#+TITLE: Measurements
:DRAWER:
#+STARTUP: overview

#+LANGUAGE: en
#+EMAIL: dehaeze.thomas@gmail.com
#+AUTHOR: Dehaeze Thomas

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#+HTML_LINK_UP: ../index.html

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#+PROPERTY: header-args:matlab  :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :results none
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :output-dir figs

#+PROPERTY: header-args:shell  :eval no-export
:END:

* Experimental conditions

| *Date*       | 2018-01-12          |
| *Sensors*    | Geophones           |
| *Excitation* | Instrumented Hammer |
| *Location*   | Laboratory          |
| *Notes*      | Unglued Granite     |

- The granite is not glued to the floor
- FS = 512Hz
- Made by Marc Lesourd on the 12 of January 2018

*Goal*:
Obtain better coherence at low frequency.

* Measurements procedure
*Geophones*
L-28LB geophones (table [[tab:L-28LB]]) are placed on
- Marle
- Tilt Stage
- Top of Hexapod

#+NAME: tab:L-28LB
#+CAPTION: L-28LB Geophone characteristics
| Natural Frequency [Hz] |  4.5 |
| Weight [g]             |  140 |
| Sensitivity [V/(m/s)]  | 31.3 |

The structure is excited using an *instrumented hammer* with impacts on
- Marble X-Y-Z
- Hexapod X-Y-Z

* Measurement Channels
#+NAME: tab:meas_channels
#+CAPTION: Description of each measurement channel
| Ch. nb | Element  | Location       | Direction |
|--------+----------+----------------+-----------|
|      1 | Hammer   | variable       |           |
|--------+----------+----------------+-----------|
|      2 | Geophone | Marble         | X-Y-Z     |
|      3 | Geophone | Tilt stage     | X-Y-Z     |
|      4 | Geophone | Top of Hexapod | X-Y-Z     |

* Experiments
#+NAME: tab:experiments
#+CAPTION: Description of the location of direction of the excitation for each measurement
| Meas. nb | Location | Direction |
|----------+----------+-----------|
|        1 | Marble   | X         |
|        2 | Hexapod  | X         |
|----------+----------+-----------|
|        3 | Marble   | Y         |
|        4 | Hexapod  | Y         |
|----------+----------+-----------|
|        5 | Marble   | Z         |
|        6 | Hexapod  | Z         |

* Data Analysis
** Loading and pre-processing of the data
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
  <<matlab-dir>>
#+end_src

#+begin_src matlab :exports none :results silent :noweb yes
  <<matlab-init>>
#+end_src

The Geophone sensitivity is defined below:
#+begin_src matlab :results none
  w0 = 4.5*2*pi; % [rad/s]
  ksi = 0.38;
  G0 = 31.3; % [V/(m/s)]
  G = G0*(s/w0)^2/((s/w0)^2 + 2*ksi*(s/w0) + 1); % [V/(m/s)]
#+end_src

We then:
- load the data
- add a minus sign when needed
- integrate the signal to have displacement instead of velocity
- scaled with the sensitivity of the Geophone
#+begin_src matlab :exports code :results none
  load('./raw_data/freq_frf.mat') % freq_frf

  w = j*2*pi*freq_frf; % j.omega in [rad/s]

  scaling = squeeze(freqresp(G, 2*pi*freq_frf))/G0;

  load('./raw_data/frf_marble_x.mat') % ReIm1
  frf_marble_x = zeros(size(ReIm1, 1), 3);
  frf_marble_x(:, 1) = -ReIm1(:, 2)./w./scaling; % marble_x
  frf_marble_x(:, 2) = -ReIm1(:, 3)./w./scaling; % tilt_x
  frf_marble_x(:, 3) = -ReIm1(:, 4)./w./scaling; % hexa_x

  load('./raw_data/frf_hexa_x.mat') % ReIm2
  frf_hexa_x = zeros(size(ReIm2, 1), 3);
  frf_hexa_x(:, 1) = -ReIm2(:, 2)./w./scaling; % marble_x
  frf_hexa_x(:, 2) = -ReIm2(:, 3)./w./scaling; % tilt_x
  frf_hexa_x(:, 3) = -ReIm2(:, 4)./w./scaling; % hexa_x

  load('./raw_data/frf_marble_y.mat') % ReIm3
  frf_marble_y = zeros(size(ReIm3, 1), 3);
  frf_marble_y(:, 1) = -ReIm3(:, 2)./w./scaling; % marble_y
  frf_marble_y(:, 2) = -ReIm3(:, 3)./w./scaling; % tilt_y
  frf_marble_y(:, 3) = -ReIm3(:, 4)./w./scaling; % hexa_y

  load('./raw_data/frf_hexa_y.mat') % ReIm4
  frf_hexa_y = zeros(size(ReIm4, 1), 3);
  frf_hexa_y(:, 1) = ReIm4(:, 2)./w./scaling; % marble_y
  frf_hexa_y(:, 2) = ReIm4(:, 3)./w./scaling; % tilt_y
  frf_hexa_y(:, 3) = ReIm4(:, 4)./w./scaling; % hexa_y

  load('./raw_data/frf_marble_z.mat') % ReIm5
  frf_marble_z = zeros(size(ReIm5, 1), 3);
  frf_marble_z(:, 1) = ReIm5(:, 2)./w./scaling; % marble_z
  frf_marble_z(:, 2) = ReIm5(:, 3)./w./scaling; % tilt_z
  frf_marble_z(:, 3) = ReIm5(:, 4)./w./scaling; % hexa_z

  load('./raw_data/frf_hexa_z.mat') % ReIm6
  frf_hexa_z = zeros(size(ReIm6, 1), 3);
  frf_hexa_z(:, 1) = ReIm6(:, 2)./w./scaling; % marble_z
  frf_hexa_z(:, 2) = ReIm6(:, 3)./w./scaling; % tilt_z
  frf_hexa_z(:, 3) = ReIm6(:, 4)./w./scaling; % hexa_z
#+end_src

#+begin_src matlab :exports code :results none
  load('./raw_data/coher_marble_x.mat') % coh1
  coh_marble_x = zeros(size(coh1, 1), 3);
  coh_marble_x(:, 1) = coh1(:, 2); % marble_x
  coh_marble_x(:, 2) = coh1(:, 3); % tilt_x
  coh_marble_x(:, 3) = coh1(:, 4); % hexa_x

  load('./raw_data/coher_hexa_x.mat') % coh2
  coh_hexa_x = zeros(size(coh2, 1), 3);
  coh_hexa_x(:, 1) = coh2(:, 2); % marble_x
  coh_hexa_x(:, 2) = coh2(:, 3); % tilt_x
  coh_hexa_x(:, 3) = coh2(:, 4); % hexa_x

  load('./raw_data/coher_marble_y.mat') % coh3
  coh_marble_y = zeros(size(coh3, 1), 3);
  coh_marble_y(:, 1) = coh3(:, 2); % marble_y
  coh_marble_y(:, 2) = coh3(:, 3); % tilt_y
  coh_marble_y(:, 3) = coh3(:, 4); % hexa_y

  load('./raw_data/coher_hexa_y.mat') % coh4
  coh_hexa_y = zeros(size(coh4, 1), 3);
  coh_hexa_y(:, 1) = coh4(:, 2); % marble_y
  coh_hexa_y(:, 2) = coh4(:, 3); % tilt_y
  coh_hexa_y(:, 3) = coh4(:, 4); % hexa_y

  load('./raw_data/coher_marble_z.mat') % coh5
  coh_marble_z = zeros(size(coh5, 1), 3);
  coh_marble_z(:, 1) = coh5(:, 2); % marble_z
  coh_marble_z(:, 2) = coh5(:, 3); % tilt_z
  coh_marble_z(:, 3) = coh5(:, 4); % hexa_z

  load('./raw_data/coher_hexa_z.mat') % coh6
  coh_hexa_z = zeros(size(coh6, 1), 3);
  coh_hexa_z(:, 1) = coh6(:, 2); % marble_z
  coh_hexa_z(:, 2) = coh6(:, 3); % tilt_z
  coh_hexa_z(:, 3) = coh6(:, 4); % hexa_z
#+end_src

** X-direction FRF
#+begin_src matlab :exports none :results none
  figure;
  hold on;
  plot(freq_frf, abs(frf_marble_x(:, 1)), 'DisplayName', 'Marble - X');
  plot(freq_frf, abs(frf_marble_x(:, 2)), 'DisplayName', 'Ry - X');
  plot(freq_frf, abs(frf_marble_x(:, 3)), 'DisplayName', 'Hexa - X');
  hold off;
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
  xlim([5, 200]); xticks([5, 10, 20, 50, 100, 200]);
  legend('Location', 'southwest');
#+end_src

#+NAME: fig:marble_x_frf
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/marble_x_frf.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:marble_x_frf
#+CAPTION: Response to a force applied on the marble in the X direction
#+RESULTS: fig:marble_x_frf
[[file:figs/marble_x_frf.png]]


#+begin_src matlab :exports none :results none
  figure;
  hold on;
  plot(freq_frf, abs(frf_hexa_x(:, 1)), 'DisplayName', 'Marble - X');
  plot(freq_frf, abs(frf_hexa_x(:, 2)), 'DisplayName', 'Ry - X');
  plot(freq_frf, abs(frf_hexa_x(:, 3)), 'DisplayName', 'Hexa - X');
  hold off;
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
  xlim([5, 200]); xticks([5, 10, 20, 50, 100, 200]);
  legend('Location', 'southwest');
#+end_src

#+NAME: fig:hexa_x_frf
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/hexa_x_frf.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:hexa_x_frf
#+CAPTION: Response to a force applied on the hexa in the X direction
#+RESULTS: fig:hexa_x_frf
[[file:figs/hexa_x_frf.png]]

** Y-direction FRF
#+begin_src matlab :exports none :results none
  figure;
  hold on;
  plot(freq_frf, abs(frf_marble_y(:, 1)), 'DisplayName', 'Marble - Y');
  plot(freq_frf, abs(frf_marble_y(:, 2)), 'DisplayName', 'Ry - Y');
  plot(freq_frf, abs(frf_marble_y(:, 3)), 'DisplayName', 'Hexa - Y');
  hold off;
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
  xlim([5, 200]); xticks([5, 10, 20, 50, 100, 200]);
  legend('Location', 'southwest');
#+end_src

#+NAME: fig:marble_y_frf
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/marble_y_frf.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:marble_y_frf
#+CAPTION: Response to a force applied on the marble in the Y direction
#+RESULTS: fig:marble_y_frf
[[file:figs/marble_y_frf.png]]

#+begin_src matlab :exports none :results none
  figure;
  hold on;
  plot(freq_frf, abs(frf_hexa_y(:, 1)), 'DisplayName', 'Marble - Y');
  plot(freq_frf, abs(frf_hexa_y(:, 2)), 'DisplayName', 'Ry - Y');
  plot(freq_frf, abs(frf_hexa_y(:, 3)), 'DisplayName', 'Hexa - Y');
  hold off;
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
  xlim([5, 200]); xticks([5, 10, 20, 50, 100, 200]);
  legend('Location', 'southwest');
#+end_src

#+NAME: fig:hexa_y_frf
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/hexa_y_frf.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:hexa_y_frf
#+CAPTION: Response to a force applied on the hexa in the Y direction
#+RESULTS: fig:hexa_y_frf
[[file:figs/hexa_y_frf.png]]

** Z-direction FRF
#+begin_src matlab :exports none :results none
  figure;
  hold on;
  plot(freq_frf, abs(frf_marble_z(:, 1)), 'DisplayName', 'Marble - Z');
  plot(freq_frf, abs(frf_marble_z(:, 2)), 'DisplayName', 'Ry - Z');
  plot(freq_frf, abs(frf_marble_z(:, 3)), 'DisplayName', 'Hexa - Z');
  hold off;
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
  xlim([5, 200]); xticks([5, 10, 20, 50, 100, 200]);
  legend('Location', 'southwest');
#+end_src

#+NAME: fig:marble_z_frf
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/marble_z_frf.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:marble_z_frf
#+CAPTION: Response to a force applied on the marble in the Z direction
#+RESULTS: fig:marble_z_frf
[[file:figs/marble_z_frf.png]]

#+begin_src matlab :exports none :results none
  figure;
  hold on;
  plot(freq_frf, abs(frf_hexa_z(:, 1)), 'DisplayName', 'Marble - Z');
  plot(freq_frf, abs(frf_hexa_z(:, 2)), 'DisplayName', 'Ry - Z');
  plot(freq_frf, abs(frf_hexa_z(:, 3)), 'DisplayName', 'Hexa - Z');
  hold off;
  set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
  xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
  xlim([5, 200]); xticks([5, 10, 20, 50, 100, 200]);
  legend('Location', 'southwest');
#+end_src

#+NAME: fig:hexa_z_frf
#+HEADER: :tangle no :exports results :results raw :noweb yes
#+begin_src matlab :var filepath="figs/hexa_z_frf.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
  <<plt-matlab>>
#+end_src

#+NAME: fig:hexa_z_frf
#+CAPTION: Response to a force applied on the hexa in the Z direction
#+RESULTS: fig:hexa_z_frf
[[file:figs/hexa_z_frf.png]]
** Save the processed data
Finally, we save the processed data.
#+begin_src matlab :results none
  save('./data/id31_microstation_2018_01_12_frf.mat', ...
         'freq_frf', ...
         'frf_marble_x', ...
         'frf_marble_y', ...
         'frf_marble_z', ...
         'frf_hexa_x', ...
         'frf_hexa_y', ...
         'frf_hexa_z');
  save('./data/id31_microstation_2018_01_12_coh.mat', ...
         'freq_frf', ...
         'coh_marble_x', ...
         'coh_marble_y', ...
         'coh_marble_z', ...
         'coh_hexa_x', ...
         'coh_hexa_y', ...
         'coh_hexa_z');
#+end_src
* Results
#+begin_important
  - Resonances at 42Hz, 70Hz and 125Hz have been identified
  - The coherence is much better than when using accelerometers
#+end_important