add all files

A3-micro-station-modal-analysis/mat/acc_pos.txt

@@ -0,0 +1,23 @@
+    23  1.5500e-001 -9.0000e-002 -5.9400e-001     
+    22  0.0000e+000  1.8000e-001 -5.9400e-001     
+    21 -1.5500e-001 -9.0000e-002 -5.9400e-001     
+    20  8.6490e-001 -5.0600e-001 -9.5060e-001     
+    19  8.7500e-001  7.9900e-001 -9.5060e-001     
+    18 -7.3500e-001  8.1400e-001 -9.5060e-001     
+    17 -7.3000e-001 -5.2600e-001 -9.5060e-001     
+    16  2.9500e-001 -4.8100e-001 -7.8560e-001     
+    15  4.5000e-001  5.3400e-001 -7.8560e-001     
+    14 -4.8000e-001  5.3400e-001 -7.8560e-001     
+    13 -3.2000e-001 -4.4600e-001 -7.8560e-001     
+    12  4.7500e-001 -4.1900e-001 -4.2730e-001     
+    11  4.7500e-001  4.2400e-001 -4.2730e-001     
+    10 -4.6500e-001  4.0700e-001 -4.2730e-001     
+     9 -4.7500e-001 -4.1400e-001 -4.2730e-001     
+     8  3.8000e-001 -3.0000e-001 -4.1680e-001     
+     7  4.2000e-001  2.8000e-001 -4.1680e-001     
+     6 -4.2000e-001  2.8000e-001 -4.1680e-001     
+     5 -3.8500e-001 -3.0000e-001 -4.1680e-001     
+     4  6.4000e-002 -6.4000e-002 -2.7000e-001     
+     3  6.4000e-002  6.4000e-002 -2.7000e-001     
+     2 -6.4000e-002  6.4000e-002 -2.7000e-001     
+     1 -6.4000e-002 -6.4000e-002 -2.7000e-001     

A3-micro-station-modal-analysis/mat/mode_damps.txt

@@ -0,0 +1,16 @@
+12.20318
+11.66888
+6.19561
+2.79104
+2.76253
+4.34928
+1.25546
+3.65470
+2.94088
+3.19084
+1.55526
+3.13166
+2.76141
+1.34304
+2.43201
+1.38400

A3-micro-station-modal-analysis/mat/mode_freqs.txt

@@ -0,0 +1,16 @@
+11.86509
+18.55747
+37.82163
+39.07850
+56.31944
+69.78452
+72.49325
+84.83446
+91.26350
+105.47266
+106.57165
+112.67669
+124.20538
+145.30034
+150.52113
+165.42632

A3-micro-station-modal-analysis/mat/mode_modal_a.txt

@@ -0,0 +1,16 @@
+4.13559e+003 +6.22828e+003
+2.76278e+002 +1.74197e+004
+-1.32270e+004 +2.17346e+004
+-2.48397e+005 -1.60998e+005
+-4.23967e+004 +7.06852e+004
+-7.36964e+003 +4.57024e+004
+1.37806e+005 +3.00336e+005
+-1.31109e+004 +2.81759e+004
+5.59259e+003 -4.27543e+004
+-5.28869e+004 +6.38436e+003
+3.71578e+004 +1.57745e+004
+-4.24659e+004 +7.90956e+003
+-3.57355e+004 +1.13161e+005
+5.24764e+004 -1.45211e+005
+1.97228e+005 +2.51758e+005
+-3.00273e+005 +3.27201e+005

A3-micro-station-modal-analysis/mat/mode_modal_b.txt

@@ -0,0 +1,16 @@
+4.98475e+005 -2.49344e+005
+2.02102e+006 +2.05017e+005
+4.96035e+006 +3.45724e+006
+-4.12180e+007 +5.98638e+007
+2.45891e+007 +1.56880e+007
+1.98796e+007 +4.09986e+006
+1.37577e+008 -6.10466e+007
+1.47532e+007 +7.53272e+006
+-2.44115e+007 -3.92655e+006
+3.11045e+006 +3.51656e+007
+1.09485e+007 -2.47140e+007
+4.65546e+006 +3.02251e+007
+8.75076e+007 +3.03162e+007
+-1.31915e+008 -4.96844e+007
+2.42567e+008 -1.80683e+008
+3.35742e+008 +3.16782e+008

A3-micro-station-modal-analysis/mat/model_solidworks_com.txt

@@ -0,0 +1,18 @@
+0.045
+0.144
+-1.251
+0.052
+0.258
+-0.778
+0.000
+0.014
+-0.600
+0.000
+-0.005
+-0.628
+0.000
+0.000
+-0.580
+-0.004
+0.006
+-0.319

A3-micro-station-modal-analysis/modal_1_meas_setup.m

@@ -0,0 +1,83 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Path for functions, data and scripts
+addpath('./mat/'); % Path for data
+
+%% Colors for the figures
+colors = colororder;
+
+%% Load Accelerometer positions
+acc_pos = readtable('mat/acc_pos.txt', 'ReadVariableNames', false);
+acc_pos = table2array(acc_pos(:, 1:4));
+[~, i] = sort(acc_pos(:, 1));
+acc_pos = acc_pos(i, 2:4);
+
+%% Load raw data
+meas1_raw = load('mat/meas_raw_1.mat');
+
+% Sampling Frequency [Hz]
+Fs = 1/meas1_raw.Track1_X_Resolution;
+
+% Time just before the impact occurs [s]
+impacts = [5.937, 11.228, 16.681, 22.205, 27.350, 32.714, 38.115, 43.888, 50.407]-0.01;
+
+% Time vector [s]
+time = linspace(0, meas1_raw.Track1_X_Resolution*length(meas1_raw.Track1), length(meas1_raw.Track1));
+
+%% Raw measurement of the Accelerometer
+figure;
+hold on;
+plot(time-22.2, meas1_raw.Track2, 'DisplayName', '$X_{1,x}$ [$m/s^2$]');
+plot(time-22.2, 1e-3*meas1_raw.Track1, 'DisplayName', '$F_{z}$ [kN]');
+hold off;
+xlabel('Time [s]');
+ylabel('Amplitude');
+xlim([0, 0.2])
+ylim([-2, 2]);
+legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
+
+%% Frequency Analysis
+Nfft = floor(5.0*Fs); % Number of frequency points
+win = hanning(Nfft); % Windowing
+Noverlap = floor(Nfft/2); % Overlap for frequency analysis
+
+%% Comnpute the power spectral density of the force and acceleration
+[pxx_force, f] = pwelch(meas1_raw.Track1, win, Noverlap, Nfft, Fs);
+[pxx_acc,   ~] = pwelch(meas1_raw.Track2, win, Noverlap, Nfft, Fs);
+
+%% Normalized Amplitude Spectral Density of the measured force and acceleration
+figure;
+hold on;
+plot(f, sqrt(pxx_acc./max(pxx_acc(f<200))), 'DisplayName', '$\Gamma_{X_{1,x}}$');
+plot(f, sqrt(pxx_force./max(pxx_force(f<200))), 'DisplayName', '$\Gamma_{F_{z}}$');
+hold off;
+set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin');
+xlabel('Frequency [Hz]'); ylabel('Normalized Spectral Density');
+xlim([0, 200]);
+xticks([0:20:200]);
+ylim([0, 1])
+legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
+
+%% Compute the transfer function and Coherence
+[G1,   f] = tfestimate(meas1_raw.Track1, meas1_raw.Track2, win, Noverlap, Nfft, Fs);
+[coh1, ~] = mscohere(  meas1_raw.Track1, meas1_raw.Track2, win, Noverlap, Nfft, Fs);
+
+%% Frequency Response Function between the force and the acceleration
+figure;
+plot(f, abs(G1));
+xlabel('Frequency [Hz]'); ylabel('FRF [$m/s^2/N$]')
+set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'log');
+xlim([0, 200]);
+xticks([0:20:200]);
+
+%% Frequency Response Function between the force and the acceleration
+figure;
+plot(f, coh1);
+xlabel('Frequency [Hz]'); ylabel('Coherence [-]')
+set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'lin');
+xlim([0, 200]); ylim([0,1]);
+xticks([0:20:200]);

A3-micro-station-modal-analysis/modal_2_frf_processing.m

@@ -0,0 +1,132 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Path for functions, data and scripts
+addpath('./mat/'); % Path for data
+
+%% Colors for the figures
+colors = colororder;
+
+%% Load frequency response matrix
+load('frf_matrix.mat', 'freqs', 'frf');
+
+%% Load Accelerometer positions
+acc_pos = readtable('mat/acc_pos.txt', 'ReadVariableNames', false);
+acc_pos = table2array(acc_pos(:, 1:4));
+[~, i] = sort(acc_pos(:, 1));
+acc_pos = acc_pos(i, 2:4);
+
+%% Accelerometers ID connected to each solid body
+solids = {};
+solids.gbot = [17, 18, 19, 20]; % bottom granite
+solids.gtop = [13, 14, 15, 16]; % top granite
+solids.ty   = [9, 10, 11, 12]; % Ty stage
+solids.ry   = [5, 6, 7, 8]; % Ry stage
+solids.rz   = [21, 22, 23]; % Rz stage
+solids.hexa = [1, 2, 3, 4]; % Hexapod
+
+% Names of the solid bodies
+solid_names = fields(solids);
+
+%% Save the accelerometer positions are well as the solid bodies
+save('mat/geometry.mat', 'solids', 'solid_names', 'acc_pos');
+
+%% Extract the CoM of considered solid bodies
+model_com = reshape(table2array(readtable('mat/model_solidworks_com.txt', 'ReadVariableNames', false)), [3, 6]);
+
+%% Frequency Response Matrix - Response expressed at the CoM of the solid bodies
+frfs_CoM = zeros(length(solid_names)*6, 3, 801);
+
+for solid_i = 1:length(solid_names)
+  % Number of accelerometers fixed to this solid body
+  solids_i = solids.(solid_names{solid_i});
+
+  % "Jacobian" matrix to go from accelerometer frame to CoM frame
+  A = zeros(3*length(solids_i), 6);
+  for i = 1:length(solids_i)
+    acc_i = solids_i(i);
+
+    acc_pos_com = acc_pos(acc_i, :).' - model_com(:, solid_i);
+
+    A(3*(i-1)+1:3*i, 1:3) = eye(3);
+    A(3*(i-1)+1:3*i, 4:6) = [ 0               acc_pos_com(3) -acc_pos_com(2) ;
+                             -acc_pos_com(3)  0               acc_pos_com(1) ;
+                              acc_pos_com(2) -acc_pos_com(1)  0];
+  end
+
+  for exc_dir = 1:3
+    frfs_CoM((solid_i-1)*6+1:solid_i*6, exc_dir, :) = A\squeeze(frf((solids_i(1)-1)*3+1:solids_i(end)*3, exc_dir, :));
+  end
+end
+
+%% Save the computed FRF at the CoM
+save('mat/frf_com.mat', 'frfs_CoM');
+
+%% Compute the FRF at the accelerometer location from the CoM reponses
+frfs_A = zeros(size(frf));
+
+% For each excitation direction
+for exc_dir = 1:3
+  % For each solid
+  for solid_i = 1:length(solid_names)
+    v0 = squeeze(frfs_CoM((solid_i-1)*6+1:(solid_i-1)*6+3, exc_dir, :));
+    W0 = squeeze(frfs_CoM((solid_i-1)*6+4:(solid_i-1)*6+6, exc_dir, :));
+
+    % For each accelerometer attached to the current solid
+    for acc_i = solids.(solid_names{solid_i})
+      % We get the position of the accelerometer expressed in frame O
+      pos = acc_pos(acc_i, :).' - model_com(:, solid_i);
+      % pos = acc_pos(acc_i, :).';
+      posX = [0 pos(3) -pos(2); -pos(3) 0 pos(1) ; pos(2) -pos(1) 0];
+
+      frfs_A(3*(acc_i-1)+1:3*(acc_i-1)+3, exc_dir, :) = v0 + posX*W0;
+    end
+  end
+end
+
+%% Comparison of the original accelerometer response and reconstructed response from the solid body response
+exc_names = {'$F_x$', '$F_y$', '$F_z$'};
+DOFs = {'x', 'y', 'z', '\theta_x', '\theta_y', '\theta_z'};
+
+solid_i = 6; % Considered solid body
+exc_dir = 1; % Excited direction
+
+accs_i = solids.(solid_names{solid_i}); % Accelerometers fixed to this solid body
+
+figure;
+tiledlayout(2, 2, 'TileSpacing', 'Tight', 'Padding', 'None');
+
+for i = 1:length(accs_i)
+  acc_i = accs_i(i);
+  nexttile();
+
+  hold on;
+  for dir_i = 1:3
+    plot(freqs, abs(squeeze(frf(3*(acc_i-1)+dir_i, exc_dir, :))), '-', 'color', [colors(dir_i,:), 0.5], 'linewidth', 2.5, 'DisplayName', sprintf('$a_{%i,%s}$ - meas', acc_i, DOFs{dir_i}));
+  end
+  for dir_i = 1:3
+    plot(freqs, abs(squeeze(frfs_A(3*(acc_i-1)+dir_i, exc_dir, :))), '-', 'color', colors(dir_i, :), 'DisplayName', sprintf('$a_{%i,%s}$ - solid body', acc_i, DOFs{dir_i}));
+  end
+  hold off;
+
+  if i > 2
+    xlabel('Frequency [Hz]');
+  else
+    set(gca, 'XTickLabel',[]);
+  end
+
+  if rem(i, 2) == 1
+    ylabel('Amplitude [$\frac{m/s^2}{N}$]');
+  else
+    set(gca, 'YTickLabel',[]);
+  end
+
+  set(gca, 'XScale', 'lin'); set(gca, 'YScale', 'log');
+  xlim([0, 200]); ylim([1e-6, 3e-2]);
+  xticks([0:20:200]);
+  leg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 2);
+  leg.ItemTokenSize(1) = 15;
+end

A3-micro-station-modal-analysis/modal_3_analysis.m

@@ -0,0 +1,151 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+%% Path for functions, data and scripts
+addpath('./mat/'); % Path for data
+
+%% Colors for the figures
+colors = colororder;
+
+%% Load frequency response matrix
+load('frf_matrix.mat', 'freqs', 'frf');
+
+%% Computation of the modal indication function
+MIF = zeros(size(frf, 2), size(frf, 2), size(frf, 3));
+
+for i = 1:length(freqs)
+  [~,S,~] = svd(frf(:, :, i));
+  MIF(:, :, i) = S'*S;
+end
+
+%% Modal Indication Function
+figure;
+hold on;
+for i = 1:size(MIF, 1)
+  plot(freqs, squeeze(MIF(i, i, :)), 'DisplayName', sprintf('MIF${}_%i$', i));
+end
+hold off;
+set(gca, 'Xscale', 'lin'); set(gca, 'Yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('CMIF Amplitude');
+xticks([0:20:200]);
+xlim([0, 200]);
+ylim([1e-6, 2e-2]);
+ldg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
+
+%% Load modal parameters
+shapes_m = readtable('mat/mode_shapes.txt',              'ReadVariableNames', false);  % [Sign / Real / Imag]
+freqs_m  = table2array(readtable('mat/mode_freqs.txt',   'ReadVariableNames', false)); % in [Hz]
+damps_m  = table2array(readtable('mat/mode_damps.txt',   'ReadVariableNames', false)); % in [%]
+modal_a  = table2array(readtable('mat/mode_modal_a.txt', 'ReadVariableNames', false)); % [Real / Imag]
+modal_b  = table2array(readtable('mat/mode_modal_b.txt', 'ReadVariableNames', false)); % [Real / Imag]
+
+%% Guess the number of modes identified from the length of the imported data.
+acc_n = 23; % Number of accelerometers
+dir_n = 3; % Number of directions
+dirs = 'XYZ';
+
+mod_n = size(shapes_m,1)/acc_n/dir_n; % Number of modes
+
+%% Mode shapes are split into 3 parts (direction plus sign, real part and imaginary part)
+% we aggregate them into one array of complex numbers
+T_sign = table2array(shapes_m(:, 1));
+T_real = table2array(shapes_m(:, 2));
+T_imag = table2array(shapes_m(:, 3));
+
+mode_shapes = zeros(mod_n, dir_n, acc_n);
+
+for mod_i = 1:mod_n
+  for acc_i = 1:acc_n
+    % Get the correct section of the signs
+    T = T_sign(acc_n*dir_n*(mod_i-1)+1:acc_n*dir_n*mod_i);
+    for dir_i = 1:dir_n
+      % Get the line corresponding to the sensor
+      i = find(contains(T, sprintf('%i%s',acc_i, dirs(dir_i))), 1, 'first')+acc_n*dir_n*(mod_i-1);
+      mode_shapes(mod_i, dir_i, acc_i) = str2num([T_sign{i}(end-1), '1'])*complex(T_real(i),T_imag(i));
+    end
+  end
+end
+
+%% Create the eigenvalue and eigenvector matrices
+eigen_val_M = diag(2*pi*freqs_m.*(-damps_m/100 + j*sqrt(1 - (damps_m/100).^2))); % Lambda = diagonal matrix
+eigen_vec_M = reshape(mode_shapes, [mod_n, acc_n*dir_n]).'; % Phi, vecnorm(eigen_vec_M) = 1
+
+% Add complex conjugate eigenvalues and eigenvectors
+eigen_val_ext_M = blkdiag(eigen_val_M, conj(eigen_val_M));
+eigen_vec_ext_M = [eigen_vec_M, conj(eigen_vec_M)];
+
+%% "Modal A" and "Modal B" matrices
+modal_a_M = diag(complex(modal_a(:, 1), modal_a(:, 2)));
+modal_b_M = diag(complex(modal_b(:, 1), modal_b(:, 2)));
+
+modal_a_ext_M = blkdiag(modal_a_M, conj(modal_a_M));
+modal_b_ext_M = blkdiag(modal_b_M, conj(modal_b_M));
+
+%% Synthesize the full FRF matrix from the modal model
+Hsyn = zeros(acc_n*dir_n, acc_n*dir_n, length(freqs));
+
+for i = 1:length(freqs)
+  Hsyn(:, :, i) = eigen_vec_ext_M*diag(1./(diag(modal_a_ext_M).*(j*2*pi*freqs(i) - diag(eigen_val_ext_M))))*eigen_vec_ext_M.';
+end
+
+%% Derivate two times to have the acceleration response
+for i = 1:size(Hsyn, 1)
+  Hsyn(i, :, :) = squeeze(Hsyn(i, :, :)).*(j*2*pi*freqs).^2;
+end
+
+acc_o = 11; dir_o = 3;
+acc_i = 11; dir_i = 3;
+
+figure;
+hold on;
+plot(freqs, abs(squeeze(frf( 3*(acc_o-1)+dir_o,             dir_i, :))), 'DisplayName', 'Measured');
+plot(freqs, abs(squeeze(Hsyn(3*(acc_o-1)+dir_o, 3*(acc_i-1)+dir_i, :))), 'DisplayName', 'Synthesized');
+hold off;
+set(gca, 'xscale', 'lin');
+set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]');
+ylabel('Magnitude [$\frac{m/s^2}{N}$]');
+ldg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
+ldg.ItemTokenSize = [10, 1];
+xticks([0:40:200]);
+xlim([1, 200]);
+ylim([1e-6, 1e-1]);
+
+acc_o = 15; dir_o = 3;
+acc_i = 11; dir_i = 3;
+
+figure;
+hold on;
+plot(freqs, abs(squeeze(frf( 3*(acc_o-1)+dir_o,             dir_i, :))), 'DisplayName', 'Measured');
+plot(freqs, abs(squeeze(Hsyn(3*(acc_o-1)+dir_o, 3*(acc_i-1)+dir_i, :))), 'DisplayName', 'Synthesized');
+hold off;
+set(gca, 'xscale', 'lin');
+set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]');
+ylabel('Magnitude [$\frac{m/s^2}{N}$]');
+ldg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
+ldg.ItemTokenSize = [10, 1];
+xticks([0:40:200]);
+xlim([1, 200]);
+ylim([1e-6, 1e-1]);
+
+acc_o = 2; dir_o = 1;
+acc_i = 11; dir_i = 2;
+
+figure;
+hold on;
+plot(freqs, abs(squeeze(frf( 3*(acc_o-1)+dir_o,             dir_i, :))), 'DisplayName', 'Measured');
+plot(freqs, abs(squeeze(Hsyn(3*(acc_o-1)+dir_o, 3*(acc_i-1)+dir_i, :))), 'DisplayName', 'Synthesized');
+hold off;
+set(gca, 'xscale', 'lin');
+set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]');
+ylabel('Magnitude [$\frac{m/s^2}{N}$]');
+ldg = legend('location', 'southeast', 'FontSize', 8, 'NumColumns', 1);
+ldg.ItemTokenSize = [10, 1];
+xticks([0:40:200]);
+xlim([1, 200]);
+ylim([1e-6, 1e-1]);