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Update ground motion analysis

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This commit is contained in:
Thomas Dehaeze
2020-01-28 15:01:32 +01:00
parent cb3f3009ed
commit b1bbae2f8f
9 changed files with 289 additions and 143 deletions
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45
ground-motion/matlab/ground_meas_id31.m
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@@ -44,9 +44,15 @@ f0 = 2; % Cut-off frequency [Hz]
S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);
freqs = logspace(-1, 2, 1000);
figure;
bodeFig({S}, logspace(-1, 2, 1000));
ylabel('Amplitude $\left[\frac{V}{m/s}\right]$')
hold on;
plot(f, abs(squeeze(freqresp(S, f, 'Hz'))));
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Magnitude $\left[\frac{V}{m/s}\right]$');
xlim([0.1, 100]);
@@ -64,19 +70,25 @@ G0 = 10^(G0_db/20); % [abs]
% We divide the ASD measured (in $\text{V}/\sqrt{\text{Hz}}$) by the gain of the voltage amplifier to obtain the ASD of the voltage across the geophone.
% We further divide the result by the sensibility of the Geophone to obtain the ASD of the velocity in $m/s/\sqrt{Hz}$.
% We divide the PSD measured (in $\text{V^2}/\sqrt{Hz}$) by the square of the gain of the voltage amplifier to obtain the PSD of the voltage across the geophone.
% We further divide the result by the square of the magnitude of sensibility of the Geophone to obtain the PSD of the velocity in $(m/s)^2/Hz$.
scaling = 1./squeeze(abs(freqresp(G0*S, f, 'Hz')));
psd_gv = px_dc./abs(squeeze(freqresp(G0*S, f, 'Hz'))).^2;
% Computation of the ASD of the velocity
% Finally, we obtain the PSD of the ground motion in $m^2/Hz$ by dividing by the square of the frequency in $rad/s$.
psd_gm = psd_gv./(2*pi*f).^2;
% Computation of the ASD of the velocity and displacement
% The ASD of the measured velocity is shown on figure [[fig:ground_motion_id31_asd_velocity]].
figure;
hold on;
plot(f, sqrt(px_dc).*scaling);
plot(f, sqrt(psd_gv));
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
@@ -92,10 +104,9 @@ xlim([0.1, 500]);
% We also plot the ASD in displacement (figure [[fig:ground_motion_id31_asd_displacement]]);
figure;
hold on;
plot(f, (sqrt(px_dc).*scaling)./(2*pi*f));
plot(f, sqrt(psd_gm));
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
@@ -107,16 +118,24 @@ xlim([0.1, 500]);
% #+CAPTION: Amplitude Spectral Density of the Displacement
% #+RESULTS: fig:ground_motion_id31_asd_displacement
% [[file:figs/ground_motion_id31_asd_displacement.png]]
% And also in $\frac{{\mu u}^2}{Hz}$ (figure [[fig:ground_motion_id31_psd_displacement]]).
% And we also plot the PSD of the displacement in $\frac{{\mu u}^2}{Hz}$ as it is a usual unit used (figure [[fig:ground_motion_id31_psd_displacement]]).
% One can then compare this curve with the figure [[fig:ground_motion_measurements]].
figure;
hold on;
plot(f, ((sqrt(px_dc).*scaling)./(2*pi*f).*1e6).^2);
plot(f, psd_gm.*1e12);
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD of the measured displacement $\left[\frac{{ \mu m }^2}{Hz}\right]$')
xlim([0.1, 500]);
xlim([0.1, 500]); ylim([1e-13, 1e3]);
% Save
% We save the PSD of the ground motion for further analysis.
save('./mat/psd_gm', 'f', 'psd_gm');
% Load the measurement data
% First we load the measurement data.
@@ -144,7 +163,7 @@ figure;
hold on;
plot(id09_f, id09_pxx, 'DisplayName', 'ID09');
plot(cern_f, cern_pxx, 'DisplayName', 'CERN');
plot(f, ((sqrt(px_dc).*scaling)./(2*pi*f)).^2, 'k', 'DisplayName', 'ID31');
plot(f, psd_gm, 'k', 'DisplayName', 'ID31');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m^2/Hz$]');