[WIP] Breaking Change - Use Update
Folder name is changed, rework the html templates Change the organisation.
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Huddle Test of the L22 Geophones</title>
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<meta name="generator" content="Org mode" />
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<meta name="author" content="Thomas Dehaeze" />
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<meta name="author" content="Dehaeze Thomas" />
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<div id="content">
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<div id="org-div-home-and-up">
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<a accesskey="h" href="../index.html"> UP </a>
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|
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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">Huddle Test of the L22 Geophones</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="#org446511b">1. Experimental Setup</a></li>
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||||
<li><a href="#org0689ed7">2. Signal Processing</a>
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<li><a href="#org214e6d8">1. Experimental Setup</a></li>
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<li><a href="#org42d6b13">2. Signal Processing</a>
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<ul>
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<li><a href="#org34a2d4c">2.1. Load data</a></li>
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<li><a href="#org28e8648">2.2. Time Domain Data</a></li>
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<li><a href="#org910f3e4">2.3. Computation of the ASD of the measured voltage</a></li>
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<li><a href="#org4e984e1">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="#org607752b">2.5. Computation of the ASD of the velocity</a></li>
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<li><a href="#org0a07c74">2.6. Transfer function between the two geophones</a></li>
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<li><a href="#orgdc03acb">2.7. Estimation of the sensor noise</a></li>
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<li><a href="#orgf4a8298">2.1. Load data</a></li>
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<li><a href="#org687ebba">2.2. Time Domain Data</a></li>
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<li><a href="#org649e300">2.3. Computation of the ASD of the measured voltage</a></li>
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||||
<li><a href="#org6148805">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="#orgfd258d8">2.5. Computation of the ASD of the velocity</a></li>
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||||
<li><a href="#org453baa3">2.6. Transfer function between the two geophones</a></li>
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<li><a href="#orgd2d293a">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="#org58e6c46">3. Compare axis</a>
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<li><a href="#orgbd963cb">3. Compare axis</a>
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<ul>
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<li><a href="#org8f74945">3.1. Load data</a></li>
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<li><a href="#orgf13f88e">3.2. Compare PSD</a></li>
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<li><a href="#orgf389e18">3.3. Compare TF</a></li>
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<li><a href="#org5ae5d71">3.1. Load data</a></li>
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<li><a href="#orgd12648a">3.2. Compare PSD</a></li>
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<li><a href="#orgf076a23">3.3. Compare TF</a></li>
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</ul>
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</li>
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<li><a href="#org1ca0f74">4. Appendix</a>
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<li><a href="#org17f5bce">4. Appendix</a>
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<ul>
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<li><a href="#org9faefb2">4.1. Computation of coherence from PSD and CSD</a></li>
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<li><a href="#org6babc5e">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-org446511b" class="outline-2">
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<h2 id="org446511b"><span class="section-number-2">1</span> Experimental Setup</h2>
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<div id="outline-container-org214e6d8" class="outline-2">
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||||
<h2 id="org214e6d8"><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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@@ -315,36 +324,46 @@ They are leveled.
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<p>
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The signals are amplified using voltage amplifier with a gain of 60dB.
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The voltage amplifiers include a low pass filter with a cut-off frequency at 1kHz.
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The voltage amplifiers includes:
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</p>
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<ul class="org-ul">
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<li>an high pass filter with a cut-off frequency at 1.5Hz (AC option)</li>
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<li>a low pass filter with a cut-off frequency at 1kHz</li>
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</ul>
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<div id="orgeab8098" class="figure">
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<p><img src="./figs/setup.jpg" alt="setup.jpg" width="500px" />
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<div id="org2edcc21" class="figure">
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||||
<p><img src="./img/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="orgdadbe53" class="figure">
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<p><img src="./figs/geophones.jpg" alt="geophones.jpg" width="500px" />
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<div id="org36e36a2" class="figure">
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<p><img src="./img/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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</div>
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</div>
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</div>
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<div id="outline-container-org0689ed7" class="outline-2">
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||||
<h2 id="org0689ed7"><span class="section-number-2">2</span> Signal Processing</h2>
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<div id="outline-container-org42d6b13" class="outline-2">
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||||
<h2 id="org42d6b13"><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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The <code>mat</code> file containing the measurement data is accessible <a href="mat/data_001.mat">here</a>.
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<a id="org7e05e6c"></a>
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</p>
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<div class="note">
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<p>
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||||
All the files (data and Matlab scripts) are accessible <a href="data/huddle_test_signal_processing.zip">here</a>.
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</p>
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</div>
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</div>
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<div id="outline-container-org34a2d4c" class="outline-3">
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||||
<h3 id="org34a2d4c"><span class="section-number-3">2.1</span> Load data</h3>
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||||
<div id="outline-container-orgf4a8298" class="outline-3">
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||||
<h3 id="orgf4a8298"><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 +377,8 @@ 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-org28e8648" class="outline-3">
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<h3 id="org28e8648"><span class="section-number-3">2.2</span> Time Domain Data</h3>
|
||||
<div id="outline-container-org687ebba" class="outline-3">
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||||
<h3 id="org687ebba"><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 +393,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
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</div>
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<div id="orgbc90092" class="figure">
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<div id="org20233d2" 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 +413,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
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</div>
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<div id="orgbb22470" class="figure">
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<div id="org1b7bc10" 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 +421,8 @@ 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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||||
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||||
<div id="outline-container-org910f3e4" class="outline-3">
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||||
<h3 id="org910f3e4"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3>
|
||||
<div id="outline-container-org649e300" class="outline-3">
|
||||
<h3 id="org649e300"><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">
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||||
<p>
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||||
We first define the parameters for the frequency domain analysis.
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||||
@@ -425,7 +444,7 @@ Then we compute the Power Spectral Density using <code>pwelch</code> function.
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||||
</div>
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||||
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||||
<p>
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||||
And we plot the result on figure <a href="#orgbf77081">5</a>.
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||||
And we plot the result on figure <a href="#org3ce04bf">5</a>.
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||||
</p>
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||||
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||||
<div class="org-src-container">
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||||
@@ -442,7 +461,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
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||||
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||||
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||||
<div id="orgbf77081" class="figure">
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||||
<div id="org3ce04bf" class="figure">
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||||
<p><img src="figs/asd_voltage.png" alt="asd_voltage.png" />
|
||||
</p>
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||||
<p><span class="figure-number">Figure 5: </span>Amplitude Spectral Density of the measured voltage</p>
|
||||
@@ -450,11 +469,11 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
</div>
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||||
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||||
<div id="outline-container-org4e984e1" class="outline-3">
|
||||
<h3 id="org4e984e1"><span class="section-number-3">2.4</span> Scaling to take into account the sensibility of the geophone and the voltage amplifier</h3>
|
||||
<div id="outline-container-org6148805" class="outline-3">
|
||||
<h3 id="org6148805"><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="#org0a867d9">6</a>.
|
||||
The Geophone used are L22. Their sensibility is shown on figure <a href="#orgd7b0965">6</a>.
|
||||
</p>
|
||||
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||||
<div class="org-src-container">
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||||
@@ -466,7 +485,7 @@ S = S0<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1
|
||||
</div>
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||||
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||||
|
||||
<div id="org0a867d9" class="figure">
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||||
<div id="orgd7b0965" class="figure">
|
||||
<p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Sensibility of the Geophone</p>
|
||||
@@ -496,11 +515,11 @@ We further divide the result by the sensibility of the Geophone to obtain the AS
|
||||
</div>
|
||||
</div>
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||||
|
||||
<div id="outline-container-org607752b" class="outline-3">
|
||||
<h3 id="org607752b"><span class="section-number-3">2.5</span> Computation of the ASD of the velocity</h3>
|
||||
<div id="outline-container-orgfd258d8" class="outline-3">
|
||||
<h3 id="orgfd258d8"><span class="section-number-3">2.5</span> Computation of the ASD of the velocity</h3>
|
||||
<div class="outline-text-3" id="text-2-5">
|
||||
<p>
|
||||
The ASD of the measured velocity is shown on figure <a href="#orgd9a4009">7</a>.
|
||||
The ASD of the measured velocity is shown on figure <a href="#org3cb06de">7</a>.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
@@ -517,14 +536,14 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgd9a4009" class="figure">
|
||||
<div id="org3cb06de" class="figure">
|
||||
<p><img src="figs/psd_velocity.png" alt="psd_velocity.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the Velocity</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We also plot the ASD in displacement (figure <a href="#orgc0b2ca5">8</a>);
|
||||
We also plot the ASD in displacement (figure <a href="#org2012a56">8</a>);
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
@@ -540,7 +559,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgc0b2ca5" class="figure">
|
||||
<div id="org2012a56" class="figure">
|
||||
<p><img src="figs/asd_displacement.png" alt="asd_displacement.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Amplitude Spectral Density of the Displacement</p>
|
||||
@@ -548,16 +567,16 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0a07c74" class="outline-3">
|
||||
<h3 id="org0a07c74"><span class="section-number-3">2.6</span> Transfer function between the two geophones</h3>
|
||||
<div id="outline-container-org453baa3" class="outline-3">
|
||||
<h3 id="org453baa3"><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="#org7d8ea2b">9</a>.
|
||||
The result is shown on figure <a href="#org8ca997a">9</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
We also compute the coherence between the two signals (figure <a href="#org628544f">10</a>).
|
||||
We also compute the coherence between the two signals (figure <a href="#org4366ab4">10</a>).
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
@@ -566,7 +585,7 @@ We also compute the coherence between the two signals (figure <a href="#org62854
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org7d8ea2b" class="figure">
|
||||
<div id="org8ca997a" class="figure">
|
||||
<p><img src="figs/tf_geophones.png" alt="tf_geophones.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Estimated transfer function between the two geophones</p>
|
||||
@@ -578,7 +597,7 @@ We also compute the coherence between the two signals (figure <a href="#org62854
|
||||
</div>
|
||||
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||||
|
||||
<div id="org628544f" class="figure">
|
||||
<div id="org4366ab4" class="figure">
|
||||
<p><img src="figs/coh_geophones.png" alt="coh_geophones.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Cohererence between the signals of the two geophones</p>
|
||||
@@ -586,8 +605,8 @@ We also compute the coherence between the two signals (figure <a href="#org62854
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgdc03acb" class="outline-3">
|
||||
<h3 id="orgdc03acb"><span class="section-number-3">2.7</span> Estimation of the sensor noise</h3>
|
||||
<div id="outline-container-orgd2d293a" class="outline-3">
|
||||
<h3 id="orgd2d293a"><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>.
|
||||
@@ -617,11 +636,11 @@ where:
|
||||
</ul>
|
||||
|
||||
<p>
|
||||
The <code>mscohere</code> function is compared with this formula on Appendix (section <a href="#orgc9ed210">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="#org956da99">4.1</a>), it is shown that it is identical.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Figure <a href="#org9b31b02">11</a> illustrate a block diagram model of the system used to determine the sensor noise of the geophone.
|
||||
Figure <a href="#orgc9be925">11</a> illustrate a block diagram model of the system used to determine the sensor noise of the geophone.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@@ -633,7 +652,7 @@ Each sensor has noise \(N\) and \(M\).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org9b31b02" class="figure">
|
||||
<div id="orgc9be925" class="figure">
|
||||
<p><img src="figs/huddle-test.png" alt="huddle-test.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>Huddle test block diagram</p>
|
||||
@@ -648,7 +667,7 @@ We also assume that \(S_1 = S_2 = 1\).
|
||||
We then obtain:
|
||||
</p>
|
||||
\begin{equation}
|
||||
\label{orgf197c52}
|
||||
\label{orgc4ca458}
|
||||
\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}
|
||||
|
||||
@@ -656,23 +675,23 @@ We then obtain:
|
||||
Since the input signal \(U\) and the instrumental noise \(N\) are incoherent:
|
||||
</p>
|
||||
\begin{equation}
|
||||
\label{org845ba9b}
|
||||
\label{orgb9a5b79}
|
||||
|G_X(\omega)| = |G_N(\omega)| + |G_U(\omega)|
|
||||
\end{equation}
|
||||
|
||||
<p>
|
||||
From equations \eqref{orgf197c52} and \eqref{org845ba9b}, we finally obtain
|
||||
From equations \eqref{orgc4ca458} and \eqref{orgb9a5b79}, we finally obtain
|
||||
</p>
|
||||
<div class="important">
|
||||
\begin{equation}
|
||||
\label{org0941f4e}
|
||||
\label{org618c850}
|
||||
|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="#orged7b0f2">12</a>.
|
||||
The instrumental noise is computed below. The result in V<sup>2</sup>/Hz is shown on figure <a href="#org8fc8f62">12</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>;
|
||||
@@ -693,14 +712,14 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orged7b0f2" class="figure">
|
||||
<div id="org8fc8f62" class="figure">
|
||||
<p><img src="figs/intrumental_noise_V.png" alt="intrumental_noise_V.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </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="#org3b9b556">13</a>)
|
||||
This is then further converted into velocity and compared with the ground velocity measurement. (figure <a href="#orgaf005ac">13</a>)
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||
@@ -716,7 +735,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org3b9b556" class="figure">
|
||||
<div id="orgaf005ac" class="figure">
|
||||
<p><img src="figs/intrumental_noise_velocity.png" alt="intrumental_noise_velocity.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 13: </span>Instrumental Noise and Measurement in \(m/s/\sqrt{Hz}\)</p>
|
||||
@@ -725,22 +744,23 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org58e6c46" class="outline-2">
|
||||
<h2 id="org58e6c46"><span class="section-number-2">3</span> Compare axis</h2>
|
||||
<div id="outline-container-orgbd963cb" class="outline-2">
|
||||
<h2 id="orgbd963cb"><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>.
|
||||
The <code>mat</code> files containing the measurement data are accessible with the following links:
|
||||
<a id="org04574c0"></a>
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>z axis: <a href="mat/data_001.mat">here</a>.</li>
|
||||
<li>east axis: <a href="mat/data_002.mat">here</a>.</li>
|
||||
<li>north axis: <a href="mat/data_003.mat">here</a>.</li>
|
||||
</ul>
|
||||
|
||||
<div class="note">
|
||||
<p>
|
||||
All the files (data and Matlab scripts) are accessible <a href="data/huddle_test_compare_axis.zip">here</a>.
|
||||
</p>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8f74945" class="outline-3">
|
||||
<h3 id="org8f74945"><span class="section-number-3">3.1</span> Load data</h3>
|
||||
<div id="outline-container-org5ae5d71" class="outline-3">
|
||||
<h3 id="org5ae5d71"><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.
|
||||
@@ -754,8 +774,8 @@ north = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="or
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf13f88e" class="outline-3">
|
||||
<h3 id="orgf13f88e"><span class="section-number-3">3.2</span> Compare PSD</h3>
|
||||
<div id="outline-container-orgd12648a" class="outline-3">
|
||||
<h3 id="orgd12648a"><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.
|
||||
@@ -773,10 +793,10 @@ The PSD for each axis of the two geophones are computed.
|
||||
</div>
|
||||
|
||||
<p>
|
||||
We compare them. The result is shown on figure <a href="#orgdfcdc16">14</a>.
|
||||
We compare them. The result is shown on figure <a href="#orgbd316c4">14</a>.
|
||||
</p>
|
||||
|
||||
<div id="orgdfcdc16" class="figure">
|
||||
<div id="orgbd316c4" class="figure">
|
||||
<p><img src="figs/compare_axis_psd.png" alt="compare_axis_psd.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 14: </span>Compare the measure PSD of the two geophones for the three axis</p>
|
||||
@@ -784,12 +804,12 @@ We compare them. The result is shown on figure <a href="#orgdfcdc16">14</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf389e18" class="outline-3">
|
||||
<h3 id="orgf389e18"><span class="section-number-3">3.3</span> Compare TF</h3>
|
||||
<div id="outline-container-orgf076a23" class="outline-3">
|
||||
<h3 id="orgf076a23"><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="#orgdd8cabb">15</a>.
|
||||
The result is shown on figure <a href="#org1278c1f">15</a>.
|
||||
</p>
|
||||
|
||||
<div class="org-src-container">
|
||||
@@ -800,7 +820,7 @@ The result is shown on figure <a href="#orgdd8cabb">15</a>.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgdd8cabb" class="figure">
|
||||
<div id="org1278c1f" class="figure">
|
||||
<p><img src="figs/compare_tf_axis.png" alt="compare_tf_axis.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 15: </span>Compare the transfer function from one geophone to the other for the 3 axis</p>
|
||||
@@ -809,15 +829,15 @@ The result is shown on figure <a href="#orgdd8cabb">15</a>.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1ca0f74" class="outline-2">
|
||||
<h2 id="org1ca0f74"><span class="section-number-2">4</span> Appendix</h2>
|
||||
<div id="outline-container-org17f5bce" class="outline-2">
|
||||
<h2 id="org17f5bce"><span class="section-number-2">4</span> Appendix</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
</div>
|
||||
<div id="outline-container-org9faefb2" class="outline-3">
|
||||
<h3 id="org9faefb2"><span class="section-number-3">4.1</span> Computation of coherence from PSD and CSD</h3>
|
||||
<div id="outline-container-org6babc5e" class="outline-3">
|
||||
<h3 id="org6babc5e"><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="orgc9ed210"></a>
|
||||
<a id="org956da99"></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>;
|
||||
@@ -848,7 +868,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgea88bec" class="figure">
|
||||
<div id="orgdd25190" class="figure">
|
||||
<p><img src="figs/comp_coherence_formula.png" alt="comp_coherence_formula.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 16: </span>Comparison of <code>mscohere</code> and manual computation</p>
|
||||
@@ -865,8 +885,8 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
||||
</p>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Thomas Dehaeze</p>
|
||||
<p class="date">Created: 2019-05-03 ven. 11:32</p>
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2019-05-10 ven. 14:24</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
</div>
|
||||
</body>
|
||||
|
||||
@@ -1,22 +1,5 @@
|
||||
#+TITLE:Huddle Test of the L22 Geophones
|
||||
:DRAWER:
|
||||
#+STARTUP: overview
|
||||
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
|
||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="../js/bootstrap.min.js"></script>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
|
||||
#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
|
||||
|
||||
#+PROPERTY: header-args:matlab :session *MATLAB*
|
||||
#+PROPERTY: header-args:matlab+ :comments org
|
||||
#+PROPERTY: header-args:matlab+ :results output
|
||||
#+PROPERTY: header-args:matlab+ :exports both
|
||||
#+PROPERTY: header-args:matlab+ :eval no-export
|
||||
#+PROPERTY: header-args:matlab+ :output-dir figs
|
||||
:END:
|
||||
#+SETUPFILE: ../config.org
|
||||
|
||||
* Experimental Setup
|
||||
Two L22 geophones are used.
|
||||
@@ -31,23 +14,40 @@ The voltage amplifiers includes:
|
||||
#+name: fig:figure_name
|
||||
#+caption: Setup
|
||||
#+attr_html: :width 500px
|
||||
[[file:./figs/setup.jpg]]
|
||||
[[file:./img/setup.jpg]]
|
||||
|
||||
#+name: fig:figure_name
|
||||
#+caption: Geophones
|
||||
#+attr_html: :width 500px
|
||||
[[file:./figs/geophones.jpg]]
|
||||
[[file:./img/geophones.jpg]]
|
||||
|
||||
* Signal Processing
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle signal_processing.m
|
||||
:header-args:matlab+: :tangle matlab/huddle_test_signal_processing.m
|
||||
:header-args:matlab+: :comments org :mkdirp yes
|
||||
:END:
|
||||
The Matlab computing file for this part is accessible [[file:signal_processing.m][here]].
|
||||
The =mat= file containing the measurement data is accessible [[file:mat/data_001.mat][here]].
|
||||
<<sec:huddle_test_signal_processing>>
|
||||
|
||||
#+begin_src bash :exports none :results none
|
||||
if [ matlab/huddle_test_signal_processing.m -nt data/huddle_test_signal_processing.zip ]; then
|
||||
cp matlab/huddle_test_signal_processing.m huddle_test_signal_processing.m;
|
||||
zip data/huddle_test_signal_processing \
|
||||
mat/data_001.mat \
|
||||
huddle_test_signal_processing.m;
|
||||
rm huddle_test_signal_processing.m;
|
||||
fi
|
||||
#+end_src
|
||||
|
||||
#+begin_note
|
||||
All the files (data and Matlab scripts) are accessible [[file:data/huddle_test_signal_processing.zip][here]].
|
||||
#+end_note
|
||||
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
#+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
|
||||
|
||||
@@ -407,17 +407,33 @@ This is then further converted into velocity and compared with the ground veloci
|
||||
|
||||
* Compare axis
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle compare_axis.m
|
||||
:header-args:matlab+: :tangle matlab/huddle_test_compare_axis.m
|
||||
:header-args:matlab+: :comments org :mkdirp yes
|
||||
:END:
|
||||
The Matlab computing file for this part is accessible [[file:compare_axis.m][here]].
|
||||
The =mat= files containing the measurement data are accessible with the following links:
|
||||
- z axis: [[file:mat/data_001.mat][here]].
|
||||
- east axis: [[file:mat/data_002.mat][here]].
|
||||
- north axis: [[file:mat/data_003.mat][here]].
|
||||
<<sec:huddle_test_compare_axis>>
|
||||
|
||||
#+begin_src bash :exports none :results none
|
||||
if [ matlab/huddle_test_compare_axis.m -nt data/huddle_test_compare_axis.zip ]; then
|
||||
cp matlab/huddle_test_compare_axis.m huddle_test_compare_axis.m;
|
||||
zip data/huddle_test_compare_axis \
|
||||
mat/data_001.mat \
|
||||
mat/data_002.mat \
|
||||
mat/data_003.mat \
|
||||
huddle_test_compare_axis.m;
|
||||
rm huddle_test_compare_axis.m;
|
||||
fi
|
||||
#+end_src
|
||||
|
||||
#+begin_note
|
||||
All the files (data and Matlab scripts) are accessible [[file:data/huddle_test_compare_axis.zip][here]].
|
||||
#+end_note
|
||||
|
||||
** Matlab Init :noexport:ignore:
|
||||
#+begin_src matlab :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
|
||||
#+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
|
||||
|
||||
|
||||
@@ -1,5 +1,10 @@
|
||||
% Matlab Init :noexport:ignore:
|
||||
|
||||
current_dir='/home/thomas/MEGA/These/meas/huddle-test-geophones/';
|
||||
%% Go to current Directory
|
||||
cd(current_dir);
|
||||
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
@@ -1,5 +1,10 @@
|
||||
% Matlab Init :noexport:ignore:
|
||||
|
||||
current_dir='/home/thomas/MEGA/These/meas/huddle-test-geophones/';
|
||||
%% Go to current Directory
|
||||
cd(current_dir);
|
||||
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
@@ -47,24 +52,44 @@ xlim([0 1]);
|
||||
% Computation of the ASD of the measured voltage
|
||||
% We first define the parameters for the frequency domain analysis.
|
||||
|
||||
win = hanning(ceil(length(x1)/100));
|
||||
Fs = 1/dt;
|
||||
Fs = 1/dt; % [Hz]
|
||||
|
||||
win = hanning(ceil(10*Fs));
|
||||
|
||||
|
||||
|
||||
% Then we compute the Power Spectral Density using =pwelch= function.
|
||||
|
||||
[pxx1, f] = pwelch(x1, win, [], [], Fs);
|
||||
[pxx2, ~] = pwelch(x2, win, [], [], Fs);
|
||||
|
||||
|
||||
|
||||
% And we plot the result on figure [[fig:asd_voltage]].
|
||||
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, sqrt(pxx1));
|
||||
plot(f, sqrt(pxx2));
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log');
|
||||
set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
|
||||
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 are shown on figure [[fig:geophone_sensibility]].
|
||||
% The Geophone used are L22. Their sensibility is shown on figure [[fig:geophone_sensibility]].
|
||||
|
||||
|
||||
S0 = 88; % Sensitivity [V/(m/s)]
|
||||
f0 = 2; % Cut-off frequnecy [Hz]
|
||||
S = (s/2/pi/f0)/(1+s/2/pi/f0);
|
||||
|
||||
S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);
|
||||
|
||||
figure;
|
||||
bodeFig({S});
|
||||
ylabel('Amplitude [V/(m/s)]')
|
||||
bodeFig({S}, logspace(-1, 2, 1000));
|
||||
ylabel('Amplitude $\left[\frac{V}{m/s}\right]$')
|
||||
|
||||
|
||||
|
||||
@@ -75,20 +100,19 @@ ylabel('Amplitude [V/(m/s)]')
|
||||
|
||||
|
||||
% We also take into account the gain of the electronics which is here set to be $60dB$.
|
||||
% The amplifiers also include a low pass filter with a cut-off frequency set at 1kHz.
|
||||
|
||||
|
||||
G0 = 60; % [dB]
|
||||
G0_db = 60; % [dB]
|
||||
|
||||
G = 10^(G0/20)/(1+s/2/pi/1000);
|
||||
G0 = 10^(60/G0_db); % [abs]
|
||||
|
||||
|
||||
|
||||
% 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 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(G*S, f, '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:psd_velocity]].
|
||||
@@ -101,13 +125,13 @@ 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]);
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
|
||||
xlim([0.1, 500]);
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:psd_velocity
|
||||
% #+CAPTION: Spectral density of the velocity
|
||||
% #+CAPTION: Amplitude Spectral Density of the Velocity
|
||||
% #+RESULTS: fig:psd_velocity
|
||||
% [[file:figs/psd_velocity.png]]
|
||||
|
||||
@@ -116,12 +140,12 @@ xlim([2, 500]);
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, (pxx1.*scaling./f).^2);
|
||||
plot(f, (pxx2.*scaling./f).^2);
|
||||
plot(f, (sqrt(pxx1).*scaling)./(2*pi*f));
|
||||
plot(f, (sqrt(pxx2).*scaling)./(2*pi*f));
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
|
||||
xlim([2, 500]);
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
|
||||
xlim([0.1, 500]);
|
||||
|
||||
% Transfer function between the two geophones
|
||||
% We here compute the transfer function from one geophone to the other.
|
||||
@@ -144,10 +168,10 @@ plot(f, mod(180+180/pi*phase(T12), 360)-180);
|
||||
set(gca, 'xscale', 'log');
|
||||
ylim([-180, 180]);
|
||||
yticks([-180, -90, 0, 90, 180]);
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase');
|
||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||
|
||||
linkaxes([ax1,ax2],'x');
|
||||
xlim([1, 500]);
|
||||
xlim([0.1, 500]);
|
||||
|
||||
|
||||
|
||||
@@ -163,7 +187,7 @@ figure;
|
||||
plot(f, coh12);
|
||||
set(gca, 'xscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Coherence');
|
||||
ylim([0,1]); xlim([1, 500]);
|
||||
ylim([0,1]); xlim([0.1, 500]);
|
||||
|
||||
% Estimation of the sensor noise
|
||||
% The technique to estimate the sensor noise is taken from cite:barzilai98_techn_measur_noise_sensor_presen.
|
||||
@@ -196,7 +220,7 @@ ylim([0,1]); xlim([1, 500]);
|
||||
% [[file:figs/huddle-test.png]]
|
||||
|
||||
% We here assume that each sensor has the same magnitude of instrumental noise ($N = M$).
|
||||
% We also assume that $H_1 = H_2 = 1$.
|
||||
% We also assume that $S_1 = S_2 = 1$.
|
||||
|
||||
% We then obtain:
|
||||
% #+NAME: eq:coh_bis
|
||||
@@ -229,8 +253,8 @@ plot(f, pxx2, '-');
|
||||
plot(f, pxxN, 'k--');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('PSD [$V^2/Hz$]');
|
||||
xlim([1, 500]);
|
||||
xlabel('Frequency [Hz]'); ylabel('PSD of the measured Voltage $\left[\frac{V^2}{Hz}\right]$');
|
||||
xlim([0.1, 500]);
|
||||
|
||||
|
||||
|
||||
@@ -248,5 +272,5 @@ plot(f, sqrt(pxx2).*scaling, '-');
|
||||
plot(f, sqrt(pxxN).*scaling, 'k--');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
|
||||
xlim([1, 500]);
|
||||
xlabel('Frequency [Hz]'); ylabel('ASD of the Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$');
|
||||
xlim([0.1, 500]);
|
||||
@@ -1,47 +0,0 @@
|
||||
tg = slrt;
|
||||
|
||||
%% TODO - Build this application if updated
|
||||
|
||||
%%
|
||||
if tg.Connected == "Yes"
|
||||
if tg.Status == "stopped"
|
||||
%% Load the application
|
||||
tg.load('test');
|
||||
|
||||
%% Run the application
|
||||
tg.start;
|
||||
pause(10);
|
||||
tg.stop;
|
||||
|
||||
%% Load the data
|
||||
f = SimulinkRealTime.openFTP(tg);
|
||||
mget(f, 'data/data_001.dat');
|
||||
close(f);
|
||||
end
|
||||
end
|
||||
|
||||
%% Convert the Data
|
||||
data = SimulinkRealTime.utils.getFileScopeData('data/data_001.dat').data;
|
||||
|
||||
t = data(:, end);
|
||||
x1 = data(:, 1);
|
||||
x2 = data(:, 2);
|
||||
|
||||
save('mat/data_003.mat', 't', 'x1', 'x2');
|
||||
|
||||
%% Plot the data
|
||||
figure;
|
||||
hold on;
|
||||
plot(t, x1);
|
||||
plot(t, x2);
|
||||
hold off
|
||||
xlabel('Time [s]');
|
||||
ylabel('Voltage [V]');
|
||||
|
||||
%% Compute the PSD
|
||||
dt = t(2)-t(1);
|
||||
|
||||
window_L = ceil(length(x1)/10);
|
||||
window_han = .5*(1 - cos(2*pi*(1:window_L)'/(window_L+1)));
|
||||
|
||||
[pxx, f] = pwelch(x1, window_han, 0, [], 1/dt);
|
||||
@@ -1 +0,0 @@
|
||||
Ts = 1e-3; % [s]
|
||||
Reference in New Issue
Block a user