merge

.gitignore

@@ -2,3 +2,49 @@ auto/
 *.tex
 **/figs/*.pdf
 **/figs/*.svg
+=======
+# Emacs
+auto/
+
+# Simulink Real Time
+*bio.m
+*pt.m
+*ref.m
+*ri.m
+*xcp.m
+*.mldatx
+*.slxc
+*.xml
+*_slrt_rtw/
+
+# data
+data/
+
+# Windows default autosave extension
+*.asv
+
+# OSX / *nix default autosave extension
+*.m~
+
+# Compiled MEX binaries (all platforms)
+*.mex*
+
+# Packaged app and toolbox files
+*.mlappinstall
+*.mltbx
+
+# Generated helpsearch folders
+helpsearch*/
+
+# Simulink code generation folders
+slprj/
+sccprj/
+
+# Matlab code generation folders
+codegen/
+
+# Simulink autosave extension
+*.autosave
+
+# Octave session info
+octave-workspace

disturbance-measurement/index.org

@@ -0,0 +1,196 @@
+#+TITLE:Measurement of the sample vibrations when rotating the Spindle
+:DRAWER:
+#+STARTUP: overview
+
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
+#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="../js/bootstrap.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
+
+#+PROPERTY: header-args:matlab  :session *MATLAB*
+#+PROPERTY: header-args:matlab+ :comments org
+#+PROPERTY: header-args:matlab+ :results output
+#+PROPERTY: header-args:matlab+ :exports both
+#+PROPERTY: header-args:matlab+ :eval no-export
+#+PROPERTY: header-args:matlab+ :output-dir figs
+:END:
+
+* Experimental Setup
+
+* Signal Processing
+** Matlab Init                                              :noexport:ignore:
+#+begin_src matlab :exports none :results silent :noweb yes
+  <<matlab-init>>
+#+end_src
+
+** Load Data
+Measurement =data_001.mat= corresponds to a measurement where the spindle is not turning and =data_002.mat= where the spindle is turning at 1rpm.
+=x1= is the signal coming from the geophone located on the marble and =x2= is the signal from the geophone located on the sample station.
+
+#+begin_src matlab :results none
+  data1 = load('mat/data_001.mat', 't', 'x1', 'x2');
+  data2 = load('mat/data_002.mat', 't', 'x1', 'x2');
+#+end_src
+
+** Time domain Data
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(data1.t, data1.x1);
+  plot(data2.t, data2.x1);
+  hold off;
+#+end_src
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(data1.t, data1.x2);
+  plot(data2.t, data2.x2)
+  hold off;
+#+end_src
+
+** ASD and Frequency domain data
+#+begin_src matlab :results none
+  dt = data1.t(2) - data1.t(1);
+  Fs = 1/dt;
+
+  windows_psd = hanning(ceil(10*Fs));
+#+end_src
+
+#+begin_src matlab :results none
+  [pxx1m, f] = pwelch(data1.x1, windows_psd, [], [], Fs); f(1) = []; pxx1m(1) = [];
+  [pxx1h, ~] = pwelch(data1.x2, windows_psd, [], [], Fs); pxx1h(1) = [];
+
+  [pxx2m, ~] = pwelch(data2.x1, windows_psd, [], [], Fs); pxx2m(1) = [];
+  [pxx2h, ~] = pwelch(data2.x2, windows_psd, [], [], Fs); pxx2h(1) = [];
+#+end_src
+
+** Some plots
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, sqrt(pxx1m));
+  plot(f, sqrt(pxx2m));
+  hold off;
+  set(gca, 'xscale', 'log');
+  set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
+#+end_src
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, sqrt(pxx1h));
+  plot(f, sqrt(pxx2h));
+  hold off;
+  set(gca, 'xscale', 'log');
+  set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
+#+end_src
+
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, sqrt(pxx2m));
+  plot(f, sqrt(pxx2h));
+  hold off;
+  set(gca, 'xscale', 'log');
+  set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
+#+end_src
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, cumtrapz(f, pxx1m))
+  plot(f, cumtrapz(f, pxx2m))
+  set(gca, 'XScale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('CAS [m]')
+#+end_src
+
+** 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 frequnecy [Hz]
+
+  S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);
+#+end_src
+
+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^(60/G0_db); % [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'))); scaling(1) = 0;
+#+end_src
+
+** Computation of the ASD of the velocity
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, sqrt(pxx1h).*scaling);
+  plot(f, sqrt(pxx2h).*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
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, (sqrt(pxx1).*scaling)./(2*pi*f));
+  plot(f, (sqrt(pxx2).*scaling)./(2*pi*f));
+  hold off;
+  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
+  xlim([0.1, 500]);
+#+end_src
+
+** RMS value of the difference between the two geophones
+We also compute the Power Spectral Density of the difference between the two geophones. This is done in order to estimate the relative displacement of the sample with respect to the granite.
+#+begin_src matlab :results none
+  [pxxd1, ~] = pwelch(data1.x2-data1.x1, windows_psd, [], [], Fs); pxxd1(1) = [];
+  [pxxd2, ~] = pwelch(data2.x2-data2.x1, windows_psd, [], [], Fs); pxxd2(1) = [];
+#+end_src
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, (sqrt(pxxd1).*scaling)./(2*pi*f));
+  plot(f, (sqrt(pxxd2).*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
+
+#+begin_src matlab :results none
+  psd_d1 = ((sqrt(pxxd1).*scaling)./(2*pi*f)).^2;
+  psd_d2 = ((sqrt(pxxd2).*scaling)./(2*pi*f)).^2;
+
+  df = f(2) - f(1);
+
+  figure;
+  hold on;
+  plot(f, sqrt(cumsum(df.*psd_d1, 'reverse')));
+  plot(f, sqrt(cumsum(df.*psd_d2, 'reverse')));
+  hold off;
+  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('CAS $\left[m\right]$')
+  xlim([0.1, 500]);
+#+end_src

disturbance-measurement/readme.org

@@ -0,0 +1,12 @@
+#+TITLE:Measurement of the sample vibrations when rotating the Spindle
+
+Measurement:
+- one geophone on the marble
+- one geophone at the sample position
+
+Every stage is powered on.
+
+| Data file    | Description                |
+|--------------+----------------------------|
+| data_001.mat | nothing is turning         |
+| data_002.mat | spindle is turning at 1rpm |

disturbance-measurement/run_test.m

@@ -0,0 +1,53 @@
+%%
+Tsim = 100; % [s]
+
+%%
+tg = slrt;
+
+%% TODO - Build this application if updated
+
+%%
+if tg.Connected == "Yes"
+    if tg.Status == "running"
+        disp('Target is Running, Stopping...');
+        tg.stop;
+        while tg.Status == "running"
+            pause(1);
+        end
+        disp('Target is Stopped');
+    end
+    if tg.Status == "stopped"
+        disp('Load the Application');
+        tg.load('disturbance_measurement');
+
+        %% Run the application
+        disp('Starting the Application');
+        tg.start;
+        pause(Tsim);
+        tg.stop;
+    end
+else
+    error("The target computer is not connected");
+end
+
+%%
+f = SimulinkRealTime.openFTP(tg);
+cd(f, 'data/disturbance_measurement/');
+mget(f, 'data_001.dat', 'data');
+close(f);
+
+data = SimulinkRealTime.utils.getFileScopeData('data/data_001.dat').data;
+
+%%
+n = 17;
+
+while isfile(['mat/data_', num2str(n, '%03d'), '.mat'])
+     disp('File exists.');
+     if input(['Are you sure you want to override the file ', 'mat/data_', ...
+            num2str(n, '%03d'), '.mat', ' ? [Y/n]']) == 'Y'
+         break;
+     end
+     n = input('What should be the measurement number?');
+end
+
+save(['mat/data_', num2str(n, '%03d'), '.mat'], 'data');

equipment/equipment.org

@@ -0,0 +1,28 @@
+#+TITLE: Equipment used to make the measurements
+
+* Geophone
+L22
+
+* Speedgoat
+ADC and DAC:
+
+* Voltage amplifier
+
+#+name: fig:voltage_amplifier
+#+caption: Picture of the voltage amplifier DLPVA
+#+attr_latex: :scale 1
+[[file:./img/DLPVA_W_R2.jpg]]
+
+
+*Specifications*:
+- Switchable gain up to 100 dB (x 100,000)
+- Bandwidth DC to 100 kHz
+- DC-drift 0.6 µV/°C
+- Input noise down to 0.4 nV/√Hz
+- Switchable AC/DC-coupling
+- Local and remote control
+- Input impedance up to 1 TΩ
+
+The documentation of the voltage amplifier is accessible [[file:documents/dlpva_datasheet.pdf][here]].
+
+The exact model is DLPVA-100-B-D

huddle-test-geophones/compare_axis.m

@@ -0,0 +1,81 @@
+% Matlab Init                                              :noexport:ignore:
+
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Initialize ans with org-babel
+ans = 0;
+
+% Load data
+% We first load the data for the three axis.
+
+z     = load('mat/data_001.mat', 't', 'x1', 'x2');
+east  = load('mat/data_002.mat', 't', 'x1', 'x2');
+north = load('mat/data_003.mat', 't', 'x1', 'x2');
+
+% Compare PSD
+% The PSD for each axis of the two geophones are computed.
+
+[pz1, fz] = pwelch(z.x1, hanning(ceil(length(z.x1)/100)), [], [], 1/(z.t(2)-z.t(1)));
+[pz2, ~]  = pwelch(z.x2, hanning(ceil(length(z.x2)/100)), [], [], 1/(z.t(2)-z.t(1)));
+
+[pe1, fe] = pwelch(east.x1, hanning(ceil(length(east.x1)/100)), [], [], 1/(east.t(2)-east.t(1)));
+[pe2, ~]  = pwelch(east.x2, hanning(ceil(length(east.x2)/100)), [], [], 1/(east.t(2)-east.t(1)));
+
+[pn1, fn] = pwelch(north.x1, hanning(ceil(length(north.x1)/100)), [], [], 1/(north.t(2)-north.t(1)));
+[pn2, ~]  = pwelch(north.x2, hanning(ceil(length(north.x2)/100)), [], [], 1/(north.t(2)-north.t(1)));
+
+
+
+% We compare them. The result is shown on figure [[fig:compare_axis_psd]].
+
+figure;
+hold on;
+plot(fz, sqrt(pz1), '-',   'Color', [0 0.4470 0.7410], 'DisplayName', 'z');
+plot(fz, sqrt(pz2), '--',  'Color', [0 0.4470 0.7410], 'HandleVisibility', 'off');
+plot(fe, sqrt(pe1), '-',   'Color', [0.8500 0.3250 0.0980], 'DisplayName', 'east');
+plot(fe, sqrt(pe2), '--',  'Color', [0.8500 0.3250 0.0980], 'HandleVisibility', 'off');
+plot(fn, sqrt(pn1), '-',   'Color', [0.9290 0.6940 0.1250], 'DisplayName', 'north');
+plot(fn, sqrt(pn2), '--',  'Color', [0.9290 0.6940 0.1250], 'HandleVisibility', 'off');
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]');
+legend('Location', 'northeast');
+xlim([0, 500]);
+
+% Compare TF
+% The transfer functions from one geophone to the other are also computed for each axis.
+% The result is shown on figure [[fig:compare_tf_axis]].
+
+
+[Tz, fz] = tfestimate(z.x1, z.x2, hanning(ceil(length(z.x1)/100)), [], [], 1/(z.t(2)-z.t(1)));
+[Te, fe] = tfestimate(east.x1, east.x2, hanning(ceil(length(east.x1)/100)), [], [], 1/(east.t(2)-east.t(1)));
+[Tn, fn] = tfestimate(north.x1, north.x2, hanning(ceil(length(north.x1)/100)), [], [], 1/(north.t(2)-north.t(1)));
+
+figure;
+ax1 = subplot(2, 1, 1);
+hold on;
+plot(fz, abs(Tz), 'DisplayName', 'z');
+plot(fe, abs(Te), 'DisplayName', 'east');
+plot(fn, abs(Tn), 'DisplayName', 'north');
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Magnitude');
+legend('Location', 'southwest');
+
+ax2 = subplot(2, 1, 2);
+hold on;
+plot(fz, mod(180+180/pi*phase(Tz), 360)-180);
+plot(fe, mod(180+180/pi*phase(Te), 360)-180);
+plot(fn, mod(180+180/pi*phase(Tn), 360)-180);
+hold off;
+set(gca, 'xscale', 'log');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase');
+
+linkaxes([ax1,ax2],'x');
+xlim([1, 500]);

huddle-test-geophones/figs/.gitignore

@@ -0,0 +1,3 @@
+*.svg
+*.pdf
+*.tex

huddle-test-geophones/index.org

@@ -0,0 +1,561 @@
+#+TITLE:Huddle Test of the L22 Geophones
+:DRAWER:
+#+STARTUP: overview
+
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
+#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="../js/bootstrap.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.stickytableheaders.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="../js/readtheorg.js"></script>
+
+#+PROPERTY: header-args:matlab  :session *MATLAB*
+#+PROPERTY: header-args:matlab+ :comments org
+#+PROPERTY: header-args:matlab+ :results output
+#+PROPERTY: header-args:matlab+ :exports both
+#+PROPERTY: header-args:matlab+ :eval no-export
+#+PROPERTY: header-args:matlab+ :output-dir figs
+:END:
+
+* Experimental Setup
+Two L22 geophones are used.
+They are placed on the ID31 granite.
+They are leveled.
+
+The signals are amplified using voltage amplifier with a gain of 60dB.
+The voltage amplifiers include a low pass filter with a cut-off frequency at 1kHz.
+
+#+name: fig:figure_name
+#+caption: Setup
+#+attr_html: :width 500px
+[[file:./figs/setup.jpg]]
+
+#+name: fig:figure_name
+#+caption: Geophones
+#+attr_html: :width 500px
+[[file:./figs/geophones.jpg]]
+
+* Signal Processing
+  :PROPERTIES:
+  :header-args:matlab+: :tangle signal_processing.m
+  :header-args:matlab+: :comments org :mkdirp yes
+  :END:
+The Matlab computing file for this part is accessible [[file:signal_processing.m][here]].
+The =mat= file containing the measurement data is accessible [[file:mat/data_001.mat][here]].
+
+** Matlab Init                                              :noexport:ignore:
+#+begin_src matlab :exports none :results silent :noweb yes
+  <<matlab-init>>
+#+end_src
+
+** Load data
+We load the data of the z axis of two geophones.
+
+#+begin_src matlab :results none
+  load('mat/data_001.mat', 't', 'x1', 'x2');
+  dt = t(2) - t(1);
+#+end_src
+
+** Time Domain Data
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(t, x1);
+  plot(t, x2);
+  hold off;
+  xlabel('Time [s]');
+  ylabel('Voltage [V]');
+  xlim([t(1), t(end)]);
+#+end_src
+
+#+NAME: fig:data_time_domain
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/data_time_domain.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:data_time_domain
+#+CAPTION: Time domain Data
+#+RESULTS: fig:data_time_domain
+[[file:figs/data_time_domain.png]]
+
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(t, x1);
+  plot(t, x2);
+  hold off;
+  xlabel('Time [s]');
+  ylabel('Voltage [V]');
+  xlim([0 1]);
+#+end_src
+
+#+NAME: fig:data_time_domain_zoom
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/data_time_domain_zoom.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:data_time_domain_zoom
+#+CAPTION: Time domain Data - Zoom
+#+RESULTS: fig:data_time_domain_zoom
+[[file:figs/data_time_domain_zoom.png]]
+
+** Computation of the ASD of the measured voltage
+We first define the parameters for the frequency domain analysis.
+#+begin_src matlab :results none
+  Fs = 1/dt; % [Hz]
+
+  win = hanning(ceil(10*Fs));
+#+end_src
+
+Then we compute the Power Spectral Density using =pwelch= function.
+#+begin_src matlab :results none
+  [pxx1, f] = pwelch(x1, win, [], [], Fs);
+  [pxx2, ~] = pwelch(x2, win, [], [], Fs);
+#+end_src
+
+And we plot the result on figure [[fig:asd_voltage]].
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, sqrt(pxx1));
+  plot(f, sqrt(pxx2));
+  hold off;
+  set(gca, 'xscale', 'log');
+  set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
+  xlim([0.1, 500]);
+#+end_src
+
+#+NAME: fig:asd_voltage
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/asd_voltage.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:asd_voltage
+#+CAPTION: Amplitude Spectral Density of the measured voltage
+#+RESULTS: fig:asd_voltage
+[[file:figs/asd_voltage.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 frequnecy [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^(60/G0_db); % [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
+The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, sqrt(pxx1).*scaling);
+  plot(f, sqrt(pxx2).*scaling);
+  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:psd_velocity
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/psd_velocity.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:psd_velocity
+#+CAPTION: Amplitude Spectral Density of the Velocity
+#+RESULTS: fig:psd_velocity
+[[file:figs/psd_velocity.png]]
+
+We also plot the ASD in displacement (figure [[fig:asd_displacement]]);
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, (sqrt(pxx1).*scaling)./(2*pi*f));
+  plot(f, (sqrt(pxx2).*scaling)./(2*pi*f));
+  hold off;
+  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
+  xlim([0.1, 500]);
+#+end_src
+
+#+NAME: fig:asd_displacement
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/asd_displacement.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:asd_displacement
+#+CAPTION: Amplitude Spectral Density of the Displacement
+#+RESULTS: fig:asd_displacement
+[[file:figs/asd_displacement.png]]
+
+** Transfer function between the two geophones
+We here compute the transfer function from one geophone to the other.
+The result is shown on figure [[fig:tf_geophones]].
+
+We also compute the coherence between the two signals (figure [[fig:coh_geophones]]).
+
+#+begin_src matlab :results none
+  [T12, ~] = tfestimate(x1, x2, win, [], [], Fs);
+#+end_src
+
+#+begin_src matlab :results none :exports none
+  figure;
+  ax1 = subplot(2, 1, 1);
+  plot(f, abs(T12));
+  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+  set(gca, 'XTickLabel',[]);
+  ylabel('Magnitude');
+
+  ax2 = subplot(2, 1, 2);
+  plot(f, mod(180+180/pi*phase(T12), 360)-180);
+  set(gca, 'xscale', 'log');
+  ylim([-180, 180]);
+  yticks([-180, -90, 0, 90, 180]);
+  xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+
+  linkaxes([ax1,ax2],'x');
+  xlim([0.1, 500]);
+#+end_src
+
+#+NAME: fig:tf_geophones
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/tf_geophones.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:tf_geophones
+#+CAPTION: Estimated transfer function between the two geophones
+#+RESULTS: fig:tf_geophones
+[[file:figs/tf_geophones.png]]
+
+#+begin_src matlab :results none
+  [coh12, ~] = mscohere(x1, x2, win, [], [], Fs);
+#+end_src
+
+#+begin_src matlab :results none :exports none
+  figure;
+  plot(f, coh12);
+  set(gca, 'xscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('Coherence');
+  ylim([0,1]); xlim([0.1, 500]);
+#+end_src
+
+#+NAME: fig:coh_geophones
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/coh_geophones.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:coh_geophones
+#+CAPTION: Cohererence between the signals of the two geophones
+#+RESULTS: fig:coh_geophones
+[[file:figs/coh_geophones.png]]
+
+** Estimation of the sensor noise
+The technique to estimate the sensor noise is taken from cite:barzilai98_techn_measur_noise_sensor_presen.
+
+The coherence between signals $X$ and $Y$ is defined as follow
+\[ \gamma^2_{XY}(\omega) = \frac{|G_{XY}(\omega)|^2}{|G_{X}(\omega)| |G_{Y}(\omega)|} \]
+where $|G_X(\omega)|$ is the output Power Spectral Density (PSD) of signal $X$ and $|G_{XY}(\omega)|$ is the Cross Spectral Density (CSD) of signal $X$ and $Y$.
+
+The PSD and CSD are defined as follow:
+\begin{align}
+  |G_X(\omega)|    &= \frac{2}{n_d T} \sum^{n_d}_{n=1} \left| X_k(\omega, T) \right|^2 \\
+  |G_{XY}(\omega)| &= \frac{2}{n_d T} \sum^{n_d}_{n=1} [ X_k^*(\omega, T) ] [ Y_k(\omega, T) ]
+\end{align}
+where:
+- $n_d$ is the number for records averaged
+- $T$ is the length of each record
+- $X_k(\omega, T)$ is the finite Fourier transform of the kth record
+- $X_k^*(\omega, T)$ is its complex conjugate
+
+The =mscohere= function is compared with this formula on Appendix (section [[sec:coherence]]), it is shown that it is identical.
+
+Figure [[fig:huddle_test]] illustrate a block diagram model of the system used to determine the sensor noise of the geophone.
+
+Two geophones are mounted side by side to ensure that they are exposed by the same motion input $U$.
+
+Each sensor has noise $N$ and $M$.
+
+#+NAME: fig:huddle_test
+#+CAPTION: Huddle test block diagram
+[[file:figs/huddle-test.png]]
+
+We here assume that each sensor has the same magnitude of instrumental noise ($N = M$).
+We also assume that $S_1 = S_2 = 1$.
+
+We then obtain:
+#+NAME: eq:coh_bis
+\begin{equation}
+  \gamma_{XY}^2(\omega) = \frac{1}{1 + 2 \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right) + \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right)^2}
+\end{equation}
+
+Since the input signal $U$ and the instrumental noise $N$ are incoherent:
+#+NAME: eq:incoherent_noise
+\begin{equation}
+  |G_X(\omega)| = |G_N(\omega)| + |G_U(\omega)|
+\end{equation}
+
+From equations [[eq:coh_bis]] and [[eq:incoherent_noise]], we finally obtain
+#+begin_important
+#+NAME: eq:noise_psd
+\begin{equation}
+  |G_N(\omega)| = |G_X(\omega)| \left( 1 - \sqrt{\gamma_{XY}^2(\omega)} \right)
+\end{equation}
+#+end_important
+
+The instrumental noise is computed below. The result in V^2/Hz is shown on figure [[fig:intrumental_noise_V]].
+#+begin_src matlab :results none
+  pxxN = pxx1.*(1 - coh12);
+#+end_src
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, pxx1, '-');
+  plot(f, pxx2, '-');
+  plot(f, pxxN, 'k--');
+  hold off;
+  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('PSD of the measured Voltage $\left[\frac{V^2}{Hz}\right]$');
+  xlim([0.1, 500]);
+#+end_src
+
+#+NAME: fig:intrumental_noise_V
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/intrumental_noise_V.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:intrumental_noise_V
+#+CAPTION: Instrumental Noise and Measurement in $V^2/Hz$
+#+RESULTS: fig:intrumental_noise_V
+[[file:figs/intrumental_noise_V.png]]
+
+This is then further converted into velocity and compared with the ground velocity measurement. (figure [[fig:intrumental_noise_velocity]])
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, sqrt(pxx1).*scaling, '-');
+  plot(f, sqrt(pxx2).*scaling, '-');
+  plot(f, sqrt(pxxN).*scaling, 'k--');
+  hold off;
+  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('ASD of the Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$');
+  xlim([0.1, 500]);
+#+end_src
+
+#+NAME: fig:intrumental_noise_velocity
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/intrumental_noise_velocity.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:intrumental_noise_velocity
+#+CAPTION: Instrumental Noise and Measurement in $m/s/\sqrt{Hz}$
+#+RESULTS: fig:intrumental_noise_velocity
+[[file:figs/intrumental_noise_velocity.png]]
+
+* Compare axis
+  :PROPERTIES:
+  :header-args:matlab+: :tangle compare_axis.m
+  :header-args:matlab+: :comments org :mkdirp yes
+  :END:
+The Matlab computing file for this part is accessible [[file:compare_axis.m][here]].
+The =mat= files containing the measurement data are accessible with the following links:
+- z axis: [[file:mat/data_001.mat][here]].
+- east axis: [[file:mat/data_002.mat][here]].
+- north axis: [[file:mat/data_003.mat][here]].
+
+** Matlab Init                                              :noexport:ignore:
+#+begin_src matlab :exports none :results silent :noweb yes
+  <<matlab-init>>
+#+end_src
+
+** Load data
+We first load the data for the three axis.
+#+begin_src matlab :results none
+  z     = load('mat/data_001.mat', 't', 'x1', 'x2');
+  east  = load('mat/data_002.mat', 't', 'x1', 'x2');
+  north = load('mat/data_003.mat', 't', 'x1', 'x2');
+#+end_src
+
+** Compare PSD
+The PSD for each axis of the two geophones are computed.
+#+begin_src matlab :results none
+  [pz1, fz] = pwelch(z.x1, hanning(ceil(length(z.x1)/100)), [], [], 1/(z.t(2)-z.t(1)));
+  [pz2, ~]  = pwelch(z.x2, hanning(ceil(length(z.x2)/100)), [], [], 1/(z.t(2)-z.t(1)));
+
+  [pe1, fe] = pwelch(east.x1, hanning(ceil(length(east.x1)/100)), [], [], 1/(east.t(2)-east.t(1)));
+  [pe2, ~]  = pwelch(east.x2, hanning(ceil(length(east.x2)/100)), [], [], 1/(east.t(2)-east.t(1)));
+
+  [pn1, fn] = pwelch(north.x1, hanning(ceil(length(north.x1)/100)), [], [], 1/(north.t(2)-north.t(1)));
+  [pn2, ~]  = pwelch(north.x2, hanning(ceil(length(north.x2)/100)), [], [], 1/(north.t(2)-north.t(1)));
+#+end_src
+
+We compare them. The result is shown on figure [[fig:compare_axis_psd]].
+#+begin_src matlab :results none :exports none
+  figure;
+  hold on;
+  plot(fz, sqrt(pz1), '-',   'Color', [0 0.4470 0.7410], 'DisplayName', 'z');
+  plot(fz, sqrt(pz2), '--',  'Color', [0 0.4470 0.7410], 'HandleVisibility', 'off');
+  plot(fe, sqrt(pe1), '-',   'Color', [0.8500 0.3250 0.0980], 'DisplayName', 'east');
+  plot(fe, sqrt(pe2), '--',  'Color', [0.8500 0.3250 0.0980], 'HandleVisibility', 'off');
+  plot(fn, sqrt(pn1), '-',   'Color', [0.9290 0.6940 0.1250], 'DisplayName', 'north');
+  plot(fn, sqrt(pn2), '--',  'Color', [0.9290 0.6940 0.1250], 'HandleVisibility', 'off');
+  hold off;
+  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+  xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]');
+  legend('Location', 'northeast');
+  xlim([0, 500]);
+#+end_src
+
+#+NAME: fig:compare_axis_psd
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/compare_axis_psd.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:compare_axis_psd
+#+CAPTION: Compare the measure PSD of the two geophones for the three axis
+#+RESULTS: fig:compare_axis_psd
+[[file:figs/compare_axis_psd.png]]
+
+** Compare TF
+The transfer functions from one geophone to the other are also computed for each axis.
+The result is shown on figure [[fig:compare_tf_axis]].
+
+#+begin_src matlab :results none
+  [Tz, fz] = tfestimate(z.x1, z.x2, hanning(ceil(length(z.x1)/100)), [], [], 1/(z.t(2)-z.t(1)));
+  [Te, fe] = tfestimate(east.x1, east.x2, hanning(ceil(length(east.x1)/100)), [], [], 1/(east.t(2)-east.t(1)));
+  [Tn, fn] = tfestimate(north.x1, north.x2, hanning(ceil(length(north.x1)/100)), [], [], 1/(north.t(2)-north.t(1)));
+#+end_src
+
+#+begin_src matlab :results none :exports none
+  figure;
+  ax1 = subplot(2, 1, 1);
+  hold on;
+  plot(fz, abs(Tz), 'DisplayName', 'z');
+  plot(fe, abs(Te), 'DisplayName', 'east');
+  plot(fn, abs(Tn), 'DisplayName', 'north');
+  hold off;
+  set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+  set(gca, 'XTickLabel',[]);
+  ylabel('Magnitude');
+  legend('Location', 'southwest');
+
+  ax2 = subplot(2, 1, 2);
+  hold on;
+  plot(fz, mod(180+180/pi*phase(Tz), 360)-180);
+  plot(fe, mod(180+180/pi*phase(Te), 360)-180);
+  plot(fn, mod(180+180/pi*phase(Tn), 360)-180);
+  hold off;
+  set(gca, 'xscale', 'log');
+  ylim([-180, 180]);
+  yticks([-180, -90, 0, 90, 180]);
+  xlabel('Frequency [Hz]'); ylabel('Phase');
+
+  linkaxes([ax1,ax2],'x');
+  xlim([1, 500]);
+#+end_src
+
+#+NAME: fig:compare_tf_axis
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/compare_tf_axis.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:compare_tf_axis
+#+CAPTION: Compare the transfer function from one geophone to the other for the 3 axis
+#+RESULTS: fig:compare_tf_axis
+[[file:figs/compare_tf_axis.png]]
+
+* Appendix
+** Computation of coherence from PSD and CSD
+  <<sec:coherence>>
+#+begin_src matlab :results none
+  load('mat/data_001.mat', 't', 'x1', 'x2');
+  dt = t(2) - t(1);
+  Fs = 1/dt;
+  win = hanning(ceil(length(x1)/100));
+#+end_src
+
+#+begin_src matlab :results none
+  pxy = cpsd(x1, x2, win, [], [], Fs);
+  pxx = pwelch(x1, win, [], [], Fs);
+  pyy = pwelch(x2, win, [], [], Fs);
+  coh = mscohere(x1, x2, win, [], [], Fs);
+#+end_src
+
+#+begin_src matlab :results none
+  figure;
+  hold on;
+  plot(f, abs(pxy).^2./abs(pxx)./abs(pyy), '-');
+  plot(f, coh, '--');
+  hold off;
+  set(gca, 'xscale', 'log');
+  xlabel('Frequency'); ylabel('Coherence');
+  xlim([1, 500]);
+#+end_src
+
+#+NAME: fig:comp_coherence_formula
+#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
+#+begin_src matlab :var filepath="figs/comp_coherence_formula.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
+  <<plt-matlab>>
+#+end_src
+
+#+NAME: fig:comp_coherence_formula
+#+CAPTION: Comparison of =mscohere= and manual computation
+#+RESULTS: fig:comp_coherence_formula
+[[file:figs/comp_coherence_formula.png]]
+
+* Bibliography                                                       :ignore:
+bibliographystyle:unsrt
+bibliography:ref.bib

huddle-test-geophones/ref.bib

@@ -0,0 +1,29 @@
+@article{barzilai98_techn_measur_noise_sensor_presen,
+  author =       {Aaron Barzilai and Tom VanZandt and Tom Kenny},
+  title =        {Technique for Measurement of the Noise of a Sensor in the
+                  Presence of Large Background Signals},
+  journal =      {Review of Scientific Instruments},
+  volume =       69,
+  number =       7,
+  pages =        {2767-2772},
+  year =         1998,
+  doi =          {10.1063/1.1149013},
+  url =          {https://doi.org/10.1063/1.1149013},
+}
+
+
+@article{kirchhoff17_huddl_test_measur_near_johns,
+  author =       {R. Kirchhoff and C. M. Mow-Lowry and V. B. Adya and G.
+                  Bergmann and S. Cooper and M. M. Hanke and P. Koch and S. M.
+                  K{\"o}hlenbeck and J. Lehmann and P. Oppermann and J.
+                  W{\"o}hler and D. S. Wu and H. L{\"u}ck and K. A. Strain},
+  title =        {Huddle Test Measurement of a Near Johnson Noise Limited
+                  Geophone},
+  journal =      {Review of Scientific Instruments},
+  volume =       88,
+  number =       11,
+  pages =        115008,
+  year =         2017,
+  doi =          {10.1063/1.5000592},
+  url =          {https://doi.org/10.1063/1.5000592},
+}

huddle-test-geophones/run_test.m

@@ -0,0 +1,47 @@
+tg = slrt;
+
+%% TODO - Build this application if updated
+
+%%
+if tg.Connected == "Yes"
+    if tg.Status == "stopped"
+        %% Load the application
+        tg.load('test');
+
+        %% Run the application
+        tg.start;
+        pause(10);
+        tg.stop;
+
+        %% Load the data
+        f = SimulinkRealTime.openFTP(tg);
+        mget(f, 'data/data_001.dat');
+        close(f);
+    end
+end
+
+%% Convert the Data
+data = SimulinkRealTime.utils.getFileScopeData('data/data_001.dat').data;
+
+t  = data(:, end);
+x1 = data(:, 1);
+x2 = data(:, 2);
+
+save('mat/data_003.mat', 't', 'x1', 'x2');
+
+%% Plot the data
+figure;
+hold on;
+plot(t, x1);
+plot(t, x2);
+hold off
+xlabel('Time [s]');
+ylabel('Voltage [V]');
+
+%% Compute the PSD
+dt = t(2)-t(1);
+
+window_L = ceil(length(x1)/10);
+window_han = .5*(1 - cos(2*pi*(1:window_L)'/(window_L+1)));
+
+[pxx, f] = pwelch(x1, window_han, 0, [], 1/dt);

huddle-test-geophones/setup.m

@@ -0,0 +1 @@
+Ts = 1e-3; % [s]

huddle-test-geophones/signal_processing.m

@@ -0,0 +1,252 @@
+% Matlab Init                                              :noexport:ignore:
+
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Initialize ans with org-babel
+ans = 0;
+
+% Load data
+% We load the data of the z axis of two geophones.
+
+
+load('mat/data_001.mat', 't', 'x1', 'x2');
+dt = t(2) - t(1);
+
+% Time Domain Data
+
+figure;
+hold on;
+plot(t, x1);
+plot(t, x2);
+hold off;
+xlabel('Time [s]');
+ylabel('Voltage [V]');
+xlim([t(1), t(end)]);
+
+
+
+% #+NAME: fig:data_time_domain
+% #+CAPTION: Time domain Data
+% #+RESULTS: fig:data_time_domain
+% [[file:figs/data_time_domain.png]]
+
+
+
+figure;
+hold on;
+plot(t, x1);
+plot(t, x2);
+hold off;
+xlabel('Time [s]');
+ylabel('Voltage [V]');
+xlim([0 1]);
+
+% Computation of the ASD of the measured voltage
+% We first define the parameters for the frequency domain analysis.
+
+win = hanning(ceil(length(x1)/100));
+Fs = 1/dt;
+
+[pxx1, f] = pwelch(x1, win, [], [], Fs);
+[pxx2, ~] = pwelch(x2, win, [], [], Fs);
+
+% Scaling to take into account the sensibility of the geophone and the voltage amplifier
+% The Geophone used are L22.
+% Their sensibility are shown on figure [[fig:geophone_sensibility]].
+
+
+S0 = 88; % Sensitivity [V/(m/s)]
+f0 = 2; % Cut-off frequnecy [Hz]
+S = (s/2/pi/f0)/(1+s/2/pi/f0);
+
+figure;
+bodeFig({S});
+ylabel('Amplitude [V/(m/s)]')
+
+
+
+% #+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 $60dB$.
+% The amplifiers also include a low pass filter with a cut-off frequency set at 1kHz.
+
+
+G0 = 60; % [dB]
+
+G = 10^(G0/20)/(1+s/2/pi/1000);
+
+
+
+% We divide the ASD measured (in $\text{V}/\sqrt{\text{Hz}}$) by the transfer function of the voltage amplifier to obtain the ASD of the voltage across the geophone.
+% We further divide the result by the sensibility of the Geophone to obtain the ASD of the velocity in $m/s/\sqrt{Hz}$.
+
+
+scaling = 1./squeeze(abs(freqresp(G*S, f, 'Hz')));
+
+% Computation of the ASD of the velocity
+% The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
+
+
+figure;
+hold on;
+plot(f, sqrt(pxx1).*scaling);
+plot(f, sqrt(pxx2).*scaling);
+hold off;
+set(gca, 'xscale', 'log');
+set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
+xlim([2, 500]);
+
+
+
+% #+NAME: fig:psd_velocity
+% #+CAPTION: Spectral density of the velocity
+% #+RESULTS: fig:psd_velocity
+% [[file:figs/psd_velocity.png]]
+
+% We also plot the ASD in displacement (figure [[fig:asd_displacement]]);
+
+
+figure;
+hold on;
+plot(f, (pxx1.*scaling./f).^2);
+plot(f, (pxx2.*scaling./f).^2);
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
+xlim([2, 500]);
+
+% Transfer function between the two geophones
+% We here compute the transfer function from one geophone to the other.
+% The result is shown on figure [[fig:tf_geophones]].
+
+% We also compute the coherence between the two signals (figure [[fig:coh_geophones]]).
+
+
+[T12, ~] = tfestimate(x1, x2, win, [], [], Fs);
+
+figure;
+ax1 = subplot(2, 1, 1);
+plot(f, abs(T12));
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Magnitude');
+
+ax2 = subplot(2, 1, 2);
+plot(f, mod(180+180/pi*phase(T12), 360)-180);
+set(gca, 'xscale', 'log');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase');
+
+linkaxes([ax1,ax2],'x');
+xlim([1, 500]);
+
+
+
+% #+NAME: fig:tf_geophones
+% #+CAPTION: Estimated transfer function between the two geophones
+% #+RESULTS: fig:tf_geophones
+% [[file:figs/tf_geophones.png]]
+
+
+[coh12, ~] = mscohere(x1, x2, win, [], [], Fs);
+
+figure;
+plot(f, coh12);
+set(gca, 'xscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Coherence');
+ylim([0,1]); xlim([1, 500]);
+
+% Estimation of the sensor noise
+% The technique to estimate the sensor noise is taken from cite:barzilai98_techn_measur_noise_sensor_presen.
+
+% The coherence between signals $X$ and $Y$ is defined as follow
+% \[ \gamma^2_{XY}(\omega) = \frac{|G_{XY}(\omega)|^2}{|G_{X}(\omega)| |G_{Y}(\omega)|} \]
+% where $|G_X(\omega)|$ is the output Power Spectral Density (PSD) of signal $X$ and $|G_{XY}(\omega)|$ is the Cross Spectral Density (CSD) of signal $X$ and $Y$.
+
+% The PSD and CSD are defined as follow:
+% \begin{align}
+%   |G_X(\omega)|    &= \frac{2}{n_d T} \sum^{n_d}_{n=1} \left| X_k(\omega, T) \right|^2 \\
+%   |G_{XY}(\omega)| &= \frac{2}{n_d T} \sum^{n_d}_{n=1} [ X_k^*(\omega, T) ] [ Y_k(\omega, T) ]
+% \end{align}
+% where:
+% - $n_d$ is the number for records averaged
+% - $T$ is the length of each record
+% - $X_k(\omega, T)$ is the finite Fourier transform of the kth record
+% - $X_k^*(\omega, T)$ is its complex conjugate
+
+% The =mscohere= function is compared with this formula on Appendix (section [[sec:coherence]]), it is shown that it is identical.
+
+% Figure [[fig:huddle_test]] illustrate a block diagram model of the system used to determine the sensor noise of the geophone.
+
+% Two geophones are mounted side by side to ensure that they are exposed by the same motion input $U$.
+
+% Each sensor has noise $N$ and $M$.
+
+% #+NAME: fig:huddle_test
+% #+CAPTION: Huddle test block diagram
+% [[file:figs/huddle-test.png]]
+
+% We here assume that each sensor has the same magnitude of instrumental noise ($N = M$).
+% We also assume that $H_1 = H_2 = 1$.
+
+% We then obtain:
+% #+NAME: eq:coh_bis
+% \begin{equation}
+%   \gamma_{XY}^2(\omega) = \frac{1}{1 + 2 \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right) + \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right)^2}
+% \end{equation}
+
+% Since the input signal $U$ and the instrumental noise $N$ are incoherent:
+% #+NAME: eq:incoherent_noise
+% \begin{equation}
+%   |G_X(\omega)| = |G_N(\omega)| + |G_U(\omega)|
+% \end{equation}
+
+% From equations [[eq:coh_bis]] and [[eq:incoherent_noise]], we finally obtain
+% #+begin_important
+% #+NAME: eq:noise_psd
+% \begin{equation}
+%   |G_N(\omega)| = |G_X(\omega)| \left( 1 - \sqrt{\gamma_{XY}^2(\omega)} \right)
+% \end{equation}
+% #+end_important
+
+% The instrumental noise is computed below. The result in V^2/Hz is shown on figure [[fig:intrumental_noise_V]].
+
+pxxN = pxx1.*(1 - coh12);
+
+figure;
+hold on;
+plot(f, pxx1, '-');
+plot(f, pxx2, '-');
+plot(f, pxxN, 'k--');
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('PSD [$V^2/Hz$]');
+xlim([1, 500]);
+
+
+
+% #+NAME: fig:intrumental_noise_V
+% #+CAPTION: Instrumental Noise and Measurement in $V^2/Hz$
+% #+RESULTS: fig:intrumental_noise_V
+% [[file:figs/intrumental_noise_V.png]]
+
+% This is then further converted into velocity and compared with the ground velocity measurement. (figure [[fig:intrumental_noise_velocity]])
+
+figure;
+hold on;
+plot(f, sqrt(pxx1).*scaling, '-');
+plot(f, sqrt(pxx2).*scaling, '-');
+plot(f, sqrt(pxxN).*scaling, 'k--');
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
+xlim([1, 500]);

index.org

@@ -2,26 +2,13 @@
 :drawer:
 #+STARTUP: overview
 
-#+OPTIONS: toc:2
-#+OPTIONS: num:2
-
-#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="css/htmlize.css"/>
-#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="css/readtheorg.css"/>
-#+HTML_HEAD: <script src="js/jquery.min.js"></script>
-#+HTML_HEAD: <script src="js/bootstrap.min.js"></script>
-#+HTML_HEAD: <script src="js/jquery.stickytableheaders.min.js"></script>
-#+HTML_HEAD: <script src="js/readtheorg.js"></script>
-
-#+LATEX_CLASS: cleanreport
-#+LaTeX_CLASS_OPTIONS: [tocnp, secbreak, minted]
-
-#+PROPERTY: header-args:matlab  :session *MATLAB*
-#+PROPERTY: header-args:matlab+ :comments org
-#+PROPERTY: header-args:matlab+ :exports both
-#+PROPERTY: header-args:matlab+ :eval no-export
-#+PROPERTY: header-args:matlab+ :noweb yes
-#+PROPERTY: header-args:matlab+ :mkdirp yes
-#+PROPERTY: header-args:matlab+ :output-dir figs
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/htmlize.css"/>
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/readtheorg.css"/>
+#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="./css/zenburn.css"/>
+#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="./js/bootstrap.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="./js/jquery.stickytableheaders.min.js"></script>
+#+HTML_HEAD: <script type="text/javascript" src="./js/readtheorg.js"></script>
 :end:
 
 * Measurements of the dynamics of the station
@@ -141,3 +128,10 @@ The goal is to estimate all the error motions induced by the Spindle
 
 * Ressources
 [[file:actuators-sensors/index.org][Actuators and Sensors]]
+
+* Other measurements
+- [[file:huddle-test-geophones/index.org][Huddle Test - Geophones]]
+- [[file:disturbance-measurement/index.org][Disturbance Measurement]]
+- [[file:slip-ring-test/index.org][Slip Ring - Noise measurement]]
+- [[file:static-measurements/index.org][Control System Measurement]]
+- [[file:equipment/equipment.org][Equipment used for the measurements]]

readme.org

@@ -0,0 +1,86 @@
+* Usefull Simulink Real Time commands
+
+* Get data from the target computer
+
+We first copy the =dat= file from the target computer to the host computer:
+
+#+begin_src matlab
+  tg=slrt;
+  f=SimulinkRealTime.openFTP(tg);
+  mget(f, 'DATA_001.dat', 'local_folder');
+  close(f);
+#+end_src
+
+We then import the =dat= file to the workspace:
+
+#+begin_src matlab
+  matlab_data = SimulinkRealTime.utils.getFileScopeData('DATA_001.dat');
+#+end_src
+
+* Commands with the target object
+https://fr.mathworks.com/help/xpc/api/simulinkrealtime.target.html
+
+| Connect | No Yes                                                      |
+| Status  | stopped runing                                              |
+| start   | Start execution of real-time application on target computer |
+| stop    | Stop execution of real-time application on target computer  |
+
+
+| tg.viewTargetScreen | Show target computer screen |
+
+| ping   | Test communication between development and target computers |
+| reboot | Restart target computer                                     |
+| close  | Close connection between development and target computers   |
+
+| load   | Download real-time application to target computer |
+| unload | Remove real-time application from target computer |
+
+| addscope              | Create a scope of specified type                                                    |
+| getscope              | Return scope identified by scope number                                             |
+| remscope              | Remove scope from target computer                                                   |
+| getlog                | Portion of output logs from target object                                           |
+| importLogData         | Import buffered logging data to the active session of the Simulation Data Inspector |
+| getsignal             | Value of signal                                                                     |
+| getsignalid           | Signal index from signal hierarchical name                                          |
+| getsignalidsfromlabel | Vector of signal indices                                                            |
+| getsignallabel        | Signal label for signal index                                                       |
+| getsignalname         | Signal name from index list                                                         |
+| getparam              | Read value of observable parameter in real-time application                         |
+| setparam              | Change value of tunable parameter in real-time application                          |
+| getparamid            | Parameter index from parameter hierarchical name                                    |
+| getparamname          | Block path and parameter name from parameter index                                  |
+| loadparamset          | Restore parameter values saved in specified file                                    |
+| saveparamset          | Save real-time application parameter values                                         |
+| startProfiler         | Start profiling service on target computer                                          |
+| stopProfiler          | Stop profiling service on target computer                                           |
+| getProfilerData       | Retrieve profile data object                                                        |
+| resetProfiler         | Reset profiling service state to Ready                                              |
+| getDiskSpace          | Return free space and total space on the drive, in bytes                            |
+
+* FTP access to the target computer
+https://fr.mathworks.com/help/xpc/api/simulinkrealtime.openftp.html?s_tid=doc_ta
+
+First run the following commands to have the =FTP= Object:
+#+begin_src matlab
+  tg=slrt;
+  f=SimulinkRealTime.openFTP(tg);
+#+end_src
+
+Then, the =f= object can be used to access the filesystem on the target computer.
+| cd     |                                            |                                      |
+| dir    |                                            |                                      |
+| mget   | Used to download data from the target host | =f.mget('data.dat', 'local_folder')= |
+| mkdir  |                                            |                                      |
+| mput   |                                            |                                      |
+| rename |                                            |                                      |
+| rmdir  |                                            |                                      |
+| close  |                                            |                                      |
+
+* ELMO
+tutorials: https://www.elmomc.com/products/application-studio/easii/easii-tutorials/
+* Low Pass Filter
+
+R = 1KOhm
+C = 1muF
+
+Fc = 1kHz

slip-ring-test/analysis.m

@@ -0,0 +1,11 @@
+data1 = load('mat/data_001.mat', 't', 'x1', 'x2');
+data2 = load('mat/data_002.mat', 't', 'x1', 'x2');
+
+figure;
+hold on;
+plot(data1.t, data1.x1-data1.x2);
+plot(data2.t, data2.x1-data2.x2);
+hold off
+xlabel('Time [s]');
+ylabel('Voltage [V]');
+legend({'Slip-ring OFF', 'Slip-ring ON'});

slip-ring-test/figs/.gitignore

@@ -0,0 +1,3 @@
+*.tex
+*.pdf
+*.svg

slip-ring-test/img/.gitignore

@@ -0,0 +1 @@
+*.mp4

slip-ring-test/img/nohup.out

@@ -0,0 +1,3 @@
+invalid color string: rgba(50, 48, 47)
+
+(termite:25037): GLib-WARNING **: 14:10:26.520: GChildWatchSource: Exit status of a child process was requested but ECHILD was received by waitpid(). See the documentation of g_child_watch_source_new() for possible causes.

slip-ring-test/low_pass_filter_measurements.m

@@ -0,0 +1,101 @@
+% Matlab Init                                             :noexport:ignore:
+
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Initialize ans with org-babel
+ans = 0;
+
+% Load data
+% We load the data of the z axis of two geophones.
+
+data = load('mat/data_018.mat', 'data'); data = data.data;
+
+% Transfer function of the LPF
+% We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
+
+dt = data(2, 3)-data(1, 3);
+
+Fs = 1/dt; % [Hz]
+
+win = hanning(ceil(10*Fs));
+
+[Glpf, f] = tfestimate(data(:, 2), data(:, 1), win, [], [], Fs);
+
+
+
+% We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of $1000rad/s$.
+% We obtain the result on figure [[fig:Glpf_bode]].
+
+Gth = 1/(1+s/1000)
+
+figure;
+ax1 = subplot(2, 1, 1);
+hold on;
+plot(f, abs(Glpf));
+plot(f, abs(squeeze(freqresp(Gth, f, 'Hz'))));
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Magnitude');
+
+ax2 = subplot(2, 1, 2);
+hold on;
+plot(f, mod(180+180/pi*phase(Glpf), 360)-180);
+plot(f, 180/pi*unwrap(angle(squeeze(freqresp(Gth, f, 'Hz')))));
+hold off;
+set(gca, 'xscale', 'log');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase');
+
+linkaxes([ax1,ax2],'x');
+xlim([1, 500]);
+
+% Load data
+% We load the data of the z axis of two geophones.
+
+data = load('mat/data_019.mat', 'data'); data = data.data;
+
+% Transfer function of the LPF
+% We compute the transfer function from the signal without the LPF to the signal measured with the LPF.
+
+dt = data(2, 3)-data(1, 3);
+
+Fs = 1/dt; % [Hz]
+
+win = hanning(ceil(10*Fs));
+
+[Glpf, f] = tfestimate(data(:, 2), data(:, 1), win, [], [], Fs);
+
+
+
+% We compare this transfer function with a transfer function corresponding to an ideal first order LPF with a cut-off frequency of $1060Hz$.
+% We obtain the result on figure [[fig:Glpf_bode_bis]].
+
+Gth = 1/(1+s/1060/2/pi);
+
+figure;
+ax1 = subplot(2, 1, 1);
+hold on;
+plot(f, abs(Glpf));
+plot(f, abs(squeeze(freqresp(Gth, f, 'Hz'))));
+hold off;
+set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Magnitude');
+
+ax2 = subplot(2, 1, 2);
+hold on;
+plot(f, mod(180+180/pi*phase(Glpf), 360)-180);
+plot(f, 180/pi*unwrap(angle(squeeze(freqresp(Gth, f, 'Hz')))));
+hold off;
+set(gca, 'xscale', 'log');
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase');
+
+linkaxes([ax1,ax2],'x');
+xlim([1, 500]);