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</div><div id="content">
<h1 class="title">Measurements</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org27cbd90">1. Experimental conditions</a></li>
<li><a href="#orgf2bb684">2. Measurements procedure</a></li>
<li><a href="#org604de72">3. Measurement Channels</a></li>
<li><a href="#orgee6f009">4. Experiments</a></li>
<li><a href="#orgc91528e">5. Data Analysis</a>
<ul>
<li><a href="#org64c9d55">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="#orgb043f14">5.3. Y-direction FRF</a></li>
<li><a href="#org63f36f4">5.4. Z-direction FRF</a></li>
<li><a href="#org9fd4cff">5.5. Save the processed data</a></li>
</ul>
</li>
<li><a href="#orge5ef1a0">6. Results</a></li>
</ul>
</div>
</div>
<div id="outline-container-org27cbd90" class="outline-2">
<h2 id="org27cbd90"><span class="section-number-2">1</span> Experimental conditions</h2>
<div class="outline-text-2" id="text-1">
<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">2018-01-12</td>
</tr>
<tr>
<td class="org-left"><b>Sensors</b></td>
<td class="org-left">Geophones</td>
</tr>
<tr>
<td class="org-left"><b>Excitation</b></td>
<td class="org-left">Instrumented Hammer</td>
</tr>
<tr>
<td class="org-left"><b>Location</b></td>
<td class="org-left">Laboratory</td>
</tr>
<tr>
<td class="org-left"><b>Notes</b></td>
<td class="org-left">Unglued Granite</td>
</tr>
</tbody>
</table>
<ul class="org-ul">
<li>The granite is not glued to the floor</li>
<li>FS = 512Hz</li>
<li>Made by Marc Lesourd on the 12 of January 2018</li>
</ul>
<p>
<b>Goal</b>:
Obtain better coherence at low frequency.
</p>
</div>
</div>
<div id="outline-container-orgf2bb684" class="outline-2">
<h2 id="orgf2bb684"><span class="section-number-2">2</span> Measurements procedure</h2>
<div class="outline-text-2" id="text-2">
<p>
<b>Geophones</b>
L-28LB geophones (table <a href="#org27c9f01">1</a>) are placed on
</p>
<ul class="org-ul">
<li>Marle</li>
<li>Tilt Stage</li>
<li>Top of Hexapod</li>
</ul>
<table id="org27c9f01" 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>
<colgroup>
<col class="org-left" />
<col class="org-right" />
</colgroup>
<tbody>
<tr>
<td class="org-left">Natural Frequency [Hz]</td>
<td class="org-right">4.5</td>
</tr>
<tr>
<td class="org-left">Weight [g]</td>
<td class="org-right">140</td>
</tr>
<tr>
<td class="org-left">Sensitivity [V/(m/s)]</td>
<td class="org-right">31.3</td>
</tr>
</tbody>
</table>
<p>
The structure is excited using an <b>instrumented hammer</b> with impacts on
</p>
<ul class="org-ul">
<li>Marble X-Y-Z</li>
<li>Hexapod X-Y-Z</li>
</ul>
</div>
</div>
<div id="outline-container-org604de72" class="outline-2">
<h2 id="org604de72"><span class="section-number-2">3</span> Measurement Channels</h2>
<div class="outline-text-2" id="text-3">
<table id="org98c14df" 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>
<colgroup>
<col class="org-right" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Ch. nb</th>
<th scope="col" class="org-left">Element</th>
<th scope="col" class="org-left">Location</th>
<th scope="col" class="org-left">Direction</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">Hammer</td>
<td class="org-left">variable</td>
<td class="org-left"> </td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-right">2</td>
<td class="org-left">Geophone</td>
<td class="org-left">Marble</td>
<td class="org-left">X-Y-Z</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">Geophone</td>
<td class="org-left">Tilt stage</td>
<td class="org-left">X-Y-Z</td>
</tr>
<tr>
<td class="org-right">4</td>
<td class="org-left">Geophone</td>
<td class="org-left">Top of Hexapod</td>
<td class="org-left">X-Y-Z</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgee6f009" class="outline-2">
<h2 id="orgee6f009"><span class="section-number-2">4</span> Experiments</h2>
<div class="outline-text-2" id="text-4">
<table id="orgd57c63a" 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>
<colgroup>
<col class="org-right" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Meas. nb</th>
<th scope="col" class="org-left">Location</th>
<th scope="col" class="org-left">Direction</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">Marble</td>
<td class="org-left">X</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">Hexapod</td>
<td class="org-left">X</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-right">3</td>
<td class="org-left">Marble</td>
<td class="org-left">Y</td>
</tr>
<tr>
<td class="org-right">4</td>
<td class="org-left">Hexapod</td>
<td class="org-left">Y</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-right">5</td>
<td class="org-left">Marble</td>
<td class="org-left">Z</td>
</tr>
<tr>
<td class="org-right">6</td>
<td class="org-left">Hexapod</td>
<td class="org-left">Z</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgc91528e" class="outline-2">
<h2 id="orgc91528e"><span class="section-number-2">5</span> Data Analysis</h2>
<div class="outline-text-2" id="text-5">
</div>
<div id="outline-container-org64c9d55" class="outline-3">
<h3 id="org64c9d55"><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">
<p>
The Geophone sensitivity is defined below:
</p>
<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>
ksi = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">38</span>;
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>
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>
</pre>
</div>
<p>
We then:
</p>
<ul class="org-ul">
<li>load the data</li>
<li>add a minus sign when needed</li>
<li>integrate the signal to have displacement instead of velocity</li>
<li>scaled with the sensitivity of the Geophone</li>
</ul>
<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>
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>
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;
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>
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<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-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-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>
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>
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<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-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-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>
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>
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<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-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-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>
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>
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<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-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-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>
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>
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<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-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-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>
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>
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<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-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-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>
</pre>
</div>
<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>
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<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-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-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>
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>
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<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-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-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>
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>
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<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-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-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>
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>
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<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-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-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>
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>
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<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-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-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>
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>
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<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-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-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>
</pre>
</div>
</div>
</div>
<div id="outline-container-org528d8bd" class="outline-3">
<h3 id="org528d8bd"><span class="section-number-3">5.2</span> X-direction FRF</h3>
<div class="outline-text-3" id="text-5-2">
<div id="orgbe46711" class="figure">
<p><img src="figs/marble_x_frf.png" alt="marble_x_frf.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Response to a force applied on the marble in the X direction</p>
</div>
<div id="org4005c39" class="figure">
<p><img src="figs/hexa_x_frf.png" alt="hexa_x_frf.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Response to a force applied on the hexa in the X direction</p>
</div>
</div>
</div>
<div id="outline-container-orgb043f14" class="outline-3">
<h3 id="orgb043f14"><span class="section-number-3">5.3</span> Y-direction FRF</h3>
<div class="outline-text-3" id="text-5-3">
<div id="org959d073" class="figure">
<p><img src="figs/marble_y_frf.png" alt="marble_y_frf.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Response to a force applied on the marble in the Y direction</p>
</div>
<div id="orge15a0ff" class="figure">
<p><img src="figs/hexa_y_frf.png" alt="hexa_y_frf.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Response to a force applied on the hexa in the Y direction</p>
</div>
</div>
</div>
<div id="outline-container-org63f36f4" class="outline-3">
<h3 id="org63f36f4"><span class="section-number-3">5.4</span> Z-direction FRF</h3>
<div class="outline-text-3" id="text-5-4">
<div id="orgf2ca329" class="figure">
<p><img src="figs/marble_z_frf.png" alt="marble_z_frf.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Response to a force applied on the marble in the Z direction</p>
</div>
<div id="orgbb33b62" class="figure">
<p><img src="figs/hexa_z_frf.png" alt="hexa_z_frf.png" />
</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 id="outline-container-org9fd4cff" class="outline-3">
<h3 id="org9fd4cff"><span class="section-number-3">5.5</span> Save the processed data</h3>
<div class="outline-text-3" id="text-5-5">
<p>
Finally, we save the processed data.
</p>
<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>
<span class="org-string">'freq_frf'</span>, <span class="org-underline">...</span>
<span class="org-string">'frf_marble_x'</span>, <span class="org-underline">...</span>
<span class="org-string">'frf_marble_y'</span>, <span class="org-underline">...</span>
<span class="org-string">'frf_marble_z'</span>, <span class="org-underline">...</span>
<span class="org-string">'frf_hexa_x'</span>, <span class="org-underline">...</span>
<span class="org-string">'frf_hexa_y'</span>, <span class="org-underline">...</span>
<span class="org-string">'frf_hexa_z'</span><span class="org-rainbow-delimiters-depth-1">)</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>
<span class="org-string">'freq_frf'</span>, <span class="org-underline">...</span>
<span class="org-string">'coh_marble_x'</span>, <span class="org-underline">...</span>
<span class="org-string">'coh_marble_y'</span>, <span class="org-underline">...</span>
<span class="org-string">'coh_marble_z'</span>, <span class="org-underline">...</span>
<span class="org-string">'coh_hexa_x'</span>, <span class="org-underline">...</span>
<span class="org-string">'coh_hexa_y'</span>, <span class="org-underline">...</span>
<span class="org-string">'coh_hexa_z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-orge5ef1a0" class="outline-2">
<h2 id="orge5ef1a0"><span class="section-number-2">6</span> Results</h2>
<div class="outline-text-2" id="text-6">
<div class="important">
<ul class="org-ul">
<li>Resonances at 42Hz, 70Hz and 125Hz have been identified</li>
<li>The coherence is much better than when using accelerometers</li>
</ul>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-14 mar. 23:06</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>