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@@ -258,23 +22,24 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orga44a9d5">1. Experimental Setup</a></li>
<li><a href="#orgb5a2f1a">2. Data Analysis</a>
<li><a href="#org2422081">1. Experimental Setup</a></li>
<li><a href="#org6220fc6">2. Data Analysis</a>
<ul>
<li><a href="#org239b200">2.1. Load data</a></li>
<li><a href="#org66889bf">2.2. Voltage to Velocity</a></li>
<li><a href="#orgd049ddc">2.3. Time domain plots</a></li>
<li><a href="#orgfee57e5">2.4. Frequency Domain</a></li>
<li><a href="#org7d3ac71">2.5. Relative Motion</a></li>
<li><a href="#org1464a72">2.6. Conclusion</a></li>
<li><a href="#org122f0e9">2.1. Load data</a></li>
<li><a href="#orgaea71b5">2.2. Voltage to Velocity</a></li>
<li><a href="#org485d23f">2.3. Time domain plots</a></li>
<li><a href="#org38cf97f">2.4. Frequency Domain</a></li>
<li><a href="#orgbaa08aa">2.5. Relative Motion</a></li>
<li><a href="#orgad3b42a">2.6. Save</a></li>
<li><a href="#org0a44924">2.7. Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orga44a9d5" class="outline-2">
<h2 id="orga44a9d5"><span class="section-number-2">1</span> Experimental Setup</h2>
<div id="outline-container-org2422081" class="outline-2">
<h2 id="org2422081"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1">
<p>
<b>Setup</b>:
@@ -383,11 +148,11 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table>
<p>
A movie showing the experiment is shown on figure <a href="#org1669ed1">1</a>.
A movie showing the experiment is shown on figure <a href="#orgc1e7286">1</a>.
</p>
<div id="org1669ed1" class="figure">
<div id="orgc1e7286" class="figure">
<p><img src="./img/VID_20190510_155655.gif" alt="VID_20190510_155655.gif" width="300px" />
</p>
<p><span class="figure-number">Figure 1: </span>Movie of the experiment, rotation speed is 6rpm</p>
@@ -395,13 +160,13 @@ A movie showing the experiment is shown on figure <a href="#org1669ed1">1</a>.
</div>
</div>
<div id="outline-container-orgb5a2f1a" class="outline-2">
<h2 id="orgb5a2f1a"><span class="section-number-2">2</span> Data Analysis</h2>
<div id="outline-container-org6220fc6" class="outline-2">
<h2 id="org6220fc6"><span class="section-number-2">2</span> Data Analysis</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org73b6124"></a>
<a id="org8446070"></a>
</p>
<div class="note">
<div class="note" id="orga7b7a45">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/spindle_slip_ring_vibrations.zip">here</a>.
</p>
@@ -409,17 +174,17 @@ All the files (data and Matlab scripts) are accessible <a href="data/spindle_sli
</div>
</div>
<div id="outline-container-org239b200" class="outline-3">
<h3 id="org239b200"><span class="section-number-3">2.1</span> Load data</h3>
<div id="outline-container-org122f0e9" class="outline-3">
<h3 id="org122f0e9"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_024.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; of = of.data;
sr = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_025.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr = sr.data;
sp = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_026.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sp = sp.data;
<pre class="src src-matlab">of = load(<span class="org-string">'mat/data_024.mat'</span>, <span class="org-string">'data'</span>); of = of.data; <span class="org-comment">% OFF</span>
sr = load(<span class="org-string">'mat/data_025.mat'</span>, <span class="org-string">'data'</span>); sr = sr.data; <span class="org-comment">% Slip Ring</span>
sp = load(<span class="org-string">'mat/data_026.mat'</span>, <span class="org-string">'data'</span>); sp = sp.data; <span class="org-comment">% Spindle</span>
</pre>
</div>
<div class="warning">
<div class="warning" id="orgb2b819c">
<p>
There is a sign error for the Geophone located on top of the Hexapod.
The problem probably comes from the wiring in the Slip-Ring.
@@ -428,54 +193,54 @@ The problem probably comes from the wiring in the Slip-Ring.
</div>
<div class="org-src-container">
<pre class="src src-matlab">of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<pre class="src src-matlab">of(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>of(<span class="org-type">:</span>, 2);
sr(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>sr(<span class="org-type">:</span>, 2);
sp(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>sp(<span class="org-type">:</span>, 2);
</pre>
</div>
</div>
</div>
<div id="outline-container-org66889bf" class="outline-3">
<h3 id="org66889bf"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div id="outline-container-orgaea71b5" class="outline-3">
<h3 id="orgaea71b5"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
<div class="outline-text-3" id="text-2-2">
<p>
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="../src/index.html">here</a>).
</p>
<div class="org-src-container">
<pre class="src src-matlab">gain = <span class="org-highlight-numbers-number">60</span>; <span class="org-comment">% [dB]</span>
<pre class="src src-matlab">gain = 60; <span class="org-comment">% [dB]</span>
of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
of(<span class="org-type">:</span>, 1) = voltageToVelocityL22(of(<span class="org-type">:</span>, 1), of(<span class="org-type">:</span>, 3), gain);
sr(<span class="org-type">:</span>, 1) = voltageToVelocityL22(sr(<span class="org-type">:</span>, 1), sr(<span class="org-type">:</span>, 3), gain);
sp(<span class="org-type">:</span>, 1) = voltageToVelocityL22(sp(<span class="org-type">:</span>, 1), sp(<span class="org-type">:</span>, 3), gain);
of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
of(<span class="org-type">:</span>, 2) = voltageToVelocityL22(of(<span class="org-type">:</span>, 2), of(<span class="org-type">:</span>, 3), gain);
sr(<span class="org-type">:</span>, 2) = voltageToVelocityL22(sr(<span class="org-type">:</span>, 2), sr(<span class="org-type">:</span>, 3), gain);
sp(<span class="org-type">:</span>, 2) = voltageToVelocityL22(sp(<span class="org-type">:</span>, 2), sp(<span class="org-type">:</span>, 3), gain);
</pre>
</div>
</div>
</div>
<div id="outline-container-orgd049ddc" class="outline-3">
<h3 id="orgd049ddc"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div id="outline-container-org485d23f" class="outline-3">
<h3 id="org485d23f"><span class="section-number-3">2.3</span> Time domain plots</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot(sp(<span class="org-type">:</span>, 3), sp(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot(sr(<span class="org-type">:</span>, 3), sr(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot(of(<span class="org-type">:</span>, 3), of(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Velocity [m/s]'</span>);
xlim([0, 100]);
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
</pre>
</div>
<div id="org4e9bed0" class="figure">
<div id="org4a00ffe" class="figure">
<p><img src="figs/slip_ring_spindle_marble_time.png" alt="slip_ring_spindle_marble_time.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Velocity as measured by the geophone located on the marble - Time domain</p>
@@ -484,25 +249,25 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle and Slip-Ring'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Only Slip-Ring'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot(sp(<span class="org-type">:</span>, 3), sp(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle and Slip-Ring'</span>);
plot(sr(<span class="org-type">:</span>, 3), sr(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Only Slip-Ring'</span>);
plot(of(<span class="org-type">:</span>, 3), of(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Velocity [m/s]'</span>);
xlim([0, 100]);
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
</pre>
</div>
<div id="org8be7963" class="figure">
<div id="orgcea5a30" class="figure">
<p><img src="figs/slip_ring_spindle_sample_time.png" alt="slip_ring_spindle_sample_time.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Velocity as measured by the geophone at the sample location - Time domain</p>
</div>
<div id="orgfc19876" class="figure">
<div id="org3c59dd5" class="figure">
<p><img src="figs/slip_ring_spindle_sample_zoom.png" alt="slip_ring_spindle_sample_zoom.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Velocity as measured by the geophone at the sample location - Time domain</p>
@@ -510,18 +275,18 @@ legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-stri
</div>
</div>
<div id="outline-container-orgfee57e5" class="outline-3">
<h3 id="orgfee57e5"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div id="outline-container-org38cf97f" class="outline-3">
<h3 id="org38cf97f"><span class="section-number-3">2.4</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-4">
<p>
We first compute some parameters that will be used for the PSD computation.
</p>
<div class="org-src-container">
<pre class="src src-matlab">dt = of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% [s]</span>
<pre class="src src-matlab">dt = of(2, 3)<span class="org-type">-</span>of(1, 3); <span class="org-comment">% [s]</span>
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Window used</span>
win = hanning(ceil(10<span class="org-type">*</span>Fs)); <span class="org-comment">% Window used</span>
</pre>
</div>
@@ -533,9 +298,9 @@ Then we compute the Power Spectral Density using <code>pwelch</code> function.
First for the geophone located on the marble
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_m, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxsp_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<pre class="src src-matlab">[pxof_m, f] = pwelch(of(<span class="org-type">:</span>, 1), win, [], [], Fs);
[pxsr_m, <span class="org-type">~</span>] = pwelch(sr(<span class="org-type">:</span>, 1), win, [], [], Fs);
[pxsp_m, <span class="org-type">~</span>] = pwelch(sp(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre>
</div>
@@ -543,9 +308,9 @@ First for the geophone located on the marble
And for the geophone located at the sample position.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxsp_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<pre class="src src-matlab">[pxof_s, <span class="org-type">~</span>] = pwelch(of(<span class="org-type">:</span>, 2), win, [], [], Fs);
[pxsr_s, <span class="org-type">~</span>] = pwelch(sr(<span class="org-type">:</span>, 2), win, [], [], Fs);
[pxsp_s, <span class="org-type">~</span>] = pwelch(sp(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre>
</div>
@@ -553,27 +318,27 @@ And for the geophone located at the sample position.
And we plot the ASD of the measured velocities:
</p>
<ul class="org-ul">
<li>figure <a href="#org704b4b4">5</a> for the geophone located on the marble</li>
<li>figure <a href="#orga078b66">6</a> for the geophone at the sample position</li>
<li>figure <a href="#orgf38cb1d">5</a> for the geophone located on the marble</li>
<li>figure <a href="#orgbe7eafc">6</a> for the geophone at the sample position</li>
</ul>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot(f, sqrt(pxsp_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot(f, sqrt(pxsr_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot(f, sqrt(pxof_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim([2, 500]);
</pre>
</div>
<div id="org704b4b4" class="figure">
<div id="orgf38cb1d" class="figure">
<p><img src="figs/sr_sp_psd_marble_compare.png" alt="sr_sp_psd_marble_compare.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Comparison of the ASD of the measured velocities from the Geophone on the marble</p>
@@ -582,52 +347,52 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot(f, sqrt(pxsp_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot(f, sqrt(pxsr_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot(f, sqrt(pxof_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim([2, 500]);
</pre>
</div>
<div id="orga078b66" class="figure">
<div id="orgbe7eafc" class="figure">
<p><img src="figs/sr_sp_psd_sample_compare.png" alt="sr_sp_psd_sample_compare.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Comparison of the ASD of the measured velocities from the Geophone at the sample location</p>
</div>
<p>
We load the ground motion to compare with the measurements (Fig. <a href="#org71cc947">7</a>).
We load the ground motion to compare with the measurements (Fig. <a href="#org71b3fba">7</a>).
We see that the motion is dominated by the ground motion below 20Hz.
</p>
<div class="org-src-container">
<pre class="src src-matlab">gm = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'../ground-motion/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gv'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<pre class="src src-matlab">gm = load(<span class="org-string">'../ground-motion/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gv'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>gm.f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>gm.psd_gv<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot(f, sqrt(pxsp_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot(f, sqrt(pxsr_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot(f, sqrt(pxof_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
plot(gm.f, sqrt(gm.psd_gv), <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ground Motion'</span>);
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim([2, 500]);
</pre>
</div>
<div id="org71cc947" class="figure">
<div id="org71b3fba" class="figure">
<p><img src="figs/ty_comp_gm.png" alt="ty_comp_gm.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Comparison of the ground velocity with the measured velocity (<a href="./figs/ty_comp_gm.png">png</a>, <a href="./figs/ty_comp_gm.pdf">pdf</a>)</p>
@@ -636,16 +401,16 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
</div>
<div id="outline-container-org7d3ac71" class="outline-3">
<h3 id="org7d3ac71"><span class="section-number-3">2.5</span> Relative Motion</h3>
<div id="outline-container-orgbaa08aa" class="outline-3">
<h3 id="orgbaa08aa"><span class="section-number-3">2.5</span> Relative Motion</h3>
<div class="outline-text-3" id="text-2-5">
<p>
The relative velocity between the sample and the marble is shown in Fig. <a href="#org21be4d0">8</a>.
The velocity is integrated to have the relative displacement in Fig. <a href="#org2d58d24">9</a>.
The relative velocity between the sample and the marble is shown in Fig. <a href="#orgb098e37">8</a>.
The velocity is integrated to have the relative displacement in Fig. <a href="#org3dac066">9</a>.
</p>
<div id="org21be4d0" class="figure">
<div id="orgb098e37" class="figure">
<p><img src="figs/rz_relative_velocity.png" alt="rz_relative_velocity.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Relative velocity between the hexapod and the marble (<a href="./figs/rz_relative_velocity.png">png</a>, <a href="./figs/rz_relative_velocity.pdf">pdf</a>)</p>
@@ -655,7 +420,7 @@ The velocity is integrated to have the relative displacement in Fig. <a href="#o
Time domain: Integration to have the displacement
</p>
<div id="org2d58d24" class="figure">
<div id="org3dac066" class="figure">
<p><img src="figs/rz_relative_motion.png" alt="rz_relative_motion.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Relative displacement between the Hexapod and the marble (<a href="./figs/rz_relative_motion.png">png</a>, <a href="./figs/rz_relative_motion.pdf">pdf</a>)</p>
@@ -665,52 +430,52 @@ Time domain: Integration to have the displacement
We compute the PSD of the relative velocity between the sample and the marble.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-rainbow-delimiters-depth-1">[</span>pxsp_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
<pre class="src src-matlab">[pxof_r, f] = pwelch(of(<span class="org-type">:</span>, 2)<span class="org-type">-</span>of(<span class="org-type">:</span>, 1), win, [], [], Fs);
[pxsr_r, <span class="org-type">~</span>] = pwelch(sr(<span class="org-type">:</span>, 2)<span class="org-type">-</span>sr(<span class="org-type">:</span>, 1), win, [], [], Fs);
[pxsp_r, <span class="org-type">~</span>] = pwelch(sp(<span class="org-type">:</span>, 2)<span class="org-type">-</span>sp(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre>
</div>
<p>
The Power Spectral Density of the Granite Velocity, Sample velocity and relative velocity are compare in Fig. <a href="#org0cfb4b3">10</a>.
The Power Spectral Density of the Granite Velocity, Sample velocity and relative velocity are compare in Fig. <a href="#orga42fb07">10</a>.
</p>
<div id="org0cfb4b3" class="figure">
<div id="orga42fb07" class="figure">
<p><img src="figs/rz_psd_sample_granite_relative_comp.png" alt="rz_psd_sample_granite_relative_comp.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Comparison of the PSD of the velocity of the Sample, Granite and relative velocity (<a href="./figs/rz_psd_sample_granite_relative_comp.png">png</a>, <a href="./figs/rz_psd_sample_granite_relative_comp.pdf">pdf</a>)</p>
</div>
<p>
Then, we display the PSD of the relative velocity for all three cases in Fig. <a href="#org9d08176">11</a>.
Then, we display the PSD of the relative velocity for all three cases in Fig. <a href="#org1f1dfc7">11</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot(f, sqrt(pxsp_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot(f, sqrt(pxsr_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot(f, sqrt(pxof_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the relative velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the relative velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim([2, 500]);
</pre>
</div>
<div id="org9d08176" class="figure">
<div id="org1f1dfc7" class="figure">
<p><img src="figs/sr_sp_psd_relative_compare.png" alt="sr_sp_psd_relative_compare.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Comparison of the ASD of the relative velocity</p>
</div>
<p>
The Cumulative Power Spectrum of the relative velocity is shown in Fig. <a href="#org76a9b23">12</a> and in Fig. <a href="#org61e2e4a">13</a> (integrated in reverse direction).
The Cumulative Power Spectrum of the relative velocity is shown in Fig. <a href="#org11a9cb7">12</a> and in Fig. <a href="#orga256753">13</a> (integrated in reverse direction).
</p>
<div id="org76a9b23" class="figure">
<div id="org11a9cb7" class="figure">
<p><img src="figs/dist_rz_cps.png" alt="dist_rz_cps.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Cumulative Power Spectrum of the relative velocity (<a href="./figs/dist_rz_cps.png">png</a>, <a href="./figs/dist_rz_cps.pdf">pdf</a>)</p>
@@ -718,7 +483,7 @@ The Cumulative Power Spectrum of the relative velocity is shown in Fig. <a href=
<div id="org61e2e4a" class="figure">
<div id="orga256753" class="figure">
<p><img src="figs/dist_rz_cps_reverse.png" alt="dist_rz_cps_reverse.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Cumulative Power Spectrum of the relative velocity (integrated from high to low frequencies) (<a href="./figs/dist_rz_cps_reverse.png">png</a>, <a href="./figs/dist_rz_cps_reverse.pdf">pdf</a>)</p>
@@ -726,43 +491,48 @@ The Cumulative Power Spectrum of the relative velocity is shown in Fig. <a href=
<p>
Finally, the Cumulative Amplitude Spectrum of the relative position between the hexapod and the marble is shown in Fig. <a href="#org454a2a7">14</a>.
Finally, the Cumulative Amplitude Spectrum of the relative position between the hexapod and the marble is shown in Fig. <a href="#orgb16a9f7">14</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>flip<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">-</span>cumtrapz<span class="org-rainbow-delimiters-depth-4">(</span>flip<span class="org-rainbow-delimiters-depth-5">(</span>f<span class="org-rainbow-delimiters-depth-5">)</span>, flip<span class="org-rainbow-delimiters-depth-5">(</span>pxsp_r<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-6">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-6">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>flip<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">-</span>cumtrapz<span class="org-rainbow-delimiters-depth-4">(</span>flip<span class="org-rainbow-delimiters-depth-5">(</span>f<span class="org-rainbow-delimiters-depth-5">)</span>, flip<span class="org-rainbow-delimiters-depth-5">(</span>pxsr_r<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-6">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-6">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>flip<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">-</span>cumtrapz<span class="org-rainbow-delimiters-depth-4">(</span>flip<span class="org-rainbow-delimiters-depth-5">(</span>f<span class="org-rainbow-delimiters-depth-5">)</span>, flip<span class="org-rainbow-delimiters-depth-5">(</span>pxof_r<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-6">(</span><span class="org-highlight-numbers-number">2</span><span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f<span class="org-rainbow-delimiters-depth-6">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
plot(f, sqrt(flip(<span class="org-type">-</span>cumtrapz(flip(f), flip(pxsp_r<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f)<span class="org-type">.^</span>2)))), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot(f, sqrt(flip(<span class="org-type">-</span>cumtrapz(flip(f), flip(pxsr_r<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f)<span class="org-type">.^</span>2)))), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot(f, sqrt(flip(<span class="org-type">-</span>cumtrapz(flip(f), flip(pxof_r<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f)<span class="org-type">.^</span>2)))), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off;
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'CAS of the relative displacement $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'CAS of the relative displacement $\left[\frac{m}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim([2, 500]);
</pre>
</div>
<div id="org454a2a7" class="figure">
<div id="orgb16a9f7" class="figure">
<p><img src="figs/dist_rz_cas.png" alt="dist_rz_cas.png" />
</p>
<p><span class="figure-number">Figure 14: </span>Cumulative Amplitude Spectrum of the relative motion Hexapod/Granite (<a href="./figs/dist_rz_cas.png">png</a>, <a href="./figs/dist_rz_cas.pdf">pdf</a>)</p>
</div>
</div>
</div>
<div id="outline-container-orgad3b42a" class="outline-3">
<h3 id="orgad3b42a"><span class="section-number-3">2.6</span> Save</h3>
<div class="outline-text-3" id="text-2-6">
<p>
The Power Spectral Density of the relative velocity is saved for further analysis.
The Power Spectral Density of the relative velocity and of the hexapod velocity is saved for further analysis.
</p>
<div class="org-src-container">
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/pxsp_r.mat'</span>, <span class="org-string">'pxsp_r'</span>, <span class="org-string">'f'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
<pre class="src src-matlab">save(<span class="org-string">'mat/pxsp_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxsp_r'</span>, <span class="org-string">'pxsp_s'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-org1464a72" class="outline-3">
<h3 id="org1464a72"><span class="section-number-3">2.6</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-6">
<div class="important">
<div id="outline-container-org0a44924" class="outline-3">
<h3 id="org0a44924"><span class="section-number-3">2.7</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-7">
<div class="important" id="orga7d722f">
<p>
The relative motion below 20Hz is dominated by another effect than the rotation of the Spindle (probably ground motion).
</p>
@@ -777,7 +547,7 @@ The Spindle rotation induces relative motion of the hexapod with respect to the
</div>
<div class="important">
<div class="important" id="orga4c2e01">
<p>
There is a huge peak at 24Hz on the sample vibration but not on the granite vibration
</p>
@@ -793,8 +563,7 @@ There is a huge peak at 24Hz on the sample vibration but not on the granite vibr
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-10-31 jeu. 16:19</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
<p class="date">Created: 2020-11-12 jeu. 10:27</p>
</div>
</body>
</html>

11
disturbance-sr-rz/index.org
View File

@@ -7,15 +7,10 @@
#+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"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/zenburn.css"/>
#+HTML_HEAD: <script type="text/javascript" src="../js/jquery.min.js"></script>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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#+HTML_MATHJAX: align: center tagside: right font: TeX