Add few curves

This commit is contained in:
Thomas Dehaeze 2019-05-03 17:33:15 +02:00
parent 7aa568e55d
commit ec07f0b91e
5 changed files with 131 additions and 19 deletions

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@ -18,6 +18,8 @@
#+PROPERTY: header-args:matlab+ :output-dir figs
:END:
* Experimental Setup
* Signal Processing
** Matlab Init :noexport:ignore:
#+begin_src matlab :exports none :results silent :noweb yes
@ -33,19 +35,6 @@ Measurement =data_001.mat= corresponds to a measurement where the spindle is not
data2 = load('mat/data_002.mat', 't', 'x1', 'x2');
#+end_src
** Pre-processing
#+begin_src matlab :results none
imax = min([length(data1.t), length(data2.t)]);
data1.t = data1.t(1:imax);
data1.x1 = data1.x1(1:imax);
data1.x2 = data1.x2(1:imax);
data2.t = data2.t(1:imax);
data2.x1 = data2.x1(1:imax);
data2.x2 = data2.x2(1:imax);
#+end_src
** Time domain Data
#+begin_src matlab :results none
figure;
@ -67,17 +56,19 @@ Measurement =data_001.mat= corresponds to a measurement where the spindle is not
#+begin_src matlab :results none
dt = data1.t(2) - data1.t(1);
Fs = 1/dt;
windows_psd = hanning(ceil(10/dt));
windows_psd = hanning(ceil(10*Fs));
#+end_src
#+begin_src matlab :results none
[pxx1m, f] = pwelch(data1.x1, windows_psd, [], [], Fs);
[pxx1h, ~] = pwelch(data1.x2, windows_psd, [], [], Fs);
[pxx1m, f] = pwelch(data1.x1, windows_psd, [], [], Fs); f(1) = []; pxx1m(1) = [];
[pxx1h, ~] = pwelch(data1.x2, windows_psd, [], [], Fs); pxx1h(1) = [];
[pxx2m, ~] = pwelch(data2.x1, windows_psd, [], [], Fs);
[pxx2h, ~] = pwelch(data2.x2, windows_psd, [], [], Fs);
[pxx2m, ~] = pwelch(data2.x1, windows_psd, [], [], Fs); pxx2m(1) = [];
[pxx2h, ~] = pwelch(data2.x2, windows_psd, [], [], Fs); pxx2h(1) = [];
#+end_src
** Some plots
#+begin_src matlab :results none
figure;
hold on;
@ -120,3 +111,86 @@ Measurement =data_001.mat= corresponds to a measurement where the spindle is not
set(gca, 'XScale', 'log');
xlabel('Frequency [Hz]'); ylabel('CAS [m]')
#+end_src
** 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]].
#+begin_src matlab :results none
S0 = 88; % Sensitivity [V/(m/s)]
f0 = 2; % Cut-off frequnecy [Hz]
S = S0*(s/2/pi/f0)/(1+s/2/pi/f0);
#+end_src
We also take into account the gain of the electronics which is here set to be $60dB$.
#+begin_src matlab :results none
G0_db = 60; % [dB]
G0 = 10^(60/G0_db); % [abs]
#+end_src
We divide the ASD measured (in $\text{V}/\sqrt{\text{Hz}}$) by the gain of the voltage amplifier to obtain the ASD of the voltage across the geophone.
We further divide the result by the sensibility of the Geophone to obtain the ASD of the velocity in $m/s/\sqrt{Hz}$.
#+begin_src matlab :results none
scaling = 1./squeeze(abs(freqresp(G0*S, f, 'Hz'))); scaling(1) = 0;
#+end_src
** Computation of the ASD of the velocity
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(pxx1h).*scaling);
plot(f, sqrt(pxx2h).*scaling);
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]);
#+end_src
#+begin_src matlab :results none
figure;
hold on;
plot(f, (sqrt(pxx1).*scaling)./(2*pi*f));
plot(f, (sqrt(pxx2).*scaling)./(2*pi*f));
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]);
#+end_src
** RMS value of the difference between the two geophones
We also compute the Power Spectral Density of the difference between the two geophones. This is done in order to estimate the relative displacement of the sample with respect to the granite.
#+begin_src matlab :results none
[pxxd1, ~] = pwelch(data1.x2-data1.x1, windows_psd, [], [], Fs); pxxd1(1) = [];
[pxxd2, ~] = pwelch(data2.x2-data2.x1, windows_psd, [], [], Fs); pxxd2(1) = [];
#+end_src
#+begin_src matlab :results none
figure;
hold on;
plot(f, (sqrt(pxxd1).*scaling)./(2*pi*f));
plot(f, (sqrt(pxxd2).*scaling)./(2*pi*f));
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]);
#+end_src
#+begin_src matlab :results none
psd_d1 = ((sqrt(pxxd1).*scaling)./(2*pi*f)).^2;
psd_d2 = ((sqrt(pxxd2).*scaling)./(2*pi*f)).^2;
df = f(2) - f(1);
figure;
hold on;
plot(f, sqrt(cumsum(df.*psd_d1, 'reverse')));
plot(f, sqrt(cumsum(df.*psd_d2, 'reverse')));
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('CAS $\left[m\right]$')
xlim([0.1, 500]);
#+end_src

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*.tex
*.pdf
*.svg

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@ -82,7 +82,7 @@ We now look at the difference between the signal directly measured by the ADC an
#+begin_src matlab :results none
figure;
hold on;
plot(sr_on.t, sr_on.x1 - sr_on.x2, 'DisplayName', 'Slip-Ring - $\omega = 1rpm$');
plot(sr_on.t, sr_on.x1 - sr_on.x2, 'DisplayName', 'Slip-Ring - $\omega = 1rpm$');
plot(sr_off.t, sr_off.x1 - sr_off.x2,'DisplayName', 'Slip-Ring off');
hold off;
xlabel('Time [s]'); ylabel('Voltage [V]');
@ -101,6 +101,41 @@ We now look at the difference between the signal directly measured by the ADC an
#+RESULTS: fig:slipring_comp_signals
[[file:figs/slipring_comp_signals.png]]
#+begin_src matlab :results none
dt = sr_on.t(2) - sr_on.t(1);
Fs = 1/dt; % [Hz]
win = hanning(ceil(1*Fs));
#+end_src
#+begin_src matlab :results none
[pxx_on, f] = pwelch(sr_on.x1 - sr_on.x2, win, [], [], Fs);
[pxx_off, ~] = pwelch(sr_off.x1 - sr_off.x2, win, [], [], Fs);
#+end_src
#+begin_src matlab :results none :exports none
figure;
hold on;
plot(f, sqrt(pxx_on), 'DisplayName', 'Slip-Ring - $\omega = 1rpm$');
plot(f, sqrt(pxx_off),'DisplayName', 'Slip-Ring off');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('PSD $\left[\frac{V}{\sqrt{Hz}}\right]$');
legend('Location', 'northeast');
xlim([1, 500]);
#+end_src
#+NAME: fig:psd_noise
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
#+begin_src matlab :var filepath="figs/psd_noise.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:psd_noise
#+CAPTION: ASD of the measured noise
#+RESULTS: fig:psd_noise
[[file:figs/psd_noise.png]]
* Conclusion
#+begin_note
*Remaining questions*: