diff --git a/disturbance-control-system/figs/psd_hexa_driver.png b/disturbance-control-system/figs/psd_hexa_driver.png index 2840793..9530d14 100644 Binary files a/disturbance-control-system/figs/psd_hexa_driver.png and b/disturbance-control-system/figs/psd_hexa_driver.png differ diff --git a/disturbance-control-system/figs/psd_hexa_driver_high_freq.png b/disturbance-control-system/figs/psd_hexa_driver_high_freq.png index 051f81d..5b92891 100644 Binary files a/disturbance-control-system/figs/psd_hexa_driver_high_freq.png and b/disturbance-control-system/figs/psd_hexa_driver_high_freq.png differ diff --git a/disturbance-control-system/figs/psd_marble_comp.png b/disturbance-control-system/figs/psd_marble_comp.png index ae7dba1..ac56732 100644 Binary files a/disturbance-control-system/figs/psd_marble_comp.png and b/disturbance-control-system/figs/psd_marble_comp.png differ diff --git a/disturbance-control-system/figs/psd_marble_comp_high_freq.png b/disturbance-control-system/figs/psd_marble_comp_high_freq.png index 79d0c6b..98ef721 100644 Binary files a/disturbance-control-system/figs/psd_marble_comp_high_freq.png and b/disturbance-control-system/figs/psd_marble_comp_high_freq.png differ diff --git a/disturbance-control-system/figs/psd_marble_comp_lpf.png b/disturbance-control-system/figs/psd_marble_comp_lpf.png index 3506ee8..8cab760 100644 Binary files a/disturbance-control-system/figs/psd_marble_comp_lpf.png and b/disturbance-control-system/figs/psd_marble_comp_lpf.png differ diff --git a/disturbance-control-system/figs/psd_marble_lpf_high_freq.png b/disturbance-control-system/figs/psd_marble_lpf_high_freq.png new file mode 100644 index 0000000..c671fa9 Binary files /dev/null and b/disturbance-control-system/figs/psd_marble_lpf_high_freq.png differ diff --git a/disturbance-control-system/figs/psd_sample_comp.png b/disturbance-control-system/figs/psd_sample_comp.png index 97ca8ea..f6717bc 100644 Binary files a/disturbance-control-system/figs/psd_sample_comp.png and b/disturbance-control-system/figs/psd_sample_comp.png differ diff --git a/disturbance-control-system/figs/psd_sample_comp_high_freq.png b/disturbance-control-system/figs/psd_sample_comp_high_freq.png index fd4fdd7..652f25f 100644 Binary files a/disturbance-control-system/figs/psd_sample_comp_high_freq.png and b/disturbance-control-system/figs/psd_sample_comp_high_freq.png differ diff --git a/disturbance-control-system/figs/psd_sample_comp_high_freq_lpf.png b/disturbance-control-system/figs/psd_sample_comp_high_freq_lpf.png index 4e35837..b12cb30 100644 Binary files a/disturbance-control-system/figs/psd_sample_comp_high_freq_lpf.png and b/disturbance-control-system/figs/psd_sample_comp_high_freq_lpf.png differ diff --git a/disturbance-control-system/figs/psd_sample_comp_lpf.png b/disturbance-control-system/figs/psd_sample_comp_lpf.png index 97f1d67..cb4cd89 100644 Binary files a/disturbance-control-system/figs/psd_sample_comp_lpf.png and b/disturbance-control-system/figs/psd_sample_comp_lpf.png differ diff --git a/disturbance-control-system/figs/time_domain_hexa_driver.png b/disturbance-control-system/figs/time_domain_hexa_driver.png index f9443ef..b78702c 100644 Binary files a/disturbance-control-system/figs/time_domain_hexa_driver.png and b/disturbance-control-system/figs/time_domain_hexa_driver.png differ diff --git a/disturbance-control-system/figs/time_domain_marble.png b/disturbance-control-system/figs/time_domain_marble.png index 755760b..3dbaea3 100644 Binary files a/disturbance-control-system/figs/time_domain_marble.png and b/disturbance-control-system/figs/time_domain_marble.png differ diff --git a/disturbance-control-system/figs/time_domain_marble_lpf.png b/disturbance-control-system/figs/time_domain_marble_lpf.png index 0549e6f..f27edc6 100644 Binary files a/disturbance-control-system/figs/time_domain_marble_lpf.png and b/disturbance-control-system/figs/time_domain_marble_lpf.png differ diff --git a/disturbance-control-system/figs/time_domain_relative_disp.png b/disturbance-control-system/figs/time_domain_relative_disp.png index 87a90f9..f71c91d 100644 Binary files a/disturbance-control-system/figs/time_domain_relative_disp.png and b/disturbance-control-system/figs/time_domain_relative_disp.png differ diff --git a/disturbance-control-system/figs/time_domain_sample.png b/disturbance-control-system/figs/time_domain_sample.png index 6518c28..78e524a 100644 Binary files a/disturbance-control-system/figs/time_domain_sample.png and b/disturbance-control-system/figs/time_domain_sample.png differ diff --git a/disturbance-control-system/figs/time_domain_sample_lpf.png b/disturbance-control-system/figs/time_domain_sample_lpf.png index c2bd996..5e875ff 100644 Binary files a/disturbance-control-system/figs/time_domain_sample_lpf.png and b/disturbance-control-system/figs/time_domain_sample_lpf.png differ diff --git a/disturbance-control-system/index.html b/disturbance-control-system/index.html index 3ec0cae..4b14d1c 100644 --- a/disturbance-control-system/index.html +++ b/disturbance-control-system/index.html @@ -1,198 +1,14 @@ + - + - Effect on the control system of each stages on the vibration of the station - @@ -200,52 +16,6 @@ -
@@ -258,79 +28,76 @@ for the JavaScript code in this tag.

Table of Contents

- -

This file is organized as follow:

-
-

1 Effect of all the control systems on the Sample vibrations

+
+

1 Effect of all the control systems on the Sample vibrations

- +

@@ -340,8 +107,8 @@ All the files (data and Matlab scripts) are accessible -

1.1 Experimental Setup

+
+

1.1 Experimental Setup

We here measure the signals of two L22 geophones: @@ -369,7 +136,7 @@ First, all the control systems are turned ON, then, they are turned one by one. Each measurement are done during 50s.

- +
@@ -489,76 +256,76 @@ Each of the mat file contains one array data with 3 co -
-

1.2 Load data

+
+

1.2 Load data

We load the data of the z axis of two geophones.

-
d3 = load('mat/data_003.mat', 'data'); d3 = d3.data;
-d4 = load('mat/data_004.mat', 'data'); d4 = d4.data;
-d5 = load('mat/data_005.mat', 'data'); d5 = d5.data;
-d6 = load('mat/data_006.mat', 'data'); d6 = d6.data;
-d7 = load('mat/data_007.mat', 'data'); d7 = d7.data;
-d8 = load('mat/data_008.mat', 'data'); d8 = d8.data;
+
d3 = load('mat/data_003.mat', 'data'); d3 = d3.data;
+d4 = load('mat/data_004.mat', 'data'); d4 = d4.data;
+d5 = load('mat/data_005.mat', 'data'); d5 = d5.data;
+d6 = load('mat/data_006.mat', 'data'); d6 = d6.data;
+d7 = load('mat/data_007.mat', 'data'); d7 = d7.data;
+d8 = load('mat/data_008.mat', 'data'); d8 = d8.data;
-
-

1.3 Analysis - Time Domain

+
+

1.3 Analysis - Time Domain

First, we can look at the time domain data and compare all the measurements:

    -
  • comparison for the geophone at the sample location (figure 1)
    • -
  • comparison for the geophone on the granite (figure 2)
    • +
  • comparison for the geophone at the sample location (figure 1)
    • +
  • comparison for the geophone on the granite (figure 2)
-
figure;
+
figure;
 hold on;
-plot(d3(:, 3), d3(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
-plot(d4(:, 3), d4(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry');
-plot(d5(:, 3), d5(:, 2), 'DisplayName', 'Hexa, Rz, SR');
-plot(d6(:, 3), d6(:, 2), 'DisplayName', 'Hexa, Rz');
-plot(d7(:, 3), d7(:, 2), 'DisplayName', 'Hexa');
-plot(d8(:, 3), d8(:, 2), 'DisplayName', 'All OFF');
+plot(d3(:, 3), d3(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
+plot(d4(:, 3), d4(:, 2), 'DisplayName', 'Hexa, Rz, SR, Ry');
+plot(d5(:, 3), d5(:, 2), 'DisplayName', 'Hexa, Rz, SR');
+plot(d6(:, 3), d6(:, 2), 'DisplayName', 'Hexa, Rz');
+plot(d7(:, 3), d7(:, 2), 'DisplayName', 'Hexa');
+plot(d8(:, 3), d8(:, 2), 'DisplayName', 'All OFF');
 hold off;
-xlabel('Time [s]'); ylabel('Voltage [V]');
-xlim([0, 50]);
-legend('Location', 'bestoutside');
+xlabel('Time [s]'); ylabel('Voltage [V]');
+xlim([0, 50]);
+legend('Location', 'bestoutside');
-
+

time_domain_sample.png

Figure 1: Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location

-
figure;
+
figure;
 hold on;
-plot(d3(:, 3), d3(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
-plot(d4(:, 3), d4(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry');
-plot(d5(:, 3), d5(:, 1), 'DisplayName', 'Hexa, Rz, SR');
-plot(d6(:, 3), d6(:, 1), 'DisplayName', 'Hexa, Rz');
-plot(d7(:, 3), d7(:, 1), 'DisplayName', 'Hexa');
-plot(d8(:, 3), d8(:, 1), 'DisplayName', 'All OFF');
+plot(d3(:, 3), d3(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
+plot(d4(:, 3), d4(:, 1), 'DisplayName', 'Hexa, Rz, SR, Ry');
+plot(d5(:, 3), d5(:, 1), 'DisplayName', 'Hexa, Rz, SR');
+plot(d6(:, 3), d6(:, 1), 'DisplayName', 'Hexa, Rz');
+plot(d7(:, 3), d7(:, 1), 'DisplayName', 'Hexa');
+plot(d8(:, 3), d8(:, 1), 'DisplayName', 'All OFF');
 hold off;
-xlabel('Time [s]'); ylabel('Voltage [V]');
-xlim([0, 50]);
-legend('Location', 'bestoutside');
+xlabel('Time [s]'); ylabel('Voltage [V]');
+xlim([0, 50]);
+legend('Location', 'bestoutside');
-
+

time_domain_marble.png

Figure 2: Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble

@@ -566,66 +333,64 @@ legend( -

1.4 Analysis - Frequency Domain

+
+

1.4 Analysis - Frequency Domain

-
dt = d3(2, 3) - d3(1, 3);
+
dt = d3(2, 3) - d3(1, 3);
 
-Fs = 1/dt;
-win = hanning(ceil(10*Fs));
+Fs = 1/dt;
+win = hanning(ceil(10*Fs));
-
-

1.4.1 Vibrations at the sample location

+
+

1.4.1 Vibrations at the sample location

First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.

-
[px3, f] = pwelch(d3(:, 2), win, [], [], Fs);
-[px4, ~] = pwelch(d4(:, 2), win, [], [], Fs);
-[px5, ~] = pwelch(d5(:, 2), win, [], [], Fs);
-[px6, ~] = pwelch(d6(:, 2), win, [], [], Fs);
-[px7, ~] = pwelch(d7(:, 2), win, [], [], Fs);
-[px8, ~] = pwelch(d8(:, 2), win, [], [], Fs);
+
[px3, f] = pwelch(d3(:, 2), win, [], [], Fs);
+[px4, ~] = pwelch(d4(:, 2), win, [], [], Fs);
+[px5, ~] = pwelch(d5(:, 2), win, [], [], Fs);
+[px6, ~] = pwelch(d6(:, 2), win, [], [], Fs);
+[px7, ~] = pwelch(d7(:, 2), win, [], [], Fs);
+[px8, ~] = pwelch(d8(:, 2), win, [], [], Fs);

-And we compare all the signals (figures 3 and 4). +And we compare all the signals (figures 3 and 4).

-
figure;
+
figure;
 hold on;
-plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
-plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
-plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
-plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
-plot(f, sqrt(px7), 'DisplayName', 'Hexa');
-plot(f, sqrt(px8), 'DisplayName', 'All OFF');
-plot(fgm, sqrt(pxxgm), '-k', 'DisplayName', 'Ground Velocity');
+plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
+plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
+plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
+plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
+plot(f, sqrt(px7), 'DisplayName', 'Hexa');
+plot(f, sqrt(px8), 'DisplayName', 'All OFF');
 hold off;
-set(gca, 'xscale', 'log');
-set(gca, 'yscale', 'log');
-xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
-xlim([0.1, 500]);
-legend('Location', 'southwest');
+set(gca, 'xscale', 'log');
+set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
+xlim([0.1, 500]);
+legend('Location', 'southwest');
-
+

psd_sample_comp.png

Figure 3: Amplitude Spectral Density of the signal coming from the top geophone

- -
+

psd_sample_comp_high_freq.png

Figure 4: Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)

@@ -633,54 +398,52 @@ legend( -

1.4.2 Vibrations on the marble

+
+

1.4.2 Vibrations on the marble

Now we plot the same curves for the geophone located on the marble.

-
[px3, f] = pwelch(d3(:, 1), win, [], [], Fs);
-[px4, ~] = pwelch(d4(:, 1), win, [], [], Fs);
-[px5, ~] = pwelch(d5(:, 1), win, [], [], Fs);
-[px6, ~] = pwelch(d6(:, 1), win, [], [], Fs);
-[px7, ~] = pwelch(d7(:, 1), win, [], [], Fs);
-[px8, ~] = pwelch(d8(:, 1), win, [], [], Fs);
+
[px3, f] = pwelch(d3(:, 1), win, [], [], Fs);
+[px4, ~] = pwelch(d4(:, 1), win, [], [], Fs);
+[px5, ~] = pwelch(d5(:, 1), win, [], [], Fs);
+[px6, ~] = pwelch(d6(:, 1), win, [], [], Fs);
+[px7, ~] = pwelch(d7(:, 1), win, [], [], Fs);
+[px8, ~] = pwelch(d8(:, 1), win, [], [], Fs);

-And we compare the Amplitude Spectral Densities (figures 5 and 6) +And we compare the Amplitude Spectral Densities (figures 5 and 6)

-
figure;
+
figure;
 hold on;
-plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
-plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
-plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
-plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
-plot(f, sqrt(px7), 'DisplayName', 'Hexa');
-plot(f, sqrt(px8), 'DisplayName', 'All OFF');
-plot(fgm, sqrt(pxxgm), '-k', 'DisplayName', 'Ground Velocity');
+plot(f, sqrt(px3), 'DisplayName', 'Hexa, Rz, SR, Ry, Ty');
+plot(f, sqrt(px4), 'DisplayName', 'Hexa, Rz, SR, Ry');
+plot(f, sqrt(px5), 'DisplayName', 'Hexa, Rz, SR');
+plot(f, sqrt(px6), 'DisplayName', 'Hexa, Rz');
+plot(f, sqrt(px7), 'DisplayName', 'Hexa');
+plot(f, sqrt(px8), 'DisplayName', 'All OFF');
 hold off;
-set(gca, 'xscale', 'log');
-set(gca, 'yscale', 'log');
-xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
-xlim([0.1, 500]);
-legend('Location', 'northeast');
+set(gca, 'xscale', 'log');
+set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{V}{\sqrt{Hz}}\right]$')
+xlim([0.1, 500]);
+legend('Location', 'northeast');
-
+

psd_marble_comp.png

Figure 5: Amplitude Spectral Density of the signal coming from the top geophone

- -
+

psd_marble_comp_high_freq.png

Figure 6: Amplitude Spectral Density of the signal coming from the top geophone (zoom at high frequencies)

@@ -689,8 +452,8 @@ legend( -

1.5 Conclusion

+
+

1.5 Conclusion

Table 1: Summary of the measurements and the states of the control systems
+
@@ -873,7 +636,7 @@ Each of the mat file contains one array data with 3 co
Table 2: Summary of the measurements and the states of the control systems
-
+

IMG_20190507_101459.jpg

Figure 7: Voltage amplifier settings for the measurement

@@ -881,129 +644,128 @@ Each of the mat file contains one array data with 3 co
-
-

2.2 Load data

+
+

2.2 Load data

We load the data of the z axis of two geophones.

-
d_of = load('mat/data_013.mat', 'data'); d_of = d_of.data;
-d_ty = load('mat/data_014.mat', 'data'); d_ty = d_ty.data;
-d_ry = load('mat/data_015.mat', 'data'); d_ry = d_ry.data;
-d_sr = load('mat/data_016.mat', 'data'); d_sr = d_sr.data;
-d_rz = load('mat/data_017.mat', 'data'); d_rz = d_rz.data;
-d_he = load('mat/data_018.mat', 'data'); d_he = d_he.data;
+
d_of = load('mat/data_013.mat', 'data'); d_of = d_of.data;
+d_ty = load('mat/data_014.mat', 'data'); d_ty = d_ty.data;
+d_ry = load('mat/data_015.mat', 'data'); d_ry = d_ry.data;
+d_sr = load('mat/data_016.mat', 'data'); d_sr = d_sr.data;
+d_rz = load('mat/data_017.mat', 'data'); d_rz = d_rz.data;
+d_he = load('mat/data_018.mat', 'data'); d_he = d_he.data;
-
-

2.3 Voltage to Velocity

+
+

2.3 Voltage to Velocity

-We convert the measured voltage to velocity using the function voltageToVelocityL22 (accessible here). +We convert the measured voltage to velocity using the function voltageToVelocityL22 (accessible here).

-
gain = 60; % [dB]
+
gain = 60; % [dB]
 
-d_of(:, 1) = voltageToVelocityL22(d_of(:, 1), d_of(:, 3), gain);
-d_ty(:, 1) = voltageToVelocityL22(d_ty(:, 1), d_ty(:, 3), gain);
-d_ry(:, 1) = voltageToVelocityL22(d_ry(:, 1), d_ry(:, 3), gain);
-d_sr(:, 1) = voltageToVelocityL22(d_sr(:, 1), d_sr(:, 3), gain);
-d_rz(:, 1) = voltageToVelocityL22(d_rz(:, 1), d_rz(:, 3), gain);
-d_he(:, 1) = voltageToVelocityL22(d_he(:, 1), d_he(:, 3), gain);
+d_of(:, 1) = voltageToVelocityL22(d_of(:, 1), d_of(:, 3), gain);
+d_ty(:, 1) = voltageToVelocityL22(d_ty(:, 1), d_ty(:, 3), gain);
+d_ry(:, 1) = voltageToVelocityL22(d_ry(:, 1), d_ry(:, 3), gain);
+d_sr(:, 1) = voltageToVelocityL22(d_sr(:, 1), d_sr(:, 3), gain);
+d_rz(:, 1) = voltageToVelocityL22(d_rz(:, 1), d_rz(:, 3), gain);
+d_he(:, 1) = voltageToVelocityL22(d_he(:, 1), d_he(:, 3), gain);
 
-d_of(:, 2) = voltageToVelocityL22(d_of(:, 2), d_of(:, 3), gain);
-d_ty(:, 2) = voltageToVelocityL22(d_ty(:, 2), d_ty(:, 3), gain);
-d_ry(:, 2) = voltageToVelocityL22(d_ry(:, 2), d_ry(:, 3), gain);
-d_sr(:, 2) = voltageToVelocityL22(d_sr(:, 2), d_sr(:, 3), gain);
-d_rz(:, 2) = voltageToVelocityL22(d_rz(:, 2), d_rz(:, 3), gain);
-d_he(:, 2) = voltageToVelocityL22(d_he(:, 2), d_he(:, 3), gain);
+d_of(:, 2) = voltageToVelocityL22(d_of(:, 2), d_of(:, 3), gain);
+d_ty(:, 2) = voltageToVelocityL22(d_ty(:, 2), d_ty(:, 3), gain);
+d_ry(:, 2) = voltageToVelocityL22(d_ry(:, 2), d_ry(:, 3), gain);
+d_sr(:, 2) = voltageToVelocityL22(d_sr(:, 2), d_sr(:, 3), gain);
+d_rz(:, 2) = voltageToVelocityL22(d_rz(:, 2), d_rz(:, 3), gain);
+d_he(:, 2) = voltageToVelocityL22(d_he(:, 2), d_he(:, 3), gain);
-
-

2.4 Analysis - Time Domain

+
+

2.4 Analysis - Time Domain

First, we can look at the time domain data and compare all the measurements:

    -
  • comparison for the geophone at the sample location (figure 8)
    • -
  • comparison for the geophone on the granite (figure 9)
    • -
  • relative displacement of the sample with respect to the marble (figure 9)
    • +
  • comparison for the geophone at the sample location (figure 8)
    • +
  • comparison for the geophone on the granite (figure 9)
    • +
  • relative displacement of the sample with respect to the marble (figure 9)
-
figure;
+
figure;
 hold on;
-plot(d_of(:, 3), d_of(:, 2), 'DisplayName', 'All OFF');
-plot(d_ty(:, 3), d_ty(:, 2), 'DisplayName', 'Ty ON');
-plot(d_ry(:, 3), d_ry(:, 2), 'DisplayName', 'Ry ON');
-plot(d_sr(:, 3), d_sr(:, 2), 'DisplayName', 'S-R ON');
-plot(d_rz(:, 3), d_rz(:, 2), 'DisplayName', 'Rz ON');
-plot(d_he(:, 3), d_he(:, 2), 'DisplayName', 'Hexa ON');
+plot(d_of(:, 3), d_of(:, 2), 'DisplayName', 'All OFF');
+plot(d_ty(:, 3), d_ty(:, 2), 'DisplayName', 'Ty ON');
+plot(d_ry(:, 3), d_ry(:, 2), 'DisplayName', 'Ry ON');
+plot(d_sr(:, 3), d_sr(:, 2), 'DisplayName', 'S-R ON');
+plot(d_rz(:, 3), d_rz(:, 2), 'DisplayName', 'Rz ON');
+plot(d_he(:, 3), d_he(:, 2), 'DisplayName', 'Hexa ON');
 hold off;
-xlabel('Time [s]'); ylabel('Velocity [m/s]');
-xlim([0, 50]);
-legend('Location', 'bestoutside');
+xlabel('Time [s]'); ylabel('Velocity [m/s]');
+xlim([0, 50]);
+legend('Location', 'bestoutside');
-
+

time_domain_sample_lpf.png

Figure 8: Comparison of the time domain data when turning off the control system of the stages - Geophone at the sample location

-
-
figure;
+
figure;
 hold on;
-plot(d_of(:, 3), d_of(:, 1), 'DisplayName', 'All OFF');
-plot(d_ty(:, 3), d_ty(:, 1), 'DisplayName', 'Ty ON');
-plot(d_ry(:, 3), d_ry(:, 1), 'DisplayName', 'Ry ON');
-plot(d_sr(:, 3), d_sr(:, 1), 'DisplayName', 'S-R ON');
-plot(d_rz(:, 3), d_rz(:, 1), 'DisplayName', 'Rz ON');
-plot(d_he(:, 3), d_he(:, 1), 'DisplayName', 'Hexa ON');
+plot(d_of(:, 3), d_of(:, 1), 'DisplayName', 'All OFF');
+plot(d_ty(:, 3), d_ty(:, 1), 'DisplayName', 'Ty ON');
+plot(d_ry(:, 3), d_ry(:, 1), 'DisplayName', 'Ry ON');
+plot(d_sr(:, 3), d_sr(:, 1), 'DisplayName', 'S-R ON');
+plot(d_rz(:, 3), d_rz(:, 1), 'DisplayName', 'Rz ON');
+plot(d_he(:, 3), d_he(:, 1), 'DisplayName', 'Hexa ON');
 hold off;
-xlabel('Time [s]'); ylabel('Velocity [m/s]');
-xlim([0, 50]);
-legend('Location', 'bestoutside');
+xlabel('Time [s]'); ylabel('Velocity [m/s]');
+xlim([0, 50]);
+legend('Location', 'bestoutside');
-
+

time_domain_marble_lpf.png

Figure 9: Comparison of the time domain data when turning off the control system of the stages - Geophone on the marble

-
figure;
+
figure;
 hold on;
-plot(d_of(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_of(:, 2)-d_of(:, 1), d_of(:, 3)), 'DisplayName', 'All OFF');
-plot(d_ty(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_ty(:, 2)-d_ty(:, 1), d_ty(:, 3)), 'DisplayName', 'Ty ON');
-plot(d_ry(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_ry(:, 2)-d_ry(:, 1), d_ry(:, 3)), 'DisplayName', 'Ry ON');
-plot(d_sr(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_sr(:, 2)-d_sr(:, 1), d_sr(:, 3)), 'DisplayName', 'S-R ON');
-plot(d_rz(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_rz(:, 2)-d_rz(:, 1), d_rz(:, 3)), 'DisplayName', 'Rz ON');
-plot(d_he(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_he(:, 2)-d_he(:, 1), d_he(:, 3)), 'DisplayName', 'Hexa ON');
+plot(d_of(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_of(:, 2)-d_of(:, 1), d_of(:, 3)), 'DisplayName', 'All OFF');
+plot(d_ty(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_ty(:, 2)-d_ty(:, 1), d_ty(:, 3)), 'DisplayName', 'Ty ON');
+plot(d_ry(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_ry(:, 2)-d_ry(:, 1), d_ry(:, 3)), 'DisplayName', 'Ry ON');
+plot(d_sr(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_sr(:, 2)-d_sr(:, 1), d_sr(:, 3)), 'DisplayName', 'S-R ON');
+plot(d_rz(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_rz(:, 2)-d_rz(:, 1), d_rz(:, 3)), 'DisplayName', 'Rz ON');
+plot(d_he(:, 3), 1e6*lsim(1/(1+s/(2*pi*0.5)), d_he(:, 2)-d_he(:, 1), d_he(:, 3)), 'DisplayName', 'Hexa ON');
 hold off;
-xlabel('Time [s]'); ylabel('Relative Displacement [$\mu m$]');
-xlim([0, 50]);
-legend('Location', 'bestoutside');
+xlabel('Time [s]'); ylabel('Relative Displacement [$\mu m$]');
+xlim([0, 50]);
+legend('Location', 'bestoutside');
-
+

time_domain_relative_disp.png

Figure 10: Relative displacement of the sample with respect to the marble

@@ -1011,57 +773,57 @@ legend( -

2.5 Analysis - Frequency Domain

+
+

2.5 Analysis - Frequency Domain

-
dt = d_of(2, 3) - d_of(1, 3);
+
dt = d_of(2, 3) - d_of(1, 3);
 
-Fs = 1/dt;
-win = hanning(ceil(10*Fs));
+Fs = 1/dt;
+win = hanning(ceil(10*Fs));
-
-

2.5.1 Vibrations at the sample location

+
+

2.5.1 Vibrations at the sample location

First, we compute the Power Spectral Density of the signals coming from the Geophone located at the sample location.

-
[px_of, f] = pwelch(d_of(:, 2), win, [], [], Fs);
-[px_ty, ~] = pwelch(d_ty(:, 2), win, [], [], Fs);
-[px_ry, ~] = pwelch(d_ry(:, 2), win, [], [], Fs);
-[px_sr, ~] = pwelch(d_sr(:, 2), win, [], [], Fs);
-[px_rz, ~] = pwelch(d_rz(:, 2), win, [], [], Fs);
-[px_he, ~] = pwelch(d_he(:, 2), win, [], [], Fs);
+
[px_of, f] = pwelch(d_of(:, 2), win, [], [], Fs);
+[px_ty, ~] = pwelch(d_ty(:, 2), win, [], [], Fs);
+[px_ry, ~] = pwelch(d_ry(:, 2), win, [], [], Fs);
+[px_sr, ~] = pwelch(d_sr(:, 2), win, [], [], Fs);
+[px_rz, ~] = pwelch(d_rz(:, 2), win, [], [], Fs);
+[px_he, ~] = pwelch(d_he(:, 2), win, [], [], Fs);

-And we compare all the signals (figures 11 and 12). +And we compare all the signals (figures 11 and 12).

-
figure;
+
figure;
 hold on;
-plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
-plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
-plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
-plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
-plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
-plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
+plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
+plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
+plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
+plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
+plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
+plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
 hold off;
-set(gca, 'xscale', 'log');
-set(gca, 'yscale', 'log');
-xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
-xlim([0.1, 500]);
-legend('Location', 'southwest');
+set(gca, 'xscale', 'log');
+set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
+xlim([0.1, 500]);
+legend('Location', 'southwest');
-
+

psd_sample_comp_lpf.png

Figure 11: Amplitude Spectral Density of the sample velocity

@@ -1069,7 +831,7 @@ legend( +

psd_sample_comp_high_freq_lpf.png

Figure 12: Amplitude Spectral Density of the sample velocity (zoom at high frequencies)

@@ -1077,54 +839,53 @@ legend( -

2.5.2 Vibrations on the marble

+
+

2.5.2 Vibrations on the marble

Now we plot the same curves for the geophone located on the marble.

-
[px_of, f] = pwelch(d_of(:, 1), win, [], [], Fs);
-[px_ty, ~] = pwelch(d_ty(:, 1), win, [], [], Fs);
-[px_ry, ~] = pwelch(d_ry(:, 1), win, [], [], Fs);
-[px_sr, ~] = pwelch(d_sr(:, 1), win, [], [], Fs);
-[px_rz, ~] = pwelch(d_rz(:, 1), win, [], [], Fs);
-[px_he, ~] = pwelch(d_he(:, 1), win, [], [], Fs);
+
[px_of, f] = pwelch(d_of(:, 1), win, [], [], Fs);
+[px_ty, ~] = pwelch(d_ty(:, 1), win, [], [], Fs);
+[px_ry, ~] = pwelch(d_ry(:, 1), win, [], [], Fs);
+[px_sr, ~] = pwelch(d_sr(:, 1), win, [], [], Fs);
+[px_rz, ~] = pwelch(d_rz(:, 1), win, [], [], Fs);
+[px_he, ~] = pwelch(d_he(:, 1), win, [], [], Fs);

-And we compare the Amplitude Spectral Densities (figures 13 and 14) +And we compare the Amplitude Spectral Densities (figures 13 and 14)

-
figure;
+
figure;
 hold on;
-plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
-plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
-plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
-plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
-plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
-plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
+plot(f, sqrt(px_of), 'DisplayName', 'All OFF');
+plot(f, sqrt(px_ty), 'DisplayName', 'Ty ON');
+plot(f, sqrt(px_ry), 'DisplayName', 'Ry ON');
+plot(f, sqrt(px_sr), 'DisplayName', 'S-R ON');
+plot(f, sqrt(px_rz), 'DisplayName', 'Rz ON');
+plot(f, sqrt(px_he), 'DisplayName', 'Hexa ON');
 hold off;
-set(gca, 'xscale', 'log');
-set(gca, 'yscale', 'log');
-xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
-xlim([0.1, 500]);
-legend('Location', 'northeast');
+set(gca, 'xscale', 'log');
+set(gca, 'yscale', 'log');
+xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
+xlim([0.1, 500]);
+legend('Location', 'northeast');
-
+

psd_marble_comp_lpf.png

Figure 13: Amplitude Spectral Density of the marble velocity

- -
-

psd_marble_comp_lpf_high_freq.png +

+

psd_marble_lpf_high_freq.png

Figure 14: Amplitude Spectral Density of the marble velocity (zoom at high frequencies)

@@ -1132,37 +893,9 @@ legend( -

2.6 Cumulative Amplitude Spectrum

+
+

2.6 Conclusion

-
-
figure;
-hold on;
-plot(f(2:end), sqrt(cumsum(px_of(2:end)./(2*pi*f(2:end)).^2).*(f(2)-f(1))), 'DisplayName', 'All OFF');
-plot(f(2:end), sqrt(cumsum(px_ty(2:end)./(2*pi*f(2:end)).^2).*(f(2)-f(1))), 'DisplayName', 'Ty ON');
-plot(f(2:end), sqrt(cumsum(px_ry(2:end)./(2*pi*f(2:end)).^2).*(f(2)-f(1))), 'DisplayName', 'Ry ON');
-plot(f(2:end), sqrt(cumsum(px_sr(2:end)./(2*pi*f(2:end)).^2).*(f(2)-f(1))), 'DisplayName', 'S-R ON');
-plot(f(2:end), sqrt(cumsum(px_rz(2:end)./(2*pi*f(2:end)).^2).*(f(2)-f(1))), 'DisplayName', 'Rz ON');
-plot(f(2:end), sqrt(cumsum(px_he(2:end)./(2*pi*f(2:end)).^2).*(f(2)-f(1))), 'DisplayName', 'Hexa ON');
-hold off;
-set(gca, 'xscale', 'log');
-set(gca, 'yscale', 'log');
-xlabel('Frequency [Hz]'); ylabel('Amplitude Spectral Density $\left[\frac{m}{\sqrt{Hz}}\right]$')
-xlim([0.1, 500]);
-legend('Location', 'northeast');
-
-
- -
-
-
-
-
-
- -
-

2.7 Conclusion

-