Add data analysis of marble dynamics
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153
dynamical-meas-granite/matlab/marble_dynamics.m
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153
dynamical-meas-granite/matlab/marble_dynamics.m
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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% Load data
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m_z = load('mat/data_037.mat', 'data'); m_z = m_z.data;
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m_n = load('mat/data_038.mat', 'data'); m_n = m_n.data;
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m_e = load('mat/data_039.mat', 'data'); m_e = m_e.data;
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% Time domain plots
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figure;
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subplot(1, 3, 1);
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hold on;
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plot(m_z(:, 3), m_z(:, 2), 'DisplayName', 'Marble - Z');
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plot(m_z(:, 3), m_z(:, 1), 'DisplayName', 'Floor - Z');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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xlim([0, 100]); ylim([-2 2]);
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legend('Location', 'northeast');
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subplot(1, 3, 2);
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hold on;
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plot(m_n(:, 3), m_n(:, 2), 'DisplayName', 'Marble - N');
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plot(m_n(:, 3), m_n(:, 1), 'DisplayName', 'Floor - N');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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xlim([0, 100]); ylim([-2 2]);
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legend('Location', 'northeast');
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subplot(1, 3, 3);
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hold on;
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plot(m_e(:, 3), m_e(:, 2), 'DisplayName', 'Marble - E');
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plot(m_e(:, 3), m_e(:, 1), 'DisplayName', 'Floor - E');
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hold off;
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xlabel('Time [s]'); ylabel('Voltage [V]');
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xlim([0, 100]); ylim([-2 2]);
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legend('Location', 'northeast');
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% Compute the power spectral densities
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% We first compute some parameters that will be used for the PSD computation.
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dt = m_z(2, 3)-m_z(1, 3);
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Fs = 1/dt; % [Hz]
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win = hanning(ceil(10*Fs));
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% Then we compute the Power Spectral Density using =pwelch= function.
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[px_fz, f] = pwelch(m_z(:, 1), win, [], [], Fs);
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[px_gz, ~] = pwelch(m_z(:, 2), win, [], [], Fs);
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[px_fn, ~] = pwelch(m_n(:, 1), win, [], [], Fs);
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[px_gn, ~] = pwelch(m_n(:, 2), win, [], [], Fs);
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[px_fe, ~] = pwelch(m_e(:, 1), win, [], [], Fs);
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[px_ge, ~] = pwelch(m_e(:, 2), win, [], [], Fs);
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% The results are shown on figure [[fig:floor_marble_psd_z]] for the Z direction, figure [[fig:floor_marble_psd_n]] for the north direction, and figure [[fig:floor_marble_psd_e]] for the east direction.
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figure;
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hold on;
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plot(f, sqrt(px_fz), 'DisplayName', 'Floor - Z');
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plot(f, sqrt(px_gz), 'DisplayName', 'Granite - Z');
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
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legend('Location', 'southwest');
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xlim([0.1, 500]);
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% #+NAME: fig:floor_marble_psd_z
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% #+CAPTION: Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - Z direction
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% #+RESULTS: fig:floor_marble_psd_z
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% [[file:figs/floor_marble_psd_z.png]]
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figure;
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hold on;
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plot(f, sqrt(px_fn), 'DisplayName', 'Floor - N');
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plot(f, sqrt(px_gn), 'DisplayName', 'Granite - N');
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
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legend('Location', 'southwest');
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xlim([0.1, 500]);
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% #+NAME: fig:floor_marble_psd_n
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% #+CAPTION: Amplitude Spectral Density of the measured voltage corresponding to the geophone located on the floor and on the marble - N direction
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% #+RESULTS: fig:floor_marble_psd_n
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% [[file:figs/floor_marble_psd_n.png]]
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figure;
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hold on;
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plot(f, sqrt(px_fe), 'DisplayName', 'Floor - E');
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plot(f, sqrt(px_ge), 'DisplayName', 'Granite - E');
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hold off;
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set(gca, 'xscale', 'log');
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set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD of the measured Voltage $\left[\frac{V}{\sqrt{Hz}}\right]$')
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legend('Location', 'southwest');
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xlim([0.1, 500]);
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% Compute the transfer function from floor motion to ground motion
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% We now compute the transfer function from the floor motion to the granite motion.
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% The result is shown on figure [[fig:tf_granite]].
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[TZ, f] = tfestimate(m_z(:, 1), -m_z(:, 2), win, [], [], Fs);
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[TN, ~] = tfestimate(m_n(:, 1), -m_n(:, 2), win, [], [], Fs);
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[TE, ~] = tfestimate(m_e(:, 1), -m_e(:, 2), win, [], [], Fs);
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figure;
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ax1 = subplot(2, 1, 1);
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hold on;
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plot(f, abs(TZ), 'DisplayName', 'Z');
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plot(f, abs(TN), 'DisplayName', 'N');
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plot(f, abs(TE), 'DisplayName', 'E');
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hold off;
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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set(gca, 'XTickLabel',[]);
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ylabel('Magnitude');
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legend('Location', 'southwest');
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ax2 = subplot(2, 1, 2);
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hold on;
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plot(f, mod(180+180/pi*phase(TZ), 360)-180);
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plot(f, mod(180+180/pi*phase(TN), 360)-180);
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plot(f, mod(180+180/pi*phase(TE), 360)-180);
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hold off;
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set(gca, 'xscale', 'log');
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ylim([-180, 180]);
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yticks([-180, -90, 0, 90, 180]);
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xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
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linkaxes([ax1,ax2],'x');
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xlim([10, 100]);
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