Change one measurement of folder
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@@ -1,4 +1,4 @@
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#+TITLE:Measurements
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#+TITLE:Effect on the control system of each stages on the vibration of the station
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:DRAWER:
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#+STARTUP: overview
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@@ -398,7 +398,11 @@ All the control systems are turned OFF, then, they are turned on one at a time.
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Each measurement are done during 100s.
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The settings of the voltage amplifier are shown on figure [[fig:amplifier_settings]].
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The settings of the voltage amplifier are shown on figure [[fig:amplifier_settings]]:
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- gain of 60dB
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- AC/DC option set on DC
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- Low pass filter set at 1kHz
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A first order low pass filter with a cut-off frequency of 1kHz is added before the voltage amplifier.
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#+name: tab:control_system_on_off
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@@ -444,22 +448,44 @@ We load the data of the z axis of two geophones.
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d_he = load('mat/data_018.mat', 'data'); d_he = d_he.data;
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#+end_src
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** Voltage to Velocity
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We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/MEGA/These/meas/src/index.org][here]]).
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#+begin_src matlab
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gain = 60; % [dB]
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d_of(:, 1) = voltageToVelocityL22(d_of(:, 1), d_of(:, 3), gain);
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d_ty(:, 1) = voltageToVelocityL22(d_ty(:, 1), d_ty(:, 3), gain);
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d_ry(:, 1) = voltageToVelocityL22(d_ry(:, 1), d_ry(:, 3), gain);
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d_sr(:, 1) = voltageToVelocityL22(d_sr(:, 1), d_sr(:, 3), gain);
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d_rz(:, 1) = voltageToVelocityL22(d_rz(:, 1), d_rz(:, 3), gain);
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d_he(:, 1) = voltageToVelocityL22(d_he(:, 1), d_he(:, 3), gain);
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d_of(:, 2) = voltageToVelocityL22(d_of(:, 2), d_of(:, 3), gain);
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d_ty(:, 2) = voltageToVelocityL22(d_ty(:, 2), d_ty(:, 3), gain);
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d_ry(:, 2) = voltageToVelocityL22(d_ry(:, 2), d_ry(:, 3), gain);
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d_sr(:, 2) = voltageToVelocityL22(d_sr(:, 2), d_sr(:, 3), gain);
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d_rz(:, 2) = voltageToVelocityL22(d_rz(:, 2), d_rz(:, 3), gain);
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d_he(:, 2) = voltageToVelocityL22(d_he(:, 2), d_he(:, 3), gain);
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#+end_src
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** Analysis - Time Domain
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First, we can look at the time domain data and compare all the measurements:
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- comparison for the geophone at the sample location (figure [[fig:time_domain_sample_lpf]])
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- comparison for the geophone on the granite (figure [[fig:time_domain_marble_lpf]])
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- relative displacement of the sample with respect to the marble (figure [[fig:time_domain_marble_lpf]])
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#+begin_src matlab :results none
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#+begin_src matlab
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figure;
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hold on;
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plot(d_of(:, 3), d_of(:, 2), 'DisplayName', 'All OFF';
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plot(d_of(:, 3), d_of(:, 2), 'DisplayName', 'All OFF');
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plot(d_ty(:, 3), d_ty(:, 2), 'DisplayName', 'Ty ON');
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plot(d_ry(:, 3), d_ry(:, 2), 'DisplayName', 'Ry ON');
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plot(d_sr(:, 3), d_sr(:, 2), 'DisplayName', 'S-R ON');
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plot(d_rz(:, 3), d_rz(:, 2), 'DisplayName', 'Rz ON');
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plot(d_he(:, 3), d_he(:, 2), 'DisplayName', 'Hexa ON');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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xlabel('Time [s]'); ylabel('Velocity [m/s]');
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xlim([0, 50]);
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legend('Location', 'bestoutside');
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#+end_src
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@@ -476,7 +502,7 @@ First, we can look at the time domain data and compare all the measurements:
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[[file:figs/time_domain_sample_lpf.png]]
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#+begin_src matlab :results none
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#+begin_src matlab
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figure;
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hold on;
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plot(d_of(:, 3), d_of(:, 1), 'DisplayName', 'All OFF');
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@@ -486,7 +512,7 @@ First, we can look at the time domain data and compare all the measurements:
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plot(d_rz(:, 3), d_rz(:, 1), 'DisplayName', 'Rz ON');
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plot(d_he(:, 3), d_he(:, 1), 'DisplayName', 'Hexa ON');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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xlabel('Time [s]'); ylabel('Velocity [m/s]');
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xlim([0, 50]);
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legend('Location', 'bestoutside');
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#+end_src
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@@ -502,6 +528,32 @@ First, we can look at the time domain data and compare all the measurements:
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#+RESULTS: fig:time_domain_marble_lpf
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[[file:figs/time_domain_marble_lpf.png]]
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#+begin_src matlab
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figure;
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hold on;
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plot(d_of(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_of(:, 2)-d_of(:, 1), d_of(:, 3)), 'DisplayName', 'All OFF');
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plot(d_ty(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_ty(:, 2)-d_ty(:, 1), d_ty(:, 3)), 'DisplayName', 'Ty ON');
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plot(d_ry(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_ry(:, 2)-d_ry(:, 1), d_ry(:, 3)), 'DisplayName', 'Ry ON');
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plot(d_sr(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_sr(:, 2)-d_sr(:, 1), d_sr(:, 3)), 'DisplayName', 'S-R ON');
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plot(d_rz(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_rz(:, 2)-d_rz(:, 1), d_rz(:, 3)), 'DisplayName', 'Rz ON');
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plot(d_he(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_he(:, 2)-d_he(:, 1), d_he(:, 3)), 'DisplayName', 'Hexa ON');
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hold off;
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xlabel('Time [s]'); ylabel('Relative Displacement [$\mu m$]');
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xlim([0, 50]);
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legend('Location', 'bestoutside');
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#+end_src
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#+NAME: fig:time_domain_relative_disp
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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/time_domain_relative_disp.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:time_domain_relative_disp
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#+CAPTION: Relative displacement of the sample with respect to the marble
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#+RESULTS: fig:time_domain_relative_disp
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[[file:figs/time_domain_relative_disp.png]]
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** Analysis - Frequency Domain
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#+begin_src matlab :results none
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dt = d_of(2, 3) - d_of(1, 3);
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@@ -534,7 +586,7 @@ And we compare all the signals (figures [[fig:psd_sample_comp_lpf]] and [[fig:ps
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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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xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
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xlim([0.1, 500]);
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legend('Location', 'southwest');
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#+end_src
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@@ -546,7 +598,7 @@ And we compare all the signals (figures [[fig:psd_sample_comp_lpf]] and [[fig:ps
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#+end_src
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#+NAME: fig:psd_sample_comp_lpf
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#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone
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#+CAPTION: Amplitude Spectral Density of the sample velocity
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#+RESULTS: fig:psd_sample_comp_lpf
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[[file:figs/psd_sample_comp_lpf.png]]
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@@ -562,7 +614,7 @@ And we compare all the signals (figures [[fig:psd_sample_comp_lpf]] and [[fig:ps
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#+end_src
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#+NAME: fig:psd_sample_comp_high_freq_lpf
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#+CAPTION: Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)
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#+CAPTION: Amplitude Spectral Density of the sample velocity (zoom at high frequencies)
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#+RESULTS: fig:psd_sample_comp_high_freq_lpf
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[[file:figs/psd_sample_comp_high_freq_lpf.png]]
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@@ -590,7 +642,7 @@ And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp_l
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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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xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
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xlim([0.1, 500]);
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legend('Location', 'northeast');
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#+end_src
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@@ -602,7 +654,7 @@ And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp_l
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#+end_src
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#+NAME: fig:psd_marble_comp_lpf
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#+CAPTION: Amplitude Spectral Density of the signal coming from geophone located on the marble
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#+CAPTION: Amplitude Spectral Density of the marble velocity
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#+RESULTS: fig:psd_marble_comp_lpf
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[[file:figs/psd_marble_comp_lpf.png]]
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@@ -619,7 +671,7 @@ And we compare the Amplitude Spectral Densities (figures [[fig:psd_marble_comp_l
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#+end_src
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#+NAME: fig:psd_marble_comp_lpf_high_freq
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#+CAPTION: Amplitude Spectral Density of the signal coming from the geophone located on the marble (zoom at high frequencies)
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#+CAPTION: Amplitude Spectral Density of the marble velocity (zoom at high frequencies)
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#+RESULTS: fig:psd_marble_comp_lpf_high_freq
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[[file:figs/psd_marble_comp_lpf_high_freq.png]]
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@@ -779,404 +831,3 @@ First, we compute the Power Spectral Density of the signals coming from the Geop
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#+begin_important
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Even tough the Hexapod's driver vibrates quite a lot, it does not generate significant vibrations of the granite when either placed on the granite or on the ground.
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#+end_important
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* Transfer function from one stage to the other
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:PROPERTIES:
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:header-args:matlab+: :tangle matlab/tf_stages_geophone.m
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:header-args:matlab+: :comments org :mkdirp yes
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:END:
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<<sec:tf_stages_geophone>>
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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/tf_stages_geophone.m -nt data/tf_stages_geophone.zip ]; then
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cp matlab/tf_stages_geophone.m tf_stages_geophone.m;
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zip data/tf_stages_geophone \
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mat/data_010.mat \
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mat/data_011.mat \
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mat/data_012.mat \
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tf_stages_geophone.m
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rm tf_stages_geophone.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/tf_stages_geophone.zip][here]].
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#+end_note
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** Experimental Setup
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For all the measurements in this section:
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- all the control stages are OFF.
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- the measurements are on the $z$ direction
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*** From Marble to Ty - =mat/meas_010.mat=
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One geophone is on the marble, one is on the Ty stage (see figures [[fig:setup_m_ty]], [[fig:setup_m_ty_zoom]] and [[fig:setup_m_ty_top]]).
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The =data= array contains the following columns:
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| Column | Description |
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|--------+-------------|
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| 1 | Ground |
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| 2 | Ty |
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| 3 | Time |
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#+name: fig:setup_m_ty
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#+caption: Setup with one geophone on the marble and one on top of the translation stage
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#+attr_html: :width 500px
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[[file:./img/IMG_20190430_155330.jpg]]
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#+name: fig:setup_m_ty_zoom
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#+caption: Setup with one geophone on the marble and one on top of the translation stage - Close up view
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#+attr_html: :width 500px
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[[file:./img/IMG_20190430_155335.jpg]]
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#+name: fig:setup_m_ty_top
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#+caption: Setup with one geophone on the marble and one on top of the translation stage - Top view
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#+attr_html: :width 500px
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[[file:./img/IMG_20190430_155342.jpg]]
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*** From Marble to Ry - =mat/meas_011.mat=
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One geophone is on the marble, one is on the Ry stage (see figure [[fig:setup_m_ry]])
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The =data= array contains the following columns:
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| Column | Description |
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|--------+-------------|
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| 1 | Ground |
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| 2 | Ry |
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| 3 | Time |
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#+name: fig:setup_m_ry
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#+caption: Setup with one geophone on the marble and one on top of the Tilt Stage
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#+attr_html: :width 500px
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[[file:./img/IMG_20190430_163919.jpg]]
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*** From Ty to Ry - =mat/meas_012.mat=
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One geophone is on the Ty stage, one is on the Ry stage (see figures [[fig:setup_ty_ry]], [[fig:setup_ty_ry_top]] and [[fig:setup_ty_ry_zoom]])
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One geophone on the Ty stage, one geophone on the Ry stage.
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The =data= array contains the following columns:
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| Column | Description |
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|--------+-------------|
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| 1 | Ty |
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| 2 | Ry |
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| 3 | Time |
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#+name: fig:setup_ty_ry
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#+caption: Setup with one geophone on the translation stage and one on top of the Tilt Stage
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#+attr_html: :width 500px
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[[file:./img/IMG_20190430_170405.jpg]]
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#+name: fig:setup_ty_ry_top
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#+caption: Setup with one geophone on the translation stage and one on top of the Tilt Stage - Top view
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#+attr_html: :width 500px
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[[file:./img/IMG_20190430_170418.jpg]]
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#+name: fig:setup_ty_ry_zoom
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#+caption: Setup with one geophone on the translation stage and one on top of the Tilt Stage - Close up view
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#+attr_html: :width 500px
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[[file:./img/IMG_20190430_170425.jpg]]
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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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We load the data of the z axis of two geophones.
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#+begin_src matlab :results none
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m_ty = load('mat/data_010.mat', 'data'); m_ty = m_ty.data;
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m_ry = load('mat/data_011.mat', 'data'); m_ry = m_ry.data;
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ty_ry = load('mat/data_012.mat', 'data'); ty_ry = ty_ry.data;
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#+end_src
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** Analysis - Time Domain
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First, we can look at the time domain data.
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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(m_ty(:, 3), m_ty(:, 1), 'DisplayName', 'Marble');
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plot(m_ty(:, 3), m_ty(:, 2), 'DisplayName', 'Ty');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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legend('Location', 'northeast');
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xlim([0, 500]);
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#+end_src
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#+NAME: fig:time_domain_m_ty
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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/time_domain_m_ty.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_m_ty
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#+CAPTION: Time domain - Marble and translation stage
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#+RESULTS: fig:time_domain_m_ty
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[[file:figs/time_domain_m_ty.png]]
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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(m_ry(:, 3), m_ry(:, 1), 'DisplayName', 'Marble');
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plot(m_ry(:, 3), m_ry(:, 2), 'DisplayName', 'Ty');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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legend('Location', 'northeast');
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xlim([0, 500]);
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#+end_src
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#+NAME: fig:time_domain_m_ry
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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/time_domain_m_ry.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_m_ry
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#+CAPTION: Time domain - Marble and tilt stage
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#+RESULTS: fig:time_domain_m_ry
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[[file:figs/time_domain_m_ry.png]]
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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(ty_ry(:, 3), ty_ry(:, 1), 'DisplayName', 'Ty');
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plot(ty_ry(:, 3), ty_ry(:, 2), 'DisplayName', 'Ry');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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legend('Location', 'northeast');
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xlim([0, 500]);
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#+end_src
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#+NAME: fig:time_domain_ty_ry
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#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/time_domain_ty_ry.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_ty_ry
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#+CAPTION: Time domain - Translation stage and tilt stage
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#+RESULTS: fig:time_domain_ty_ry
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||||
[[file:figs/time_domain_ty_ry.png]]
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||||
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||||
** Analysis - Frequency Domain
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||||
#+begin_src matlab :results none
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dt = m_ty(2, 3) - m_ty(1, 3);
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||||
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||||
Fs = 1/dt;
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||||
win = hanning(ceil(1*Fs));
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||||
#+end_src
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||||
|
||||
First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure [[fig:compare_tf_geophones]]). We also plot their coherence (figure [[fig:coherence_two_geophones]]).
|
||||
#+begin_src matlab :results none
|
||||
[T_m_ty, f] = tfestimate(m_ty(:, 1), m_ty(:, 2), win, [], [], Fs);
|
||||
[T_m_ry, ~] = tfestimate(m_ry(:, 1), m_ry(:, 2), win, [], [], Fs);
|
||||
[T_ty_ry, ~] = tfestimate(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
ax1 = subplot(2, 1, 1);
|
||||
hold on;
|
||||
plot(f, abs(T_m_ty), 'DisplayName', 'Marble - Ty');
|
||||
plot(f, abs(T_m_ry), 'DisplayName', 'Marble - Ry');
|
||||
plot(f, abs(T_ty_ry), 'DisplayName', 'Ty - Ry');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
set(gca, 'XTickLabel',[]);
|
||||
ylabel('Magnitude');
|
||||
legend('Location', 'northwest');
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
hold on;
|
||||
plot(f, mod(180+180/pi*phase(T_m_ty), 360)-180);
|
||||
plot(f, mod(180+180/pi*phase(T_m_ry), 360)-180);
|
||||
plot(f, mod(180+180/pi*phase(T_ty_ry), 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([10, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:compare_tf_geophones
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/compare_tf_geophones.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:compare_tf_geophones
|
||||
#+CAPTION: Transfer function from the first geophone to the second geophone for the three experiments
|
||||
#+RESULTS: fig:compare_tf_geophones
|
||||
[[file:figs/compare_tf_geophones.png]]
|
||||
|
||||
|
||||
#+begin_src matlab :results none
|
||||
[coh_m_ty, f] = mscohere(m_ty(:, 1), m_ty(:, 2), win, [], [], Fs);
|
||||
[coh_m_ry, ~] = mscohere(m_ry(:, 1), m_ry(:, 2), win, [], [], Fs);
|
||||
[coh_ty_ry, ~] = mscohere(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results none :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, coh_m_ty, 'DisplayName', 'Marble - Ty');
|
||||
plot(f, coh_m_ry, 'DisplayName', 'Marble - Ry');
|
||||
plot(f, coh_ty_ry, 'DisplayName', 'Ty - Ry');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Coherence');
|
||||
ylim([0, 1]); xlim([1, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:coherence_two_geophones
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/coherence_two_geophones.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:coherence_two_geophones
|
||||
#+CAPTION: Coherence between the two geophones for the three experiments
|
||||
#+RESULTS: fig:coherence_two_geophones
|
||||
[[file:figs/coherence_two_geophones.png]]
|
||||
|
||||
** Conclusion
|
||||
#+begin_important
|
||||
These measurements are not relevant.
|
||||
#+end_important
|
||||
|
||||
* Effect of the Ty Control System on the vibration of the Sample :noexport:ignore:
|
||||
** Experimental Setup
|
||||
One geophone is on the marble, the other at the sample location (see figures [[fig:setup_ty]]).
|
||||
|
||||
The signal from the top geophone goes through the slip-ring.
|
||||
|
||||
#+name: fig:setup_ty
|
||||
#+caption: Experimental Setup
|
||||
#+attr_html: :width 500px
|
||||
[[file:./img/IMG_20190430_112615.jpg]]
|
||||
|
||||
Two measurements are done:
|
||||
| Setup | Data File |
|
||||
|----------------------+--------------------|
|
||||
| Control of Ty is on | =mat/data_001.mat= |
|
||||
| Control of Ty is off | =mat/data_002.mat= |
|
||||
|
||||
For each of the measurements, the data are:
|
||||
| Variable | Description |
|
||||
|----------+--------------------------------------------------------------------|
|
||||
| =t= | Time Vector |
|
||||
| =x1= | Voltage measured across the geophone placed on the marble |
|
||||
| =x2= | Voltage measured across the geophone placed at the sample location |
|
||||
|
||||
Measurements are 50s long.
|
||||
|
||||
** 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
|
||||
We load the data of the z axis of two geophones.
|
||||
#+begin_src matlab :results none
|
||||
tyOn = load('mat/data_001.mat', 't', 'x1', 'x2');
|
||||
tyOff = load('mat/data_002.mat', 't', 'x1', 'x2');
|
||||
#+end_src
|
||||
|
||||
** Analysis - Time Domain
|
||||
#+begin_src matlab :results none
|
||||
dt = tyOn.t(2)-tyOn.t(1);
|
||||
Fs = 1/dt;
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
subplot(1, 2, 1);
|
||||
hold on;
|
||||
plot(tyOn.t, tyOn.x1, 'DisplayName', 'Ty ON - Marble');
|
||||
plot(tyOff.t, tyOff.x1, 'DisplayName', 'Ty OFF - Marble');
|
||||
hold off;
|
||||
legend();
|
||||
xlabel('Time [s]'); ylabel('Voltage [V]');
|
||||
xlim([0, 50]);
|
||||
|
||||
subplot(1, 2, 2);
|
||||
hold on;
|
||||
plot(tyOn.t, tyOn.x2, 'DisplayName', 'Ty ON - Sample');
|
||||
plot(tyOff.t, tyOff.x2, 'DisplayName', 'Ty OFF - Sample');
|
||||
hold off;
|
||||
legend();
|
||||
xlabel('Time [s]'); ylabel('Voltage [V]');
|
||||
xlim([0, 50]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:time_domain_effect_ty
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/time_domain_effect_ty.pdf" :var figsize="full-normal" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:time_domain_effect_ty
|
||||
#+CAPTION: Effect of the Ty control system on the vibrations of the marble and sample
|
||||
#+RESULTS: fig:time_domain_effect_ty
|
||||
[[file:figs/time_domain_effect_ty.png]]
|
||||
|
||||
** Analysis - Frequency Domain
|
||||
#+begin_src matlab :results none
|
||||
Fs = 1/dt;
|
||||
win = hanning(ceil(10*Fs));
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results none
|
||||
[pxOn1, f] = pwelch(tyOn.x1, win, [], [], Fs);
|
||||
[pxOn2, ~] = pwelch(tyOn.x2, win, [], [], Fs);
|
||||
|
||||
[pxOff1, ~] = pwelch(tyOff.x1, win, [], [], Fs);
|
||||
[pxOff2, ~] = pwelch(tyOff.x2, win, [], [], Fs);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
subplot(1, 2, 1);
|
||||
hold on;
|
||||
plot(f, sqrt(pxOn1), 'DisplayName', 'Ty ON - Marble');
|
||||
plot(f, sqrt(pxOff1), 'DisplayName', 'Ty OFF - Marble');
|
||||
hold off;
|
||||
legend();
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
xlim([0.1, 500]); ylim([1e-4, 1]);
|
||||
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
|
||||
|
||||
subplot(1, 2, 2);
|
||||
hold on;
|
||||
plot(f, sqrt(pxOn2), 'DisplayName', 'Ty ON - Sample');
|
||||
plot(f, sqrt(pxOff2), 'DisplayName', 'Ty OFF - Sample');
|
||||
hold off;
|
||||
legend();
|
||||
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]); ylim([1e-4, 1]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:psd_effect_ty
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/psd_effect_ty.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:psd_effect_ty
|
||||
#+CAPTION: Amplitude Spectral Density - Effect of the Ty control system
|
||||
#+RESULTS: fig:psd_effect_ty
|
||||
[[file:figs/psd_effect_ty.png]]
|
||||
|
||||
** Conclusion
|
||||
File renamed without changes.
File renamed without changes.
File renamed without changes.
File renamed without changes.
File renamed without changes.
File renamed without changes.
File renamed without changes.
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File renamed without changes.
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File renamed without changes.
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@@ -0,0 +1,124 @@
|
||||
%% Clear Workspace and Close figures
|
||||
clear; close all; clc;
|
||||
|
||||
%% Intialize Laplace variable
|
||||
s = zpk('s');
|
||||
|
||||
% Load data
|
||||
% We load the data of the z axis of two geophones.
|
||||
|
||||
m_ty = load('mat/data_010.mat', 'data'); m_ty = m_ty.data;
|
||||
m_ry = load('mat/data_011.mat', 'data'); m_ry = m_ry.data;
|
||||
ty_ry = load('mat/data_012.mat', 'data'); ty_ry = ty_ry.data;
|
||||
|
||||
% Analysis - Time Domain
|
||||
% First, we can look at the time domain data.
|
||||
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(m_ty(:, 3), m_ty(:, 1), 'DisplayName', 'Marble');
|
||||
plot(m_ty(:, 3), m_ty(:, 2), 'DisplayName', 'Ty');
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Voltage [V]');
|
||||
legend('Location', 'northeast');
|
||||
xlim([0, 500]);
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:time_domain_m_ty
|
||||
% #+CAPTION: Time domain - Marble and translation stage
|
||||
% #+RESULTS: fig:time_domain_m_ty
|
||||
% [[file:figs/time_domain_m_ty.png]]
|
||||
|
||||
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(m_ry(:, 3), m_ry(:, 1), 'DisplayName', 'Marble');
|
||||
plot(m_ry(:, 3), m_ry(:, 2), 'DisplayName', 'Ty');
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Voltage [V]');
|
||||
legend('Location', 'northeast');
|
||||
xlim([0, 500]);
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:time_domain_m_ry
|
||||
% #+CAPTION: Time domain - Marble and tilt stage
|
||||
% #+RESULTS: fig:time_domain_m_ry
|
||||
% [[file:figs/time_domain_m_ry.png]]
|
||||
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(ty_ry(:, 3), ty_ry(:, 1), 'DisplayName', 'Ty');
|
||||
plot(ty_ry(:, 3), ty_ry(:, 2), 'DisplayName', 'Ry');
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Voltage [V]');
|
||||
legend('Location', 'northeast');
|
||||
xlim([0, 500]);
|
||||
|
||||
% Analysis - Frequency Domain
|
||||
|
||||
dt = m_ty(2, 3) - m_ty(1, 3);
|
||||
|
||||
Fs = 1/dt;
|
||||
win = hanning(ceil(1*Fs));
|
||||
|
||||
|
||||
|
||||
% First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure [[fig:compare_tf_geophones]]). We also plot their coherence (figure [[fig:coherence_two_geophones]]).
|
||||
|
||||
[T_m_ty, f] = tfestimate(m_ty(:, 1), m_ty(:, 2), win, [], [], Fs);
|
||||
[T_m_ry, ~] = tfestimate(m_ry(:, 1), m_ry(:, 2), win, [], [], Fs);
|
||||
[T_ty_ry, ~] = tfestimate(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);
|
||||
|
||||
figure;
|
||||
ax1 = subplot(2, 1, 1);
|
||||
hold on;
|
||||
plot(f, abs(T_m_ty), 'DisplayName', 'Marble - Ty');
|
||||
plot(f, abs(T_m_ry), 'DisplayName', 'Marble - Ry');
|
||||
plot(f, abs(T_ty_ry), 'DisplayName', 'Ty - Ry');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
set(gca, 'XTickLabel',[]);
|
||||
ylabel('Magnitude');
|
||||
legend('Location', 'northwest');
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
hold on;
|
||||
plot(f, mod(180+180/pi*phase(T_m_ty), 360)-180);
|
||||
plot(f, mod(180+180/pi*phase(T_m_ry), 360)-180);
|
||||
plot(f, mod(180+180/pi*phase(T_ty_ry), 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([10, 500]);
|
||||
|
||||
|
||||
|
||||
% #+NAME: fig:compare_tf_geophones
|
||||
% #+CAPTION: Transfer function from the first geophone to the second geophone for the three experiments
|
||||
% #+RESULTS: fig:compare_tf_geophones
|
||||
% [[file:figs/compare_tf_geophones.png]]
|
||||
|
||||
|
||||
|
||||
[coh_m_ty, f] = mscohere(m_ty(:, 1), m_ty(:, 2), win, [], [], Fs);
|
||||
[coh_m_ry, ~] = mscohere(m_ry(:, 1), m_ry(:, 2), win, [], [], Fs);
|
||||
[coh_ty_ry, ~] = mscohere(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);
|
||||
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, coh_m_ty, 'DisplayName', 'Marble - Ty');
|
||||
plot(f, coh_m_ry, 'DisplayName', 'Marble - Ry');
|
||||
plot(f, coh_ty_ry, 'DisplayName', 'Ty - Ry');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Coherence');
|
||||
ylim([0, 1]); xlim([1, 500]);
|
||||
@@ -0,0 +1,686 @@
|
||||
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||||
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||||
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||||
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|
||||
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||
<title>Transfer function from velocity of one stage to the velocity of another stage using geophones</title>
|
||||
<meta name="generator" content="Org mode" />
|
||||
<meta name="author" content="Dehaeze Thomas" />
|
||||
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||||
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||||
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||||
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
|
||||
</div><div id="content">
|
||||
<h1 class="title">Transfer function from velocity of one stage to the velocity of another stage using geophones</h1>
|
||||
<div id="table-of-contents">
|
||||
<h2>Table of Contents</h2>
|
||||
<div id="text-table-of-contents">
|
||||
<ul>
|
||||
<li><a href="#orgbdb27eb">1. Experimental Setup</a>
|
||||
<ul>
|
||||
<li><a href="#org8dbd49b">1.1. From Marble to Ty - <code>mat/meas_010.mat</code></a></li>
|
||||
<li><a href="#orgf538b5e">1.2. From Marble to Ry - <code>mat/meas_011.mat</code></a></li>
|
||||
<li><a href="#orga48e2bc">1.3. From Ty to Ry - <code>mat/meas_012.mat</code></a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a href="#org3ea309e">2. Measurement Analysis</a>
|
||||
<ul>
|
||||
<li><a href="#org1638277">2.1. Load data</a></li>
|
||||
<li><a href="#org0d3cc48">2.2. Analysis - Time Domain</a></li>
|
||||
<li><a href="#org65a5a79">2.3. Analysis - Frequency Domain</a></li>
|
||||
<li><a href="#orgbbc525b">2.4. Conclusion</a></li>
|
||||
</ul>
|
||||
</li>
|
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|
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|
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<div id="outline-container-orgbdb27eb" class="outline-2">
|
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<h2 id="orgbdb27eb"><span class="section-number-2">1</span> Experimental Setup</h2>
|
||||
<div class="outline-text-2" id="text-1">
|
||||
<p>
|
||||
For all the measurements in this section:
|
||||
</p>
|
||||
<ul class="org-ul">
|
||||
<li>all the control stages are OFF.</li>
|
||||
<li>the measurements are on the \(z\) direction</li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8dbd49b" class="outline-3">
|
||||
<h3 id="org8dbd49b"><span class="section-number-3">1.1</span> From Marble to Ty - <code>mat/meas_010.mat</code></h3>
|
||||
<div class="outline-text-3" id="text-1-1">
|
||||
<p>
|
||||
One geophone is on the marble, one is on the Ty stage (see figures <a href="#orgee9d1f3">1</a>, <a href="#org0acaa0d">2</a> and <a href="#orgec4ad6b">3</a>).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The <code>data</code> array contains the following columns:
|
||||
</p>
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<td class="org-right">1</td>
|
||||
<td class="org-left">Ground</td>
|
||||
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|
||||
|
||||
<tr>
|
||||
<td class="org-right">2</td>
|
||||
<td class="org-left">Ty</td>
|
||||
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|
||||
|
||||
<tr>
|
||||
<td class="org-right">3</td>
|
||||
<td class="org-left">Time</td>
|
||||
</tr>
|
||||
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|
||||
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|
||||
|
||||
|
||||
<div id="orgee9d1f3" class="figure">
|
||||
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|
||||
</p>
|
||||
<p><span class="figure-number">Figure 1: </span>Setup with one geophone on the marble and one on top of the translation stage</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org0acaa0d" class="figure">
|
||||
<p><img src="./img/IMG_20190430_155335.jpg" alt="IMG_20190430_155335.jpg" width="500px" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 2: </span>Setup with one geophone on the marble and one on top of the translation stage - Close up view</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgec4ad6b" class="figure">
|
||||
<p><img src="./img/IMG_20190430_155342.jpg" alt="IMG_20190430_155342.jpg" width="500px" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 3: </span>Setup with one geophone on the marble and one on top of the translation stage - Top view</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgf538b5e" class="outline-3">
|
||||
<h3 id="orgf538b5e"><span class="section-number-3">1.2</span> From Marble to Ry - <code>mat/meas_011.mat</code></h3>
|
||||
<div class="outline-text-3" id="text-1-2">
|
||||
<p>
|
||||
One geophone is on the marble, one is on the Ry stage (see figure <a href="#orgd643390">4</a>)
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The <code>data</code> array contains the following columns:
|
||||
</p>
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
|
||||
|
||||
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|
||||
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|
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<td class="org-left">Ground</td>
|
||||
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|
||||
|
||||
<tr>
|
||||
<td class="org-right">2</td>
|
||||
<td class="org-left">Ry</td>
|
||||
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|
||||
|
||||
<tr>
|
||||
<td class="org-right">3</td>
|
||||
<td class="org-left">Time</td>
|
||||
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|
||||
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|
||||
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|
||||
|
||||
|
||||
<div id="orgd643390" class="figure">
|
||||
<p><img src="./img/IMG_20190430_163919.jpg" alt="IMG_20190430_163919.jpg" width="500px" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 4: </span>Setup with one geophone on the marble and one on top of the Tilt Stage</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga48e2bc" class="outline-3">
|
||||
<h3 id="orga48e2bc"><span class="section-number-3">1.3</span> From Ty to Ry - <code>mat/meas_012.mat</code></h3>
|
||||
<div class="outline-text-3" id="text-1-3">
|
||||
<p>
|
||||
One geophone is on the Ty stage, one is on the Ry stage (see figures <a href="#org4038125">5</a>, <a href="#orge841934">6</a> and <a href="#org7715257">7</a>)
|
||||
One geophone on the Ty stage, one geophone on the Ry stage.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The <code>data</code> array contains the following columns:
|
||||
</p>
|
||||
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
||||
|
||||
|
||||
<colgroup>
|
||||
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|
||||
|
||||
<col class="org-left" />
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
</tr>
|
||||
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|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="org-right">1</td>
|
||||
<td class="org-left">Ty</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">2</td>
|
||||
<td class="org-left">Ry</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td class="org-right">3</td>
|
||||
<td class="org-left">Time</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
|
||||
<div id="org4038125" class="figure">
|
||||
<p><img src="./img/IMG_20190430_170405.jpg" alt="IMG_20190430_170405.jpg" width="500px" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orge841934" class="figure">
|
||||
<p><img src="./img/IMG_20190430_170418.jpg" alt="IMG_20190430_170418.jpg" width="500px" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Top view</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org7715257" class="figure">
|
||||
<p><img src="./img/IMG_20190430_170425.jpg" alt="IMG_20190430_170425.jpg" width="500px" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Setup with one geophone on the translation stage and one on top of the Tilt Stage - Close up view</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org3ea309e" class="outline-2">
|
||||
<h2 id="org3ea309e"><span class="section-number-2">2</span> Measurement Analysis</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="org88007a9"></a>
|
||||
</p>
|
||||
<div class="note">
|
||||
<p>
|
||||
All the files (data and Matlab scripts) are accessible <a href="data/tf_stages_geophone.zip">here</a>.
|
||||
</p>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org1638277" class="outline-3">
|
||||
<h3 id="org1638277"><span class="section-number-3">2.1</span> Load data</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<p>
|
||||
We load the data of the z axis of two geophones.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">m_ty = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_010.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_ty = m_ty.data;
|
||||
m_ry = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_011.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; m_ry = m_ry.data;
|
||||
ty_ry = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_012.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ty_ry = ty_ry.data;
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org0d3cc48" class="outline-3">
|
||||
<h3 id="org0d3cc48"><span class="section-number-3">2.2</span> Analysis - Time Domain</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
First, we can look at the time domain data.
|
||||
</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>m_ty<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>, m_ty<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-string">'DisplayName', 'Marble'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<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>, m_ty<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-2">)</span>, <span class="org-string">'DisplayName', 'Ty'</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>;
|
||||
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">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org6d8a0eb" class="figure">
|
||||
<p><img src="figs/time_domain_m_ty.png" alt="time_domain_m_ty.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Time domain - Marble and translation stage</p>
|
||||
</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>m_ry<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>, m_ry<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-string">'DisplayName', 'Marble'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<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>, m_ry<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-2">)</span>, <span class="org-string">'DisplayName', 'Ty'</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>;
|
||||
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">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org8700a74" class="figure">
|
||||
<p><img src="figs/time_domain_m_ry.png" alt="time_domain_m_ry.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Time domain - Marble and tilt stage</p>
|
||||
</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>ty_ry<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>, ty_ry<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-string">'DisplayName', 'Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<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>, ty_ry<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-2">)</span>, <span class="org-string">'DisplayName', 'Ry'</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>;
|
||||
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">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
</pre>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgcb2e12d" class="figure">
|
||||
<p><img src="figs/time_domain_ty_ry.png" alt="time_domain_ty_ry.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>Time domain - Translation stage and tilt stage</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org65a5a79" class="outline-3">
|
||||
<h3 id="org65a5a79"><span class="section-number-3">2.3</span> Analysis - Frequency Domain</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">dt = m_ty<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> m_ty<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">1</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>
|
||||
|
||||
<p>
|
||||
First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure <a href="#orgc25589d">11</a>). We also plot their coherence (figure <a href="#org6b84c12">12</a>).
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>T_m_ty, f<span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<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>, m_ty<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-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>;
|
||||
<span class="org-rainbow-delimiters-depth-1">[</span>T_m_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<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>, m_ry<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-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>;
|
||||
<span class="org-rainbow-delimiters-depth-1">[</span>T_ty_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = tfestimate<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<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>, ty_ry<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-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>;
|
||||
ax1 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
hold on;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T_m_ty<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ty'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T_m_ry<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Marble - Ry'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, abs<span class="org-rainbow-delimiters-depth-2">(</span>T_ty_ry<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName', 'Ty - Ry'</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>;
|
||||
<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">'XTickLabel'</span>,<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><span class="org-string">'Magnitude'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', 'northwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
|
||||
ax2 = subplot<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
hold on;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T_m_ty<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T_m_ry<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, mod<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">180</span><span class="org-type">+</span><span class="org-highlight-numbers-number">180</span><span class="org-type">/</span><span class="org-constant">pi</span><span class="org-type">*</span>phase<span class="org-rainbow-delimiters-depth-3">(</span>T_ty_ry<span class="org-rainbow-delimiters-depth-3">)</span>, <span class="org-highlight-numbers-number">360</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</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>;
|
||||
ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
yticks<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">180</span>, <span class="org-type">-</span><span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">90</span>, <span class="org-highlight-numbers-number">180</span><span class="org-rainbow-delimiters-depth-2">]</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">'Phase'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||
|
||||
linkaxes<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span>ax1,ax2<span class="org-rainbow-delimiters-depth-2">]</span>,<span class="org-string">'x'</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">10</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="orgc25589d" class="figure">
|
||||
<p><img src="figs/compare_tf_geophones.png" alt="compare_tf_geophones.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>Transfer function from the first geophone to the second geophone for the three experiments</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>coh_m_ty, f<span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>m_ty<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>, m_ty<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-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>;
|
||||
<span class="org-rainbow-delimiters-depth-1">[</span>coh_m_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>m_ry<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>, m_ry<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-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>;
|
||||
<span class="org-rainbow-delimiters-depth-1">[</span>coh_ty_ry, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = mscohere<span class="org-rainbow-delimiters-depth-1">(</span>ty_ry<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>, ty_ry<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-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 id="org6b84c12" class="figure">
|
||||
<p><img src="figs/coherence_two_geophones.png" alt="coherence_two_geophones.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </span>Coherence between the two geophones for the three experiments</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgbbc525b" class="outline-3">
|
||||
<h3 id="orgbbc525b"><span class="section-number-3">2.4</span> Conclusion</h3>
|
||||
<div class="outline-text-3" id="text-2-4">
|
||||
<div class="important">
|
||||
<p>
|
||||
These measurements are not relevant.
|
||||
</p>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2019-05-15 mer. 17:22</p>
|
||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,301 @@
|
||||
#+TITLE: Transfer function from velocity of one stage to the velocity of another stage using geophones
|
||||
:DRAWER:
|
||||
#+STARTUP: overview
|
||||
|
||||
#+LANGUAGE: en
|
||||
#+EMAIL: dehaeze.thomas@gmail.com
|
||||
#+AUTHOR: Dehaeze Thomas
|
||||
|
||||
#+HTML_LINK_HOME: ../index.html
|
||||
#+HTML_LINK_UP: ../index.html
|
||||
|
||||
#+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>
|
||||
|
||||
#+HTML_MATHJAX: align: center tagside: right font: TeX
|
||||
|
||||
#+PROPERTY: header-args:matlab :session *MATLAB*
|
||||
#+PROPERTY: header-args:matlab+ :comments org
|
||||
#+PROPERTY: header-args:matlab+ :results none
|
||||
#+PROPERTY: header-args:matlab+ :exports both
|
||||
#+PROPERTY: header-args:matlab+ :eval no-export
|
||||
#+PROPERTY: header-args:matlab+ :output-dir figs
|
||||
|
||||
#+PROPERTY: header-args:shell :eval no-export
|
||||
:END:
|
||||
|
||||
* Experimental Setup
|
||||
For all the measurements in this section:
|
||||
- all the control stages are OFF.
|
||||
- the measurements are on the $z$ direction
|
||||
|
||||
** From Marble to Ty - =mat/meas_010.mat=
|
||||
One geophone is on the marble, one is on the Ty stage (see figures [[fig:setup_m_ty]], [[fig:setup_m_ty_zoom]] and [[fig:setup_m_ty_top]]).
|
||||
|
||||
The =data= array contains the following columns:
|
||||
| Column | Description |
|
||||
|--------+-------------|
|
||||
| 1 | Ground |
|
||||
| 2 | Ty |
|
||||
| 3 | Time |
|
||||
|
||||
#+name: fig:setup_m_ty
|
||||
#+caption: Setup with one geophone on the marble and one on top of the translation stage
|
||||
#+attr_html: :width 500px
|
||||
[[file:./img/IMG_20190430_155330.jpg]]
|
||||
|
||||
#+name: fig:setup_m_ty_zoom
|
||||
#+caption: Setup with one geophone on the marble and one on top of the translation stage - Close up view
|
||||
#+attr_html: :width 500px
|
||||
[[file:./img/IMG_20190430_155335.jpg]]
|
||||
|
||||
#+name: fig:setup_m_ty_top
|
||||
#+caption: Setup with one geophone on the marble and one on top of the translation stage - Top view
|
||||
#+attr_html: :width 500px
|
||||
[[file:./img/IMG_20190430_155342.jpg]]
|
||||
|
||||
** From Marble to Ry - =mat/meas_011.mat=
|
||||
One geophone is on the marble, one is on the Ry stage (see figure [[fig:setup_m_ry]])
|
||||
|
||||
The =data= array contains the following columns:
|
||||
| Column | Description |
|
||||
|--------+-------------|
|
||||
| 1 | Ground |
|
||||
| 2 | Ry |
|
||||
| 3 | Time |
|
||||
|
||||
#+name: fig:setup_m_ry
|
||||
#+caption: Setup with one geophone on the marble and one on top of the Tilt Stage
|
||||
#+attr_html: :width 500px
|
||||
[[file:./img/IMG_20190430_163919.jpg]]
|
||||
|
||||
** From Ty to Ry - =mat/meas_012.mat=
|
||||
One geophone is on the Ty stage, one is on the Ry stage (see figures [[fig:setup_ty_ry]], [[fig:setup_ty_ry_top]] and [[fig:setup_ty_ry_zoom]])
|
||||
One geophone on the Ty stage, one geophone on the Ry stage.
|
||||
|
||||
The =data= array contains the following columns:
|
||||
| Column | Description |
|
||||
|--------+-------------|
|
||||
| 1 | Ty |
|
||||
| 2 | Ry |
|
||||
| 3 | Time |
|
||||
|
||||
#+name: fig:setup_ty_ry
|
||||
#+caption: Setup with one geophone on the translation stage and one on top of the Tilt Stage
|
||||
#+attr_html: :width 500px
|
||||
[[file:./img/IMG_20190430_170405.jpg]]
|
||||
|
||||
#+name: fig:setup_ty_ry_top
|
||||
#+caption: Setup with one geophone on the translation stage and one on top of the Tilt Stage - Top view
|
||||
#+attr_html: :width 500px
|
||||
[[file:./img/IMG_20190430_170418.jpg]]
|
||||
|
||||
#+name: fig:setup_ty_ry_zoom
|
||||
#+caption: Setup with one geophone on the translation stage and one on top of the Tilt Stage - Close up view
|
||||
#+attr_html: :width 500px
|
||||
[[file:./img/IMG_20190430_170425.jpg]]
|
||||
|
||||
* Measurement Analysis
|
||||
:PROPERTIES:
|
||||
:header-args:matlab+: :tangle matlab/tf_stages_geophone.m
|
||||
:header-args:matlab+: :comments org :mkdirp yes
|
||||
:END:
|
||||
<<sec:tf_stages_geophone>>
|
||||
|
||||
** ZIP file containing the data and matlab files :ignore:
|
||||
#+begin_src bash :exports none :results none
|
||||
if [ matlab/tf_stages_geophone.m -nt data/tf_stages_geophone.zip ]; then
|
||||
cp matlab/tf_stages_geophone.m tf_stages_geophone.m;
|
||||
zip data/tf_stages_geophone \
|
||||
mat/data_010.mat \
|
||||
mat/data_011.mat \
|
||||
mat/data_012.mat \
|
||||
tf_stages_geophone.m
|
||||
rm tf_stages_geophone.m;
|
||||
fi
|
||||
#+end_src
|
||||
|
||||
#+begin_note
|
||||
All the files (data and Matlab scripts) are accessible [[file:data/tf_stages_geophone.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
|
||||
We load the data of the z axis of two geophones.
|
||||
#+begin_src matlab :results none
|
||||
m_ty = load('mat/data_010.mat', 'data'); m_ty = m_ty.data;
|
||||
m_ry = load('mat/data_011.mat', 'data'); m_ry = m_ry.data;
|
||||
ty_ry = load('mat/data_012.mat', 'data'); ty_ry = ty_ry.data;
|
||||
#+end_src
|
||||
|
||||
** Analysis - Time Domain
|
||||
First, we can look at the time domain data.
|
||||
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
hold on;
|
||||
plot(m_ty(:, 3), m_ty(:, 1), 'DisplayName', 'Marble');
|
||||
plot(m_ty(:, 3), m_ty(:, 2), 'DisplayName', 'Ty');
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Voltage [V]');
|
||||
legend('Location', 'northeast');
|
||||
xlim([0, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:time_domain_m_ty
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/time_domain_m_ty.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:time_domain_m_ty
|
||||
#+CAPTION: Time domain - Marble and translation stage
|
||||
#+RESULTS: fig:time_domain_m_ty
|
||||
[[file:figs/time_domain_m_ty.png]]
|
||||
|
||||
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
hold on;
|
||||
plot(m_ry(:, 3), m_ry(:, 1), 'DisplayName', 'Marble');
|
||||
plot(m_ry(:, 3), m_ry(:, 2), 'DisplayName', 'Ty');
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Voltage [V]');
|
||||
legend('Location', 'northeast');
|
||||
xlim([0, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:time_domain_m_ry
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/time_domain_m_ry.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:time_domain_m_ry
|
||||
#+CAPTION: Time domain - Marble and tilt stage
|
||||
#+RESULTS: fig:time_domain_m_ry
|
||||
[[file:figs/time_domain_m_ry.png]]
|
||||
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
hold on;
|
||||
plot(ty_ry(:, 3), ty_ry(:, 1), 'DisplayName', 'Ty');
|
||||
plot(ty_ry(:, 3), ty_ry(:, 2), 'DisplayName', 'Ry');
|
||||
hold off;
|
||||
xlabel('Time [s]'); ylabel('Voltage [V]');
|
||||
legend('Location', 'northeast');
|
||||
xlim([0, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:time_domain_ty_ry
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/time_domain_ty_ry.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:time_domain_ty_ry
|
||||
#+CAPTION: Time domain - Translation stage and tilt stage
|
||||
#+RESULTS: fig:time_domain_ty_ry
|
||||
[[file:figs/time_domain_ty_ry.png]]
|
||||
|
||||
** Analysis - Frequency Domain
|
||||
#+begin_src matlab :results none
|
||||
dt = m_ty(2, 3) - m_ty(1, 3);
|
||||
|
||||
Fs = 1/dt;
|
||||
win = hanning(ceil(1*Fs));
|
||||
#+end_src
|
||||
|
||||
First, we compute the transfer function estimate between the two geophones for the 3 experiments (figure [[fig:compare_tf_geophones]]). We also plot their coherence (figure [[fig:coherence_two_geophones]]).
|
||||
#+begin_src matlab :results none
|
||||
[T_m_ty, f] = tfestimate(m_ty(:, 1), m_ty(:, 2), win, [], [], Fs);
|
||||
[T_m_ry, ~] = tfestimate(m_ry(:, 1), m_ry(:, 2), win, [], [], Fs);
|
||||
[T_ty_ry, ~] = tfestimate(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results none
|
||||
figure;
|
||||
ax1 = subplot(2, 1, 1);
|
||||
hold on;
|
||||
plot(f, abs(T_m_ty), 'DisplayName', 'Marble - Ty');
|
||||
plot(f, abs(T_m_ry), 'DisplayName', 'Marble - Ry');
|
||||
plot(f, abs(T_ty_ry), 'DisplayName', 'Ty - Ry');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||
set(gca, 'XTickLabel',[]);
|
||||
ylabel('Magnitude');
|
||||
legend('Location', 'northwest');
|
||||
|
||||
ax2 = subplot(2, 1, 2);
|
||||
hold on;
|
||||
plot(f, mod(180+180/pi*phase(T_m_ty), 360)-180);
|
||||
plot(f, mod(180+180/pi*phase(T_m_ry), 360)-180);
|
||||
plot(f, mod(180+180/pi*phase(T_ty_ry), 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([10, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:compare_tf_geophones
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/compare_tf_geophones.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:compare_tf_geophones
|
||||
#+CAPTION: Transfer function from the first geophone to the second geophone for the three experiments
|
||||
#+RESULTS: fig:compare_tf_geophones
|
||||
[[file:figs/compare_tf_geophones.png]]
|
||||
|
||||
|
||||
#+begin_src matlab :results none
|
||||
[coh_m_ty, f] = mscohere(m_ty(:, 1), m_ty(:, 2), win, [], [], Fs);
|
||||
[coh_m_ry, ~] = mscohere(m_ry(:, 1), m_ry(:, 2), win, [], [], Fs);
|
||||
[coh_ty_ry, ~] = mscohere(ty_ry(:, 1), ty_ry(:, 2), win, [], [], Fs);
|
||||
#+end_src
|
||||
|
||||
#+begin_src matlab :results none :exports none
|
||||
figure;
|
||||
hold on;
|
||||
plot(f, coh_m_ty, 'DisplayName', 'Marble - Ty');
|
||||
plot(f, coh_m_ry, 'DisplayName', 'Marble - Ry');
|
||||
plot(f, coh_ty_ry, 'DisplayName', 'Ty - Ry');
|
||||
hold off;
|
||||
set(gca, 'xscale', 'log');
|
||||
xlabel('Frequency [Hz]'); ylabel('Coherence');
|
||||
ylim([0, 1]); xlim([1, 500]);
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:coherence_two_geophones
|
||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||
#+begin_src matlab :var filepath="figs/coherence_two_geophones.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
|
||||
<<plt-matlab>>
|
||||
#+end_src
|
||||
|
||||
#+NAME: fig:coherence_two_geophones
|
||||
#+CAPTION: Coherence between the two geophones for the three experiments
|
||||
#+RESULTS: fig:coherence_two_geophones
|
||||
[[file:figs/coherence_two_geophones.png]]
|
||||
|
||||
** Conclusion
|
||||
#+begin_important
|
||||
These measurements are not relevant.
|
||||
#+end_important
|
||||
+1
-1
@@ -76,7 +76,7 @@ This Matlab function is accessible [[file:voltageToDisplacementL22.m][here]].
|
||||
#+begin_src matlab
|
||||
velocity = voltageToVelocityL22(voltage, time, gain);
|
||||
|
||||
disp = lsim(1/s, velocity, time);
|
||||
disp = lsim(1/(1+s/(2*pi*0.5)), velocity, time);
|
||||
#+end_src
|
||||
* getGroundVelocity
|
||||
:PROPERTIES:
|
||||
|
||||
@@ -15,4 +15,4 @@ s = zpk('s');
|
||||
|
||||
velocity = voltageToVelocityL22(voltage, time, gain);
|
||||
|
||||
disp = lsim(1/s, velocity, time);
|
||||
disp = lsim(1/(1+s/(2*pi*0.5)), velocity, time);
|
||||
Reference in new issue
Block a user