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<div id="content">
<h1 class="title">Measurement of the sample vibrations when rotating the Spindle</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgdf465ae">1. Signal Processing</a>
<ul>
<li><a href="#org4996901">1.1. Load Data</a></li>
<li><a href="#org533857f">1.2. Pre-processing</a></li>
<li><a href="#org7af64b7">1.3. Time domain Data</a></li>
<li><a href="#orga48afa8">1.4. ASD and Frequency domain data</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orgdf465ae" class="outline-2">
<h2 id="orgdf465ae"><span class="section-number-2">1</span> Signal Processing</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-org4996901" class="outline-3">
<h3 id="org4996901"><span class="section-number-3">1.1</span> Load Data</h3>
<div class="outline-text-3" id="text-1-1">
<p>
Measurement <code>data_001.mat</code> corresponds to a measurement where the spindle is not turning and <code>data_002.mat</code> where the spindle is turning at 1rpm.
<code>x1</code> is the signal coming from the geophone located on the marble and <code>x2</code> is the signal from the geophone located on the sample station.
</p>
<div class="org-src-container">
<pre class="src src-matlab">data1 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
data2 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_002.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org533857f" class="outline-3">
<h3 id="org533857f"><span class="section-number-3">1.2</span> Pre-processing</h3>
<div class="outline-text-3" id="text-1-2">
<div class="org-src-container">
<pre class="src src-matlab">imax = min<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>length<span class="org-rainbow-delimiters-depth-3">(</span>data1.t<span class="org-rainbow-delimiters-depth-3">)</span>, length<span class="org-rainbow-delimiters-depth-3">(</span>data2.t<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
data1.t = data1.t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>imax<span class="org-rainbow-delimiters-depth-1">)</span>;
data1.x1 = data1.x1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>imax<span class="org-rainbow-delimiters-depth-1">)</span>;
data1.x2 = data1.x2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>imax<span class="org-rainbow-delimiters-depth-1">)</span>;
data2.t = data2.t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>imax<span class="org-rainbow-delimiters-depth-1">)</span>;
data2.x1 = data2.x1<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>imax<span class="org-rainbow-delimiters-depth-1">)</span>;
data2.x2 = data2.x2<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">:</span>imax<span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org7af64b7" class="outline-3">
<h3 id="org7af64b7"><span class="section-number-3">1.3</span> Time domain Data</h3>
<div class="outline-text-3" id="text-1-3">
<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>data1.t, data1.x1<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>data2.t, data2.x1<span class="org-rainbow-delimiters-depth-1">)</span>;
hold off;
</pre>
</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>data1.t, data1.x2<span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>data2.t, data2.x2<span class="org-rainbow-delimiters-depth-1">)</span>
hold off;
</pre>
</div>
</div>
</div>
<div id="outline-container-orga48afa8" class="outline-3">
<h3 id="orga48afa8"><span class="section-number-3">1.4</span> ASD and Frequency domain data</h3>
<div class="outline-text-3" id="text-1-4">
<div class="org-src-container">
<pre class="src src-matlab">dt = data1.t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> data1.t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt;
windows_psd = 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>dt<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxx1m, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>data1.x1, windows_psd, <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>pxx1h, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>data1.x2, windows_psd, <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>pxx2m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>data2.x1, windows_psd, <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>pxx2h, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>data2.x2, windows_psd, <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 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>pxx1m<span class="org-rainbow-delimiters-depth-2">)</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>pxx2m<span class="org-rainbow-delimiters-depth-2">)</span><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">'PSD </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s/sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">(</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></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>
</pre>
</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>pxx1h<span class="org-rainbow-delimiters-depth-2">)</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>pxx2h<span class="org-rainbow-delimiters-depth-2">)</span><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">'PSD </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s/sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">(</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></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>
</pre>
</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>pxx2m<span class="org-rainbow-delimiters-depth-2">)</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>pxx2h<span class="org-rainbow-delimiters-depth-2">)</span><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">'PSD </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s/sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">(</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></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>
</pre>
</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, cumtrapz<span class="org-rainbow-delimiters-depth-2">(</span>f, pxx1m<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, cumtrapz<span class="org-rainbow-delimiters-depth-2">(</span>f, pxx2m<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>
<span class="org-type">set</span><span class="org-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>;
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">'CAS </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>
</pre>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-05-02 jeu. 14:11</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
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<div id="content"> <div id="content">
<h1 class="title">SpeedGoat</h1> <h1 class="title">Huddle Test of the L22 Geophones</h1>
<div id="table-of-contents"> <div id="table-of-contents">
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org3e6baac">1. Experimental Setup</a></li> <li><a href="#orge5c8cc5">1. Experimental Setup</a></li>
<li><a href="#org924e227">2. Signal Processing</a> <li><a href="#org8b7c96e">2. Signal Processing</a>
<ul> <ul>
<li><a href="#org8f54945">2.1. Load data</a></li> <li><a href="#org7cb3283">2.1. Load data</a></li>
<li><a href="#org26953ea">2.2. Time Domain Data</a></li> <li><a href="#org0a3a0d0">2.2. Time Domain Data</a></li>
<li><a href="#orgea14a3e">2.3. Computation of the ASD of the measured voltage</a></li> <li><a href="#org89016b8">2.3. Computation of the ASD of the measured voltage</a></li>
<li><a href="#org10d59fe">2.4. Scaling to take into account the sensibility of the geophone and the voltage amplifier</a></li> <li><a href="#orga26e03c">2.4. Scaling to take into account the sensibility of the geophone and the voltage amplifier</a></li>
<li><a href="#orgca371f4">2.5. Computation of the ASD of the velocity</a></li> <li><a href="#orgfd3ab32">2.5. Computation of the ASD of the velocity</a></li>
<li><a href="#orgd108d7b">2.6. Transfer function between the two geophones</a></li> <li><a href="#orgcd33ee8">2.6. Transfer function between the two geophones</a></li>
<li><a href="#orgd3b08ee">2.7. Estimation of the sensor noise</a></li> <li><a href="#org244b412">2.7. Estimation of the sensor noise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgdb15af9">3. Compare axis</a> <li><a href="#org6beee86">3. Compare axis</a>
<ul> <ul>
<li><a href="#orgba2e891">3.1. Load data</a></li> <li><a href="#org53cf537">3.1. Load data</a></li>
<li><a href="#org4fa1ea3">3.2. Compare PSD</a></li> <li><a href="#org8e12607">3.2. Compare PSD</a></li>
<li><a href="#org413e0a4">3.3. Compare TF</a></li> <li><a href="#org90e5861">3.3. Compare TF</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org47dea1f">4. Appendix</a> <li><a href="#org7c0ad67">4. Appendix</a>
<ul> <ul>
<li><a href="#orgc970c0a">4.1. Computation of coherence from PSD and CSD</a></li> <li><a href="#orgd75efe3">4.1. Computation of coherence from PSD and CSD</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org3e6baac" class="outline-2"> <div id="outline-container-orge5c8cc5" class="outline-2">
<h2 id="org3e6baac"><span class="section-number-2">1</span> Experimental Setup</h2> <h2 id="orge5c8cc5"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
Two L22 geophones are used. Two L22 geophones are used.
@ -319,14 +319,14 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
</p> </p>
<div id="org1834fe1" class="figure"> <div id="org32e95c2" class="figure">
<p><img src="./figs/setup.jpg" alt="setup.jpg" width="500px" /> <p><img src="./figs/setup.jpg" alt="setup.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Setup</p> <p><span class="figure-number">Figure 1: </span>Setup</p>
</div> </div>
<div id="orgd38e8c5" class="figure"> <div id="orgdd8ca8c" class="figure">
<p><img src="./figs/geophones.jpg" alt="geophones.jpg" width="500px" /> <p><img src="./figs/geophones.jpg" alt="geophones.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Geophones</p> <p><span class="figure-number">Figure 2: </span>Geophones</p>
@ -334,8 +334,8 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
</div> </div>
</div> </div>
<div id="outline-container-org924e227" class="outline-2"> <div id="outline-container-org8b7c96e" class="outline-2">
<h2 id="org924e227"><span class="section-number-2">2</span> Signal Processing</h2> <h2 id="org8b7c96e"><span class="section-number-2">2</span> Signal Processing</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
The Matlab computing file for this part is accessible <a href="signal_processing.m">here</a>. The Matlab computing file for this part is accessible <a href="signal_processing.m">here</a>.
@ -343,8 +343,8 @@ The <code>mat</code> file containing the measurement data is accessible <a href=
</p> </p>
</div> </div>
<div id="outline-container-org8f54945" class="outline-3"> <div id="outline-container-org7cb3283" class="outline-3">
<h3 id="org8f54945"><span class="section-number-3">2.1</span> Load data</h3> <h3 id="org7cb3283"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
@ -358,8 +358,8 @@ dt = t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-high
</div> </div>
</div> </div>
<div id="outline-container-org26953ea" class="outline-3"> <div id="outline-container-org0a3a0d0" class="outline-3">
<h3 id="org26953ea"><span class="section-number-3">2.2</span> Time Domain Data</h3> <h3 id="org0a3a0d0"><span class="section-number-3">2.2</span> Time Domain Data</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
@ -374,7 +374,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="orge43c98a" class="figure"> <div id="org09ad879" class="figure">
<p><img src="figs/data_time_domain.png" alt="data_time_domain.png" /> <p><img src="figs/data_time_domain.png" alt="data_time_domain.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Time domain Data</p> <p><span class="figure-number">Figure 3: </span>Time domain Data</p>
@ -394,7 +394,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="orgb1d4c24" class="figure"> <div id="org04c8d74" class="figure">
<p><img src="figs/data_time_domain_zoom.png" alt="data_time_domain_zoom.png" /> <p><img src="figs/data_time_domain_zoom.png" alt="data_time_domain_zoom.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Time domain Data - Zoom</p> <p><span class="figure-number">Figure 4: </span>Time domain Data - Zoom</p>
@ -402,8 +402,8 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-orgea14a3e" class="outline-3"> <div id="outline-container-org89016b8" class="outline-3">
<h3 id="orgea14a3e"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3> <h3 id="org89016b8"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
We first define the parameters for the frequency domain analysis. We first define the parameters for the frequency domain analysis.
@ -422,12 +422,12 @@ Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/
</div> </div>
</div> </div>
<div id="outline-container-org10d59fe" class="outline-3"> <div id="outline-container-orga26e03c" class="outline-3">
<h3 id="org10d59fe"><span class="section-number-3">2.4</span> Scaling to take into account the sensibility of the geophone and the voltage amplifier</h3> <h3 id="orga26e03c"><span class="section-number-3">2.4</span> Scaling to take into account the sensibility of the geophone and the voltage amplifier</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
The Geophone used are L22. The Geophone used are L22.
Their sensibility are shown on figure <a href="#org542fee1">5</a>. Their sensibility are shown on figure <a href="#orgb86dfe6">5</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -438,7 +438,7 @@ S = <span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type"
</div> </div>
<div id="org542fee1" class="figure"> <div id="orgb86dfe6" class="figure">
<p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" /> <p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Sensibility of the Geophone</p> <p><span class="figure-number">Figure 5: </span>Sensibility of the Geophone</p>
@ -469,11 +469,11 @@ We further divide the result by the sensibility of the Geophone to obtain the AS
</div> </div>
</div> </div>
<div id="outline-container-orgca371f4" class="outline-3"> <div id="outline-container-orgfd3ab32" class="outline-3">
<h3 id="orgca371f4"><span class="section-number-3">2.5</span> Computation of the ASD of the velocity</h3> <h3 id="orgfd3ab32"><span class="section-number-3">2.5</span> Computation of the ASD of the velocity</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<p> <p>
The ASD of the measured velocity is shown on figure <a href="#orga342d1d">6</a>. The ASD of the measured velocity is shown on figure <a href="#org204dcef">6</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -490,14 +490,14 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="orga342d1d" class="figure"> <div id="org204dcef" class="figure">
<p><img src="figs/psd_velocity.png" alt="psd_velocity.png" /> <p><img src="figs/psd_velocity.png" alt="psd_velocity.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>Spectral density of the velocity</p> <p><span class="figure-number">Figure 6: </span>Spectral density of the velocity</p>
</div> </div>
<p> <p>
We also plot the ASD in displacement (figure <a href="#orgb224e73">7</a>); We also plot the ASD in displacement (figure <a href="#org9967b3b">7</a>);
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -513,7 +513,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="orgb224e73" class="figure"> <div id="org9967b3b" class="figure">
<p><img src="figs/asd_displacement.png" alt="asd_displacement.png" /> <p><img src="figs/asd_displacement.png" alt="asd_displacement.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the displacement as measured by the geophones</p> <p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the displacement as measured by the geophones</p>
@ -521,16 +521,16 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-orgd108d7b" class="outline-3"> <div id="outline-container-orgcd33ee8" class="outline-3">
<h3 id="orgd108d7b"><span class="section-number-3">2.6</span> Transfer function between the two geophones</h3> <h3 id="orgcd33ee8"><span class="section-number-3">2.6</span> Transfer function between the two geophones</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-6">
<p> <p>
We here compute the transfer function from one geophone to the other. We here compute the transfer function from one geophone to the other.
The result is shown on figure <a href="#org9006692">8</a>. The result is shown on figure <a href="#org5faacba">8</a>.
</p> </p>
<p> <p>
We also compute the coherence between the two signals (figure <a href="#org9200232">9</a>). We also compute the coherence between the two signals (figure <a href="#orgf374e25">9</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -539,7 +539,7 @@ We also compute the coherence between the two signals (figure <a href="#org92002
</div> </div>
<div id="org9006692" class="figure"> <div id="org5faacba" class="figure">
<p><img src="figs/tf_geophones.png" alt="tf_geophones.png" /> <p><img src="figs/tf_geophones.png" alt="tf_geophones.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>Estimated transfer function between the two geophones</p> <p><span class="figure-number">Figure 8: </span>Estimated transfer function between the two geophones</p>
@ -551,7 +551,7 @@ We also compute the coherence between the two signals (figure <a href="#org92002
</div> </div>
<div id="org9200232" class="figure"> <div id="orgf374e25" class="figure">
<p><img src="figs/coh_geophones.png" alt="coh_geophones.png" /> <p><img src="figs/coh_geophones.png" alt="coh_geophones.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>Cohererence between the signals of the two geophones</p> <p><span class="figure-number">Figure 9: </span>Cohererence between the signals of the two geophones</p>
@ -559,8 +559,8 @@ We also compute the coherence between the two signals (figure <a href="#org92002
</div> </div>
</div> </div>
<div id="outline-container-orgd3b08ee" class="outline-3"> <div id="outline-container-org244b412" class="outline-3">
<h3 id="orgd3b08ee"><span class="section-number-3">2.7</span> Estimation of the sensor noise</h3> <h3 id="org244b412"><span class="section-number-3">2.7</span> Estimation of the sensor noise</h3>
<div class="outline-text-3" id="text-2-7"> <div class="outline-text-3" id="text-2-7">
<p> <p>
The technique to estimate the sensor noise is taken from <a class='org-ref-reference' href="#barzilai98_techn_measur_noise_sensor_presen">barzilai98_techn_measur_noise_sensor_presen</a>. The technique to estimate the sensor noise is taken from <a class='org-ref-reference' href="#barzilai98_techn_measur_noise_sensor_presen">barzilai98_techn_measur_noise_sensor_presen</a>.
@ -590,11 +590,11 @@ where:
</ul> </ul>
<p> <p>
The <code>mscohere</code> function is compared with this formula on Appendix (section <a href="#org550fd32">4.1</a>), it is shown that it is identical. The <code>mscohere</code> function is compared with this formula on Appendix (section <a href="#orge316ad4">4.1</a>), it is shown that it is identical.
</p> </p>
<p> <p>
Figure <a href="#org72885b4">10</a> illustrate a block diagram model of the system used to determine the sensor noise of the geophone. Figure <a href="#org57a5459">10</a> illustrate a block diagram model of the system used to determine the sensor noise of the geophone.
</p> </p>
<p> <p>
@ -606,7 +606,7 @@ Each sensor has noise \(N\) and \(M\).
</p> </p>
<div id="org72885b4" class="figure"> <div id="org57a5459" class="figure">
<p><img src="figs/huddle-test.png" alt="huddle-test.png" /> <p><img src="figs/huddle-test.png" alt="huddle-test.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Huddle test block diagram</p> <p><span class="figure-number">Figure 10: </span>Huddle test block diagram</p>
@ -614,14 +614,14 @@ Each sensor has noise \(N\) and \(M\).
<p> <p>
We here assume that each sensor has the same magnitude of instrumental noise (\(N = M\)). We here assume that each sensor has the same magnitude of instrumental noise (\(N = M\)).
We also assume that \(H_1 = H_2 = 1\). We also assume that \(S_1 = S_2 = 1\).
</p> </p>
<p> <p>
We then obtain: We then obtain:
</p> </p>
\begin{equation} \begin{equation}
\label{orgb78feac} \label{org5b2976f}
\gamma_{XY}^2(\omega) = \frac{1}{1 + 2 \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right) + \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right)^2} \gamma_{XY}^2(\omega) = \frac{1}{1 + 2 \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right) + \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right)^2}
\end{equation} \end{equation}
@ -629,23 +629,23 @@ We then obtain:
Since the input signal \(U\) and the instrumental noise \(N\) are incoherent: Since the input signal \(U\) and the instrumental noise \(N\) are incoherent:
</p> </p>
\begin{equation} \begin{equation}
\label{org8419580} \label{orgb493a2c}
|G_X(\omega)| = |G_N(\omega)| + |G_U(\omega)| |G_X(\omega)| = |G_N(\omega)| + |G_U(\omega)|
\end{equation} \end{equation}
<p> <p>
From equations \eqref{orgb78feac} and \eqref{org8419580}, we finally obtain From equations \eqref{org5b2976f} and \eqref{orgb493a2c}, we finally obtain
</p> </p>
<div class="important"> <div class="important">
\begin{equation} \begin{equation}
\label{orgbe05867} \label{org4f59d30}
|G_N(\omega)| = |G_X(\omega)| \left( 1 - \sqrt{\gamma_{XY}^2(\omega)} \right) |G_N(\omega)| = |G_X(\omega)| \left( 1 - \sqrt{\gamma_{XY}^2(\omega)} \right)
\end{equation} \end{equation}
</div> </div>
<p> <p>
The instrumental noise is computed below. The result in V<sup>2</sup>/Hz is shown on figure <a href="#org40db312">11</a>. The instrumental noise is computed below. The result in V<sup>2</sup>/Hz is shown on figure <a href="#org9584668">11</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">pxxN = pxx1<span class="org-type">.*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">-</span> coh12<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">pxxN = pxx1<span class="org-type">.*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">-</span> coh12<span class="org-rainbow-delimiters-depth-1">)</span>;
@ -666,14 +666,14 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="org40db312" class="figure"> <div id="org9584668" class="figure">
<p><img src="figs/intrumental_noise_V.png" alt="intrumental_noise_V.png" /> <p><img src="figs/intrumental_noise_V.png" alt="intrumental_noise_V.png" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Instrumental Noise and Measurement in \(V^2/Hz\)</p> <p><span class="figure-number">Figure 11: </span>Instrumental Noise and Measurement in \(V^2/Hz\)</p>
</div> </div>
<p> <p>
This is then further converted into velocity and compared with the ground velocity measurement. (figure <a href="#org2a811b0">12</a>) This is then further converted into velocity and compared with the ground velocity measurement. (figure <a href="#orgdd66b8f">12</a>)
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
@ -689,7 +689,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="org2a811b0" class="figure"> <div id="orgdd66b8f" class="figure">
<p><img src="figs/intrumental_noise_velocity.png" alt="intrumental_noise_velocity.png" /> <p><img src="figs/intrumental_noise_velocity.png" alt="intrumental_noise_velocity.png" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Instrumental Noise and Measurement in \(m/s/\sqrt{Hz}\)</p> <p><span class="figure-number">Figure 12: </span>Instrumental Noise and Measurement in \(m/s/\sqrt{Hz}\)</p>
@ -698,8 +698,8 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-orgdb15af9" class="outline-2"> <div id="outline-container-org6beee86" class="outline-2">
<h2 id="orgdb15af9"><span class="section-number-2">3</span> Compare axis</h2> <h2 id="org6beee86"><span class="section-number-2">3</span> Compare axis</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
The Matlab computing file for this part is accessible <a href="compare_axis.m">here</a>. The Matlab computing file for this part is accessible <a href="compare_axis.m">here</a>.
@ -712,8 +712,8 @@ The <code>mat</code> files containing the measurement data are accessible with t
</ul> </ul>
</div> </div>
<div id="outline-container-orgba2e891" class="outline-3"> <div id="outline-container-org53cf537" class="outline-3">
<h3 id="orgba2e891"><span class="section-number-3">3.1</span> Load data</h3> <h3 id="org53cf537"><span class="section-number-3">3.1</span> Load data</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
We first load the data for the three axis. We first load the data for the three axis.
@ -727,8 +727,8 @@ north = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="or
</div> </div>
</div> </div>
<div id="outline-container-org4fa1ea3" class="outline-3"> <div id="outline-container-org8e12607" class="outline-3">
<h3 id="org4fa1ea3"><span class="section-number-3">3.2</span> Compare PSD</h3> <h3 id="org8e12607"><span class="section-number-3">3.2</span> Compare PSD</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
The PSD for each axis of the two geophones are computed. The PSD for each axis of the two geophones are computed.
@ -746,10 +746,10 @@ The PSD for each axis of the two geophones are computed.
</div> </div>
<p> <p>
We compare them. The result is shown on figure <a href="#org8d0a71b">13</a>. We compare them. The result is shown on figure <a href="#org4b31119">13</a>.
</p> </p>
<div id="org8d0a71b" class="figure"> <div id="org4b31119" class="figure">
<p><img src="figs/compare_axis_psd.png" alt="compare_axis_psd.png" /> <p><img src="figs/compare_axis_psd.png" alt="compare_axis_psd.png" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Compare the measure PSD of the two geophones for the three axis</p> <p><span class="figure-number">Figure 13: </span>Compare the measure PSD of the two geophones for the three axis</p>
@ -757,12 +757,12 @@ We compare them. The result is shown on figure <a href="#org8d0a71b">13</a>.
</div> </div>
</div> </div>
<div id="outline-container-org413e0a4" class="outline-3"> <div id="outline-container-org90e5861" class="outline-3">
<h3 id="org413e0a4"><span class="section-number-3">3.3</span> Compare TF</h3> <h3 id="org90e5861"><span class="section-number-3">3.3</span> Compare TF</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<p> <p>
The transfer functions from one geophone to the other are also computed for each axis. The transfer functions from one geophone to the other are also computed for each axis.
The result is shown on figure <a href="#org167ce04">14</a>. The result is shown on figure <a href="#org76b2565">14</a>.
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -773,7 +773,7 @@ The result is shown on figure <a href="#org167ce04">14</a>.
</div> </div>
<div id="org167ce04" class="figure"> <div id="org76b2565" class="figure">
<p><img src="figs/compare_tf_axis.png" alt="compare_tf_axis.png" /> <p><img src="figs/compare_tf_axis.png" alt="compare_tf_axis.png" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Compare the transfer function from one geophone to the other for the 3 axis</p> <p><span class="figure-number">Figure 14: </span>Compare the transfer function from one geophone to the other for the 3 axis</p>
@ -782,15 +782,15 @@ The result is shown on figure <a href="#org167ce04">14</a>.
</div> </div>
</div> </div>
<div id="outline-container-org47dea1f" class="outline-2"> <div id="outline-container-org7c0ad67" class="outline-2">
<h2 id="org47dea1f"><span class="section-number-2">4</span> Appendix</h2> <h2 id="org7c0ad67"><span class="section-number-2">4</span> Appendix</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
</div> </div>
<div id="outline-container-orgc970c0a" class="outline-3"> <div id="outline-container-orgd75efe3" class="outline-3">
<h3 id="orgc970c0a"><span class="section-number-3">4.1</span> Computation of coherence from PSD and CSD</h3> <h3 id="orgd75efe3"><span class="section-number-3">4.1</span> Computation of coherence from PSD and CSD</h3>
<div class="outline-text-3" id="text-4-1"> <div class="outline-text-3" id="text-4-1">
<p> <p>
<a id="org550fd32"></a> <a id="orge316ad4"></a>
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
@ -821,7 +821,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="org229a280" class="figure"> <div id="org5c602bf" class="figure">
<p><img src="figs/comp_coherence_formula.png" alt="comp_coherence_formula.png" /> <p><img src="figs/comp_coherence_formula.png" alt="comp_coherence_formula.png" />
</p> </p>
<p><span class="figure-number">Figure 15: </span>Comparison of <code>mscohere</code> and manual computation</p> <p><span class="figure-number">Figure 15: </span>Comparison of <code>mscohere</code> and manual computation</p>
@ -839,7 +839,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p> <p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-04-18 jeu. 17:24</p> <p class="date">Created: 2019-05-02 jeu. 14:11</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>
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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>
<!-- 2019-04-17 mer. 18:25 --> <!-- 2019-05-02 jeu. 14:11 -->
<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>SpeedGoat</title> <title>SpeedGoat</title>
@ -250,27 +250,17 @@ for the JavaScript code in this tag.
<body> <body>
<div id="content"> <div id="content">
<h1 class="title">SpeedGoat</h1> <h1 class="title">SpeedGoat</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgc3dbb11">1. Folders</a></li>
</ul>
</div>
</div>
<div id="outline-container-orgc3dbb11" class="outline-2">
<h2 id="orgc3dbb11"><span class="section-number-2">1</span> Folders</h2>
<div class="outline-text-2" id="text-1">
<ul class="org-ul"> <ul class="org-ul">
<li><a href="huddle-test-geophones/index.html">Huddle Test - Geophones</a></li> <li><a href="huddle-test-geophones/index.html">Huddle Test - Geophones</a></li>
<li><a href="disturbance-measurement/index.html">Disturbance Measurement</a></li>
<li><a href="slip-ring-test/index.html">Slip Ring - Noise measurement</a></li>
<li><a href="static-measurements/index.html">Control System Measurement</a></li>
</ul> </ul>
</div> </div>
</div>
</div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p> <p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-04-17 mer. 18:25</p> <p class="date">Created: 2019-05-02 jeu. 14:11</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>
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@ -11,6 +11,7 @@
#+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script> #+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
:END: :END:
* Folders
- [[file:huddle-test-geophones/index.org][Huddle Test - Geophones]] - [[file:huddle-test-geophones/index.org][Huddle Test - Geophones]]
- [[file:disturbance-measurement/index.org][Disturbance Measurement]]
- [[file:slip-ring-test/index.org][Slip Ring - Noise measurement]]
- [[file:static-measurements/index.org][Control System Measurement]]

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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>
<!-- 2019-05-02 jeu. 14:08 --> <!-- 2019-05-02 jeu. 14:12 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<title>Effect of the rotation of the Slip-Ring</title> <title>Effect of the rotation of the Slip-Ring</title>
@ -254,16 +254,16 @@ 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="#org6cf5814">1. Measurement Description</a></li> <li><a href="#org4210b03">1. Measurement Description</a></li>
<li><a href="#orgd40e7ef">2. Load data</a></li> <li><a href="#org28261aa">2. Load data</a></li>
<li><a href="#org4ee458b">3. Analysis</a></li> <li><a href="#org79cb6de">3. Analysis</a></li>
<li><a href="#org7c09cda">4. Conclusion</a></li> <li><a href="#org30f1cc1">4. Conclusion</a></li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org6cf5814" class="outline-2"> <div id="outline-container-org4210b03" class="outline-2">
<h2 id="org6cf5814"><span class="section-number-2">1</span> Measurement Description</h2> <h2 id="org4210b03"><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>
Random Signal is generated by one DAC of the SpeedGoat. Random Signal is generated by one DAC of the SpeedGoat.
@ -352,8 +352,8 @@ Here, the rotation speed of the Slip-Ring is set to 1rpm.
</div> </div>
</div> </div>
<div id="outline-container-orgd40e7ef" class="outline-2"> <div id="outline-container-org28261aa" class="outline-2">
<h2 id="orgd40e7ef"><span class="section-number-2">2</span> Load data</h2> <h2 id="org28261aa"><span class="section-number-2">2</span> Load data</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
@ -366,11 +366,11 @@ sr_on = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="o
</div> </div>
</div> </div>
<div id="outline-container-org4ee458b" class="outline-2"> <div id="outline-container-org79cb6de" class="outline-2">
<h2 id="org4ee458b"><span class="section-number-2">3</span> Analysis</h2> <h2 id="org79cb6de"><span class="section-number-2">3</span> Analysis</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
Let's first look at the signal produced by the DAC (figure <a href="#org7a29853">1</a>). Let's first look at the signal produced by the DAC (figure <a href="#orgf3a4e2b">1</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -384,14 +384,14 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="org7a29853" class="figure"> <div id="orgf3a4e2b" class="figure">
<p><img src="figs/random_signal.png" alt="random_signal.png" /> <p><img src="figs/random_signal.png" alt="random_signal.png" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Random signal produced by the DAC</p> <p><span class="figure-number">Figure 1: </span>Random signal produced by the DAC</p>
</div> </div>
<p> <p>
We now look at the difference between the signal directly measured by the ADC and the signal that goes through the slip-ring (figure <a href="#org88cd8db">2</a>). We now look at the difference between the signal directly measured by the ADC and the signal that goes through the slip-ring (figure <a href="#org07de8c8">2</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -407,7 +407,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org88cd8db" class="figure"> <div id="org07de8c8" class="figure">
<p><img src="figs/slipring_comp_signals.png" alt="slipring_comp_signals.png" /> <p><img src="figs/slipring_comp_signals.png" alt="slipring_comp_signals.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Alteration of the signal when the slip-ring is turning</p> <p><span class="figure-number">Figure 2: </span>Alteration of the signal when the slip-ring is turning</p>
@ -415,8 +415,8 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-org7c09cda" class="outline-2"> <div id="outline-container-org30f1cc1" class="outline-2">
<h2 id="org7c09cda"><span class="section-number-2">4</span> Conclusion</h2> <h2 id="org30f1cc1"><span class="section-number-2">4</span> Conclusion</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
<div class="note"> <div class="note">
<p> <p>
@ -433,7 +433,7 @@ legend<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: Thomas Dehaeze</p> <p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-05-02 jeu. 14:08</p> <p class="date">Created: 2019-05-02 jeu. 14:12</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>
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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>
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<title>Measurements</title> <title>Measurements</title>
@ -276,43 +276,43 @@ 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="#org5efded7">1. Effect of the Slip-Ring on the signal</a> <li><a href="#org1ec9040">1. Effect of the Slip-Ring on the signal</a>
<ul> <ul>
<li><a href="#org05d3b24">1.1. Experimental Setup</a></li> <li><a href="#orga86437c">1.1. Experimental Setup</a></li>
<li><a href="#org77b1246">1.2. Load data</a></li> <li><a href="#orgd5025b8">1.2. Load data</a></li>
<li><a href="#orgd60d3c7">1.3. Analysis - Time Domain</a></li> <li><a href="#org733b9d4">1.3. Analysis - Time Domain</a></li>
<li><a href="#orgc8caaf3">1.4. Analysis - Frequency Domain</a></li> <li><a href="#org561e53f">1.4. Analysis - Frequency Domain</a></li>
<li><a href="#org131b000">1.5. Conclusion</a></li> <li><a href="#orge6dd817">1.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org4762833">2. Effect of all the control systems on the Sample vibrations</a> <li><a href="#orgb89af3a">2. Effect of all the control systems on the Sample vibrations</a>
<ul> <ul>
<li><a href="#org085a657">2.1. Experimental Setup</a></li> <li><a href="#org0b19b98">2.1. Experimental Setup</a></li>
<li><a href="#org0368a1a">2.2. Load data</a></li> <li><a href="#org3fe03db">2.2. Load data</a></li>
<li><a href="#org465131e">2.3. Analysis - Time Domain</a></li> <li><a href="#org3fdec7a">2.3. Analysis - Time Domain</a></li>
<li><a href="#org41c1a51">2.4. Analysis - Frequency Domain</a> <li><a href="#org6b5f0ed">2.4. Analysis - Frequency Domain</a>
<ul> <ul>
<li><a href="#org5416fa1">2.4.1. Vibrations at the sample location</a></li> <li><a href="#orgfda4e64">2.4.1. Vibrations at the sample location</a></li>
<li><a href="#org64cfb89">2.4.2. Vibrations on the marble</a></li> <li><a href="#orgc2f810b">2.4.2. Vibrations on the marble</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org42553b0">2.5. Effect of the control system on the transmissibility from ground to sample</a></li> <li><a href="#org43b187d">2.5. Effect of the control system on the transmissibility from ground to sample</a></li>
<li><a href="#org9ad50de">2.6. Conclusion</a></li> <li><a href="#org8ffc99d">2.6. Conclusion</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org089e6c4">3. Transfer function from one stage to the other</a> <li><a href="#orge358e9f">3. Transfer function from one stage to the other</a>
<ul> <ul>
<li><a href="#org5af1ad1">3.1. Experimental Setup</a> <li><a href="#org8671c9c">3.1. Experimental Setup</a>
<ul> <ul>
<li><a href="#org266aa09">3.1.1. From Marble to Ty - <code>mat/meas_010.mat</code></a></li> <li><a href="#orgb8620d5">3.1.1. From Marble to Ty - <code>mat/meas_010.mat</code></a></li>
<li><a href="#org51f3cb6">3.1.2. From Marble to Ry - <code>mat/meas_011.mat</code></a></li> <li><a href="#org3ca3b63">3.1.2. From Marble to Ry - <code>mat/meas_011.mat</code></a></li>
<li><a href="#orgd9c5a6f">3.1.3. From Ty to Ry - <code>mat/meas_012.mat</code></a></li> <li><a href="#orgff3cde2">3.1.3. From Ty to Ry - <code>mat/meas_012.mat</code></a></li>
</ul> </ul>
</li> </li>
<li><a href="#org3523b58">3.2. Load data</a></li> <li><a href="#org185b0f5">3.2. Load data</a></li>
<li><a href="#org2c086d0">3.3. Analysis - Time Domain</a></li> <li><a href="#org1dfb0b9">3.3. Analysis - Time Domain</a></li>
<li><a href="#org63bd941">3.4. Analysis - Frequency Domain</a></li> <li><a href="#org388dc28">3.4. Analysis - Frequency Domain</a></li>
<li><a href="#orgc82b7b0">3.5. Conclusion</a></li> <li><a href="#org26a82a2">3.5. Conclusion</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
@ -328,23 +328,23 @@ For all the measurements shown here:
<li>the voltage amplifiers include a low pass filter with a cut-off frequency at 1kHz</li> <li>the voltage amplifiers include a low pass filter with a cut-off frequency at 1kHz</li>
</ul> </ul>
<div id="outline-container-org5efded7" class="outline-2"> <div id="outline-container-org1ec9040" class="outline-2">
<h2 id="org5efded7"><span class="section-number-2">1</span> Effect of the Slip-Ring on the signal</h2> <h2 id="org1ec9040"><span class="section-number-2">1</span> Effect of the Slip-Ring on the signal</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
</div> </div>
<div id="outline-container-org05d3b24" class="outline-3"> <div id="outline-container-orga86437c" class="outline-3">
<h3 id="org05d3b24"><span class="section-number-3">1.1</span> Experimental Setup</h3> <h3 id="orga86437c"><span class="section-number-3">1.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
Two measurements are made with the control systems of all the stages turned OFF. Two measurements are made with the control systems of all the stages turned OFF.
</p> </p>
<p> <p>
One geophone is located on the marble while the other is located at the sample location (figure <a href="#orgd14e0b4">1</a>). One geophone is located on the marble while the other is located at the sample location (figure <a href="#org5ef91e0">1</a>).
</p> </p>
<div id="orgd14e0b4" class="figure"> <div id="org5ef91e0" class="figure">
<p><img src="./img/IMG_20190430_112615.jpg" alt="IMG_20190430_112615.jpg" width="500px" /> <p><img src="./img/IMG_20190430_112615.jpg" alt="IMG_20190430_112615.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 1: </span>Experimental Setup</p> <p><span class="figure-number">Figure 1: </span>Experimental Setup</p>
@ -417,8 +417,8 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</div> </div>
</div> </div>
<div id="outline-container-org77b1246" class="outline-3"> <div id="outline-container-orgd5025b8" class="outline-3">
<h3 id="org77b1246"><span class="section-number-3">1.2</span> Load data</h3> <h3 id="orgd5025b8"><span class="section-number-3">1.2</span> Load data</h3>
<div class="outline-text-3" id="text-1-2"> <div class="outline-text-3" id="text-1-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
@ -432,11 +432,11 @@ d9 = load<span class="org-rainbow-delimiters-depth-1">(</span>'mat<span class="o
</div> </div>
</div> </div>
<div id="outline-container-orgd60d3c7" class="outline-3"> <div id="outline-container-org733b9d4" class="outline-3">
<h3 id="orgd60d3c7"><span class="section-number-3">1.3</span> Analysis - Time Domain</h3> <h3 id="org733b9d4"><span class="section-number-3">1.3</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-1-3"> <div class="outline-text-3" id="text-1-3">
<p> <p>
First, we compare the time domain signals for the two experiments (figure <a href="#org6ba0e72">2</a>). First, we compare the time domain signals for the two experiments (figure <a href="#orgc28e2b2">2</a>).
</p> </p>
@ -453,7 +453,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org6ba0e72" class="figure"> <div id="orgc28e2b2" class="figure">
<p><img src="figs/slipring_time.png" alt="slipring_time.png" /> <p><img src="figs/slipring_time.png" alt="slipring_time.png" />
</p> </p>
<p><span class="figure-number">Figure 2: </span>Effect of the Slip-Ring on the measured signal - Time domain</p> <p><span class="figure-number">Figure 2: </span>Effect of the Slip-Ring on the measured signal - Time domain</p>
@ -461,11 +461,11 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-orgc8caaf3" class="outline-3"> <div id="outline-container-org561e53f" class="outline-3">
<h3 id="orgc8caaf3"><span class="section-number-3">1.4</span> Analysis - Frequency Domain</h3> <h3 id="org561e53f"><span class="section-number-3">1.4</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-1-4"> <div class="outline-text-3" id="text-1-4">
<p> <p>
We then compute the Power Spectral Density of the two signals and we compare them (figure <a href="#org3e50fec">3</a>). We then compute the Power Spectral Density of the two signals and we compare them (figure <a href="#orgcc1d3ae">3</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = d8<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> d8<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = d8<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> d8<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>;
@ -496,7 +496,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org3e50fec" class="figure"> <div id="orgcc1d3ae" class="figure">
<p><img src="figs/slipring_asd.png" alt="slipring_asd.png" /> <p><img src="figs/slipring_asd.png" alt="slipring_asd.png" />
</p> </p>
<p><span class="figure-number">Figure 3: </span>Effect of the Slip-Ring on the measured signal - Frequency domain</p> <p><span class="figure-number">Figure 3: </span>Effect of the Slip-Ring on the measured signal - Frequency domain</p>
@ -504,8 +504,8 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-org131b000" class="outline-3"> <div id="outline-container-orge6dd817" class="outline-3">
<h3 id="org131b000"><span class="section-number-3">1.5</span> Conclusion</h3> <h3 id="orge6dd817"><span class="section-number-3">1.5</span> Conclusion</h3>
<div class="outline-text-3" id="text-1-5"> <div class="outline-text-3" id="text-1-5">
<div class="important"> <div class="important">
<ul class="org-ul"> <ul class="org-ul">
@ -529,12 +529,12 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-org4762833" class="outline-2"> <div id="outline-container-orgb89af3a" class="outline-2">
<h2 id="org4762833"><span class="section-number-2">2</span> Effect of all the control systems on the Sample vibrations</h2> <h2 id="orgb89af3a"><span class="section-number-2">2</span> Effect of all the control systems on the Sample vibrations</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
</div> </div>
<div id="outline-container-org085a657" class="outline-3"> <div id="outline-container-org0b19b98" class="outline-3">
<h3 id="org085a657"><span class="section-number-3">2.1</span> Experimental Setup</h3> <h3 id="org0b19b98"><span class="section-number-3">2.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
We here measure the signals of two geophones: We here measure the signals of two geophones:
@ -553,7 +553,7 @@ First, all the control systems are turned ON, then, they are turned one by one.
Each measurement are done during 50s. Each measurement are done during 50s.
</p> </p>
<table id="org6235ad0" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> <table id="org0b1da98" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Summary of the measurements and the states of the control systems</caption> <caption class="t-above"><span class="table-number">Table 1:</span> Summary of the measurements and the states of the control systems</caption>
<colgroup> <colgroup>
@ -673,8 +673,8 @@ Each of the <code>mat</code> file contains one array <code>data</code> with 3 co
</div> </div>
</div> </div>
<div id="outline-container-org0368a1a" class="outline-3"> <div id="outline-container-org3fe03db" class="outline-3">
<h3 id="org0368a1a"><span class="section-number-3">2.2</span> Load data</h3> <h3 id="org3fe03db"><span class="section-number-3">2.2</span> Load data</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
@ -691,15 +691,15 @@ d8 = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-s
</div> </div>
</div> </div>
<div id="outline-container-org465131e" class="outline-3"> <div id="outline-container-org3fdec7a" class="outline-3">
<h3 id="org465131e"><span class="section-number-3">2.3</span> Analysis - Time Domain</h3> <h3 id="org3fdec7a"><span class="section-number-3">2.3</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
First, we can look at the time domain data and compare all the measurements: First, we can look at the time domain data and compare all the measurements:
</p> </p>
<ul class="org-ul"> <ul class="org-ul">
<li>comparison for the geophone at the sample location (figure <a href="#org335e162">4</a>)</li> <li>comparison for the geophone at the sample location (figure <a href="#org96fa0ed">4</a>)</li>
<li>comparison for the geophone on the granite (figure <a href="#orgbe9208d">5</a>)</li> <li>comparison for the geophone on the granite (figure <a href="#org9f51b4a">5</a>)</li>
</ul> </ul>
<div class="org-src-container"> <div class="org-src-container">
@ -719,7 +719,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org335e162" class="figure"> <div id="org96fa0ed" class="figure">
<p><img src="figs/time_domain_sample.png" alt="time_domain_sample.png" /> <p><img src="figs/time_domain_sample.png" alt="time_domain_sample.png" />
</p> </p>
<p><span class="figure-number">Figure 4: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p> <p><span class="figure-number">Figure 4: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location</p>
@ -743,7 +743,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="orgbe9208d" class="figure"> <div id="org9f51b4a" class="figure">
<p><img src="figs/time_domain_marble.png" alt="time_domain_marble.png" /> <p><img src="figs/time_domain_marble.png" alt="time_domain_marble.png" />
</p> </p>
<p><span class="figure-number">Figure 5: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p> <p><span class="figure-number">Figure 5: </span>Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble</p>
@ -751,8 +751,8 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-org41c1a51" class="outline-3"> <div id="outline-container-org6b5f0ed" class="outline-3">
<h3 id="org41c1a51"><span class="section-number-3">2.4</span> Analysis - Frequency Domain</h3> <h3 id="org6b5f0ed"><span class="section-number-3">2.4</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = d3<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> d3<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = d3<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> d3<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>;
@ -763,8 +763,8 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
</div> </div>
</div> </div>
<div id="outline-container-org5416fa1" class="outline-4"> <div id="outline-container-orgfda4e64" class="outline-4">
<h4 id="org5416fa1"><span class="section-number-4">2.4.1</span> Vibrations at the sample location</h4> <h4 id="orgfda4e64"><span class="section-number-4">2.4.1</span> Vibrations at the sample location</h4>
<div class="outline-text-4" id="text-2-4-1"> <div class="outline-text-4" id="text-2-4-1">
<p> <p>
First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location. First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.
@ -780,7 +780,7 @@ First, we compute the Power Spectral Density of the signals coming from the Geop
</div> </div>
<p> <p>
And we compare all the signals (figures <a href="#org4625dfd">6</a> and <a href="#org7ea2a57">7</a>). And we compare all the signals (figures <a href="#org89b13c6">6</a> and <a href="#org308e055">7</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
@ -801,7 +801,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="org4625dfd" class="figure"> <div id="org89b13c6" class="figure">
<p><img src="figs/psd_sample_comp.png" alt="psd_sample_comp.png" /> <p><img src="figs/psd_sample_comp.png" alt="psd_sample_comp.png" />
</p> </p>
<p><span class="figure-number">Figure 6: </span>PSD of the signal coming from the top geophone</p> <p><span class="figure-number">Figure 6: </span>PSD of the signal coming from the top geophone</p>
@ -809,7 +809,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
<div id="org7ea2a57" class="figure"> <div id="org308e055" class="figure">
<p><img src="figs/psd_sample_comp_high_freq.png" alt="psd_sample_comp_high_freq.png" /> <p><img src="figs/psd_sample_comp_high_freq.png" alt="psd_sample_comp_high_freq.png" />
</p> </p>
<p><span class="figure-number">Figure 7: </span>PSD of the signal coming from the top geophone (zoom at high frequencies)</p> <p><span class="figure-number">Figure 7: </span>PSD of the signal coming from the top geophone (zoom at high frequencies)</p>
@ -817,8 +817,8 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
<div id="outline-container-org64cfb89" class="outline-4"> <div id="outline-container-orgc2f810b" class="outline-4">
<h4 id="org64cfb89"><span class="section-number-4">2.4.2</span> Vibrations on the marble</h4> <h4 id="orgc2f810b"><span class="section-number-4">2.4.2</span> Vibrations on the marble</h4>
<div class="outline-text-4" id="text-2-4-2"> <div class="outline-text-4" id="text-2-4-2">
<p> <p>
Now we plot the same curves for the geophone located on the marble. Now we plot the same curves for the geophone located on the marble.
@ -834,7 +834,7 @@ Now we plot the same curves for the geophone located on the marble.
</div> </div>
<p> <p>
And we compare the ASD (figures <a href="#orge9b59a5">8</a> and <a href="#org8caf60f">9</a>) And we compare the ASD (figures <a href="#orgbe8f7be">8</a> and <a href="#orgd5c44ba">9</a>)
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>; <pre class="src src-matlab"><span class="org-type">figure</span>;
@ -855,7 +855,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
<div id="orge9b59a5" class="figure"> <div id="orgbe8f7be" class="figure">
<p><img src="figs/psd_marble_comp.png" alt="psd_marble_comp.png" /> <p><img src="figs/psd_marble_comp.png" alt="psd_marble_comp.png" />
</p> </p>
<p><span class="figure-number">Figure 8: </span>PSD of the signal coming from the top geophone</p> <p><span class="figure-number">Figure 8: </span>PSD of the signal coming from the top geophone</p>
@ -863,7 +863,7 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
<div id="org8caf60f" class="figure"> <div id="orgd5c44ba" class="figure">
<p><img src="figs/psd_marble_comp_high_freq.png" alt="psd_marble_comp_high_freq.png" /> <p><img src="figs/psd_marble_comp_high_freq.png" alt="psd_marble_comp_high_freq.png" />
</p> </p>
<p><span class="figure-number">Figure 9: </span>PSD of the signal coming from the top geophone (zoom at high frequencies)</p> <p><span class="figure-number">Figure 9: </span>PSD of the signal coming from the top geophone (zoom at high frequencies)</p>
@ -871,11 +871,11 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org42553b0" class="outline-3"> <div id="outline-container-org43b187d" class="outline-3">
<h3 id="org42553b0"><span class="section-number-3">2.5</span> Effect of the control system on the transmissibility from ground to sample</h3> <h3 id="org43b187d"><span class="section-number-3">2.5</span> Effect of the control system on the transmissibility from ground to sample</h3>
<div class="outline-text-3" id="text-2-5"> <div class="outline-text-3" id="text-2-5">
<p> <p>
As the feedback loops change the dynamics of the system, we should see differences on the transfer function from marble velocity to sample velocity when turning off the control systems (figure <a href="#orgbeaac3f">10</a>). As the feedback loops change the dynamics of the system, we should see differences on the transfer function from marble velocity to sample velocity when turning off the control systems (figure <a href="#org5664b0a">10</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
@ -935,15 +935,15 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="orgbeaac3f" class="figure"> <div id="org5664b0a" class="figure">
<p><img src="figs/trans_comp.png" alt="trans_comp.png" /> <p><img src="figs/trans_comp.png" alt="trans_comp.png" />
</p> </p>
<p><span class="figure-number">Figure 10: </span>Comparison of the transfer function from the geophone on the marble to the geophone at the sample location</p> <p><span class="figure-number">Figure 10: </span>Comparison of the transfer function from the geophone on the marble to the geophone at the sample location</p>
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-org9ad50de" class="outline-3"> <div id="outline-container-org8ffc99d" class="outline-3">
<h3 id="org9ad50de"><span class="section-number-3">2.6</span> Conclusion</h3> <h3 id="org8ffc99d"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6"> <div class="outline-text-3" id="text-2-6">
<div class="important"> <div class="important">
<ul class="org-ul"> <ul class="org-ul">
@ -962,12 +962,12 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-org089e6c4" class="outline-2"> <div id="outline-container-orge358e9f" class="outline-2">
<h2 id="org089e6c4"><span class="section-number-2">3</span> Transfer function from one stage to the other</h2> <h2 id="orge358e9f"><span class="section-number-2">3</span> Transfer function from one stage to the other</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
</div> </div>
<div id="outline-container-org5af1ad1" class="outline-3"> <div id="outline-container-org8671c9c" class="outline-3">
<h3 id="org5af1ad1"><span class="section-number-3">3.1</span> Experimental Setup</h3> <h3 id="org8671c9c"><span class="section-number-3">3.1</span> Experimental Setup</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
For all the measurements in this section: For all the measurements in this section:
@ -978,11 +978,11 @@ For all the measurements in this section:
</ul> </ul>
</div> </div>
<div id="outline-container-org266aa09" class="outline-4"> <div id="outline-container-orgb8620d5" class="outline-4">
<h4 id="org266aa09"><span class="section-number-4">3.1.1</span> From Marble to Ty - <code>mat/meas_010.mat</code></h4> <h4 id="orgb8620d5"><span class="section-number-4">3.1.1</span> From Marble to Ty - <code>mat/meas_010.mat</code></h4>
<div class="outline-text-4" id="text-3-1-1"> <div class="outline-text-4" id="text-3-1-1">
<p> <p>
One geophone is on the marble, one is on the Ty stage (see figures <a href="#org0f2eb79">11</a>, <a href="#orgcdf6183">12</a> and <a href="#orga6a9a3a">13</a>). One geophone is on the marble, one is on the Ty stage (see figures <a href="#org6500e1d">11</a>, <a href="#org3ecc8bf">12</a> and <a href="#org9e84f58">13</a>).
</p> </p>
<p> <p>
@ -1021,21 +1021,21 @@ The <code>data</code> array contains the following columns:
</table> </table>
<div id="org0f2eb79" class="figure"> <div id="org6500e1d" class="figure">
<p><img src="./img/IMG_20190430_155330.jpg" alt="IMG_20190430_155330.jpg" width="500px" /> <p><img src="./img/IMG_20190430_155330.jpg" alt="IMG_20190430_155330.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 11: </span>Setup with one geophone on the marble and one on top of the translation stage</p> <p><span class="figure-number">Figure 11: </span>Setup with one geophone on the marble and one on top of the translation stage</p>
</div> </div>
<div id="orgcdf6183" class="figure"> <div id="org3ecc8bf" class="figure">
<p><img src="./img/IMG_20190430_155335.jpg" alt="IMG_20190430_155335.jpg" width="500px" /> <p><img src="./img/IMG_20190430_155335.jpg" alt="IMG_20190430_155335.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 12: </span>Setup with one geophone on the marble and one on top of the translation stage - Close up view</p> <p><span class="figure-number">Figure 12: </span>Setup with one geophone on the marble and one on top of the translation stage - Close up view</p>
</div> </div>
<div id="orga6a9a3a" class="figure"> <div id="org9e84f58" class="figure">
<p><img src="./img/IMG_20190430_155342.jpg" alt="IMG_20190430_155342.jpg" width="500px" /> <p><img src="./img/IMG_20190430_155342.jpg" alt="IMG_20190430_155342.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 13: </span>Setup with one geophone on the marble and one on top of the translation stage - Top view</p> <p><span class="figure-number">Figure 13: </span>Setup with one geophone on the marble and one on top of the translation stage - Top view</p>
@ -1043,11 +1043,11 @@ The <code>data</code> array contains the following columns:
</div> </div>
</div> </div>
<div id="outline-container-org51f3cb6" class="outline-4"> <div id="outline-container-org3ca3b63" class="outline-4">
<h4 id="org51f3cb6"><span class="section-number-4">3.1.2</span> From Marble to Ry - <code>mat/meas_011.mat</code></h4> <h4 id="org3ca3b63"><span class="section-number-4">3.1.2</span> From Marble to Ry - <code>mat/meas_011.mat</code></h4>
<div class="outline-text-4" id="text-3-1-2"> <div class="outline-text-4" id="text-3-1-2">
<p> <p>
One geophone is on the marble, one is on the Ry stage (see figure <a href="#org7d8f6dd">14</a>) One geophone is on the marble, one is on the Ry stage (see figure <a href="#orgb45486f">14</a>)
</p> </p>
<p> <p>
@ -1086,7 +1086,7 @@ The <code>data</code> array contains the following columns:
</table> </table>
<div id="org7d8f6dd" class="figure"> <div id="orgb45486f" class="figure">
<p><img src="./img/IMG_20190430_163919.jpg" alt="IMG_20190430_163919.jpg" width="500px" /> <p><img src="./img/IMG_20190430_163919.jpg" alt="IMG_20190430_163919.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 14: </span>Setup with one geophone on the marble and one on top of the Tilt Stage</p> <p><span class="figure-number">Figure 14: </span>Setup with one geophone on the marble and one on top of the Tilt Stage</p>
@ -1094,11 +1094,11 @@ The <code>data</code> array contains the following columns:
</div> </div>
</div> </div>
<div id="outline-container-orgd9c5a6f" class="outline-4"> <div id="outline-container-orgff3cde2" class="outline-4">
<h4 id="orgd9c5a6f"><span class="section-number-4">3.1.3</span> From Ty to Ry - <code>mat/meas_012.mat</code></h4> <h4 id="orgff3cde2"><span class="section-number-4">3.1.3</span> From Ty to Ry - <code>mat/meas_012.mat</code></h4>
<div class="outline-text-4" id="text-3-1-3"> <div class="outline-text-4" id="text-3-1-3">
<p> <p>
One geophone is on the Ty stage, one is on the Ry stage (see figures <a href="#orgba2d3e3">15</a>, <a href="#orge407959">16</a> and <a href="#org6526dff">17</a>) One geophone is on the Ty stage, one is on the Ry stage (see figures <a href="#orgf7603bb">15</a>, <a href="#orgea56cfb">16</a> and <a href="#orga7b7318">17</a>)
One geophone on the Ty stage, one geophone on the Ry stage. One geophone on the Ty stage, one geophone on the Ry stage.
</p> </p>
@ -1138,21 +1138,21 @@ The <code>data</code> array contains the following columns:
</table> </table>
<div id="orgba2d3e3" class="figure"> <div id="orgf7603bb" class="figure">
<p><img src="./img/IMG_20190430_170405.jpg" alt="IMG_20190430_170405.jpg" width="500px" /> <p><img src="./img/IMG_20190430_170405.jpg" alt="IMG_20190430_170405.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 15: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage</p> <p><span class="figure-number">Figure 15: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage</p>
</div> </div>
<div id="orge407959" class="figure"> <div id="orgea56cfb" class="figure">
<p><img src="./img/IMG_20190430_170418.jpg" alt="IMG_20190430_170418.jpg" width="500px" /> <p><img src="./img/IMG_20190430_170418.jpg" alt="IMG_20190430_170418.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 16: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Top view</p> <p><span class="figure-number">Figure 16: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Top view</p>
</div> </div>
<div id="org6526dff" class="figure"> <div id="orga7b7318" class="figure">
<p><img src="./img/IMG_20190430_170425.jpg" alt="IMG_20190430_170425.jpg" width="500px" /> <p><img src="./img/IMG_20190430_170425.jpg" alt="IMG_20190430_170425.jpg" width="500px" />
</p> </p>
<p><span class="figure-number">Figure 17: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Close up view</p> <p><span class="figure-number">Figure 17: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Close up view</p>
@ -1161,8 +1161,8 @@ The <code>data</code> array contains the following columns:
</div> </div>
</div> </div>
<div id="outline-container-org3523b58" class="outline-3"> <div id="outline-container-org185b0f5" class="outline-3">
<h3 id="org3523b58"><span class="section-number-3">3.2</span> Load data</h3> <h3 id="org185b0f5"><span class="section-number-3">3.2</span> Load data</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
We load the data of the z axis of two geophones. We load the data of the z axis of two geophones.
@ -1176,8 +1176,8 @@ ty_ry = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="or
</div> </div>
</div> </div>
<div id="outline-container-org2c086d0" class="outline-3"> <div id="outline-container-org1dfb0b9" class="outline-3">
<h3 id="org2c086d0"><span class="section-number-3">3.3</span> Analysis - Time Domain</h3> <h3 id="org1dfb0b9"><span class="section-number-3">3.3</span> Analysis - Time Domain</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<p> <p>
First, we can look at the time domain data. First, we can look at the time domain data.
@ -1196,7 +1196,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="org28c5ecf" class="figure"> <div id="org091d427" class="figure">
<p><img src="figs/time_domain_m_ty.png" alt="time_domain_m_ty.png" /> <p><img src="figs/time_domain_m_ty.png" alt="time_domain_m_ty.png" />
</p> </p>
<p><span class="figure-number">Figure 18: </span>Time domain - Marble and translation stage</p> <p><span class="figure-number">Figure 18: </span>Time domain - Marble and translation stage</p>
@ -1216,7 +1216,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="orgc219487" class="figure"> <div id="org64705f0" class="figure">
<p><img src="figs/time_domain_m_ry.png" alt="time_domain_m_ry.png" /> <p><img src="figs/time_domain_m_ry.png" alt="time_domain_m_ry.png" />
</p> </p>
<p><span class="figure-number">Figure 19: </span>Time domain - Marble and tilt stage</p> <p><span class="figure-number">Figure 19: </span>Time domain - Marble and tilt stage</p>
@ -1235,7 +1235,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="org0dbd78b" class="figure"> <div id="orga9c5a81" class="figure">
<p><img src="figs/time_domain_ty_ry.png" alt="time_domain_ty_ry.png" /> <p><img src="figs/time_domain_ty_ry.png" alt="time_domain_ty_ry.png" />
</p> </p>
<p><span class="figure-number">Figure 20: </span>Time domain - Translation stage and tilt stage</p> <p><span class="figure-number">Figure 20: </span>Time domain - Translation stage and tilt stage</p>
@ -1243,8 +1243,8 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-org63bd941" class="outline-3"> <div id="outline-container-org388dc28" class="outline-3">
<h3 id="org63bd941"><span class="section-number-3">3.4</span> Analysis - Frequency Domain</h3> <h3 id="org388dc28"><span class="section-number-3">3.4</span> Analysis - Frequency Domain</h3>
<div class="outline-text-3" id="text-3-4"> <div class="outline-text-3" id="text-3-4">
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab">dt = m_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> m_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab">dt = m_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> m_ty<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
@ -1255,7 +1255,7 @@ win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span clas
</div> </div>
<p> <p>
First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure <a href="#orgcd25676">21</a>). We also plot their coherence (figure <a href="#org0202f2c">22</a>). First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure <a href="#orgb44305f">21</a>). We also plot their coherence (figure <a href="#orgf8b4679">22</a>).
</p> </p>
<div class="org-src-container"> <div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>T_m_ty, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>; <pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>T_m_ty, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, m_ty<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
@ -1294,7 +1294,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="orgcd25676" class="figure"> <div id="orgb44305f" class="figure">
<p><img src="figs/compare_tf_geophones.png" alt="compare_tf_geophones.png" /> <p><img src="figs/compare_tf_geophones.png" alt="compare_tf_geophones.png" />
</p> </p>
<p><span class="figure-number">Figure 21: </span>Transfer function from the first geophone to the second geophone for the three experiments</p> <p><span class="figure-number">Figure 21: </span>Transfer function from the first geophone to the second geophone for the three experiments</p>
@ -1309,7 +1309,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
<div id="org0202f2c" class="figure"> <div id="orgf8b4679" class="figure">
<p><img src="figs/coherence_two_geophones.png" alt="coherence_two_geophones.png" /> <p><img src="figs/coherence_two_geophones.png" alt="coherence_two_geophones.png" />
</p> </p>
<p><span class="figure-number">Figure 22: </span>Coherence between the two geophones for the three experiments</p> <p><span class="figure-number">Figure 22: </span>Coherence between the two geophones for the three experiments</p>
@ -1317,14 +1317,14 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div> </div>
</div> </div>
<div id="outline-container-orgc82b7b0" class="outline-3"> <div id="outline-container-org26a82a2" class="outline-3">
<h3 id="orgc82b7b0"><span class="section-number-3">3.5</span> Conclusion</h3> <h3 id="org26a82a2"><span class="section-number-3">3.5</span> Conclusion</h3>
</div> </div>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p> <p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-05-02 jeu. 14:06</p> <p class="date">Created: 2019-05-02 jeu. 14:12</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>