371 lines
13 KiB
Org Mode
371 lines
13 KiB
Org Mode
#+TITLE: Ground Motion Measurements
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:DRAWER:
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#+STARTUP: overview
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#+LANGUAGE: en
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#+EMAIL: dehaeze.thomas@gmail.com
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#+AUTHOR: Dehaeze Thomas
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#+HTML_LINK_HOME: ../index.html
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#+HTML_LINK_UP: ../index.html
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
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#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="../js/bootstrap.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
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#+HTML_MATHJAX: align: center tagside: right font: TeX
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#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:matlab+ :results none
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#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :output-dir figs
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#+PROPERTY: header-args:shell :eval no-export
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:END:
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* Experimental Setup
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The goal here is to compare the ground motion at the location of the micro-station (ID31 beamline at ESRF) with other measurements of the ground motion.
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This will also permit to confirm that the device use for the measurement (geophones, amplifiers, ADC) are working well and that the data processing is correct.
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One L22 geophone is put on the ID31 floor.
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The signal is then filtered with a first order low pass filter with a cut-off frequency of $1kHz$.
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Then the signal is amplified by a Voltage Amplifier with the following settings:
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- AC/DC option set to DC
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- Amplification of 60dB (1000)
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- Low pass filter at the output with a cut-off frequency of $1kHz$
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On figure [[fig:ground_motion_measurements]] is an overview of multiple measurements made at famous location.
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#+name: fig:ground_motion_measurements
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#+caption: Power spectral density of ground vibration in the vertical direction at multiple locations ([[https://vibration.desy.de/][source]])
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#+attr_html: :width 800px
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[[file:./img/ground_motion_measurements.png]]
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* Measurement Analysis
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/ground_meas_id31.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:ground_meas_id31>>
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** ZIP file containing the data and matlab files :ignore:
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#+begin_src bash :exports none :results none
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if [ matlab/ground_meas_id31.m -nt data/ground_meas_id31.zip ]; then
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cp matlab/ground_meas_id31.m ground_meas_id31.m;
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zip data/ground_meas_id31 \
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mat/data_028.mat \
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mat/id09_floor_september2018.mat \
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mat/ground_motion_dist.mat \
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ground_meas_id31.m
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rm ground_meas_id31.m;
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fi
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#+end_src
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#+begin_note
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All the files (data and Matlab scripts) are accessible [[file:data/ground_meas_id31.zip][here]].
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#+end_note
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** Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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** Load data
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#+begin_src matlab
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data = load('mat/data_028.mat', 'data'); data = data.data;
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#+end_src
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** Time domain plots of the measured voltage
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#+begin_src matlab
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figure;
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hold on;
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plot(data(:, 3), data(:, 1));
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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xlim([0, 100]);
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#+end_src
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#+NAME: fig:ground_motion_id31_time
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/ground_motion_id31_time.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:ground_motion_id31_time
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#+CAPTION: Measurement of the ground motion - Time domain
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#+RESULTS: fig:ground_motion_id31_time
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[[file:figs/ground_motion_id31_time.png]]
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** Computation of the ASD of the measured voltage
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#+begin_src matlab :results none
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dt = data(2, 3) - data(1, 3);
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Fs = 1/dt;
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win = hanning(ceil(10*Fs));
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#+end_src
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#+begin_src matlab :results none
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[px_dc, f] = pwelch(data(:, 1), win, [], [], Fs);
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#+end_src
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(f, sqrt(px_dc));
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
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xlim([0.1, 500]);
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#+end_src
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#+NAME: fig:ground_motion_id31_asd_volt
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/ground_motion_id31_asd_volt.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:ground_motion_id31_asd_volt
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#+CAPTION: Amplitude Spectral Density of the measured Voltage
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#+RESULTS: fig:ground_motion_id31_asd_volt
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[[file:figs/ground_motion_id31_asd_volt.png]]
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** Scaling to take into account the sensibility of the geophone and the voltage amplifier
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The Geophone used are L22. Their sensibility is shown on figure [[fig:geophone_sensibility]].
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#+begin_src matlab :results none
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S0 = 88; % Sensitivity [V/(m/s)]
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f0 = 2; % Cut-off frequency [Hz]
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S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);
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#+end_src
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#+begin_src matlab :results none
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freqs = logspace(-1, 2, 1000);
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figure;
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hold on;
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plot(f, abs(squeeze(freqresp(S, f, 'Hz'))));
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Magnitude $\left[\frac{V}{m/s}\right]$');
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xlim([0.1, 100]);
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#+end_src
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#+NAME: fig:geophone_sensibility
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/geophone_sensibility.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:geophone_sensibility
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#+CAPTION: Sensibility of the Geophone
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#+RESULTS: fig:geophone_sensibility
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[[file:figs/geophone_sensibility.png]]
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We also take into account the gain of the electronics which is here set to be $60dB$.
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#+begin_src matlab :results none
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G0_db = 60; % [dB]
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G0 = 10^(G0_db/20); % [abs]
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#+end_src
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We divide the PSD measured (in $\text{V^2}/\sqrt{Hz}$) by the square of the gain of the voltage amplifier to obtain the PSD of the voltage across the geophone.
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We further divide the result by the square of the magnitude of sensibility of the Geophone to obtain the PSD of the velocity in $(m/s)^2/Hz$.
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#+begin_src matlab :results none
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psd_gv = px_dc./abs(squeeze(freqresp(G0*S, f, 'Hz'))).^2;
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#+end_src
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Finally, we obtain the PSD of the ground motion in $m^2/Hz$ by dividing by the square of the frequency in $rad/s$.
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#+begin_src matlab
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psd_gm = psd_gv./(2*pi*f).^2;
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#+end_src
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** Time domain plots of the ground motion
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We can inverse the dynamics of the geophone to convert the measured voltage into the estimated ground motion.
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#+begin_src matlab
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est_vel = lsim(inv(G0*S)*(s/2/pi)/(1+s/2/pi), data(:, 1), data(:, 3)); % Estimated velocity above 1Hz
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est_vel = est_vel - mean(est_vel(data(:,3)>10)); % The mean value of the velocity if removed
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est_dis = lsim(1/(1+s/2/pi), est_vel, data(:, 3)); % The velocity is integrated above 1Hz
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#+end_src
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(data(:, 3), est_vel);
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hold off;
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xlabel('Time [s]'); ylabel('Velocity [m/s]');
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xlim([10, 100]);
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#+end_src
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/time_domain_velocity.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:time_domain_velocity
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#+CAPTION: Time domain velocity ([[./figs/time_domain_velocity.png][png]], [[./figs/time_domain_velocity.pdf][pdf]])
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[[file:figs/time_domain_velocity.png]]
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#+begin_src matlab :exports none
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figure;
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hold on;
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plot(data(:, 3), est_dis);
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hold off;
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xlabel('Time [s]'); ylabel('Displacement [m]');
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xlim([10, 100]);
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#+end_src
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#+HEADER: :tangle no :exports results :results none :noweb yes
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#+begin_src matlab :var filepath="figs/time_domain_displacement.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:time_domain_displacement
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#+CAPTION: Time domain absolute displacement ([[./figs/time_domain_displacement.png][png]], [[./figs/time_domain_displacement.pdf][pdf]])
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[[file:figs/time_domain_displacement.png]]
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** Computation of the ASD of the velocity and displacement
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The ASD of the measured velocity is shown on figure [[fig:ground_motion_id31_asd_velocity]].
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(f, sqrt(psd_gv));
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD of the measured Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
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xlim([0.1, 500]);
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#+end_src
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#+NAME: fig:ground_motion_id31_asd_velocity
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/ground_motion_id31_asd_velocity.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:ground_motion_id31_asd_velocity
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#+CAPTION: Amplitude Spectral Density of the Velocity
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#+RESULTS: fig:ground_motion_id31_asd_velocity
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[[file:figs/ground_motion_id31_asd_velocity.png]]
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We also plot the ASD in displacement (figure [[fig:ground_motion_id31_asd_displacement]]);
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(f, sqrt(psd_gm));
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
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xlim([0.1, 500]);
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#+end_src
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#+NAME: fig:ground_motion_id31_asd_displacement
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/ground_motion_id31_asd_displacement.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:ground_motion_id31_asd_displacement
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#+CAPTION: Amplitude Spectral Density of the Displacement
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#+RESULTS: fig:ground_motion_id31_asd_displacement
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[[file:figs/ground_motion_id31_asd_displacement.png]]
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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]]).
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One can then compare this curve with the figure [[fig:ground_motion_measurements]].
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#+begin_src matlab :results none
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figure;
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hold on;
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plot(f, psd_gm.*1e12);
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('PSD of the measured displacement $\left[\frac{{ \mu m }^2}{Hz}\right]$')
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xlim([0.1, 500]); ylim([1e-13, 1e3]);
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#+end_src
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#+NAME: fig:ground_motion_id31_psd_displacement
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/ground_motion_id31_psd_displacement.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:ground_motion_id31_psd_displacement
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#+CAPTION: Power Spectral Density of the measured displacement
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#+RESULTS: fig:ground_motion_id31_psd_displacement
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[[file:figs/ground_motion_id31_psd_displacement.png]]
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** Save
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We save the PSD of the ground motion for further analysis.
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#+begin_src matlab
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save('./mat/psd_gm.mat', 'f', 'psd_gm', 'psd_gv');
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#+end_src
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** Comparison with other measurements of ground motion
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Now we will compare with other measurements.
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*** Load the measurement data
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First we load the measurement data.
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Here we have one measurement of the floor motion made at the ESRF in 2018, and one measurement made at CERN.
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#+begin_src matlab
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id09 = load('./mat/id09_floor_september2018.mat');
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cern = load('./mat/ground_motion_dist.mat');
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#+end_src
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*** Compute PSD of the measurements
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We compute the Power Spectral Densities of the measurements.
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#+begin_src matlab
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Fs_id09 = 1/(id09.time3(2)-id09.time3(1));
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win_id09 = hanning(ceil(10*Fs_id09));
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[id09_pxx, id09_f] = pwelch(1e-6*id09.x_y_z(:, 3), win_id09, [], [], Fs_id09);
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#+end_src
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#+begin_src matlab
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Fs_cern = 1/(cern.gm.time(2)-cern.gm.time(1));
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win_cern = hanning(ceil(10*Fs_cern));
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[cern_pxx, cern_f] = pwelch(cern.gm.signal, win_cern, [], [], Fs_cern);
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#+end_src
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*** Compare PSD of Cern, ID09 and ID31
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And we compare all the measurements (figure [[fig:ground_motion_compare]]).
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#+begin_src matlab :results silent
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figure;
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hold on;
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plot(id09_f, id09_pxx, 'DisplayName', 'ID09');
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plot(cern_f, cern_pxx, 'DisplayName', 'CERN');
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plot(f, psd_gm, 'k', 'DisplayName', 'ID31');
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hold off;
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set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
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xlabel('Frequency [Hz]'); ylabel('PSD [$m^2/Hz$]');
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legend('Location', 'northeast');
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xlim([0.1, 500]);
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#+end_src
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#+NAME: fig:ground_motion_compare
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
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#+begin_src matlab :var filepath="figs/ground_motion_compare.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:ground_motion_compare
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#+CAPTION: Comparison of the PSD of the ground motion measured at different location
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#+RESULTS: fig:ground_motion_compare
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[[file:figs/ground_motion_compare.png]]
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