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Reworked the ground motion page

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This commit is contained in:
Thomas Dehaeze 2019-05-10 17:52:14 +02:00
parent ed61db2f86
commit 5208373cf6
34 changed files with 1071 additions and 1397 deletions
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2
2018-01-12 - Marc/index.html
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@ -467,7 +467,7 @@ The Geophone sensitivity is defined below:
<pre class="src src-matlab">w0 = <span class="org-highlight-numbers-number">4</span>.<span class="org-highlight-numbers-number">5</span><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-comment">% [rad/s]</span>
ksi = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">38</span>;
G0 = <span class="org-highlight-numbers-number">31</span>.<span class="org-highlight-numbers-number">3</span>; <span class="org-comment">% [V/(m/s)]</span>
G = G0<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type">/</span>w0<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span>s<span class="org-type">/</span>w0<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span> <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>ksi<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>s<span class="org-type">/</span>w0<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-1">)</span>; <span class="org-comment">% [V/(m/s)]</span>
[Omitted long matching line]
</pre>
</div>

2
2018-10-15 - Marc/index.html
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@ -539,7 +539,7 @@ Measurements will be normalized by the inverse of this transfer function in orde
<pre class="src src-matlab">L4C_w0 = <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span>; <span class="org-comment">% [rad/s]</span>
L4C_ksi = <span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">28</span>;
L4C_G0 = <span class="org-highlight-numbers-number">276</span>.<span class="org-highlight-numbers-number">8</span>; <span class="org-comment">% [V/(m/s)]</span>
L4C_G = L4C_G0<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type">/</span>L4C_w0<span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">(</span>s<span class="org-type">/</span>L4C_w0<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">^</span><span class="org-highlight-numbers-number">2</span> <span class="org-type">+</span> <span class="org-highlight-numbers-number">2</span><span class="org-type">*</span>L4C_ksi<span class="org-type">*</span><span class="org-rainbow-delimiters-depth-2">(</span>s<span class="org-type">/</span>L4C_w0<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-1">)</span>;
[Omitted long matching line]
</pre>
</div>

31
Ground Motion/analyze_ground_motion.m
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@ -1,31 +0,0 @@
%%
clear; close all; clc;
%%
id31 = load('ground_motion_psd.mat');
id09 = load('id09_floor_september2018.mat');
cern = load('ground_motion_dist.mat');
%% ID09 Measurements - Time Domain
figure;
hold on;
plot(id09.time3, 1e-6*id09.x_y_z(:, 1), 'DisplayName', 'dx');
plot(id09.time3, 1e-6*id09.x_y_z(:, 2), 'DisplayName', 'dy');
plot(id09.time3, 1e-6*id09.x_y_z(:, 3), 'DisplayName', 'dz');
hold off;
xlabel('Time [s]'); ylabel('Velocity [$m/s$]');
legend();
% Compute PSD of ID09 ground motion
[id09_pxx, id09_f] = pwelch(1e-6*id09.x_y_z(:, 1), hanning(ceil(length(1e-6*id09.x_y_z(:, 1))/10)), 0, [], 1/(id09.time3(end)/(length(id09.time3) - 1)));
%% Compare PSD of Cern, ID09 and ID31
figure;
hold on;
plot(cern.gm.freq, cern.gm.psd, 'DisplayName', 'CERN');
plot(id31.freqs, id31.psd_dx, 'DisplayName', 'ID31');
plot(id09_f, id09_pxx, 'DisplayName', 'ID09');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m^2/Hz$]');
legend('Location', 'northeast');

24
Ground Motion/convert_txt_to_mat.m
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@ -1,24 +0,0 @@
%%
clear; close all; clc;
%%
% 1st column is frequency in Hz
% Then PSD's in (um/s)^2/Hz) for the x,y,z axis respectively.
%%
data = table2array(readtable('id31_camac_floor_PSD_october2014.txt'));
%%
gm.freqs = data(:, 1);
gm.psd_vx = 1e-12*data(:, 2); % [(um/s)^2/Hz] => [(m/s)^2/Hz]
gm.psd_vy = 1e-12*data(:, 3); % [(um/s)^2/Hz] => [(m/s)^2/Hz]
gm.psd_vz = 1e-12*data(:, 4); % [(um/s)^2/Hz] => [(m/s)^2/Hz]
gm.psd_dx = gm.psd_vx./(2*pi*gm.freqs); % velocity to displacement [m^2/Hz]
gm.psd_dy = gm.psd_vy./(2*pi*gm.freqs); % velocity to displacement [m^2/Hz]
gm.psd_dz = gm.psd_vz./(2*pi*gm.freqs); % velocity to displacement [m^2/Hz]
%%
save('../../Matlab/data/signals/gm_esrf.mat', 'gm');

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Ground Motion/data/ground_motion_psd.mat
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800
Ground Motion/data/id31_camac_floor_PSD_october2014.txt
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@ -1,800 +0,0 @@
0.0000000000000000e+00 2.5332081562015230e-03 9.7646056705452092e-04 8.1899913100021734e-04
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<div id="content">
<h1 class="title">Ground Motion Measurements</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org51a66d9">1. Preprocessing of id31 ground motion measurement</a></li>
<li><a href="#orga36c9a4">2. Plots</a>
<ul>
<li><a href="#orgd4b4350">2.1. ID09 Measurements - Time Domain</a></li>
<li><a href="#org13c38c6">2.2. Compute PSD of ID09 ground motion</a></li>
<li><a href="#org8526d27">2.3. Compare PSD of Cern, ID09 and ID31</a></li>
</ul>
</li>
</ul>
</div>
</div>
<p>
<a href="../index.html">Back to main page</a>.
</p>
<div id="outline-container-org51a66d9" class="outline-2">
<h2 id="org51a66d9"><span class="section-number-2">1</span> Preprocessing of id31 ground motion measurement</h2>
<div class="outline-text-2" id="text-1">
<div class="org-src-container">
<pre class="src src-matlab">data = table2array<span style="color: #DCDCCC;">(</span>readtable<span style="color: #BFEBBF;">(</span><span style="color: #CC9393;">'./data/id31_camac_floor_PSD_october2014.txt'</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<p>
The first column is the frequency vector in Hz.
</p>
<div class="org-src-container">
<pre class="src src-matlab">gm.freqs = data<span style="color: #DCDCCC;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<p>
The other colmns are the PSD of the ground velocity in \(\frac{(\mu m/s)^2}{Hz}\) for the x,y,z axis.
It is converted to \(\frac{(m/s)^2}{Hz}\).
</p>
<div class="org-src-container">
<pre class="src src-matlab">gm.psd_vx = <span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">12</span><span style="color: #7CB8BB;">*</span>data<span style="color: #DCDCCC;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">)</span>;
gm.psd_vy = <span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">12</span><span style="color: #7CB8BB;">*</span>data<span style="color: #DCDCCC;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">3</span><span style="color: #DCDCCC;">)</span>;
gm.psd_vz = <span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">12</span><span style="color: #7CB8BB;">*</span>data<span style="color: #DCDCCC;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">4</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<p>
Finally, we integrate the signal to obtain the power spectral density of the ground displacement.
</p>
<div class="org-src-container">
<pre class="src src-matlab">gm.psd_dx = gm.psd_vx<span style="color: #7CB8BB;">./</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">*</span>gm.freqs<span style="color: #DCDCCC;">)</span>;
gm.psd_dy = gm.psd_vy<span style="color: #7CB8BB;">./</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">*</span>gm.freqs<span style="color: #DCDCCC;">)</span>;
gm.psd_dz = gm.psd_vz<span style="color: #7CB8BB;">./</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">pi</span><span style="color: #7CB8BB;">*</span>gm.freqs<span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<p>
The pre-processed data are saved.
</p>
<div class="org-src-container">
<pre class="src src-matlab">save<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./data/gm_esrf.mat', 'gm'</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orga36c9a4" class="outline-2">
<h2 id="orga36c9a4"><span class="section-number-2">2</span> Plots</h2>
<div class="outline-text-2" id="text-2">
<p>
We load measurements made:
</p>
<ul class="org-ul">
<li>at ID31</li>
<li>at ID09</li>
<li>at CERN</li>
</ul>
<div class="org-src-container">
<pre class="src src-matlab">id31 = load<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./data/ground_motion_psd.mat'</span><span style="color: #DCDCCC;">)</span>;
id09 = load<span style="color: #DCDCCC;">(</span>'<span style="color: #7CB8BB;">./</span>data<span style="color: #7CB8BB;">/</span>id09_floor_september2018.mat'<span style="color: #DCDCCC;">)</span>;
cern = load<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'./data/ground_motion_dist.mat'</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
</div>
<div id="outline-container-orgd4b4350" class="outline-3">
<h3 id="orgd4b4350"><span class="section-number-3">2.1</span> ID09 Measurements - Time Domain</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
plot<span style="color: #DCDCCC;">(</span>id09.time3, <span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span><span style="color: #7CB8BB;">*</span>id09.x_y_z<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span>, <span style="color: #CC9393;">'DisplayName', 'dx'</span><span style="color: #DCDCCC;">)</span>;
plot<span style="color: #DCDCCC;">(</span>id09.time3, <span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span><span style="color: #7CB8BB;">*</span>id09.x_y_z<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span>, <span style="color: #CC9393;">'DisplayName', 'dy'</span><span style="color: #DCDCCC;">)</span>;
plot<span style="color: #DCDCCC;">(</span>id09.time3, <span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span><span style="color: #7CB8BB;">*</span>id09.x_y_z<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span>, <span style="color: #CC9393;">'DisplayName', 'dz'</span><span style="color: #DCDCCC;">)</span>;
hold off;
xlabel<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Time </span><span style="color: #BFEBBF;">[</span><span style="color: #CC9393;">s</span><span style="color: #BFEBBF;">]</span><span style="color: #CC9393;">'</span><span style="color: #DCDCCC;">)</span><span style="color: #CC9393;">; ylabel</span><span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Velocity </span><span style="color: #BFEBBF;">[</span><span style="color: #CC9393;">$m/s$</span><span style="color: #BFEBBF;">]</span><span style="color: #CC9393;">'</span><span style="color: #DCDCCC;">)</span>;
legend<span style="color: #DCDCCC;">()</span>;
</pre>
</div>
<div id="orgce3682d" class="figure">
<p><img src="figs/id09_time_domain.png" alt="id09_time_domain.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Time domain data - ID09</p>
</div>
</div>
</div>
<div id="outline-container-org13c38c6" class="outline-3">
<h3 id="org13c38c6"><span class="section-number-3">2.2</span> Compute PSD of ID09 ground motion</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #DCDCCC;">[</span>id09_pxx, id09_f<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span><span style="color: #7CB8BB;">*</span>id09.x_y_z<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span>, hanning<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span>length<span style="color: #93E0E3;">(</span><span style="color: #BFEBBF;">1e</span><span style="color: #7CB8BB;">-</span><span style="color: #BFEBBF;">6</span><span style="color: #7CB8BB;">*</span>id09.x_y_z<span style="color: #9FC59F;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #9FC59F;">)</span><span style="color: #93E0E3;">)</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">10</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, <span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">/</span><span style="color: #BFEBBF;">(</span>id09.time3<span style="color: #D0BF8F;">(</span>end<span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">/</span><span style="color: #D0BF8F;">(</span>length<span style="color: #93E0E3;">(</span>id09.time3<span style="color: #93E0E3;">)</span> <span style="color: #7CB8BB;">-</span> <span style="color: #BFEBBF;">1</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org8526d27" class="outline-3">
<h3 id="org8526d27"><span class="section-number-3">2.3</span> Compare PSD of Cern, ID09 and ID31</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
plot<span style="color: #DCDCCC;">(</span>cern.gm.freq, cern.gm.psd, <span style="color: #CC9393;">'DisplayName', 'CERN'</span><span style="color: #DCDCCC;">)</span>;
plot<span style="color: #DCDCCC;">(</span>id31.freqs, id31.psd_dx, <span style="color: #CC9393;">'DisplayName', 'ID31'</span><span style="color: #DCDCCC;">)</span>;
plot<span style="color: #DCDCCC;">(</span>id09_f, id09_pxx, <span style="color: #CC9393;">'DisplayName', '</span>ID09'<span style="color: #DCDCCC;">)</span>;
hold off;
<span style="color: #7CB8BB;">set</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">gca</span>, <span style="color: #CC9393;">'XScale', 'log'</span><span style="color: #DCDCCC;">)</span><span style="color: #CC9393;">; set</span><span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">gca, 'YScale', 'log'</span><span style="color: #DCDCCC;">)</span>;
xlabel<span style="color: #DCDCCC;">(</span>'Frequency <span style="color: #BFEBBF;">[</span>Hz<span style="color: #BFEBBF;">]</span>'<span style="color: #DCDCCC;">)</span>; ylabel<span style="color: #DCDCCC;">(</span>'PSD <span style="color: #BFEBBF;">[</span>$m<span style="color: #7CB8BB;">^</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">/</span>Hz$<span style="color: #BFEBBF;">]</span>'<span style="color: #DCDCCC;">)</span>;
legend<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Location', 'northeast'</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<div id="orgd6dc880" class="figure">
<p><img src="figs/psd_comparison.png" alt="psd_comparison.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Comparison of the PSD of ground motion</p>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-03-15 ven. 11:42</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>

106
Ground Motion/index.org
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@ -1,106 +0,0 @@
#+TITLE: Ground Motion Measurements
#+SETUPFILE: ../config.org
* 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
* Preprocessing of id31 ground motion measurement
#+begin_src matlab :exports code :results silent
data = table2array(readtable('./data/id31_camac_floor_PSD_october2014.txt'));
#+end_src
The first column is the frequency vector in Hz.
#+begin_src matlab :exports code :results silent
gm.freqs = data(:, 1);
#+end_src
The other colmns are the PSD of the ground velocity in $\frac{(\mu m/s)^2}{Hz}$ for the x,y,z axis.
It is converted to $\frac{(m/s)^2}{Hz}$.
#+begin_src matlab :exports code :results silent
gm.psd_vx = 1e-12*data(:, 2);
gm.psd_vy = 1e-12*data(:, 3);
gm.psd_vz = 1e-12*data(:, 4);
#+end_src
Finally, we integrate the signal to obtain the power spectral density of the ground displacement.
#+begin_src matlab :results silent
gm.psd_dx = gm.psd_vx./(2*pi*gm.freqs);
gm.psd_dy = gm.psd_vy./(2*pi*gm.freqs);
gm.psd_dz = gm.psd_vz./(2*pi*gm.freqs);
#+end_src
The pre-processed data are saved.
#+begin_src matlab :results silent
save('./data/gm_esrf.mat', 'gm');
#+end_src
* Plots
We load measurements made:
- at ID31
- at ID09
- at CERN
#+begin_src matlab :results silent
id31 = load('./data/ground_motion_psd.mat');
id09 = load('./data/id09_floor_september2018.mat');
cern = load('./data/ground_motion_dist.mat');
#+end_src
** ID09 Measurements - Time Domain
#+begin_src matlab :results silent
figure;
hold on;
plot(id09.time3, 1e-6*id09.x_y_z(:, 1), 'DisplayName', 'dx');
plot(id09.time3, 1e-6*id09.x_y_z(:, 2), 'DisplayName', 'dy');
plot(id09.time3, 1e-6*id09.x_y_z(:, 3), 'DisplayName', 'dz');
hold off;
xlabel('Time [s]'); ylabel('Velocity [$m/s$]');
legend();
#+end_src
#+NAME: fig:id09_time_domain
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/id09_time_domain.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:id09_time_domain
#+CAPTION: Time domain data - ID09
#+RESULTS: fig:id09_time_domain
[[file:figs/id09_time_domain.png]]
** Compute PSD of ID09 ground motion
#+begin_src matlab :results silent
[id09_pxx, id09_f] = pwelch(1e-6*id09.x_y_z(:, 1), hanning(ceil(length(1e-6*id09.x_y_z(:, 1))/10)), 0, [], 1/(id09.time3(end)/(length(id09.time3) - 1)));
#+end_src
** Compare PSD of Cern, ID09 and ID31
#+begin_src matlab :results silent
figure;
hold on;
plot(cern.gm.freq, cern.gm.psd, 'DisplayName', 'CERN');
plot(id31.freqs, id31.psd_dx, 'DisplayName', 'ID31');
plot(id09_f, id09_pxx, 'DisplayName', 'ID09');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m^2/Hz$]');
legend('Location', 'northeast');
#+end_src
#+NAME: fig:psd_comparison
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/psd_comparison.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:psd_comparison
#+CAPTION: Comparison of the PSD of ground motion
#+RESULTS: fig:psd_comparison
[[file:figs/psd_comparison.png]]

4
actuators-sensors/index.html
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@ -530,7 +530,7 @@ We define the parameters of the geophone and we plot its bode plot (figure <a hr
<pre class="src src-matlab">w0 = <span style="color: #BFEBBF;">4</span>.<span style="color: #BFEBBF;">5</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">pi</span>; <span style="color: #7F9F7F;">% [rad/s]</span>
ksi = <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">38</span>;
G0 = <span style="color: #BFEBBF;">31</span>.<span style="color: #BFEBBF;">3</span>; <span style="color: #7F9F7F;">% [V/(m/s)]</span>
G = G0<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">(</span>s<span style="color: #7CB8BB;">/</span>w0<span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">^</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">/</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">(</span>s<span style="color: #7CB8BB;">/</span>w0<span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">^</span><span style="color: #BFEBBF;">2</span> <span style="color: #7CB8BB;">+</span> <span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span>ksi<span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">(</span>s<span style="color: #7CB8BB;">/</span>w0<span style="color: #BFEBBF;">)</span> <span style="color: #7CB8BB;">+</span> <span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>;
[Omitted long matching line]
</pre>
</div>
@ -596,7 +596,7 @@ Its bode plot is shown on figure <a href="#orga651aed">4</a>.
<pre class="src src-matlab">w0 = <span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">pi</span>; <span style="color: #7F9F7F;">% [rad/s]</span>
ksi = <span style="color: #BFEBBF;">0</span>.<span style="color: #BFEBBF;">28</span>;
G0 = <span style="color: #BFEBBF;">276</span>.<span style="color: #BFEBBF;">8</span>; <span style="color: #7F9F7F;">% [V/(m/s)]</span>
G = G0<span style="color: #7CB8BB;">*</span><span style="color: #DCDCCC;">(</span>s<span style="color: #7CB8BB;">/</span>w0<span style="color: #DCDCCC;">)</span><span style="color: #7CB8BB;">^</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">/</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">(</span>s<span style="color: #7CB8BB;">/</span>w0<span style="color: #BFEBBF;">)</span><span style="color: #7CB8BB;">^</span><span style="color: #BFEBBF;">2</span> <span style="color: #7CB8BB;">+</span> <span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">*</span>ksi<span style="color: #7CB8BB;">*</span><span style="color: #BFEBBF;">(</span>s<span style="color: #7CB8BB;">/</span>w0<span style="color: #BFEBBF;">)</span> <span style="color: #7CB8BB;">+</span> <span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>;
[Omitted long matching line]
</pre>
</div>

2
disturbance-measurement/index.org
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@ -114,7 +114,7 @@ We also take into account the gain of the electronics which is here set to be $6
#+begin_src matlab :results none
G0_db = 60; % [dB]
G0 = 10^(60/G0_db); % [abs]
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.

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<head>
<!-- 2019-05-10 ven. 17:51 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<h1 class="title">Ground Motion Measurements</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgddb7761">1. Experimental Setup</a></li>
<li><a href="#org828fff9">2. Measurement Analysis</a>
<ul>
<li><a href="#orgadf99c0">2.1. Load data</a></li>
<li><a href="#org93551bb">2.2. Time domain plots</a></li>
<li><a href="#orgfd0b3a8">2.3. Computation of the ASD of the measured voltage</a></li>
<li><a href="#org4d7ad21">2.4. Scaling to take into account the sensibility of the geophone and the voltage amplifier</a></li>
<li><a href="#org1b04be0">2.5. Computation of the ASD of the velocity and displacement</a></li>
<li><a href="#orge570bf0">2.6. Comparison with other measurements of ground motion</a>
<ul>
<li><a href="#org9008f38">2.6.1. Load the measurement data</a></li>
<li><a href="#org906cad8">2.6.2. Compute PSD of the measurements</a></li>
<li><a href="#orgab58013">2.6.3. Compare PSD of Cern, ID09 and ID31</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orgddb7761" class="outline-2">
<h2 id="orgddb7761"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1">
<p>
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.
</p>
<p>
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.
</p>
<p>
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:
</p>
<ul class="org-ul">
<li>AC/DC option set to DC</li>
<li>Amplification of 60dB (1000)</li>
<li>Low pass filter at the output with a cut-off frequency of \(1kHz\)</li>
</ul>
<p>
On figure <a href="#org3e1d768">1</a> is an overview of multiple measurements made at famous location.
</p>
<div id="org3e1d768" class="figure">
<p><img src="./img/ground_motion_measurements.png" alt="ground_motion_measurements.png" width="800px" />
</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>

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#+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]]

0
Ground Motion/mat/data_027.mat → ground-motion/mat/data_027.mat
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0
Ground Motion/mat/data_028.mat → ground-motion/mat/data_028.mat
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0
Ground Motion/data/ground_motion_dist.mat → ground-motion/mat/ground_motion_dist.mat
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0
Ground Motion/data/id09_floor_september2018.mat → ground-motion/mat/id09_floor_september2018.mat
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152
ground-motion/matlab/ground_meas_id31.m Normal file
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@ -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]);

0
Ground Motion/readme.org → ground-motion/readme.org
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2
huddle-test-geophones/index.html
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@ -509,7 +509,7 @@ We further divide the result by the sensibility of the Geophone to obtain the AS
</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>;
[Omitted long matching line]
</pre>
</div>
</div>

2
huddle-test-geophones/index.org
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@ -177,7 +177,7 @@ We also take into account the gain of the electronics which is here set to be $6
#+begin_src matlab :results none
G0_db = 60; % [dB]
G0 = 10^(60/G0_db); % [abs]
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.

2
huddle-test-geophones/matlab/huddle_test_signal_processing.m
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@ -104,7 +104,7 @@ ylabel('Amplitude $\left[\frac{V}{m/s}\right]$')
G0_db = 60; % [dB]
G0 = 10^(60/G0_db); % [abs]
G0 = 10^(G0_db/20); % [abs]