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Add data analysis of marble dynamics

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Thomas Dehaeze 2019-05-14 14:11:31 +02:00
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disturbance-sr-rz/index.html
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2019-05-13 lun. 13:24 --> <!-- 2019-05-14 mar. 10:53 -->
<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 Slip-Ring and the Spindle</title> <title>Vibrations induced by the Slip-Ring and the Spindle</title>
@ -258,22 +258,26 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org371ff02">1. Experimental Setup</a></li> <li><a href="#orgae707b1">1. Experimental Setup</a></li>
<li><a href="#orgecddaf0">2. Data Analysis</a> <li><a href="#org78dded5">2. Data Analysis</a>
<ul> <ul>
<li><a href="#orgc4627de">2.1. Load data</a></li> <li><a href="#orgaf48712">2.1. Load data</a></li>
<li><a href="#orgb8a6467">2.2. Time domain plots</a></li> <li><a href="#orga3184c9">2.2. Time domain plots</a></li>
<li><a href="#org27d9d17">2.3. Frequency Domain</a></li> <li><a href="#org66e3cd4">2.3. Frequency Domain</a></li>
<li><a href="#org6127e14">2.4. Conclusion</a></li> <li><a href="#orgbe56ee4">2.4. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org371ff02" class="outline-2"> <div id="outline-container-orgae707b1" class="outline-2">
<h2 id="org371ff02"><span class="section-number-2">1</span> Experimental Setup</h2> <h2 id="orgae707b1"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
</div>
<ol class="org-ol">
<li><a id="orgd4a8f25"></a>Setup<br />
<div class="outline-text-6" id="text-1-0-0-0-1">
<p> <p>
All the stages are OFF. All the stages are OFF.
</p> </p>
@ -306,7 +310,9 @@ A first order low pass filter is also added at the input of the voltage amplifie
<li>Identify the vibrations induced by the rotation of the Slip-Ring and Spindle</li> <li>Identify the vibrations induced by the rotation of the Slip-Ring and Spindle</li>
</ul> </ul>
<p> <p>
<b>Measurements</b>:
Three measurements are done: Three measurements are done:
</p> </p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
@ -377,23 +383,25 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table> </table>
<p> <p>
A movie showing the experiment is shown on figure <a href="#orgc3a4296">1</a>. A movie showing the experiment is shown on figure <a href="#orgb52ab90">1</a>.
</p> </p>
<div id="orgc3a4296" class="figure"> <div id="orgb52ab90" class="figure">
<p><img src="./img/VID_20190510_155655.gif" alt="VID_20190510_155655.gif" width="300px" /> <p><img src="./img/VID_20190510_155655.gif" alt="VID_20190510_155655.gif" width="300px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Movie of the experiment, rotation speed is 6rpm</p> <p><span class="figure-number">Figure 1: </span>Movie of the experiment, rotation speed is 6rpm</p>
</div> </div>
</div> </div>
</li>
</ol>
</div> </div>
<div id="outline-container-orgecddaf0" class="outline-2"> <div id="outline-container-org78dded5" class="outline-2">
<h2 id="orgecddaf0"><span class="section-number-2">2</span> Data Analysis</h2> <h2 id="org78dded5"><span class="section-number-2">2</span> Data Analysis</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
<a id="orgc194b61"></a> <a id="org66307ff"></a>
</p> </p>
<div class="note"> <div class="note">
@ -404,8 +412,8 @@ All the files (data and Matlab scripts) are accessible <a href="data/spindle_sli
</div> </div>
</div> </div>
<div id="outline-container-orgc4627de" class="outline-3"> <div id="outline-container-orgaf48712" class="outline-3">
<h3 id="orgc4627de"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="orgaf48712"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_024.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; of = of.data; <pre class="src src-matlab">of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_024.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; of = of.data;
@ -416,8 +424,8 @@ sp = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-s
</div> </div>
</div> </div>
<div id="outline-container-orgb8a6467" class="outline-3"> <div id="outline-container-orga3184c9" class="outline-3">
<h3 id="orgb8a6467"><span class="section-number-3">2.2</span> Time domain plots</h3> <h3 id="orga3184c9"><span class="section-number-3">2.2</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
@ -433,7 +441,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org914392c" class="figure"> <div id="orga435a98" class="figure">
<p><img src="figs/slip_ring_spindle_marble_time.png" alt="slip_ring_spindle_marble_time.png" /> <p><img src="figs/slip_ring_spindle_marble_time.png" alt="slip_ring_spindle_marble_time.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Measurement of the geophone located on the marble - Time domain</p> <p><span class="figure-number">Figure 2: </span>Measurement of the geophone located on the marble - Time domain</p>
@ -453,7 +461,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="orge34f253" class="figure"> <div id="org2bafcfa" class="figure">
<p><img src="figs/slip_ring_spindle_sample_time.png" alt="slip_ring_spindle_sample_time.png" /> <p><img src="figs/slip_ring_spindle_sample_time.png" alt="slip_ring_spindle_sample_time.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Measurement of the geophone at the sample location - Time domain</p> <p><span class="figure-number">Figure 3: </span>Measurement of the geophone at the sample location - Time domain</p>
@ -461,8 +469,8 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-org27d9d17" class="outline-3"> <div id="outline-container-org66e3cd4" class="outline-3">
<h3 id="org27d9d17"><span class="section-number-3">2.3</span> Frequency Domain</h3> <h3 id="org66e3cd4"><span class="section-number-3">2.3</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
We first compute some parameters that will be used for the PSD computation. We first compute some parameters that will be used for the PSD computation.
@ -504,8 +512,8 @@ And for the geophone located at the sample position.
And we plot the ASD of the measured signals: And we plot the ASD of the measured signals:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>figure <a href="#orgf453585">4</a> for the geophone located on the marble</li> <li>figure <a href="#org3fb6d61">4</a> for the geophone located on the marble</li>
<li>figure <a href="#org3aa1b94">5</a> for the geophone at the sample position</li> <li>figure <a href="#orge9619ee">5</a> for the geophone at the sample position</li>
</ul> </ul>
<div class="org-src-container"> <div class="org-src-container">
@ -524,7 +532,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="orgf453585" class="figure"> <div id="org3fb6d61" class="figure">
<p><img src="figs/sr_sp_psd_marble_compare.png" alt="sr_sp_psd_marble_compare.png" /> <p><img src="figs/sr_sp_psd_marble_compare.png" alt="sr_sp_psd_marble_compare.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Comparison of the ASD of the measured voltage from the Geophone on the marble</p> <p><span class="figure-number">Figure 4: </span>Comparison of the ASD of the measured voltage from the Geophone on the marble</p>
@ -546,7 +554,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="org3aa1b94" class="figure"> <div id="orge9619ee" class="figure">
<p><img src="figs/sr_sp_psd_sample_compare.png" alt="sr_sp_psd_sample_compare.png" /> <p><img src="figs/sr_sp_psd_sample_compare.png" alt="sr_sp_psd_sample_compare.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Comparison of the ASD of the measured voltage from the Geophone at the sample location</p> <p><span class="figure-number">Figure 5: </span>Comparison of the ASD of the measured voltage from the Geophone at the sample location</p>
@ -554,8 +562,8 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-org6127e14" class="outline-3"> <div id="outline-container-orgbe56ee4" class="outline-3">
<h3 id="org6127e14"><span class="section-number-3">2.4</span> Conclusion</h3> <h3 id="orgbe56ee4"><span class="section-number-3">2.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<div class="important"> <div class="important">
<p> <p>
@ -574,7 +582,7 @@ There is a huge peak at 24Hz on the sample vibration but not on the granite vibr
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-13 lun. 13:24</p> <p class="date">Created: 2019-05-14 mar. 10:53</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>

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:END: :END:
* Experimental Setup * Experimental Setup
*Setup*:
All the stages are OFF. All the stages are OFF.
Two geophone are use: Two geophone are use:
@ -43,9 +44,12 @@ Two voltage amplifiers are used, their setup is:
A first order low pass filter is also added at the input of the voltage amplifiers. A first order low pass filter is also added at the input of the voltage amplifiers.
*Goal*: *Goal*:
- Identify the vibrations induced by the rotation of the Slip-Ring and Spindle - Identify the vibrations induced by the rotation of the Slip-Ring and Spindle
*Measurements*:
Three measurements are done: Three measurements are done:
| Measurement File | Description | | Measurement File | Description |
|--------------------+----------------------------------------------------------------------| |--------------------+----------------------------------------------------------------------|

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#+TITLE:Measurements #+TITLE:Vibrations induced by both the translation stage and the slip-ring
:DRAWER: :DRAWER:
#+STARTUP: overview #+STARTUP: overview

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<h1 class="title">Vibrations induced by the Slip-Ring and the Spindle</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org2ead7e9">1. Experimental Setup</a></li>
<li><a href="#org8e5682f">2. Data Analysis</a>
<ul>
<li><a href="#org71d31f6">2.1. Load data</a></li>
<li><a href="#org36715e9">2.2. Time domain plots</a></li>
<li><a href="#org32ab030">2.3. Compute the power spectral densities</a></li>
<li><a href="#orgb8b258a">2.4. Compute the transfer function from floor motion to ground motion</a></li>
<li><a href="#org806c2da">2.5. Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org2ead7e9" class="outline-2">
<h2 id="org2ead7e9"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1">
<p>
<b>Setup</b>:
One geophone is located on the marble, the other one on the floor (see figure <a href="#org04c2f7b">1</a>).
</p>
<p>
Two geophone are use:
</p>
<ul class="org-ul">
<li>One on the floor (corresponding to the first column in the data)</li>
<li>One at the marble location (corresponding to the second column in the data)</li>
</ul>
<p>
Two voltage amplifiers are used, their setup is:
</p>
<ul class="org-ul">
<li>gain of 60dB</li>
<li>AC/DC switch on AC</li>
<li>Low pass filter at 1kHz</li>
</ul>
<p>
A first order low pass filter is also added at the input of the voltage amplifiers.
</p>
<p>
<b>Goal</b>:
</p>
<ul class="org-ul">
<li>Identify the marble dynamics in all the directions</li>
</ul>
<p>
<b>Measurements</b>:
Three measurements are done:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Measurement File</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>mat/data_037.mat</code></td>
<td class="org-left">Z direction</td>
</tr>
<tr>
<td class="org-left"><code>mat/data_038.mat</code></td>
<td class="org-left">N direction</td>
</tr>
<tr>
<td class="org-left"><code>mat/data_039.mat</code></td>
<td class="org-left">E direction</td>
</tr>
</tbody>
</table>
<p>
Each of the measurement <code>mat</code> file contains one <code>data</code> array with 3 columns:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Column number</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">Geophone - Floor</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">Geophone - Marble</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">Time</td>
</tr>
</tbody>
</table>
<div id="org04c2f7b" class="figure">
<p><img src="./img/IMG_20190513_161729.jpg" alt="IMG_20190513_161729.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 1: </span>Picture of the experimental setup</p>
</div>
<div id="orge39c59f" class="figure">
<p><img src="./img/IMG_20190513_161718.jpg" alt="IMG_20190513_161718.jpg" width="500px" />
</p>
<p><span class="figure-number">Figure 2: </span>Picture of the experimental setup</p>
</div>
</div>
</div>
<div id="outline-container-org8e5682f" class="outline-2">
<h2 id="org8e5682f"><span class="section-number-2">2</span> Data Analysis</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org4b537af"></a>
</p>
<div class="note">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/marble_dynamics.zip">here</a>.
</p>
</div>
</div>
<div id="outline-container-org71d31f6" class="outline-3">
<h3 id="org71d31f6"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">m_z = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_037.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_z = m_z.data;
m_n = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_038.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_n = m_n.data;
m_e = load<span class="org-rainbow-delimiters-depth-1">(</span>'mat<span class="org-type">/</span>data_039.mat', <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_e = m_e.data;
</pre>
</div>
</div>
</div>
<div id="outline-container-org36715e9" class="outline-3">
<h3 id="org36715e9"><span class="section-number-3">2.2</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Floor - Z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">2</span> <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - N'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Floor - N'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">2</span> <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - E'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Floor - E'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">2</span> <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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>
</div>
<div id="org10ef412" class="figure">
<p><img src="figs/marble_floor_motion_time.png" alt="marble_floor_motion_time.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Floor and ground motion</p>
</div>
</div>
</div>
<div id="outline-container-org32ab030" class="outline-3">
<h3 id="org32ab030"><span class="section-number-3">2.3</span> Compute the power spectral densities</h3>
<div class="outline-text-3" id="text-2-3">
<p>
We first compute some parameters that will be used for the PSD computation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = m_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>m_z<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
Then we compute the Power Spectral Density using <code>pwelch</code> function.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px_fz, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px_gz, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px_fn, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px_gn, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px_fe, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>px_ge, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<p>
The results are shown on figure <a href="#org0484222">4</a> for the Z direction, figure <a href="#org691dab7">5</a> for the north direction, and figure <a href="#org0047fc8">6</a> for the east direction.
</p>
<div id="org0484222" class="figure">
<p><img src="figs/floor_marble_psd_z.png" alt="floor_marble_psd_z.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - Z direction</p>
</div>
<div id="org691dab7" class="figure">
<p><img src="figs/floor_marble_psd_n.png" alt="floor_marble_psd_n.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - N direction</p>
</div>
<div id="org0047fc8" class="figure">
<p><img src="figs/floor_marble_psd_e.png" alt="floor_marble_psd_e.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - E direction</p>
</div>
</div>
</div>
<div id="outline-container-orgb8b258a" class="outline-3">
<h3 id="orgb8b258a"><span class="section-number-3">2.4</span> Compute the transfer function from floor motion to ground motion</h3>
<div class="outline-text-3" id="text-2-4">
<p>
We now compute the transfer function from the floor motion to the granite motion.
</p>
<p>
The result is shown on figure <a href="#orgac80e8a">7</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>TZ, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">-</span>m_z<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>TN, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">-</span>m_n<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>TE, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-type">-</span>m_e<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div id="orgac80e8a" class="figure">
<p><img src="figs/tf_granite.png" alt="tf_granite.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Transfer function from floor motion to granite motion</p>
</div>
</div>
</div>
<div id="outline-container-org806c2da" class="outline-3">
<h3 id="org806c2da"><span class="section-number-3">2.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-5">
<div class="important">
<ul class="org-ul">
<li>We see resonance of the granite at 33Hz in the horizontal directions</li>
<li>We see two resonances for the z direction: at 60Hz and 75Hz</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-14 mar. 11:25</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>

284
dynamical-meas-granite/index.org
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@ -29,17 +29,281 @@
#+PROPERTY: header-args:shell :eval no-export #+PROPERTY: header-args:shell :eval no-export
:END: :END:
* Experimental Setup
*Setup*:
One geophone is located on the marble, the other one on the floor (see figure [[fig:experimental_setup]]).
One geophone is located on the marble, the other one on the floor.
col1: floor Two geophone are use:
col2: marble - One on the floor (corresponding to the first column in the data)
- One at the marble location (corresponding to the second column in the data)
Each of the signal is amplified by voltage amplifier: Two voltage amplifiers are used, their setup is:
- 60db - gain of 60dB
- AC - AC/DC switch on AC
- 1kHz - Low pass filter at 1kHz
- meas 37: Z direction A first order low pass filter is also added at the input of the voltage amplifiers.
- meas 38: N direction
- meas 39: E direction *Goal*:
- Identify the marble dynamics in all the directions
*Measurements*:
Three measurements are done:
| Measurement File | Description |
|--------------------+-------------|
| =mat/data_037.mat= | Z direction |
| =mat/data_038.mat= | N direction |
| =mat/data_039.mat= | E direction |
Each of the measurement =mat= file contains one =data= array with 3 columns:
| Column number | Description |
|---------------+-------------------|
| 1 | Geophone - Floor |
| 2 | Geophone - Marble |
| 3 | Time |
#+name: fig:experimental_setup
#+caption: Picture of the experimental setup
#+attr_html: :width 500px
[[file:./img/IMG_20190513_161729.jpg]]
#+name: fig:experimental_setup_bix
#+caption: Picture of the experimental setup
#+attr_html: :width 500px
[[file:./img/IMG_20190513_161718.jpg]]
* Data Analysis
:PROPERTIES:
:header-args:matlab+: :tangle matlab/marble_dynamics.m
:header-args:matlab+: :comments org :mkdirp yes
:END:
<<sec:marble_dynamics>>
** ZIP file containing the data and matlab files :ignore:
#+begin_src bash :exports none :results none
if [ matlab/marble_dynamics.m -nt data/marble_dynamics.zip ]; then
cp matlab/marble_dynamics.m marble_dynamics.m;
zip data/marble_dynamics \
mat/data_037.mat \
mat/data_038.mat \
mat/data_039.mat \
marble_dynamics.m
rm marble_dynamics.m;
fi
#+end_src
#+begin_note
All the files (data and Matlab scripts) are accessible [[file:data/marble_dynamics.zip][here]].
#+end_note
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
** Load data
#+begin_src matlab
m_z = load('mat/data_037.mat', 'data'); m_z = m_z.data;
m_n = load('mat/data_038.mat', 'data'); m_n = m_n.data;
m_e = load('mat/data_039.mat', 'data'); m_e = m_e.data;
#+end_src
** Time domain plots
#+begin_src matlab
figure;
subplot(1, 3, 1);
hold on;
plot(m_z(:, 3), m_z(:, 2), 'DisplayName', 'Marble - Z');
plot(m_z(:, 3), m_z(:, 1), 'DisplayName', 'Floor - Z');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 100]); ylim([-2 2]);
legend('Location', 'northeast');
subplot(1, 3, 2);
hold on;
plot(m_n(:, 3), m_n(:, 2), 'DisplayName', 'Marble - N');
plot(m_n(:, 3), m_n(:, 1), 'DisplayName', 'Floor - N');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 100]); ylim([-2 2]);
legend('Location', 'northeast');
subplot(1, 3, 3);
hold on;
plot(m_e(:, 3), m_e(:, 2), 'DisplayName', 'Marble - E');
plot(m_e(:, 3), m_e(:, 1), 'DisplayName', 'Floor - E');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 100]); ylim([-2 2]);
legend('Location', 'northeast');
#+end_src
#+NAME: fig:marble_floor_motion_time
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/marble_floor_motion_time.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:marble_floor_motion_time
#+CAPTION: Floor and ground motion
#+RESULTS: fig:marble_floor_motion_time
[[file:figs/marble_floor_motion_time.png]]
** Compute the power spectral densities
We first compute some parameters that will be used for the PSD computation.
#+begin_src matlab :results none
dt = m_z(2, 3)-m_z(1, 3);
Fs = 1/dt; % [Hz]
win = hanning(ceil(10*Fs));
#+end_src
Then we compute the Power Spectral Density using =pwelch= function.
#+begin_src matlab
[px_fz, f] = pwelch(m_z(:, 1), win, [], [], Fs);
[px_gz, ~] = pwelch(m_z(:, 2), win, [], [], Fs);
[px_fn, ~] = pwelch(m_n(:, 1), win, [], [], Fs);
[px_gn, ~] = pwelch(m_n(:, 2), win, [], [], Fs);
[px_fe, ~] = pwelch(m_e(:, 1), win, [], [], Fs);
[px_ge, ~] = pwelch(m_e(:, 2), win, [], [], Fs);
#+end_src
The results are shown on figure [[fig:floor_marble_psd_z]] for the Z direction, figure [[fig:floor_marble_psd_n]] for the north direction, and figure [[fig:floor_marble_psd_e]] for the east direction.
#+begin_src matlab :exports none
figure;
hold on;
plot(f, sqrt(px_fz), 'DisplayName', 'Floor - Z');
plot(f, sqrt(px_gz), 'DisplayName', 'Granite - Z');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([0.1, 500]);
#+end_src
#+NAME: fig:floor_marble_psd_z
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/floor_marble_psd_z.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:floor_marble_psd_z
#+CAPTION: Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - Z direction
#+RESULTS: fig:floor_marble_psd_z
[[file:figs/floor_marble_psd_z.png]]
#+begin_src matlab :exports none
figure;
hold on;
plot(f, sqrt(px_fn), 'DisplayName', 'Floor - N');
plot(f, sqrt(px_gn), 'DisplayName', 'Granite - N');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([0.1, 500]);
#+end_src
#+NAME: fig:floor_marble_psd_n
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/floor_marble_psd_n.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:floor_marble_psd_n
#+CAPTION: Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - N direction
#+RESULTS: fig:floor_marble_psd_n
[[file:figs/floor_marble_psd_n.png]]
#+begin_src matlab :exports none
figure;
hold on;
plot(f, sqrt(px_fe), 'DisplayName', 'Floor - E');
plot(f, sqrt(px_ge), 'DisplayName', 'Granite - E');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([0.1, 500]);
#+end_src
#+NAME: fig:floor_marble_psd_e
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/floor_marble_psd_e.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:floor_marble_psd_e
#+CAPTION: Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - E direction
#+RESULTS: fig:floor_marble_psd_e
[[file:figs/floor_marble_psd_e.png]]
** Compute the transfer function from floor motion to ground motion
We now compute the transfer function from the floor motion to the granite motion.
The result is shown on figure [[fig:tf_granite]].
#+begin_src matlab :results none
[TZ, f] = tfestimate(m_z(:, 1), -m_z(:, 2), win, [], [], Fs);
[TN, ~] = tfestimate(m_n(:, 1), -m_n(:, 2), win, [], [], Fs);
[TE, ~] = tfestimate(m_e(:, 1), -m_e(:, 2), win, [], [], Fs);
#+end_src
#+begin_src matlab :results none :exports none
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(f, abs(TZ), 'DisplayName', 'Z');
plot(f, abs(TN), 'DisplayName', 'N');
plot(f, abs(TE), 'DisplayName', 'E');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
set(gca, 'XTickLabel',[]);
ylabel('Magnitude');
legend('Location', 'southwest');
ax2 = subplot(2, 1, 2);
hold on;
plot(f, mod(180+180/pi*phase(TZ), 360)-180);
plot(f, mod(180+180/pi*phase(TN), 360)-180);
plot(f, mod(180+180/pi*phase(TE), 360)-180);
hold off;
set(gca, 'xscale', 'log');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
linkaxes([ax1,ax2],'x');
xlim([10, 100]);
#+end_src
#+NAME: fig:tf_granite
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/tf_granite.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:tf_granite
#+CAPTION: Transfer function from floor motion to granite motion
#+RESULTS: fig:tf_granite
[[file:figs/tf_granite.png]]
** Conclusion
#+begin_important
- We see resonance of the granite at 33Hz in the horizontal directions
- We see two resonances for the z direction: at 60Hz and 75Hz
#+end_important

153
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@ -0,0 +1,153 @@
%% Clear Workspace and Close figures
clear; close all; clc;
%% Intialize Laplace variable
s = zpk('s');
% Load data
m_z = load('mat/data_037.mat', 'data'); m_z = m_z.data;
m_n = load('mat/data_038.mat', 'data'); m_n = m_n.data;
m_e = load('mat/data_039.mat', 'data'); m_e = m_e.data;
% Time domain plots
figure;
subplot(1, 3, 1);
hold on;
plot(m_z(:, 3), m_z(:, 2), 'DisplayName', 'Marble - Z');
plot(m_z(:, 3), m_z(:, 1), 'DisplayName', 'Floor - Z');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 100]); ylim([-2 2]);
legend('Location', 'northeast');
subplot(1, 3, 2);
hold on;
plot(m_n(:, 3), m_n(:, 2), 'DisplayName', 'Marble - N');
plot(m_n(:, 3), m_n(:, 1), 'DisplayName', 'Floor - N');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 100]); ylim([-2 2]);
legend('Location', 'northeast');
subplot(1, 3, 3);
hold on;
plot(m_e(:, 3), m_e(:, 2), 'DisplayName', 'Marble - E');
plot(m_e(:, 3), m_e(:, 1), 'DisplayName', 'Floor - E');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 100]); ylim([-2 2]);
legend('Location', 'northeast');
% Compute the power spectral densities
% We first compute some parameters that will be used for the PSD computation.
dt = m_z(2, 3)-m_z(1, 3);
Fs = 1/dt; % [Hz]
win = hanning(ceil(10*Fs));
% Then we compute the Power Spectral Density using =pwelch= function.
[px_fz, f] = pwelch(m_z(:, 1), win, [], [], Fs);
[px_gz, ~] = pwelch(m_z(:, 2), win, [], [], Fs);
[px_fn, ~] = pwelch(m_n(:, 1), win, [], [], Fs);
[px_gn, ~] = pwelch(m_n(:, 2), win, [], [], Fs);
[px_fe, ~] = pwelch(m_e(:, 1), win, [], [], Fs);
[px_ge, ~] = pwelch(m_e(:, 2), win, [], [], Fs);
% The results are shown on figure [[fig:floor_marble_psd_z]] for the Z direction, figure [[fig:floor_marble_psd_n]] for the north direction, and figure [[fig:floor_marble_psd_e]] for the east direction.
figure;
hold on;
plot(f, sqrt(px_fz), 'DisplayName', 'Floor - Z');
plot(f, sqrt(px_gz), 'DisplayName', 'Granite - Z');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([0.1, 500]);
% #+NAME: fig:floor_marble_psd_z
% #+CAPTION: Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - Z direction
% #+RESULTS: fig:floor_marble_psd_z
% [[file:figs/floor_marble_psd_z.png]]
figure;
hold on;
plot(f, sqrt(px_fn), 'DisplayName', 'Floor - N');
plot(f, sqrt(px_gn), 'DisplayName', 'Granite - N');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([0.1, 500]);
% #+NAME: fig:floor_marble_psd_n
% #+CAPTION: Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - N direction
% #+RESULTS: fig:floor_marble_psd_n
% [[file:figs/floor_marble_psd_n.png]]
figure;
hold on;
plot(f, sqrt(px_fe), 'DisplayName', 'Floor - E');
plot(f, sqrt(px_ge), 'DisplayName', 'Granite - E');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([0.1, 500]);
% Compute the transfer function from floor motion to ground motion
% We now compute the transfer function from the floor motion to the granite motion.
% The result is shown on figure [[fig:tf_granite]].
[TZ, f] = tfestimate(m_z(:, 1), -m_z(:, 2), win, [], [], Fs);
[TN, ~] = tfestimate(m_n(:, 1), -m_n(:, 2), win, [], [], Fs);
[TE, ~] = tfestimate(m_e(:, 1), -m_e(:, 2), win, [], [], Fs);
figure;
ax1 = subplot(2, 1, 1);
hold on;
plot(f, abs(TZ), 'DisplayName', 'Z');
plot(f, abs(TN), 'DisplayName', 'N');
plot(f, abs(TE), 'DisplayName', 'E');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
set(gca, 'XTickLabel',[]);
ylabel('Magnitude');
legend('Location', 'southwest');
ax2 = subplot(2, 1, 2);
hold on;
plot(f, mod(180+180/pi*phase(TZ), 360)-180);
plot(f, mod(180+180/pi*phase(TN), 360)-180);
plot(f, mod(180+180/pi*phase(TE), 360)-180);
hold off;
set(gca, 'xscale', 'log');
ylim([-180, 180]);
yticks([-180, -90, 0, 90, 180]);
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
linkaxes([ax1,ax2],'x');
xlim([10, 100]);