Add ASD of displacement
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huddle-test-geophones/figs/asd_displacement.png
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huddle-test-geophones/figs/asd_displacement.png
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@ -3,7 +3,7 @@
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2019-04-18 jeu. 17:11 -->
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<!-- 2019-04-18 jeu. 17:24 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>SpeedGoat</title>
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@ -276,36 +276,36 @@ for the JavaScript code in this tag.
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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="#orgeb3ab60">1. Experimental Setup</a></li>
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<li><a href="#org17b1fa2">2. Signal Processing</a>
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<li><a href="#org3e6baac">1. Experimental Setup</a></li>
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<li><a href="#org924e227">2. Signal Processing</a>
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<ul>
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<li><a href="#orge77a4ee">2.1. Load data</a></li>
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<li><a href="#org6b7befd">2.2. Time Domain Data</a></li>
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<li><a href="#org4e41681">2.3. Computation of the ASD of the measured voltage</a></li>
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<li><a href="#org83cd67f">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="#orge0f93a9">2.5. Computation of the ASD of the velocity</a></li>
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<li><a href="#orgd178821">2.6. Transfer function between the two geophones</a></li>
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<li><a href="#orgaf0dac1">2.7. Estimation of the sensor noise</a></li>
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<li><a href="#org8f54945">2.1. Load data</a></li>
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<li><a href="#org26953ea">2.2. Time Domain Data</a></li>
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<li><a href="#orgea14a3e">2.3. Computation of the ASD of the measured voltage</a></li>
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<li><a href="#org10d59fe">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="#orgca371f4">2.5. Computation of the ASD of the velocity</a></li>
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<li><a href="#orgd108d7b">2.6. Transfer function between the two geophones</a></li>
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<li><a href="#orgd3b08ee">2.7. Estimation of the sensor noise</a></li>
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</ul>
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</li>
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<li><a href="#org126e178">3. Compare axis</a>
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<li><a href="#orgdb15af9">3. Compare axis</a>
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<ul>
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<li><a href="#org3f6cac8">3.1. Load data</a></li>
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<li><a href="#org608de0c">3.2. Compare PSD</a></li>
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<li><a href="#org4db3872">3.3. Compare TF</a></li>
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<li><a href="#orgba2e891">3.1. Load data</a></li>
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<li><a href="#org4fa1ea3">3.2. Compare PSD</a></li>
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<li><a href="#org413e0a4">3.3. Compare TF</a></li>
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</ul>
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</li>
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<li><a href="#org66ca70f">4. Appendix</a>
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<li><a href="#org47dea1f">4. Appendix</a>
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<ul>
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<li><a href="#org7492edb">4.1. Computation of coherence from PSD and CSD</a></li>
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<li><a href="#orgc970c0a">4.1. Computation of coherence from PSD and CSD</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orgeb3ab60" class="outline-2">
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<h2 id="orgeb3ab60"><span class="section-number-2">1</span> Experimental Setup</h2>
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<div id="outline-container-org3e6baac" class="outline-2">
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<h2 id="org3e6baac"><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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Two L22 geophones are used.
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@ -319,14 +319,14 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
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</p>
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<div id="orgfe0dca3" class="figure">
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<div id="org1834fe1" class="figure">
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<p><img src="./figs/setup.jpg" alt="setup.jpg" width="500px" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Setup</p>
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</div>
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<div id="orgbcec6a9" class="figure">
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<div id="orgd38e8c5" class="figure">
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<p><img src="./figs/geophones.jpg" alt="geophones.jpg" width="500px" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Geophones</p>
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@ -334,8 +334,8 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
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</div>
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</div>
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<div id="outline-container-org17b1fa2" class="outline-2">
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<h2 id="org17b1fa2"><span class="section-number-2">2</span> Signal Processing</h2>
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<div id="outline-container-org924e227" class="outline-2">
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<h2 id="org924e227"><span class="section-number-2">2</span> Signal Processing</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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The Matlab computing file for this part is accessible <a href="signal_processing.m">here</a>.
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@ -343,8 +343,8 @@ The <code>mat</code> file containing the measurement data is accessible <a href=
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</p>
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</div>
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<div id="outline-container-orge77a4ee" class="outline-3">
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<h3 id="orge77a4ee"><span class="section-number-3">2.1</span> Load data</h3>
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<div id="outline-container-org8f54945" class="outline-3">
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<h3 id="org8f54945"><span class="section-number-3">2.1</span> Load data</h3>
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<div class="outline-text-3" id="text-2-1">
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<p>
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We load the data of the z axis of two geophones.
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@ -358,8 +358,8 @@ dt = t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-high
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</div>
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</div>
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<div id="outline-container-org6b7befd" class="outline-3">
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<h3 id="org6b7befd"><span class="section-number-3">2.2</span> Time Domain Data</h3>
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<div id="outline-container-org26953ea" class="outline-3">
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<h3 id="org26953ea"><span class="section-number-3">2.2</span> Time Domain Data</h3>
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<div class="outline-text-3" id="text-2-2">
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-type">figure</span>;
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@ -374,7 +374,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
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</div>
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<div id="org0161433" class="figure">
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<div id="orge43c98a" class="figure">
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<p><img src="figs/data_time_domain.png" alt="data_time_domain.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Time domain Data</p>
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@ -394,7 +394,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
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</div>
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<div id="orgab64b52" class="figure">
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<div id="orgb1d4c24" class="figure">
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<p><img src="figs/data_time_domain_zoom.png" alt="data_time_domain_zoom.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Time domain Data - Zoom</p>
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@ -402,8 +402,8 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
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</div>
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</div>
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<div id="outline-container-org4e41681" class="outline-3">
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<h3 id="org4e41681"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3>
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<div id="outline-container-orgea14a3e" class="outline-3">
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<h3 id="orgea14a3e"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3>
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<div class="outline-text-3" id="text-2-3">
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<p>
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We first define the parameters for the frequency domain analysis.
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@ -422,12 +422,12 @@ Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/
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</div>
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</div>
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<div id="outline-container-org83cd67f" class="outline-3">
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<h3 id="org83cd67f"><span class="section-number-3">2.4</span> Scaling to take into account the sensibility of the geophone and the voltage amplifier</h3>
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<div id="outline-container-org10d59fe" class="outline-3">
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<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>
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<div class="outline-text-3" id="text-2-4">
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<p>
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The Geophone used are L22.
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Their sensibility are shown on figure <a href="#orgf03c4b4">5</a>.
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Their sensibility are shown on figure <a href="#org542fee1">5</a>.
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</p>
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<div class="org-src-container">
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@ -438,7 +438,7 @@ S = <span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type"
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</div>
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<div id="orgf03c4b4" class="figure">
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<div id="org542fee1" class="figure">
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<p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Sensibility of the Geophone</p>
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@ -453,7 +453,7 @@ The amplifiers also include a low pass filter with a cut-off frequency set at 1k
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<div class="org-src-container">
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<pre class="src src-matlab">G0 = <span class="org-highlight-numbers-number">60</span>; <span class="org-comment">% [dB]</span>
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G = G0<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><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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G = <span class="org-highlight-numbers-number">10</span><span class="org-type">^</span><span class="org-rainbow-delimiters-depth-1">(</span>G0<span class="org-type">/</span><span class="org-highlight-numbers-number">20</span><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><span class="org-highlight-numbers-number">1000</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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</pre>
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</div>
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@ -463,24 +463,24 @@ We further divide the result by the sensibility of the Geophone to obtain the AS
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</p>
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<div class="org-src-container">
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<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>G, f, <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 class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">./squeeze</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">abs</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">(</span></span><span class="org-string">freqresp</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">(</span></span><span class="org-string">S, f, '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>;
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<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>G<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>;
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-orge0f93a9" class="outline-3">
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<h3 id="orge0f93a9"><span class="section-number-3">2.5</span> Computation of the ASD of the velocity</h3>
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<div id="outline-container-orgca371f4" class="outline-3">
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<h3 id="orgca371f4"><span class="section-number-3">2.5</span> Computation of the ASD of the velocity</h3>
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<div class="outline-text-3" id="text-2-5">
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<p>
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The ASD of the measured velocity is shown on figure <a href="#org9a56511">6</a>.
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The ASD of the measured velocity is shown on figure <a href="#orga342d1d">6</a>.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"><span class="org-type">figure</span>;
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hold on;
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plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx1<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>scaling<span class="org-rainbow-delimiters-depth-1">)</span>;
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plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx2<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">./</span>scaling<span class="org-rainbow-delimiters-depth-1">)</span>;
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plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx1<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-1">)</span>;
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plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxx2<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">.*</span>scaling<span class="org-rainbow-delimiters-depth-1">)</span>;
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hold off;
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<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>;
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<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>;
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@ -490,24 +490,47 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
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</div>
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<div id="org9a56511" class="figure">
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<div id="orga342d1d" class="figure">
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<p><img src="figs/psd_velocity.png" alt="psd_velocity.png" />
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</p>
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<p><span class="figure-number">Figure 6: </span>Spectral density of the velocity</p>
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</div>
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<p>
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We also plot the ASD in displacement (figure <a href="#orgb224e73">7</a>);
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</p>
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<div class="org-src-container">
|
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<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>pxx1<span class="org-type">.*</span>scaling<span class="org-type">./</span>f<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>;
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plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-rainbow-delimiters-depth-2">(</span>pxx2<span class="org-type">.*</span>scaling<span class="org-type">./</span>f<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>;
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hold off;
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<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>;
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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>
|
||||
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</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="orgb224e73" class="figure">
|
||||
<p><img src="figs/asd_displacement.png" alt="asd_displacement.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the displacement as measured by the geophones</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd178821" class="outline-3">
|
||||
<h3 id="orgd178821"><span class="section-number-3">2.6</span> Transfer function between the two geophones</h3>
|
||||
<div id="outline-container-orgd108d7b" class="outline-3">
|
||||
<h3 id="orgd108d7b"><span class="section-number-3">2.6</span> Transfer function between the two geophones</h3>
|
||||
<div class="outline-text-3" id="text-2-6">
|
||||
<p>
|
||||
We here compute the transfer function from one geophone to the other.
|
||||
The result is shown on figure <a href="#orgb6c07f9">7</a>.
|
||||
The result is shown on figure <a href="#org9006692">8</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
We also compute the coherence between the two signals (figure <a href="#org1b45a36">8</a>).
|
||||
We also compute the coherence between the two signals (figure <a href="#org9200232">9</a>).
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
@ -516,10 +539,10 @@ We also compute the coherence between the two signals (figure <a href="#org1b45a
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgb6c07f9" class="figure">
|
||||
<div id="org9006692" class="figure">
|
||||
<p><img src="figs/tf_geophones.png" alt="tf_geophones.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </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>
|
||||
</div>
|
||||
|
||||
<div class="org-src-container">
|
||||
@ -528,16 +551,16 @@ We also compute the coherence between the two signals (figure <a href="#org1b45a
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org1b45a36" class="figure">
|
||||
<div id="org9200232" class="figure">
|
||||
<p><img src="figs/coh_geophones.png" alt="coh_geophones.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgaf0dac1" class="outline-3">
|
||||
<h3 id="orgaf0dac1"><span class="section-number-3">2.7</span> Estimation of the sensor noise</h3>
|
||||
<div id="outline-container-orgd3b08ee" class="outline-3">
|
||||
<h3 id="orgd3b08ee"><span class="section-number-3">2.7</span> Estimation of the sensor noise</h3>
|
||||
<div class="outline-text-3" id="text-2-7">
|
||||
<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>.
|
||||
@ -567,11 +590,11 @@ where:
|
||||
</ul>
|
||||
|
||||
<p>
|
||||
The <code>mscohere</code> function is compared with this formula on Appendix (section <a href="#orgd085438">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="#org550fd32">4.1</a>), it is shown that it is identical.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Figure <a href="#orga4af110">9</a> illustrate a block diagram model of the system used to determine the sensor noise of the geophone.
|
||||
Figure <a href="#org72885b4">10</a> illustrate a block diagram model of the system used to determine the sensor noise of the geophone.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -583,10 +606,10 @@ Each sensor has noise \(N\) and \(M\).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orga4af110" class="figure">
|
||||
<div id="org72885b4" class="figure">
|
||||
<p><img src="figs/huddle-test.png" alt="huddle-test.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Huddle test block diagram</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Huddle test block diagram</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
@ -598,7 +621,7 @@ We also assume that \(H_1 = H_2 = 1\).
|
||||
We then obtain:
|
||||
</p>
|
||||
\begin{equation}
|
||||
\label{org65b3ddf}
|
||||
\label{orgb78feac}
|
||||
\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}
|
||||
|
||||
@ -606,23 +629,23 @@ We then obtain:
|
||||
Since the input signal \(U\) and the instrumental noise \(N\) are incoherent:
|
||||
</p>
|
||||
\begin{equation}
|
||||
\label{org14038cd}
|
||||
\label{org8419580}
|
||||
|G_X(\omega)| = |G_N(\omega)| + |G_U(\omega)|
|
||||
\end{equation}
|
||||
|
||||
<p>
|
||||
From equations \eqref{org65b3ddf} and \eqref{org14038cd}, we finally obtain
|
||||
From equations \eqref{orgb78feac} and \eqref{org8419580}, we finally obtain
|
||||
</p>
|
||||
<div class="important">
|
||||
\begin{equation}
|
||||
\label{org84c455c}
|
||||
\label{orgbe05867}
|
||||
|G_N(\omega)| = |G_X(\omega)| \left( 1 - \sqrt{\gamma_{XY}^2(\omega)} \right)
|
||||
\end{equation}
|
||||
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The instrumental noise is computed below. The result in V<sup>2</sup>/Hz is shown on figure <a href="#orgd0b903d">10</a>.
|
||||
The instrumental noise is computed below. The result in V<sup>2</sup>/Hz is shown on figure <a href="#org40db312">11</a>.
|
||||
</p>
|
||||
<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>;
|
||||
@ -643,14 +666,14 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgd0b903d" class="figure">
|
||||
<div id="org40db312" class="figure">
|
||||
<p><img src="figs/intrumental_noise_V.png" alt="intrumental_noise_V.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </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>
|
||||
|
||||
<p>
|
||||
This is then further converted into velocity and compared with the ground velocity measurement. (figure <a href="#org0542ab9">11</a>)
|
||||
This is then further converted into velocity and compared with the ground velocity measurement. (figure <a href="#org2a811b0">12</a>)
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
@ -666,17 +689,17 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org0542ab9" class="figure">
|
||||
<div id="org2a811b0" class="figure">
|
||||
<p><img src="figs/intrumental_noise_velocity.png" alt="intrumental_noise_velocity.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org126e178" class="outline-2">
|
||||
<h2 id="org126e178"><span class="section-number-2">3</span> Compare axis</h2>
|
||||
<div id="outline-container-orgdb15af9" class="outline-2">
|
||||
<h2 id="orgdb15af9"><span class="section-number-2">3</span> Compare axis</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
The Matlab computing file for this part is accessible <a href="compare_axis.m">here</a>.
|
||||
@ -689,8 +712,8 @@ The <code>mat</code> files containing the measurement data are accessible with t
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3f6cac8" class="outline-3">
|
||||
<h3 id="org3f6cac8"><span class="section-number-3">3.1</span> Load data</h3>
|
||||
<div id="outline-container-orgba2e891" class="outline-3">
|
||||
<h3 id="orgba2e891"><span class="section-number-3">3.1</span> Load data</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<p>
|
||||
We first load the data for the three axis.
|
||||
@ -704,8 +727,8 @@ north = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="or
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org608de0c" class="outline-3">
|
||||
<h3 id="org608de0c"><span class="section-number-3">3.2</span> Compare PSD</h3>
|
||||
<div id="outline-container-org4fa1ea3" class="outline-3">
|
||||
<h3 id="org4fa1ea3"><span class="section-number-3">3.2</span> Compare PSD</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<p>
|
||||
The PSD for each axis of the two geophones are computed.
|
||||
@ -723,23 +746,23 @@ The PSD for each axis of the two geophones are computed.
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We compare them. The result is shown on figure <a href="#orge0ebe78">12</a>.
|
||||
We compare them. The result is shown on figure <a href="#org8d0a71b">13</a>.
|
||||
</p>
|
||||
|
||||
<div id="orge0ebe78" class="figure">
|
||||
<div id="org8d0a71b" class="figure">
|
||||
<p><img src="figs/compare_axis_psd.png" alt="compare_axis_psd.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4db3872" class="outline-3">
|
||||
<h3 id="org4db3872"><span class="section-number-3">3.3</span> Compare TF</h3>
|
||||
<div id="outline-container-org413e0a4" class="outline-3">
|
||||
<h3 id="org413e0a4"><span class="section-number-3">3.3</span> Compare TF</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<p>
|
||||
The transfer functions from one geophone to the other are also computed for each axis.
|
||||
The result is shown on figure <a href="#org2a4c622">13</a>.
|
||||
The result is shown on figure <a href="#org167ce04">14</a>.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
@ -750,24 +773,24 @@ The result is shown on figure <a href="#org2a4c622">13</a>.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org2a4c622" class="figure">
|
||||
<div id="org167ce04" class="figure">
|
||||
<p><img src="figs/compare_tf_axis.png" alt="compare_tf_axis.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 13: </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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org66ca70f" class="outline-2">
|
||||
<h2 id="org66ca70f"><span class="section-number-2">4</span> Appendix</h2>
|
||||
<div id="outline-container-org47dea1f" class="outline-2">
|
||||
<h2 id="org47dea1f"><span class="section-number-2">4</span> Appendix</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
</div>
|
||||
<div id="outline-container-org7492edb" class="outline-3">
|
||||
<h3 id="org7492edb"><span class="section-number-3">4.1</span> Computation of coherence from PSD and CSD</h3>
|
||||
<div id="outline-container-orgc970c0a" class="outline-3">
|
||||
<h3 id="orgc970c0a"><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">
|
||||
<p>
|
||||
<a id="orgd085438"></a>
|
||||
<a id="org550fd32"></a>
|
||||
</p>
|
||||
<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>;
|
||||
@ -798,10 +821,10 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org0bcdbf7" class="figure">
|
||||
<div id="org229a280" class="figure">
|
||||
<p><img src="figs/comp_coherence_formula.png" alt="comp_coherence_formula.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 14: </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>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
@ -816,7 +839,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Thomas Dehaeze</p>
|
||||
<p class="date">Created: 2019-04-18 jeu. 17:11</p>
|
||||
<p class="date">Created: 2019-04-18 jeu. 17:24</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
</div>
|
||||
</body>
|
||||
|
||||
@ -149,14 +149,14 @@ The amplifiers also include a low pass filter with a cut-off frequency set at 1k
|
||||
#+begin_src matlab :results none
|
||||
G0 = 60; % [dB]
|
||||
|
||||
G = G0/(1+s/2/pi/1000);
|
||||
G = 10^(G0/20)/(1+s/2/pi/1000);
|
||||
#+end_src
|
||||
|
||||
We divide the ASD measured (in $\text{V}/\sqrt{\text{Hz}}$) by the transfer function 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(G, f, 'Hz')))./squeeze(abs(freqresp(S, f, 'Hz')));
|
||||
scaling = 1./squeeze(abs(freqresp(G*S, f, 'Hz')));
|
||||
#+end_src
|
||||
|
||||
** Computation of the ASD of the velocity
|
||||
@ -165,8 +165,8 @@ The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(pxx1)./scaling);
|
||||
plot(f, sqrt(pxx2)./scaling);
|
||||
plot(f, sqrt(pxx1).*scaling);
|
||||
plot(f, sqrt(pxx2).*scaling);
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log');
|
||||
set(gca, 'yscale', 'log');
|
||||
@ -176,7 +176,7 @@ The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
|
||||
|
||||
#+NAME: fig:psd_velocity
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/psd_velocity.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
#+begin_src matlab :var filepath="figs/psd_velocity.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
@ -185,6 +185,30 @@ The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
|
||||
#+RESULTS: fig:psd_velocity
|
||||
[[file:figs/psd_velocity.png]]
|
||||
|
||||
We also plot the ASD in displacement (figure [[fig:asd_displacement]]);
|
||||
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, (pxx1.*scaling./f).^2);
|
||||
plot(f, (pxx2.*scaling./f).^2);
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
|
||||
xlim([2, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:asd_displacement
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/asd_displacement.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:asd_displacement
|
||||
#+CAPTION: Amplitude Spectral Density of the displacement as measured by the geophones
|
||||
#+RESULTS: fig:asd_displacement
|
||||
[[file:figs/asd_displacement.png]]
|
||||
|
||||
** Transfer function between the two geophones
|
||||
We here compute the transfer function from one geophone to the other.
|
||||
The result is shown on figure [[fig:tf_geophones]].
|
||||
|
||||
@ -80,7 +80,7 @@ ylabel('Amplitude [V/(m/s)]')
|
||||
|
||||
G0 = 60; % [dB]
|
||||
|
||||
G = G0/(1+s/2/pi/1000);
|
||||
G = 10^(G0/20)/(1+s/2/pi/1000);
|
||||
|
||||
|
||||
|
||||
@ -88,7 +88,7 @@ G = G0/(1+s/2/pi/1000);
|
||||
% 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(G, f, 'Hz')))./squeeze(abs(freqresp(S, f, 'Hz')));
|
||||
scaling = 1./squeeze(abs(freqresp(G*S, f, 'Hz')));
|
||||
|
||||
% Computation of the ASD of the velocity
|
||||
% The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
|
||||
@ -96,14 +96,33 @@ scaling = 1./squeeze(abs(freqresp(G, f, 'Hz')))./squeeze(abs(freqresp(S, f, 'Hz'
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(pxx1)./scaling);
|
||||
plot(f, sqrt(pxx2)./scaling);
|
||||
plot(f, sqrt(pxx1).*scaling);
|
||||
plot(f, sqrt(pxx2).*scaling);
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log');
|
||||
set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
|
||||
xlim([2, 500]);
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:psd_velocity
|
||||
% #+CAPTION: Spectral density of the velocity
|
||||
% #+RESULTS: fig:psd_velocity
|
||||
% [[file:figs/psd_velocity.png]]
|
||||
|
||||
% We also plot the ASD in displacement (figure [[fig:asd_displacement]]);
|
||||
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, (pxx1.*scaling./f).^2);
|
||||
plot(f, (pxx2.*scaling./f).^2);
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
|
||||
xlim([2, 500]);
|
||||
|
||||
% Transfer function between the two geophones
|
||||
% We here compute the transfer function from one geophone to the other.
|
||||
% The result is shown on figure [[fig:tf_geophones]].
|
||||
|
||||
Loading…
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Reference in New Issue
Block a user