Finish the file about measurements. Add raw measurements to git

modal-analysis/index.org

@@ -20,7 +20,31 @@
 #+HTML_MATHJAX: align: center tagside: right font: TeX
 :END:
 
-The modal analysis of the ID31 Micro-station consists of several parts:
+The goal is to experimentally extract a *Spatial Model* (mass, damping, stiffness) of the structure (shown on figure [[fig:nass_picture]]) in order to tune the Multi-Body model.
+
+#+name: fig:nass_picture
+#+caption: Picture of the ID31 Micro-Station. (1) Granite (2) Translation Stage (3) Tilt Stage (4) Hexapod (5) Dummy Mass
+#+attr_html: :width 500px
+[[file:img/nass_picture.png]]
+
+The procedure is represented on figure [[fig:vibration_analysis_procedure]] where we go from left to right.
+
+#+name: fig:vibration_analysis_procedure
+#+caption: Vibration Analysis Procedure
+#+attr_html: :width 400px
+[[file:img/vibration_analysis_procedure.png]]
+
+The steps are:
+- we obtain a *Response Model* (Frequency Response Functions) from measurements (described [[file:measurement.org][here]])
+- the response model is further converted into a *Modal Model* (Natural Frequencies and Mode Shapes) (described [[file:modal_extraction.org][here]])
+- this is converted into a *Spatial Model* with the Mass/Damping/Stiffness matrices (described [[file:mathematical_model.org][here]])
+
+Theses matrices will be used to tune the Simscape (multi-body) model.
+
+The modes we want to identify are those in the frequency range between 0Hz and 150Hz.
+
+
+The modal analysis of the ID31 Micro-station thus consists of several parts:
 - [[file:measurement.org][Frequency Response Measurements]]
 - [[file:modal_extraction.org][Modal Parameter Extraction]]
 - [[file:mathematical_model.org][Derivation of Mathematical Model]]

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 -2.9600e-001     
+     3  6.4000e-002  6.4000e-002 -2.9600e-001     
+     2 -6.4000e-002  6.4000e-002 -2.9600e-001     
+     1 -6.4000e-002 -6.4000e-002 -2.9600e-001     

modal-analysis/mat/id31_nanostation.cfg

@@ -0,0 +1,90 @@
+This file was saved by N-Modal automatically.
+16:49:47, Monday, July 01, 2019
+
+HEADER
+Data are imported from UFF files. 
+
+
+FREQVEC
+UFF
+
+RES_TYPE
+ACCELERATION
+
+COOR_SYS
+     1     0  0.0000e+000  0.0000e+000  0.0000e+000  0.0000e+000  0.0000e+000  0.0000e+000  0.0000e+000  0.0000e+000  0.0000e+000   Cartesian1
+
+NODES
+    23  1.5500e-001 -9.0000e-002 -5.9400e-001      0          bot
+    22  0.0000e+000  1.8000e-001 -5.9400e-001      0          bot
+    21 -1.5500e-001 -9.0000e-002 -5.9400e-001      0          bot
+    20  8.6490e-001 -5.0600e-001 -9.5060e-001      0          low
+    19  8.7500e-001  7.9900e-001 -9.5060e-001      0          low
+    18 -7.3500e-001  8.1400e-001 -9.5060e-001      0          low
+    17 -7.3000e-001 -5.2600e-001 -9.5060e-001      0          low
+    16  2.9500e-001 -4.8100e-001 -7.8560e-001      0          top
+    15  4.5000e-001  5.3400e-001 -7.8560e-001      0          top
+    14 -4.8000e-001  5.3400e-001 -7.8560e-001      0          top
+    13 -3.2000e-001 -4.4600e-001 -7.8560e-001      0          top
+    12  4.7500e-001 -4.1900e-001 -4.2730e-001      0        outer
+    11  4.7500e-001  4.2400e-001 -4.2730e-001      0        outer
+    10 -4.6500e-001  4.0700e-001 -4.2730e-001      0        outer
+     9 -4.7500e-001 -4.1400e-001 -4.2730e-001      0        outer
+     8  3.8000e-001 -3.0000e-001 -4.1680e-001      0        inner
+     7  4.2000e-001  2.8000e-001 -4.1680e-001      0        inner
+     6 -4.2000e-001  2.8000e-001 -4.1680e-001      0        inner
+     5 -3.8500e-001 -3.0000e-001 -4.1680e-001      0        inner
+     4  6.4000e-002 -6.4000e-002 -2.7000e-001      0          Top
+     3  6.4000e-002  6.4000e-002 -2.7000e-001      0          Top
+     2 -6.4000e-002  6.4000e-002 -2.7000e-001      0          Top
+     1 -6.4000e-002 -6.4000e-002 -2.7000e-001      0          Top
+
+LINES
+     1      4
+     4      3
+     3      2
+     2      1
+     1     21
+    21     23
+    23     22
+    22     21
+    21      5
+     5      6
+     6      7
+     7      8
+     8      5
+     6     10
+    10     11
+    11     12
+    12      9
+     9     10
+    10     14
+    14     15
+    15     16
+    16     13
+    13     14
+    14     18
+    18     19
+    19     20
+    20     17
+    17     18
+     5      9
+     9     13
+    12     16
+    16     20
+    17     13
+     8     12
+    23      8
+     2     22
+    22      3
+     7     22
+    22      6
+     7     11
+    11     15
+    15     19
+     4     23
+
+SETUP
+Setup 1
+FILE
+C:\Users\lesourd\Downloads\id31_modal_analysis\uff_data\Measurement1.uff|Measurement2.uff|Measurement3.uff|Measurement4.uff|Measurement5.uff|Measurement6.uff|Measurement7.uff|Measurement8.uff|Measurement9.uff|Measurement10.uff|Measurement11.uff|Measurement12.uff|Measurement13.uff|Measurement14.uff|Measurement15.uff|Measurement16.uff|Measurement17.uff|Measurement18.uff|Measurement19.uff|Measurement20.uff|Measurement21.uff|Measurement22.uff|Measurement23.uff|Measurement24.uff

modal-analysis/mat/mode_damps.txt

@@ -0,0 +1,21 @@
+8.72664
+11.75321
+6.44322
+3.60695
+0.24170
+2.83603
+4.60472
+0.64145
+1.58544
+3.56361
+0.26865
+2.86851
+3.30737
+3.27213
+1.89158
+3.02795
+2.71094
+0.56008
+1.64638
+2.17368
+1.39142

modal-analysis/mat/mode_freqs.txt

@@ -0,0 +1,21 @@
+11.41275
+18.51409
+37.58431
+39.43487
+53.99524
+56.14871
+69.68561
+71.58533
+72.35341
+84.92538
+90.56538
+91.00542
+95.76079
+105.43696
+106.76771
+112.58508
+116.84928
+124.13356
+145.35893
+150.10734
+164.65885

modal-analysis/mat/mode_modal_a.txt

@@ -0,0 +1,21 @@
+-4.50556e+003 -9.41744e+003
+-1.56119e+003 -1.64408e+004
+1.24918e+004 -2.00022e+004
+-1.83730e+004 +8.73583e+004
+-6.02120e+005 -5.53574e+004
+-8.13722e+003 -4.17194e+004
+9.12802e+003 -3.78264e+004
+1.83523e+005 -5.45837e+005
+-1.85481e+005 -8.15852e+004
+-6.44647e+003 -3.91843e+004
+2.02548e+005 -4.85436e+005
+-1.54209e+002 -3.09920e+004
+2.10759e+004 -1.47578e+004
+-8.03639e+003 -7.00743e+004
+1.73222e+005 +1.94075e+005
+5.46351e+003 -9.46357e+003
+-2.00775e+004 +5.23111e+004
+-6.04037e+004 -8.70001e+004
+1.50266e+004 -1.61655e+005
+1.66427e+005 +1.73772e+005
+-2.41033e+005 +2.81618e+005

modal-analysis/mat/mode_modal_b.txt

@@ -0,0 +1,21 @@
+-7.00928e+005 +2.62922e+005
+-1.92061e+006 -4.44325e+004
+-4.52363e+006 -3.24813e+006
+2.14671e+007 +5.33018e+006
+-1.92744e+007 +2.04231e+008
+-1.47938e+007 +2.45218e+006
+-1.63606e+007 -4.75508e+006
+-2.44974e+008 -8.41188e+007
+-3.84216e+007 +8.37228e+007
+-2.10181e+007 +2.69256e+006
+-2.75921e+008 -1.15999e+008
+-1.77166e+007 -4.20197e+005
+-8.45524e+006 -1.29677e+007
+-4.65722e+007 +3.80208e+006
+1.32368e+008 -1.13721e+008
+-6.57437e+006 -4.06578e+006
+3.79924e+007 +1.57763e+007
+-6.81189e+007 +4.67313e+007
+-1.47397e+008 -1.61530e+007
+1.67266e+008 -1.53366e+008
+2.87859e+008 +2.53398e+008

modal-analysis/mat/nohup.out

@@ -0,0 +1,2 @@
+
+(termite:6464): GLib-WARNING **: 10:26:13.129: GChildWatchSource: Exit status of a child process was requested but ECHILD was received by waitpid(). See the documentation of g_child_watch_source_new() for possible causes.

modal-analysis/mathematical_model.org

@@ -7,7 +7,7 @@
 #+AUTHOR: Dehaeze Thomas
 
 #+HTML_LINK_HOME: ../index.html
-#+HTML_LINK_UP: ../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"/>
@@ -38,3 +38,25 @@
 #+PROPERTY: header-args:latex+ :mkdirp yes
 #+PROPERTY: header-args:latex+ :output-dir figs
 :END:
+
+* Type of Model
+The model that we want to obtain is a *multi-body model*.
+It is composed of several *solid bodies connected with springs and dampers*.
+The solid bodies are represented with different colors on figure [[fig:nass_solidworks]].
+
+In the simscape model, the solid bodies are:
+- the granite (1 or 2 solids)
+- the translation stage
+- the tilt stage
+- the spindle and slip-ring
+- the hexapod
+
+#+name: fig:nass_solidworks
+#+caption: CAD view of the ID31 Micro-Station
+#+attr_html: :width 800px
+[[file:img/nass_solidworks.png]]
+
+However, each of the DOF of the system may not be relevant for the modes present in the frequency band of interest.
+For instance, the translation stage may not vibrate in the Z direction for all the modes identified. Then, we can block this DOF and this simplifies the model.
+
+The modal identification done here will thus permit us to determine *which DOF can be neglected*.

modal-analysis/matlab/modal_frf_coh.m

@@ -0,0 +1,317 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+% Windowing
+% Windowing is used on the force and response signals.
+
+% A boxcar window (figure [[fig:windowing_force_signal]]) is used for the force signal as once the impact on the structure is done, the measured signal is meaningless.
+% The parameters are:
+% - *Start*: $3\%$
+% - *Stop*: $7\%$
+
+
+figure;
+plot(100*[0, 0.03, 0.03, 0.07, 0.07, 1], [0, 0, 1, 1, 0, 0]);
+xlabel('Time [%]'); ylabel('Amplitude');
+xlim([0, 100]); ylim([0, 1]);
+
+
+
+% #+NAME: fig:windowing_force_signal
+% #+CAPTION: Window used for the force signal
+% [[file:figs/windowing_force_signal.png]]
+
+% An exponential window (figure [[fig:windowing_response_signal]]) is used for the response signal as we are measuring transient signals and most of the information is located at the beginning of the signal.
+% The parameters are:
+% - FlatTop:
+%   - *Start*: $3\%$
+%   - *Stop*: $2.96\%$
+% - Decreasing point:
+%   - *X*: $60.4\%$
+%   - *Y*: $14.7\%$
+
+
+x0 = 0.296;
+xd = 0.604;
+yd = 0.147;
+
+alpha = log(yd)/(x0 - xd);
+
+t = x0:0.01:1.01;
+y = exp(-alpha*(t-x0));
+
+figure;
+plot(100*[0, 0.03, 0.03, x0, t], [0, 0, 1, 1, y]);
+xlabel('Time [%]'); ylabel('Amplitude');
+xlim([0, 100]); ylim([0, 1]);
+
+% Force and Response signals
+% Let's load some obtained data to look at the force and response signals.
+
+
+meas1_raw = load('mat/meas_raw_1.mat');
+
+% Raw Force Data
+% The force input for the first measurement is shown on figure [[fig:raw_data_force]]. We can see 10 impacts, one zoom on one impact is shown on figure [[fig:raw_data_force_zoom]].
+
+% The Fourier transform of the force is shown on figure [[fig:fourier_transfor_force_impact]]. This has been obtained without any windowing.
+
+
+time = linspace(0, meas1_raw.Track1_X_Resolution*length(meas1_raw.Track1), length(meas1_raw.Track1));
+
+figure;
+plot(time, meas1_raw.Track1);
+xlabel('Time [s]');
+ylabel('Force [N]');
+
+
+
+% #+NAME: fig:raw_data_force
+% #+CAPTION: Raw Force Data from Hammer Blow
+% [[file:figs/raw_data_force.png]]
+
+
+figure;
+plot(time, meas1_raw.Track1);
+xlabel('Time [s]');
+ylabel('Force [N]');
+xlim([22.1, 22.3]);
+
+
+
+% #+NAME: fig:raw_data_force_zoom
+% #+CAPTION: Raw Force Data from Hammer Blow - Zoom
+% [[file:figs/raw_data_force_zoom.png]]
+
+
+Fs = 1/meas1_raw.Track1_X_Resolution; % Sampling Frequency [Hz]
+impacts = [5.9, 11.2, 16.6, 22.2, 27.3, 32.7, 38.1, 43.8, 50.4]; % Time just before the impact occurs [s]
+
+L = 8194;
+f = Fs*(0:(L/2))/L; % Frequency vector [Hz]
+
+F_fft = zeros((8193+1)/2+1, length(impacts));
+
+for i = 1:length(impacts)
+  t0 = impacts(i);
+  [~, i_start] = min(abs(time-t0));
+  i_end = i_start + 8193;
+
+  Y = fft(meas1_raw.Track1(i_start:i_end));
+
+  P2 = abs(Y/L);
+  P1 = P2(1:L/2+1);
+  P1(2:end-1) = 2*P1(2:end-1);
+  F_fft(:, i) = P1;
+end
+
+figure;
+hold on;
+for i = 1:length(impacts)
+  plot(f, F_fft(:, i), '-k');
+end
+hold off;
+xlim([0, 200]);
+xlabel('Frequency [Hz]'); ylabel('Force [N]');
+
+% Raw Response Data
+% The response signal for the first measurement is shown on figure [[fig:raw_data_acceleration]]. One zoom on one response is shown on figure [[fig:raw_data_acceleration_zoom]].
+
+% The Fourier transform of the response signals is shown on figure [[fig:fourier_transform_response_signals]]. This has been obtained without any windowing.
+
+
+figure;
+plot(time, meas1_raw.Track2);
+xlabel('Time [s]');
+ylabel('Acceleration [m/s2]');
+
+
+
+% #+NAME: fig:raw_data_acceleration
+% #+CAPTION: Raw Acceleration Data from Accelerometer
+% [[file:figs/raw_data_acceleration.png]]
+
+
+figure;
+plot(time, meas1_raw.Track2);
+xlabel('Time [s]');
+ylabel('Acceleration [m/s2]');
+xlim([22.1, 22.5]);
+
+
+
+% #+NAME: fig:raw_data_acceleration_zoom
+% #+CAPTION: Raw Acceleration Data from Accelerometer - Zoom
+% [[file:figs/raw_data_acceleration_zoom.png]]
+
+
+X_fft = zeros((8193+1)/2+1, length(impacts));
+
+for i = 1:length(impacts)
+  t0 = impacts(i);
+  [~, i_start] = min(abs(time-t0));
+  i_end = i_start + 8193;
+
+  Y = fft(meas1_raw.Track2(i_start:i_end));
+
+  P2 = abs(Y/L);
+  P1 = P2(1:L/2+1);
+  P1(2:end-1) = 2*P1(2:end-1);
+  X_fft(:, i) = P1;
+end
+
+figure;
+hold on;
+for i = 1:length(impacts)
+  plot(f, X_fft(:, i), '-k');
+end
+hold off;
+xlim([0, 200]);
+set(gca, 'Yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Acceleration [$m/s^2$]');
+
+% Computation of one Frequency Response Function
+% Now that we have obtained the Fourier transform of both the force input and the response signal, we can compute the Frequency Response Function from the force to the acceleration.
+
+% We then compare the result obtained with the FRF computed by the modal software (figure [[fig:frf_comparison_software]]).
+
+% The slight difference can probably be explained by the use of windows.
+
+% In the following analysis, FRF computed from the software will be used.
+
+
+meas1 = load('mat/meas_frf_coh_1.mat');
+
+figure;
+hold on;
+for i = 1:length(impacts)
+  plot(f, X_fft(:, i)./F_fft(:, i), '-k');
+end
+plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_AvSpc_2_RMS_Y_Val)
+hold off;
+xlim([0, 200]);
+set(gca, 'Yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Acceleration/Force [$m/s^2/N$]');
+
+% Frequency Response Functions and Coherence Results
+% Let's see one computed Frequency Response Function and one coherence in order to attest the quality of the measurement.
+
+% First, we load the data.
+
+meas1 = load('mat/meas_frf_coh_1.mat');
+
+
+
+% And we plot on figure [[fig:frf_result_example]] the frequency response function from the force applied in the $X$ direction at the location of the accelerometer number 11 to the acceleration in the $X$ direction as measured by the first accelerometer located on the top platform of the hexapod.
+
+% The coherence associated is shown on figure [[fig:frf_result_example]].
+
+
+figure;
+ax1 = subplot(2, 1, 1);
+plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_AvXSpc_2_1_RMS_Y_Mod);
+set(gca, 'Yscale', 'log');
+set(gca, 'XTickLabel',[]);
+ylabel('Magnitude');
+
+ax2 = subplot(2, 1, 2);
+plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_AvXSpc_2_1_RMS_Y_Phas);
+ylim([-180, 180]);
+yticks([-180, -90, 0, 90, 180]);
+xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
+
+linkaxes([ax1,ax2],'x');
+
+
+
+% #+NAME: fig:frf_result_example
+% #+CAPTION: Example of one measured FRF
+% [[file:figs/frf_result_example.png]]
+
+
+figure;
+plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_Coh_2_1_RMS_Y_Val);
+xlabel('Frequency [Hz]');
+ylabel('Coherence');
+
+% Generation of a FRF matrix and a Coherence matrix from the measurements
+% We want here to combine all the Frequency Response Functions measured into one big array called the *Frequency Response Matrix*.
+
+% The frequency response matrix is an $n \times p \times q$:
+% - $n$ is the number of measurements: $23 \times 3$ (23 accelerometers measuring 3 directions each)
+% - $p$ is the number of excitation inputs: $3$
+% - $q$ is the number of frequency points $\omega_i$
+
+% Thus, the FRF matrix is an $69 \times 3 \times 801$ matrix.
+
+
+% #+begin_important
+% For each frequency point $\omega_i$, we obtain a 2D matrix:
+% \begin{equation}
+%   \text{FRF}(\omega_i) = \begin{bmatrix}
+%   \frac{D_{1_x}}{F_x}(\omega_i) & \frac{D_{1_x}}{F_y}(\omega_i) & \frac{D_{1_x}}{F_z}(\omega_i) \\
+%   \frac{D_{1_y}}{F_x}(\omega_i) & \frac{D_{1_y}}{F_y}(\omega_i) & \frac{D_{1_y}}{F_z}(\omega_i) \\
+%   \frac{D_{1_z}}{F_x}(\omega_i) & \frac{D_{1_z}}{F_y}(\omega_i) & \frac{D_{1_z}}{F_z}(\omega_i) \\
+%   \frac{D_{2_x}}{F_x}(\omega_i) & \frac{D_{2_x}}{F_y}(\omega_i) & \frac{D_{2_x}}{F_z}(\omega_i) \\
+%   \vdots              & \vdots              & \vdots              \\
+%   \frac{D_{23_z}}{F_x}(\omega_i) & \frac{D_{23_z}}{F_y}(\omega_i) & \frac{D_{23_z}}{F_z}(\omega_i) \\
+% \end{bmatrix}
+% \end{equation}
+% #+end_important
+
+% We generate such FRF matrix from the measurements using the following script.
+
+n_meas = 24;
+n_acc = 23;
+
+dirs = 'XYZ';
+
+% Number of Accelerometer * DOF for each acccelerometer / Number of excitation / frequency points
+FRFs = zeros(3*n_acc, 3, 801);
+COHs = zeros(3*n_acc, 3, 801);
+
+% Loop through measurements
+for i = 1:n_meas
+  % Load the measurement file
+  meas = load(sprintf('mat/meas_frf_coh_%i.mat', i));
+
+  % First: determine what is the exitation (direction and sign)
+  exc_dir = meas.FFT1_AvXSpc_2_1_RMS_RfName(end);
+  exc_sign = meas.FFT1_AvXSpc_2_1_RMS_RfName(end-1);
+  % Determine what is the correct excitation sign
+  exc_factor = str2num([exc_sign, '1']);
+  if exc_dir ~= 'Z'
+    exc_factor = exc_factor*(-1);
+  end
+
+  % Then: loop through the nine measurements and store them at the correct location
+  for j = 2:10
+    % Determine what is the accelerometer and direction
+    [indices_acc_i] = strfind(meas.(sprintf('FFT1_H1_%i_1_RpName', j)), '.');
+    acc_i = str2num(meas.(sprintf('FFT1_H1_%i_1_RpName', j))(indices_acc_i(1)+1:indices_acc_i(2)-1));
+
+    meas_dir  = meas.(sprintf('FFT1_H1_%i_1_RpName', j))(end);
+    meas_sign = meas.(sprintf('FFT1_H1_%i_1_RpName', j))(end-1);
+    % Determine what is the correct measurement sign
+    meas_factor = str2num([meas_sign, '1']);
+    if meas_dir ~= 'Z'
+      meas_factor = meas_factor*(-1);
+    end
+
+    % FRFs(acc_i+n_acc*(find(dirs==meas_dir)-1), find(dirs==exc_dir), :) = exc_factor*meas_factor*meas.(sprintf('FFT1_H1_%i_1_Y_ReIm', j));
+    % COHs(acc_i+n_acc*(find(dirs==meas_dir)-1), find(dirs==exc_dir), :) = meas.(sprintf('FFT1_Coh_%i_1_RMS_Y_Val', j));
+
+    FRFs(find(dirs==meas_dir)+3*(acc_i-1), find(dirs==exc_dir), :) = exc_factor*meas_factor*meas.(sprintf('FFT1_H1_%i_1_Y_ReIm', j));
+    COHs(find(dirs==meas_dir)+3*(acc_i-1), find(dirs==exc_dir), :) = meas.(sprintf('FFT1_Coh_%i_1_RMS_Y_Val', j));
+  end
+end
+freqs = meas.FFT1_Coh_10_1_RMS_X_Val;
+
+
+
+% And we save the obtained FRF matrix and Coherence matrix in a =.mat= file.
+
+save('./mat/frf_coh_matrices.mat', 'FRFs', 'COHs', 'freqs');