nass-micro-station-measurements/ground-motion/matlab/ground_meas_id31.m

%% Clear Workspace and Close figures
clear; close all; clc;

%% Intialize Laplace variable
s = zpk('s');

% Load data

data = load('mat/data_028.mat', 'data'); data = data.data;

% Time domain plots of the measured voltage

figure;
hold on;
plot(data(:, 3), data(:, 1));
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
xlim([0, 100]);

% Computation of the ASD of the measured voltage

dt = data(2, 3) - data(1, 3);

Fs = 1/dt;
win = hanning(ceil(10*Fs));

[px_dc, f] = pwelch(data(:, 1), win, [], [], Fs);

figure;
hold on;
plot(f, sqrt(px_dc));
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);

% Scaling to take into account the sensibility of the geophone and the voltage amplifier
% The Geophone used are L22. Their sensibility is shown on figure [[fig:geophone_sensibility]].


S0 = 88; % Sensitivity [V/(m/s)]
f0 = 2; % Cut-off frequency [Hz]

S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);

freqs = logspace(-1, 2, 1000);

figure;
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]);



% #+NAME: fig:geophone_sensibility
% #+CAPTION: Sensibility of the Geophone
% #+RESULTS: fig:geophone_sensibility
% [[file:figs/geophone_sensibility.png]]

% We also take into account the gain of the electronics which is here set to be $60dB$.


G0_db = 60; % [dB]

G0 = 10^(G0_db/20); % [abs]



% We divide the 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 $(m/s)^2/Hz$.


psd_gv = px_dc./abs(squeeze(freqresp(G0*S, f, 'Hz'))).^2;



% 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;

% Time domain plots of the ground motion
% We can inverse the dynamics of the geophone to convert the measured voltage into the estimated ground motion.


est_vel = lsim(inv(G0*S)*(s/2/pi)/(1+s/2/pi), data(:, 1), data(:, 3)); % Estimated velocity above 1Hz
est_vel = est_vel - mean(est_vel(data(:,3)>10)); % The mean value of the velocity if removed
est_dis = lsim(1/(1+s/2/pi), est_vel, data(:, 3)); % The velocity is integrated above 1Hz

figure;
hold on;
plot(data(:, 3), est_vel);
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([10, 100]);



% #+NAME: fig:time_domain_velocity
% #+CAPTION: Time domain velocity ([[./figs/time_domain_velocity.png][png]], [[./figs/time_domain_velocity.pdf][pdf]])
% [[file:figs/time_domain_velocity.png]]


figure;
hold on;
plot(data(:, 3), est_dis);
hold off;
xlabel('Time [s]'); ylabel('Displacement [m]');
xlim([10, 100]);

% 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(psd_gv));
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured Velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);



% #+NAME: fig:ground_motion_id31_asd_velocity
% #+CAPTION: Amplitude Spectral Density of the Velocity
% #+RESULTS: fig:ground_motion_id31_asd_velocity
% [[file:figs/ground_motion_id31_asd_velocity.png]]

% We also plot the ASD in displacement (figure [[fig:ground_motion_id31_asd_displacement]]);

figure;
hold on;
plot(f, sqrt(psd_gm));
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
xlim([0.1, 500]);



% #+NAME: fig:ground_motion_id31_asd_displacement
% #+CAPTION: Amplitude Spectral Density of the Displacement
% #+RESULTS: fig:ground_motion_id31_asd_displacement
% [[file:figs/ground_motion_id31_asd_displacement.png]]

% And 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, 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]); ylim([1e-13, 1e3]);

% Save
% We save the PSD of the ground motion for further analysis.

save('./mat/psd_gm.mat', 'f', 'psd_gm', 'psd_gv');

% Load the measurement data
% First we load the measurement data.
% Here we have one measurement of the floor motion made at the ESRF in 2018, and one measurement made at CERN.

id09 = load('./mat/id09_floor_september2018.mat');
cern = load('./mat/ground_motion_dist.mat');

% Compute PSD of the measurements
% We compute the Power Spectral Densities of the measurements.

Fs_id09 = 1/(id09.time3(2)-id09.time3(1));
win_id09 = hanning(ceil(10*Fs_id09));
[id09_pxx, id09_f] = pwelch(1e-6*id09.x_y_z(:, 3), win_id09, [], [], Fs_id09);

Fs_cern = 1/(cern.gm.time(2)-cern.gm.time(1));
win_cern = hanning(ceil(10*Fs_cern));
[cern_pxx, cern_f] = pwelch(cern.gm.signal, win_cern, [], [], Fs_cern);

% Compare PSD of Cern, ID09 and ID31
% And we compare all the measurements (figure [[fig:ground_motion_compare]]).


figure;
hold on;
plot(id09_f, id09_pxx, 'DisplayName', 'ID09');
plot(cern_f, cern_pxx, 'DisplayName', 'CERN');
plot(f, psd_gm, 'k', 'DisplayName', 'ID31');
hold off;
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD [$m^2/Hz$]');
legend('Location', 'northeast');
xlim([0.1, 500]);