Reworked the ground motion page
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Ground Motion Measurements</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgddb7761">1. Experimental Setup</a></li>
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<li><a href="#org828fff9">2. Measurement Analysis</a>
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<ul>
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<li><a href="#orgadf99c0">2.1. Load data</a></li>
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<li><a href="#org93551bb">2.2. Time domain plots</a></li>
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<li><a href="#orgfd0b3a8">2.3. Computation of the ASD of the measured voltage</a></li>
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<li><a href="#org4d7ad21">2.4. Scaling to take into account the sensibility of the geophone and the voltage amplifier</a></li>
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<li><a href="#org1b04be0">2.5. Computation of the ASD of the velocity and displacement</a></li>
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<li><a href="#orge570bf0">2.6. Comparison with other measurements of ground motion</a>
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<ul>
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<li><a href="#org9008f38">2.6.1. Load the measurement data</a></li>
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<li><a href="#org906cad8">2.6.2. Compute PSD of the measurements</a></li>
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<li><a href="#orgab58013">2.6.3. Compare PSD of Cern, ID09 and ID31</a></li>
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</ul>
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</li>
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<h2 id="orgddb7761"><span class="section-number-2">1</span> Experimental Setup</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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The goal here is to compare the ground motion at the location of the micro-station (ID31 beamline at ESRF) with other measurements of the ground motion.
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</p>
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<p>
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This will also permit to confirm that the device use for the measurement (geophones, amplifiers, ADC) are working well and that the data processing is correct.
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</p>
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<p>
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One L22 geophone is put on the ID31 floor.
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The signal is then filtered with a first order low pass filter with a cut-off frequency of \(1kHz\).
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Then the signal is amplified by a Voltage Amplifier with the following settings:
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</p>
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<ul class="org-ul">
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<li>AC/DC option set to DC</li>
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<li>Amplification of 60dB (1000)</li>
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<li>Low pass filter at the output with a cut-off frequency of \(1kHz\)</li>
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</ul>
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<p>
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On figure <a href="#org3e1d768">1</a> is an overview of multiple measurements made at famous location.
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</p>
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<div id="org3e1d768" class="figure">
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<p><img src="./img/ground_motion_measurements.png" alt="ground_motion_measurements.png" width="800px" />
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</p>
|
||||
<p><span class="figure-number">Figure 1: </span>Power spectral density of ground vibration in the vertical direction at multiple locations (<a href="https://vibration.desy.de/">source</a>)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org828fff9" class="outline-2">
|
||||
<h2 id="org828fff9"><span class="section-number-2">2</span> Measurement Analysis</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="org1ffac8a"></a>
|
||||
</p>
|
||||
|
||||
<div class="note">
|
||||
<p>
|
||||
All the files (data and Matlab scripts) are accessible <a href="data/ground_meas_id31.zip">here</a>.
|
||||
</p>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgadf99c0" class="outline-3">
|
||||
<h3 id="orgadf99c0"><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">data = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_028.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; data = data.data;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org93551bb" class="outline-3">
|
||||
<h3 id="org93551bb"><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>;
|
||||
hold on;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><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>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orga85fb0d" class="figure">
|
||||
<p><img src="figs/ground_motion_id31_time.png" alt="ground_motion_id31_time.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Measurement of the ground motion - Time domain</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgfd0b3a8" class="outline-3">
|
||||
<h3 id="orgfd0b3a8"><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="org-src-container">
|
||||
<pre class="src src-matlab">dt = data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span> <span class="org-type">-</span> data<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
|
||||
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt;
|
||||
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">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>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>px_dc, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>data<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, 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 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>px_dc<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">'</span>Amplitude Spectral Density $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
||||
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org6f3989c" class="figure">
|
||||
<p><img src="figs/ground_motion_id31_asd_volt.png" alt="ground_motion_id31_asd_volt.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>Amplitude Spectral Density of the measured Voltage</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4d7ad21" class="outline-3">
|
||||
<h3 id="org4d7ad21"><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">
|
||||
<p>
|
||||
The Geophone used are L22. Their sensibility is shown on figure <a href="#org137d089">4</a>.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">S0 = <span class="org-highlight-numbers-number">88</span>; <span class="org-comment">% Sensitivity [V/(m/s)]</span>
|
||||
f0 = <span class="org-highlight-numbers-number">2</span>; <span class="org-comment">% Cut-off frequency [Hz]</span>
|
||||
|
||||
S = S0<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>f0<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span><span class="org-type">+</span>s<span class="org-type">/</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">/</span>f0<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org137d089" class="figure">
|
||||
<p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Sensibility of the Geophone</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We also take into account the gain of the electronics which is here set to be \(60dB\).
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">G0_db = <span class="org-highlight-numbers-number">60</span>; <span class="org-comment">% [dB]</span>
|
||||
|
||||
G0 = <span class="org-highlight-numbers-number">10</span><span class="org-type">^</span><span class="org-rainbow-delimiters-depth-1">(</span>G0_db<span class="org-type">/</span><span class="org-highlight-numbers-number">20</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% [abs]</span>
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We divide the ASD measured (in \(\text{V}/\sqrt{\text{Hz}}\)) by the gain of the voltage amplifier to obtain the ASD of the voltage across the geophone.
|
||||
We further divide the result by the sensibility of the Geophone to obtain the ASD of the velocity in \(m/s/\sqrt{Hz}\).
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">scaling = <span class="org-highlight-numbers-number">1</span><span class="org-type">./</span>squeeze<span class="org-rainbow-delimiters-depth-1">(</span>abs<span class="org-rainbow-delimiters-depth-2">(</span>freqresp<span class="org-rainbow-delimiters-depth-3">(</span>G0<span class="org-type">*</span>S, f, <span class="org-string">'Hz'</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1b04be0" class="outline-3">
|
||||
<h3 id="org1b04be0"><span class="section-number-3">2.5</span> Computation of the ASD of the velocity and displacement</h3>
|
||||
<div class="outline-text-3" id="text-2-5">
|
||||
<p>
|
||||
The ASD of the measured velocity is shown on figure <a href="#orgcf7bd1e">5</a>.
|
||||
</p>
|
||||
|
||||
<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>px_dc<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
hold off;
|
||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Velocity $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-type">/</span>s<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
||||
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgcf7bd1e" class="figure">
|
||||
<p><img src="figs/ground_motion_id31_asd_velocity.png" alt="ground_motion_id31_asd_velocity.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the Velocity</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We also plot the ASD in displacement (figure <a href="#orge1d92c4">6</a>);
|
||||
</p>
|
||||
|
||||
<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, <span class="org-rainbow-delimiters-depth-2">(</span>sqrt<span class="org-rainbow-delimiters-depth-3">(</span>px_dc<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span><span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
hold off;
|
||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the displacement $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>m<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
||||
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orge1d92c4" class="figure">
|
||||
<p><img src="figs/ground_motion_id31_asd_displacement.png" alt="ground_motion_id31_asd_displacement.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Amplitude Spectral Density of the Displacement</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
And we also plot the PSD of the displacement in \(\frac{{\mu u}^2}{Hz}\) as it is a usual unit used (figure <a href="#org149605d">7</a>).
|
||||
One can then compare this curve with the figure <a href="#org3e1d768">1</a>.
|
||||
</p>
|
||||
|
||||
<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, <span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">(</span>sqrt<span class="org-rainbow-delimiters-depth-4">(</span>px_dc<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">./</span><span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">.*</span><span class="org-highlight-numbers-number">1e6</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-rainbow-delimiters-depth-1">)</span>;
|
||||
hold off;
|
||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>PSD of the measured displacement $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span><span class="org-rainbow-delimiters-depth-4">{</span> <span class="org-type">\</span>mu m <span class="org-rainbow-delimiters-depth-4">}</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-3">}{</span>Hz<span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
|
||||
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org149605d" class="figure">
|
||||
<p><img src="figs/ground_motion_id31_psd_displacement.png" alt="ground_motion_id31_psd_displacement.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Power Spectral Density of the measured displacement</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orge570bf0" class="outline-3">
|
||||
<h3 id="orge570bf0"><span class="section-number-3">2.6</span> Comparison with other measurements of ground motion</h3>
|
||||
<div class="outline-text-3" id="text-2-6">
|
||||
<p>
|
||||
Now we will compare with other measurements.
|
||||
</p>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org9008f38" class="outline-4">
|
||||
<h4 id="org9008f38"><span class="section-number-4">2.6.1</span> Load the measurement data</h4>
|
||||
<div class="outline-text-4" id="text-2-6-1">
|
||||
<p>
|
||||
First we load the measurement data.
|
||||
Here we have one measurement of the floor motion made at the ESRF in 2018, and one measurement made at CERN.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">id09 = load<span class="org-rainbow-delimiters-depth-1">(</span>'<span class="org-type">./</span>mat<span class="org-type">/</span>id09_floor_september2018.mat'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
cern = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./mat/ground_motion_dist.mat'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org906cad8" class="outline-4">
|
||||
<h4 id="org906cad8"><span class="section-number-4">2.6.2</span> Compute PSD of the measurements</h4>
|
||||
<div class="outline-text-4" id="text-2-6-2">
|
||||
<p>
|
||||
We compute the Power Spectral Densities of the measurements.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Fs_id09 = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span>id09.time3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>id09.time3<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
win_id09 = 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_id09<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-rainbow-delimiters-depth-1">[</span>id09_pxx, id09_f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1e</span><span class="org-type">-</span><span class="org-highlight-numbers-number">6</span><span class="org-type">*</span>id09.x_y_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>, win_id09, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs_id09<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Fs_cern = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span>cern.gm.time<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>cern.gm.time<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
win_cern = 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_cern<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
<span class="org-rainbow-delimiters-depth-1">[</span>cern_pxx, cern_f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>cern.gm.signal, win_cern, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs_cern<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgab58013" class="outline-4">
|
||||
<h4 id="orgab58013"><span class="section-number-4">2.6.3</span> Compare PSD of Cern, ID09 and ID31</h4>
|
||||
<div class="outline-text-4" id="text-2-6-3">
|
||||
<p>
|
||||
And we compare all the measurements (figure <a href="#org2a2b94e">8</a>).
|
||||
</p>
|
||||
|
||||
<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>id09_f, id09_pxx, <span class="org-string">'DisplayName', '</span>ID09'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>cern_f, cern_pxx, <span class="org-string">'DisplayName', 'CERN'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-rainbow-delimiters-depth-2">(</span><span class="org-rainbow-delimiters-depth-3">(</span>sqrt<span class="org-rainbow-delimiters-depth-4">(</span>px_dc<span class="org-rainbow-delimiters-depth-4">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">./</span><span class="org-rainbow-delimiters-depth-3">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-3">)</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-string">'k', 'DisplayName', 'ID31'</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-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'YScale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
xlabel<span class="org-rainbow-delimiters-depth-1">(</span>'Frequency <span class="org-rainbow-delimiters-depth-2">[</span>Hz<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span>'PSD <span class="org-rainbow-delimiters-depth-2">[</span>$m<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span>Hz$<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>;
|
||||
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org2a2b94e" class="figure">
|
||||
<p><img src="figs/ground_motion_compare.png" alt="ground_motion_compare.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Comparison of the PSD of the ground motion measured at different location</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2019-05-10 ven. 17:51</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
280
ground-motion/index.org
Normal file
280
ground-motion/index.org
Normal file
@@ -0,0 +1,280 @@
|
||||
#+TITLE: Ground Motion Measurements
|
||||
#+SETUPFILE: ../config.org
|
||||
|
||||
* Experimental Setup
|
||||
The goal here is to compare the ground motion at the location of the micro-station (ID31 beamline at ESRF) with other measurements of the ground motion.
|
||||
|
||||
This will also permit to confirm that the device use for the measurement (geophones, amplifiers, ADC) are working well and that the data processing is correct.
|
||||
|
||||
One L22 geophone is put on the ID31 floor.
|
||||
The signal is then filtered with a first order low pass filter with a cut-off frequency of $1kHz$.
|
||||
Then the signal is amplified by a Voltage Amplifier with the following settings:
|
||||
- AC/DC option set to DC
|
||||
- Amplification of 60dB (1000)
|
||||
- Low pass filter at the output with a cut-off frequency of $1kHz$
|
||||
|
||||
On figure [[fig:ground_motion_measurements]] is an overview of multiple measurements made at famous location.
|
||||
|
||||
#+name: fig:ground_motion_measurements
|
||||
#+caption: Power spectral density of ground vibration in the vertical direction at multiple locations ([[https://vibration.desy.de/][source]])
|
||||
#+attr_html: :width 800px
|
||||
[[file:./img/ground_motion_measurements.png]]
|
||||
|
||||
* Measurement Analysis
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle matlab/ground_meas_id31.m
|
||||
:header-args:matlab+: :comments org :mkdirp yes
|
||||
:END:
|
||||
<<sec:ground_meas_id31>>
|
||||
|
||||
#+begin_src bash :exports none :results none
|
||||
if [ matlab/ground_meas_id31.m -nt data/ground_meas_id31.zip ]; then
|
||||
cp matlab/ground_meas_id31.m ground_meas_id31.m;
|
||||
zip data/ground_meas_id31 \
|
||||
mat/data_028.mat \
|
||||
mat/id09_floor_september2018.mat \
|
||||
mat/ground_motion_dist.mat \
|
||||
ground_meas_id31.m
|
||||
rm ground_meas_id31.m;
|
||||
fi
|
||||
#+end_src
|
||||
|
||||
#+begin_note
|
||||
All the files (data and Matlab scripts) are accessible [[file:data/ground_meas_id31.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
|
||||
data = load('mat/data_028.mat', 'data'); data = data.data;
|
||||
#+end_src
|
||||
|
||||
** Time domain plots
|
||||
#+begin_src matlab
|
||||
figure;
|
||||
hold on;
|
||||
plot(data(:, 3), data(:, 1));
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Voltage [V]');
|
||||
xlim([0, 100]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:ground_motion_id31_time
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/ground_motion_id31_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:ground_motion_id31_time
|
||||
#+CAPTION: Measurement of the ground motion - Time domain
|
||||
#+RESULTS: fig:ground_motion_id31_time
|
||||
[[file:figs/ground_motion_id31_time.png]]
|
||||
|
||||
** Computation of the ASD of the measured voltage
|
||||
#+begin_src matlab :results none
|
||||
dt = data(2, 3) - data(1, 3);
|
||||
|
||||
Fs = 1/dt;
|
||||
win = hanning(ceil(10*Fs));
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results none
|
||||
[px_dc, f] = pwelch(data(:, 1), win, [], [], Fs);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(px_dc));
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log');
|
||||
set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
|
||||
xlim([0.1, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:ground_motion_id31_asd_volt
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/ground_motion_id31_asd_volt.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:ground_motion_id31_asd_volt
|
||||
#+CAPTION: Amplitude Spectral Density of the measured Voltage
|
||||
#+RESULTS: fig:ground_motion_id31_asd_volt
|
||||
[[file:figs/ground_motion_id31_asd_volt.png]]
|
||||
|
||||
** Scaling to take into account the sensibility of the geophone and the voltage amplifier
|
||||
The Geophone used are L22. Their sensibility is shown on figure [[fig:geophone_sensibility]].
|
||||
|
||||
#+begin_src matlab :results none
|
||||
S0 = 88; % Sensitivity [V/(m/s)]
|
||||
f0 = 2; % Cut-off frequency [Hz]
|
||||
|
||||
S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results none :exports none
|
||||
figure;
|
||||
bodeFig({S}, logspace(-1, 2, 1000));
|
||||
ylabel('Amplitude $\left[\frac{V}{m/s}\right]$')
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:geophone_sensibility
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/geophone_sensibility.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:geophone_sensibility
|
||||
#+CAPTION: Sensibility of the Geophone
|
||||
#+RESULTS: fig:geophone_sensibility
|
||||
[[file:figs/geophone_sensibility.png]]
|
||||
|
||||
We also take into account the gain of the electronics which is here set to be $60dB$.
|
||||
|
||||
#+begin_src matlab :results none
|
||||
G0_db = 60; % [dB]
|
||||
|
||||
G0 = 10^(G0_db/20); % [abs]
|
||||
#+end_src
|
||||
|
||||
We divide the ASD measured (in $\text{V}/\sqrt{\text{Hz}}$) by the gain of the voltage amplifier to obtain the ASD of the voltage across the geophone.
|
||||
We further divide the result by the sensibility of the Geophone to obtain the ASD of the velocity in $m/s/\sqrt{Hz}$.
|
||||
|
||||
#+begin_src matlab :results none
|
||||
scaling = 1./squeeze(abs(freqresp(G0*S, f, 'Hz')));
|
||||
#+end_src
|
||||
|
||||
** Computation of the ASD of the velocity and displacement
|
||||
The ASD of the measured velocity is shown on figure [[fig:ground_motion_id31_asd_velocity]].
|
||||
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(px_dc).*scaling);
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log');
|
||||
set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
|
||||
xlim([0.1, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:ground_motion_id31_asd_velocity
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/ground_motion_id31_asd_velocity.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:ground_motion_id31_asd_velocity
|
||||
#+CAPTION: Amplitude Spectral Density of the Velocity
|
||||
#+RESULTS: fig:ground_motion_id31_asd_velocity
|
||||
[[file:figs/ground_motion_id31_asd_velocity.png]]
|
||||
|
||||
We also plot the ASD in displacement (figure [[fig:ground_motion_id31_asd_displacement]]);
|
||||
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, (sqrt(px_dc).*scaling)./(2*pi*f));
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
|
||||
xlim([0.1, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:ground_motion_id31_asd_displacement
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/ground_motion_id31_asd_displacement.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:ground_motion_id31_asd_displacement
|
||||
#+CAPTION: Amplitude Spectral Density of the Displacement
|
||||
#+RESULTS: fig:ground_motion_id31_asd_displacement
|
||||
[[file:figs/ground_motion_id31_asd_displacement.png]]
|
||||
|
||||
And we also plot the PSD of the displacement in $\frac{{\mu u}^2}{Hz}$ as it is a usual unit used (figure [[fig:ground_motion_id31_psd_displacement]]).
|
||||
One can then compare this curve with the figure [[fig:ground_motion_measurements]].
|
||||
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, ((sqrt(px_dc).*scaling)./(2*pi*f).*1e6).^2);
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log');
|
||||
set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('PSD of the measured displacement $\left[\frac{{ \mu m }^2}{Hz}\right]$')
|
||||
xlim([0.1, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:ground_motion_id31_psd_displacement
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/ground_motion_id31_psd_displacement.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:ground_motion_id31_psd_displacement
|
||||
#+CAPTION: Power Spectral Density of the measured displacement
|
||||
#+RESULTS: fig:ground_motion_id31_psd_displacement
|
||||
[[file:figs/ground_motion_id31_psd_displacement.png]]
|
||||
|
||||
** Comparison with other measurements of ground motion
|
||||
Now we will compare with other measurements.
|
||||
|
||||
*** Load the measurement data
|
||||
First we load the measurement data.
|
||||
Here we have one measurement of the floor motion made at the ESRF in 2018, and one measurement made at CERN.
|
||||
#+begin_src matlab
|
||||
id09 = load('./mat/id09_floor_september2018.mat');
|
||||
cern = load('./mat/ground_motion_dist.mat');
|
||||
#+end_src
|
||||
|
||||
*** Compute PSD of the measurements
|
||||
We compute the Power Spectral Densities of the measurements.
|
||||
#+begin_src matlab
|
||||
Fs_id09 = 1/(id09.time3(2)-id09.time3(1));
|
||||
win_id09 = hanning(ceil(10*Fs_id09));
|
||||
[id09_pxx, id09_f] = pwelch(1e-6*id09.x_y_z(:, 3), win_id09, [], [], Fs_id09);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab
|
||||
Fs_cern = 1/(cern.gm.time(2)-cern.gm.time(1));
|
||||
win_cern = hanning(ceil(10*Fs_cern));
|
||||
[cern_pxx, cern_f] = pwelch(cern.gm.signal, win_cern, [], [], Fs_cern);
|
||||
#+end_src
|
||||
|
||||
*** Compare PSD of Cern, ID09 and ID31
|
||||
And we compare all the measurements (figure [[fig:ground_motion_compare]]).
|
||||
|
||||
#+begin_src matlab :results silent
|
||||
figure;
|
||||
hold on;
|
||||
plot(id09_f, id09_pxx, 'DisplayName', 'ID09');
|
||||
plot(cern_f, cern_pxx, 'DisplayName', 'CERN');
|
||||
plot(f, ((sqrt(px_dc).*scaling)./(2*pi*f)).^2, 'k', 'DisplayName', 'ID31');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('PSD [$m^2/Hz$]');
|
||||
legend('Location', 'northeast');
|
||||
xlim([0.1, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:ground_motion_compare
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/ground_motion_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:ground_motion_compare
|
||||
#+CAPTION: Comparison of the PSD of the ground motion measured at different location
|
||||
#+RESULTS: fig:ground_motion_compare
|
||||
[[file:figs/ground_motion_compare.png]]
|
||||
BIN
ground-motion/mat/data_027.mat
Normal file
BIN
ground-motion/mat/data_027.mat
Normal file
Binary file not shown.
BIN
ground-motion/mat/data_028.mat
Normal file
BIN
ground-motion/mat/data_028.mat
Normal file
Binary file not shown.
BIN
ground-motion/mat/ground_motion_dist.mat
Normal file
BIN
ground-motion/mat/ground_motion_dist.mat
Normal file
Binary file not shown.
BIN
ground-motion/mat/id09_floor_september2018.mat
Normal file
BIN
ground-motion/mat/id09_floor_september2018.mat
Normal file
Binary file not shown.
152
ground-motion/matlab/ground_meas_id31.m
Normal file
152
ground-motion/matlab/ground_meas_id31.m
Normal file
@@ -0,0 +1,152 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
% Load data
|
||||
|
||||
data = load('mat/data_028.mat', 'data'); data = data.data;
|
||||
|
||||
% Time domain plots
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(data(:, 3), data(:, 1));
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Voltage [V]');
|
||||
xlim([0, 100]);
|
||||
|
||||
% Computation of the ASD of the measured voltage
|
||||
|
||||
dt = data(2, 3) - data(1, 3);
|
||||
|
||||
Fs = 1/dt;
|
||||
win = hanning(ceil(10*Fs));
|
||||
|
||||
[px_dc, f] = pwelch(data(:, 1), win, [], [], Fs);
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(px_dc));
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log');
|
||||
set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
|
||||
xlim([0.1, 500]);
|
||||
|
||||
% Scaling to take into account the sensibility of the geophone and the voltage amplifier
|
||||
% The Geophone used are L22. Their sensibility is shown on figure [[fig:geophone_sensibility]].
|
||||
|
||||
|
||||
S0 = 88; % Sensitivity [V/(m/s)]
|
||||
f0 = 2; % Cut-off frequency [Hz]
|
||||
|
||||
S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);
|
||||
|
||||
figure;
|
||||
bodeFig({S}, logspace(-1, 2, 1000));
|
||||
ylabel('Amplitude $\left[\frac{V}{m/s}\right]$')
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:geophone_sensibility
|
||||
% #+CAPTION: Sensibility of the Geophone
|
||||
% #+RESULTS: fig:geophone_sensibility
|
||||
% [[file:figs/geophone_sensibility.png]]
|
||||
|
||||
% We also take into account the gain of the electronics which is here set to be $60dB$.
|
||||
|
||||
|
||||
G0_db = 60; % [dB]
|
||||
|
||||
G0 = 10^(G0_db/20); % [abs]
|
||||
|
||||
|
||||
|
||||
% We divide the ASD measured (in $\text{V}/\sqrt{\text{Hz}}$) by the gain of the voltage amplifier to obtain the ASD of the voltage across the geophone.
|
||||
% We further divide the result by the sensibility of the Geophone to obtain the ASD of the velocity in $m/s/\sqrt{Hz}$.
|
||||
|
||||
|
||||
scaling = 1./squeeze(abs(freqresp(G0*S, f, 'Hz')));
|
||||
|
||||
% Computation of the ASD of the velocity
|
||||
% The ASD of the measured velocity is shown on figure [[fig:ground_motion_id31_asd_velocity]].
|
||||
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(px_dc).*scaling);
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log');
|
||||
set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
|
||||
xlim([0.1, 500]);
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:ground_motion_id31_asd_velocity
|
||||
% #+CAPTION: Amplitude Spectral Density of the Velocity
|
||||
% #+RESULTS: fig:ground_motion_id31_asd_velocity
|
||||
% [[file:figs/ground_motion_id31_asd_velocity.png]]
|
||||
|
||||
% We also plot the ASD in displacement (figure [[fig:ground_motion_id31_asd_displacement]]);
|
||||
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, (sqrt(px_dc).*scaling)./(2*pi*f));
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
|
||||
xlim([0.1, 500]);
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:ground_motion_id31_asd_displacement
|
||||
% #+CAPTION: Amplitude Spectral Density of the Displacement
|
||||
% #+RESULTS: fig:ground_motion_id31_asd_displacement
|
||||
% [[file:figs/ground_motion_id31_asd_displacement.png]]
|
||||
% And also in $\frac{{\mu u}^2}{Hz}$ (figure [[fig:ground_motion_id31_psd_displacement]]).
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, ((sqrt(px_dc).*scaling)./(2*pi*f).*1e6).^2);
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log');
|
||||
set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('PSD of the measured displacement $\left[\frac{{ \mu m }^2}{Hz}\right]$')
|
||||
xlim([0.1, 500]);
|
||||
|
||||
% Load the measurement data
|
||||
% First we load the measurement data.
|
||||
% Here we have one measurement of the floor motion made at the ESRF in 2018, and one measurement made at CERN.
|
||||
|
||||
id09 = load('./mat/id09_floor_september2018.mat');
|
||||
cern = load('./mat/ground_motion_dist.mat');
|
||||
|
||||
% Compute PSD of the measurements
|
||||
% We compute the Power Spectral Densities of the measurements.
|
||||
|
||||
Fs_id09 = 1/(id09.time3(2)-id09.time3(1));
|
||||
win_id09 = hanning(ceil(10*Fs_id09));
|
||||
[id09_pxx, id09_f] = pwelch(1e-6*id09.x_y_z(:, 3), win_id09, [], [], Fs_id09);
|
||||
|
||||
Fs_cern = 1/(cern.gm.time(2)-cern.gm.time(1));
|
||||
win_cern = hanning(ceil(10*Fs_cern));
|
||||
[cern_pxx, cern_f] = pwelch(cern.gm.signal, win_cern, [], [], Fs_cern);
|
||||
|
||||
% Compare PSD of Cern, ID09 and ID31
|
||||
% And we compare all the measurements (figure [[fig:ground_motion_compare]]).
|
||||
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(id09_f, id09_pxx, 'DisplayName', 'ID09');
|
||||
plot(cern_f, cern_pxx, 'DisplayName', 'CERN');
|
||||
plot(f, ((sqrt(px_dc).*scaling)./(2*pi*f)).^2, 'k', 'DisplayName', 'ID31');
|
||||
hold off;
|
||||
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('PSD [$m^2/Hz$]');
|
||||
legend('Location', 'northeast');
|
||||
xlim([0.1, 500]);
|
||||
13
ground-motion/readme.org
Normal file
13
ground-motion/readme.org
Normal file
@@ -0,0 +1,13 @@
|
||||
Measure of the ground vibration with the L22
|
||||
|
||||
MEAS27
|
||||
|
||||
60dB
|
||||
AC
|
||||
1kHz
|
||||
|
||||
LPF at 1kHz
|
||||
|
||||
|
||||
MEAS28
|
||||
same but DC
|
||||
Reference in New Issue
Block a user