
</div> </div>
<div id="outline-container-org8623e83" class="outline-3"> <div id="outline-container-org7fc6c17" class="outline-3">
<h3 id="org8623e83"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="org7fc6c17"><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', '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-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_040.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; z_ty = z_ty.data;
@ -428,8 +428,8 @@ e_of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org
</div> </div>
</div> </div>
<div id="outline-container-org29ed1af" class="outline-3"> <div id="outline-container-orga70e282" class="outline-3">
<h3 id="org29ed1af"><span class="section-number-3">2.2</span> Voltage to Velocity</h3> <h3 id="orga70e282"><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/MEGA/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/MEGA/These/meas/src/index.html">here</a>).
@ -448,9 +448,17 @@ e_of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">
</div> </div>
</div> </div>
<div id="outline-container-orgc0653a4" class="outline-3"> <div id="outline-container-org4e85d3b" class="outline-3">
<h3 id="orgc0653a4"><span class="section-number-3">2.3</span> Time domain plots</h3> <h3 id="org4e85d3b"><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>
We plot the measured velocity of the marble and sample in the vertical direction (figure <a href="#org9602ab5">2</a>) and in the X direction (figure <a href="#orgcc783df">3</a>).
</p>
<p>
We also integrate the relative velocity to obtain the relative displacement (figure <a href="#org00d44bf">4</a> in the X direction and figure <a href="#org8cb0d85">5</a> in the Z direction).
</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;
@ -458,26 +466,18 @@ plot<span class="org-rainbow-delimiters-depth-1">(</span>z_ty<span class="org-ra
plot<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">3</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">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<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">3</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">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - Z'</span><span class="org-rainbow-delimiters-depth-1">)</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-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>;
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<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>;
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-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
<div id="org66c8a67" class="figure"> <div id="org9602ab5" 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="orgde211b5" class="figure">
<p><img src="figs/ty_z_time_zoom.png" alt="ty_z_time_zoom.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Z velocity of the sample and marble when scanning with the translation stage - Zoom</p>
</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;
@ -485,29 +485,52 @@ plot<span class="org-rainbow-delimiters-depth-1">(</span>e_ty<span class="org-ra
plot<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">3</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">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - X'</span><span class="org-rainbow-delimiters-depth-1">)</span>; plot<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">3</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">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Sample - X'</span><span class="org-rainbow-delimiters-depth-1">)</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-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>;
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<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>;
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-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre> </pre>
</div> </div>
<div id="orgc1e7b3a" class="figure"> <div id="orgcc783df" 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 4: </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 class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
plot<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">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1e6</span><span class="org-type">*</span>lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, e_ty<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>e_ty<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>, e_ty<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>;
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">'</span>X Relative Displacement <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>;
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>;
</pre>
</div> </div>
<div id="orgff260b2" class="figure"> <div id="org00d44bf" class="figure">
<p><img src="figs/ty_e_time_zoom.png" alt="ty_e_time_zoom.png" /> <p><img src="figs/x_relative_disp.png" alt="x_relative_disp.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Velocity of the sample and marble in the east direction when scanning with the translation stage - Zoom</p> <p><span class="figure-number">Figure 4: </span>X relative displacement of the sample with respect to the marble</p>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
plot<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">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-highlight-numbers-number">1e6</span><span class="org-type">*</span>lsim<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>s, z_ty<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>z_ty<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>, z_ty<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>;
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">'</span>Z Relative Displacement <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>;
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>;
</pre>
</div>
<div id="org8cb0d85" class="figure">
<p><img src="figs/z_relative_disp.png" alt="z_relative_disp.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Z relative disp of the sample with respect to the marble</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orgaa04452" class="outline-3"> <div id="outline-container-org121abe7" class="outline-3">
<h3 id="orgaa04452"><span class="section-number-3">2.4</span> Frequency Domain analysis</h3> <h3 id="org121abe7"><span class="section-number-3">2.4</span> Frequency Domain analysis</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
We get the typical ground velocity to compare with the velocities measured. We get the typical ground velocity to compare with the velocities measured.
@ -547,19 +570,30 @@ 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, 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>, 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"><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>;
<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>; <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>;
<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>; <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>;
</pre> </pre>
</div> </div>
<p>
And finally for the relative velocity between the sample and the marble.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxz_ty_r, <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><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>;
<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>;
<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>;
</pre>
</div>
<p> <p>
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="#org5fbea6a">6</a> compares the marble velocity in the east direction when scanning and when Ty is OFF</li> <li>figure <a href="#org72aa28e">6</a> compares the marble velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#org2010bd4">7</a> compares the sample velocity in the east direction when scanning and when Ty is OFF</li> <li>figure <a href="#orgd1eabc6">7</a> compares the sample velocity in the east direction when scanning and when Ty is OFF</li>
<li>figure <a href="#org40d5824">8</a> shows the marble and sample velocities in the Z direction when scanning with the translation stage</li> <li>figure <a href="#org22a9555">8</a> shows the marble and sample velocities in the Z direction when scanning with the translation stage</li>
<li>figure <a href="#org3c552b8">9</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</li>
</ul> </ul>
<div class="org-src-container"> <div class="org-src-container">
@ -578,7 +612,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="org5fbea6a" class="figure"> <div id="org72aa28e" 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>
@ -601,7 +635,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="org2010bd4" class="figure"> <div id="orgd1eabc6" 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>
@ -624,23 +658,45 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="org40d5824" class="figure"> <div id="org22a9555" 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 class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
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', 'Ty OFF - Relative - E'</span><span class="org-rainbow-delimiters-depth-1">)</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>, 'DisplayName', 'Ty <span class="org-highlight-numbers-number">1Hz</span> <span class="org-type">-</span> Relative <span class="org-type">-</span> E'<span class="org-rainbow-delimiters-depth-1">)</span>;
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-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>;
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>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</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>;
</pre>
</div>
<div id="org3c552b8" class="figure">
<p><img src="figs/asd_e_relative.png" alt="asd_e_relative.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Amplitude spectral density of the measured relative velocity in the X direction</p>
</div>
</div> </div>
</div> </div>
<div id="outline-container-org0579205" class="outline-3"> <div id="outline-container-org9bb2e68" class="outline-3">
<h3 id="org0579205"><span class="section-number-3">2.5</span> Transfer function from marble motion in the East direction to sample motion in the East direction</h3> <h3 id="org9bb2e68"><span class="section-number-3">2.5</span> Transfer function from marble motion in the East direction to sample motion in the East direction</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<p> <p>
Let's compute the transfer function for the marble velocity in the east direction to the sample velocity in the east direction. Let's compute the transfer function for the marble velocity in the east direction to the sample velocity in the east direction.
</p> </p>
<p> <p>
We first plot the time domain motions when every stage is off (figure <a href="#org8d02455">9</a>). We first plot the time domain motions when every stage is off (figure <a href="#org52fbb44">10</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -656,10 +712,10 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org8d02455" class="figure"> <div id="org52fbb44" class="figure">
<p><img src="figs/east_marble_sample.png" alt="east_marble_sample.png" /> <p><img src="figs/east_marble_sample.png" alt="east_marble_sample.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Velocity in the east direction of the marble and sample when all the stages are OFF</p> <p><span class="figure-number">Figure 10: </span>Velocity in the east direction of the marble and sample when all the stages are OFF</p>
</div> </div>
@ -677,27 +733,27 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
<p> <p>
The result is shown on figure <a href="#org1b6386e">10</a>. The result is shown on figure <a href="#org2cef692">11</a>.
</p> </p>
<div id="org1b6386e" class="figure"> <div id="org2cef692" class="figure">
<p><img src="figs/tf_east_marble_sample.png" alt="tf_east_marble_sample.png" /> <p><img src="figs/tf_east_marble_sample.png" alt="tf_east_marble_sample.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Estimation of the transfer function from marble velocity in the east direction to sample velocity in the east direction</p> <p><span class="figure-number">Figure 11: </span>Estimation of the transfer function from marble velocity in the east direction to sample velocity in the east direction</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org540379b" class="outline-3"> <div id="outline-container-org3557c4c" class="outline-3">
<h3 id="org540379b"><span class="section-number-3">2.6</span> Position of the translation stage and Current</h3> <h3 id="org3557c4c"><span class="section-number-3">2.6</span> Position of the translation stage and Current</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-6">
<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-orgf590ed7" class="outline-4"> <div id="outline-container-orgda3ab01" class="outline-4">
<h4 id="orgf590ed7"><span class="section-number-4">2.6.1</span> Data pre-processing</h4> <h4 id="orgda3ab01"><span class="section-number-4">2.6.1</span> Data pre-processing</h4>
<div class="outline-text-4" id="text-2-6-1"> <div class="outline-text-4" id="text-2-6-1">
<p> <p>
Let's look at at the start of the csv file. Let's look at at the start of the csv file.
@ -720,13 +776,13 @@ We then load this <code>cvs</code> file starting at line 29.
</div> </div>
</div> </div>
<div id="outline-container-org0f186e6" class="outline-4"> <div id="outline-container-orgc12f6b8" class="outline-4">
<h4 id="org0f186e6"><span class="section-number-4">2.6.2</span> Time domain data</h4> <h4 id="orgc12f6b8"><span class="section-number-4">2.6.2</span> Time domain data</h4>
<div class="outline-text-4" id="text-2-6-2"> <div class="outline-text-4" id="text-2-6-2">
<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="#org064acde">11</a>. The result is shown on figure <a href="#org1e26376">12</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -740,21 +796,21 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org064acde" class="figure"> <div id="org1e26376" 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 11: </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="org33956fc" class="figure"> <div id="orgbbcae78" 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 12: </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="#org436454e">13</a>. We also plot the current as function of the time on figure <a href="#org12f65b1">14</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -768,24 +824,24 @@ xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org436454e" class="figure"> <div id="org12f65b1" 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 13: </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="org9e37388" class="figure"> <div id="orgc92d4f4" 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 14: </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>
</div> </div>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org4f5f98f" class="outline-3"> <div id="outline-container-orgd2aa958" class="outline-3">
<h3 id="org4f5f98f"><span class="section-number-3">2.7</span> Conclusion</h3> <h3 id="orgd2aa958"><span class="section-number-3">2.7</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-7"> <div class="outline-text-3" id="text-2-7">
<div class="important"> <div class="important">
<ul class="org-ul"> <ul class="org-ul">
@ -800,7 +856,7 @@ 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: 2019-05-15 mer. 14:37</p> <p class="date">Created: 2019-05-15 mer. 16:35</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>

96
disturbance-ty/index.org
View File

@ -131,6 +131,10 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
#+end_src #+end_src
** Time domain plots ** Time domain plots
We plot the measured velocity of the marble and sample in the vertical direction (figure [[fig:ty_z_time]]) and in the X direction (figure [[fig:ty_e_time]]).
We also integrate the relative velocity to obtain the relative displacement (figure [[fig:x_relative_disp]] in the X direction and figure [[fig:z_relative_disp]] in the Z direction).
#+begin_src matlab #+begin_src matlab
figure; figure;
hold on; hold on;
@ -138,7 +142,7 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
plot(z_ty(:, 3), z_ty(:, 2), 'DisplayName', 'Sample - Z'); plot(z_ty(:, 3), z_ty(:, 2), 'DisplayName', 'Sample - Z');
hold off; hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]); xlim([0, 2]);
legend('Location', 'northeast'); legend('Location', 'northeast');
#+end_src #+end_src
@ -153,22 +157,6 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
#+RESULTS: fig:ty_z_time #+RESULTS: fig:ty_z_time
[[file:figs/ty_z_time.png]] [[file:figs/ty_z_time.png]]
#+begin_src matlab :exports none
xlim([0, 1]);
#+end_src
#+NAME: fig:ty_z_time_zoom
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_z_time_zoom.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_z_time_zoom
#+CAPTION: Z velocity of the sample and marble when scanning with the translation stage - Zoom
#+RESULTS: fig:ty_z_time_zoom
[[file:figs/ty_z_time_zoom.png]]
#+begin_src matlab #+begin_src matlab
figure; figure;
hold on; hold on;
@ -176,7 +164,7 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
plot(e_ty(:, 3), e_ty(:, 2), 'DisplayName', 'Sample - X'); plot(e_ty(:, 3), e_ty(:, 2), 'DisplayName', 'Sample - X');
hold off; hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]); xlim([0, 2]);
legend('Location', 'northeast'); legend('Location', 'northeast');
#+end_src #+end_src
@ -191,20 +179,41 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
#+RESULTS: fig:ty_e_time #+RESULTS: fig:ty_e_time
[[file:figs/ty_e_time.png]] [[file:figs/ty_e_time.png]]
#+begin_src matlab :exports none #+begin_src matlab
xlim([0, 1]); figure;
plot(e_ty(:, 3), 1e6*lsim(1/s, e_ty(:, 2)-e_ty(:, 1), e_ty(:, 3)));
xlabel('Time [s]'); ylabel('X Relative Displacement [$\mu m$]');
xlim([0, 2]);
#+end_src #+end_src
#+NAME: fig:ty_e_time_zoom #+NAME: fig:x_relative_disp
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes #+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/ty_e_time_zoom.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png") #+begin_src matlab :var filepath="figs/x_relative_disp.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>> <<plt-matlab>>
#+end_src #+end_src
#+NAME: fig:ty_e_time_zoom #+NAME: fig:x_relative_disp
#+CAPTION: Velocity of the sample and marble in the east direction when scanning with the translation stage - Zoom #+CAPTION: X relative displacement of the sample with respect to the marble
#+RESULTS: fig:ty_e_time_zoom #+RESULTS: fig:x_relative_disp
[[file:figs/ty_e_time_zoom.png]] [[file:figs/x_relative_disp.png]]
#+begin_src matlab
figure;
plot(z_ty(:, 3), 1e6*lsim(1/s, z_ty(:, 2)-z_ty(:, 1), z_ty(:, 3)));
xlabel('Time [s]'); ylabel('Z Relative Displacement [$\mu m$]');
xlim([0, 2]);
#+end_src
#+NAME: fig:z_relative_disp
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/z_relative_disp.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:z_relative_disp
#+CAPTION: Z relative disp of the sample with respect to the marble
#+RESULTS: fig:z_relative_disp
[[file:figs/z_relative_disp.png]]
** Frequency Domain analysis ** Frequency Domain analysis
We get the typical ground velocity to compare with the velocities measured. We get the typical ground velocity to compare with the velocities measured.
@ -232,15 +241,23 @@ 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.
#+begin_src matlab #+begin_src matlab
[pxz_ty_s, f] = pwelch(z_ty(:, 2), win, [], [], Fs); [pxz_ty_s, ~] = pwelch(z_ty(:, 2), win, [], [], Fs);
[pxe_ty_s, ~] = pwelch(e_ty(:, 2), win, [], [], Fs); [pxe_ty_s, ~] = pwelch(e_ty(:, 2), win, [], [], Fs);
[pxe_of_s, ~] = pwelch(e_of(:, 2), win, [], [], Fs); [pxe_of_s, ~] = pwelch(e_of(:, 2), win, [], [], Fs);
#+end_src #+end_src
And finally for the relative velocity between the sample and the marble.
#+begin_src matlab
[pxz_ty_r, ~] = pwelch(z_ty(:, 2)-z_ty(:, 1), win, [], [], Fs);
[pxe_ty_r, ~] = pwelch(e_ty(:, 2)-e_ty(:, 1), win, [], [], Fs);
[pxe_of_r, ~] = pwelch(e_of(:, 2)-e_of(:, 1), win, [], [], Fs);
#+end_src
And we plot the ASD of the measured velocities: And we plot the ASD of the measured velocities:
- figure [[fig:asd_east_marble]] compares the marble velocity in the east direction when scanning and when Ty is OFF - figure [[fig:asd_east_marble]] compares the marble velocity in the east direction when scanning and when Ty is OFF
- figure [[fig:asd_east_sample]] compares the sample velocity in the east direction when scanning and when Ty is OFF - figure [[fig:asd_east_sample]] compares the sample velocity in the east direction when scanning and when Ty is OFF
- figure [[fig:asd_z_direction]] shows the marble and sample velocities in the Z direction when scanning with the translation stage - figure [[fig:asd_z_direction]] shows the marble and sample velocities in the Z direction when scanning with the translation stage
- figure [[fig:asd_e_relative]] 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
#+begin_src matlab #+begin_src matlab
figure; figure;
@ -319,6 +336,31 @@ And we plot the ASD of the measured velocities:
#+RESULTS: fig:asd_z_direction #+RESULTS: fig:asd_z_direction
[[file:figs/asd_z_direction.png]] [[file:figs/asd_z_direction.png]]
#+begin_src matlab
figure;
hold on;
plot(f, sqrt(pxe_of_r), 'DisplayName', 'Ty OFF - Relative - E');
plot(f, sqrt(pxe_ty_r), 'DisplayName', 'Ty 1Hz - Relative - E');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'northwest');
xlim([0.1, 500]);
#+end_src
#+NAME: fig:asd_e_relative
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/asd_e_relative.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:asd_e_relative
#+CAPTION: Amplitude spectral density of the measured relative velocity in the X direction
#+RESULTS: fig:asd_e_relative
[[file:figs/asd_e_relative.png]]
** Transfer function from marble motion in the East direction to sample motion in the East direction ** Transfer function from marble motion in the East direction to sample motion in the East direction
Let's compute the transfer function for the marble velocity in the east direction to the sample velocity in the east direction. Let's compute the transfer function for the marble velocity in the east direction to the sample velocity in the east direction.

70
disturbance-ty/matlab/disturbance_ty.m
View File

@ -23,6 +23,10 @@ e_ty(:, 2) = voltageToVelocityL22(e_ty(:, 2), e_ty(:, 3), 40);
e_of(:, 2) = voltageToVelocityL22(e_of(:, 2), e_of(:, 3), 40); e_of(:, 2) = voltageToVelocityL22(e_of(:, 2), e_of(:, 3), 40);
% Time domain plots % Time domain plots
% We plot the measured velocity of the marble and sample in the vertical direction (figure [[fig:ty_z_time]]) and in the X direction (figure [[fig:ty_e_time]]).
% We also integrate the relative velocity to obtain the relative displacement (figure [[fig:x_relative_disp]] in the X direction and figure [[fig:z_relative_disp]] in the Z direction).
figure; figure;
hold on; hold on;
@ -30,7 +34,7 @@ plot(z_ty(:, 3), z_ty(:, 1), 'DisplayName', 'Marble - Z');
plot(z_ty(:, 3), z_ty(:, 2), 'DisplayName', 'Sample - Z'); plot(z_ty(:, 3), z_ty(:, 2), 'DisplayName', 'Sample - Z');
hold off; hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]); xlim([0, 2]);
legend('Location', 'northeast'); legend('Location', 'northeast');
@ -41,24 +45,13 @@ legend('Location', 'northeast');
% [[file:figs/ty_z_time.png]] % [[file:figs/ty_z_time.png]]
xlim([0, 1]);
% #+NAME: fig:ty_z_time_zoom
% #+CAPTION: Z velocity of the sample and marble when scanning with the translation stage - Zoom
% #+RESULTS: fig:ty_z_time_zoom
% [[file:figs/ty_z_time_zoom.png]]
figure; figure;
hold on; hold on;
plot(e_ty(:, 3), e_ty(:, 1), 'DisplayName', 'Marble - X'); plot(e_ty(:, 3), e_ty(:, 1), 'DisplayName', 'Marble - X');
plot(e_ty(:, 3), e_ty(:, 2), 'DisplayName', 'Sample - X'); plot(e_ty(:, 3), e_ty(:, 2), 'DisplayName', 'Sample - X');
hold off; hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]'); xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]); xlim([0, 2]);
legend('Location', 'northeast'); legend('Location', 'northeast');
@ -69,7 +62,23 @@ legend('Location', 'northeast');
% [[file:figs/ty_e_time.png]] % [[file:figs/ty_e_time.png]]
xlim([0, 1]) figure;
plot(e_ty(:, 3), 1e6*lsim(1/s, e_ty(:, 2)-e_ty(:, 1), e_ty(:, 3)));
xlabel('Time [s]'); ylabel('X Relative Displacement [$\mu m$]');
xlim([0, 2]);
% #+NAME: fig:x_relative_disp
% #+CAPTION: X relative displacement of the sample with respect to the marble
% #+RESULTS: fig:x_relative_disp
% [[file:figs/x_relative_disp.png]]
figure;
plot(z_ty(:, 3), 1e6*lsim(1/s, z_ty(:, 2)-z_ty(:, 1), z_ty(:, 3)));
xlabel('Time [s]'); ylabel('Z Relative Displacement [$\mu m$]');
xlim([0, 2]);
% Frequency Domain analysis % Frequency Domain analysis
% We get the typical ground velocity to compare with the velocities measured. % We get the typical ground velocity to compare with the velocities measured.
@ -100,16 +109,25 @@ win = hanning(ceil(10*Fs));
% And for the geophone located at the sample position. % And for the geophone located at the sample position.
[pxz_ty_s, f] = pwelch(z_ty(:, 2), win, [], [], Fs); [pxz_ty_s, ~] = pwelch(z_ty(:, 2), win, [], [], Fs);
[pxe_ty_s, ~] = pwelch(e_ty(:, 2), win, [], [], Fs); [pxe_ty_s, ~] = pwelch(e_ty(:, 2), win, [], [], Fs);
[pxe_of_s, ~] = pwelch(e_of(:, 2), win, [], [], Fs); [pxe_of_s, ~] = pwelch(e_of(:, 2), win, [], [], Fs);
% And finally for the relative velocity between the sample and the marble.
[pxz_ty_r, ~] = pwelch(z_ty(:, 2)-z_ty(:, 1), win, [], [], Fs);
[pxe_ty_r, ~] = pwelch(e_ty(:, 2)-e_ty(:, 1), win, [], [], Fs);
[pxe_of_r, ~] = pwelch(e_of(:, 2)-e_of(:, 1), win, [], [], Fs);
% And we plot the ASD of the measured velocities: % And we plot the ASD of the measured velocities:
% - figure [[fig:asd_east_marble]] compares the marble velocity in the east direction when scanning and when Ty is OFF % - figure [[fig:asd_east_marble]] compares the marble velocity in the east direction when scanning and when Ty is OFF
% - figure [[fig:asd_east_sample]] compares the sample velocity in the east direction when scanning and when Ty is OFF % - figure [[fig:asd_east_sample]] compares the sample velocity in the east direction when scanning and when Ty is OFF
% - figure [[fig:asd_z_direction]] shows the marble and sample velocities in the Z direction when scanning with the translation stage % - figure [[fig:asd_z_direction]] shows the marble and sample velocities in the Z direction when scanning with the translation stage
% - figure [[fig:asd_e_relative]] 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
figure; figure;
@ -162,7 +180,27 @@ plot(f_gm, sqrt(pxx_gm), 'k--', 'DisplayName', 'Ground Motion');
hold off; hold off;
set(gca, 'xscale', 'log'); set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$') xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'northwest');
xlim([0.1, 500]);
% #+NAME: fig:asd_z_direction
% #+CAPTION: 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
% #+RESULTS: fig:asd_z_direction
% [[file:figs/asd_z_direction.png]]
figure;
hold on;
plot(f, sqrt(pxe_of_r), 'DisplayName', 'Ty OFF - Relative - E');
plot(f, sqrt(pxe_ty_r), 'DisplayName', 'Ty 1Hz - Relative - E');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'northwest'); legend('Location', 'northwest');
xlim([0.1, 500]); xlim([0.1, 500]);