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<div id="content">
<h1 class="title">Static Measurements</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgceaa13e">1. Notes</a></li>
<li><a href="#org8d8d266">2. Data Pre-processing</a></li>
<li><a href="#orgc36603f">3. Matlab - Data Import</a></li>
<li><a href="#orgf7ebbe2">4. Data - Plot</a></li>
<li><a href="#orgd305b40">5. Translate to time domain</a></li>
<li><a href="#orgbc4466d">6. Compute the PSD</a></li>
</ul>
</div>
</div>
<p>
<a href="../index.html">Back to main page</a>.
</p>
<div id="outline-container-orgceaa13e" class="outline-2">
<h2 id="orgceaa13e"><span class="section-number-2">1</span> Notes</h2>
<div class="outline-text-2" id="text-1">
<ul class="org-ul">
<li><b>5530</b>: Straightness Plot: Yz</li>
<li><b>Filename</b>: <code>r:\home\PDMU\PEL\Measurement_library\ID31\ID31_u_station\TY\12_12_2018\linear deviation _tyz_401_points.txt</code></li>
<li><b>Acquisition date</b>: 09/01/2019 13:49:42</li>
<li><b>Current date</b>: 08/03/2019 08:46:35</li>
<li><b>Measurement Type</b>: STRAIGHTNESS vertical</li>
<li><b>Travel Mode</b>: Bidirectional</li>
<li><b>Number of Target Positions</b>: 401</li>
<li><b>Number of total data pairs</b>: 2406</li>
<li><b>Number of total data runs</b>:6</li>
<li><b>Position Value Units</b>: millimeters</li>
<li><b>Error Value Units</b>: micrometers</li>
</ul>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Environmental Data</th>
<th scope="col" class="org-left">Min</th>
<th scope="col" class="org-left">Max</th>
<th scope="col" class="org-left">Avg</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Air Temp (C)</td>
<td class="org-left">024,57</td>
<td class="org-left">024,61</td>
<td class="org-left">024,59</td>
</tr>
<tr>
<td class="org-left">Air Prs (mm)</td>
<td class="org-left">742,56</td>
<td class="org-left">743,29</td>
<td class="org-left">742,83</td>
</tr>
<tr>
<td class="org-left">Air Hmd (%)</td>
<td class="org-left">024,00</td>
<td class="org-left">024,00</td>
<td class="org-left">024,00</td>
</tr>
<tr>
<td class="org-left">MT1 Temp (C)</td>
<td class="org-left"> </td>
<td class="org-left"> </td>
<td class="org-left">020,00</td>
</tr>
<tr>
<td class="org-left">MT2 Temp (C)</td>
<td class="org-left">024,40</td>
<td class="org-left">024,44</td>
<td class="org-left">024,42</td>
</tr>
<tr>
<td class="org-left">MT3 Temp (C)</td>
<td class="org-left">024,32</td>
<td class="org-left">024,36</td>
<td class="org-left">024,34</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org8d8d266" class="outline-2">
<h2 id="org8d8d266"><span class="section-number-2">2</span> Data Pre-processing</h2>
<div class="outline-text-2" id="text-2">
<div class="org-src-container">
<pre class="src src-shell">sed <span style="color: #CC9393;">'s/\t/ /g;s/\,/./g'</span> <span style="color: #CC9393;">"data/linear deviation _tyz_401_points.txt"</span> > data/data.txt
</pre>
</div>
<div class="org-src-container">
<pre class="src src-shell">head <span style="color: #CC9393;">"data/data.txt"</span>
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-right" />
<col class="org-right" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Run</th>
<th scope="col" class="org-right">Pos</th>
<th scope="col" class="org-right">TargetValue</th>
<th scope="col" class="org-right">ErrorValue</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-right">1</td>
<td class="org-right">-4.5E+00</td>
<td class="org-right">7.5377892E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">2</td>
<td class="org-right">-4.4775E+00</td>
<td class="org-right">7.5422246E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">3</td>
<td class="org-right">-4.455E+00</td>
<td class="org-right">7.5655617E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">4</td>
<td class="org-right">-4.4325E+00</td>
<td class="org-right">7.5149518E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">5</td>
<td class="org-right">-4.41E+00</td>
<td class="org-right">7.4886377E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">6</td>
<td class="org-right">-4.3875E+00</td>
<td class="org-right">7.437007E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">7</td>
<td class="org-right">-4.365E+00</td>
<td class="org-right">7.4449354E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">8</td>
<td class="org-right">-4.3425E+00</td>
<td class="org-right">7.3937387E+00</td>
</tr>
<tr>
<td class="org-right">1</td>
<td class="org-right">9</td>
<td class="org-right">-4.32E+00</td>
<td class="org-right">7.3287468E+00</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgc36603f" class="outline-2">
<h2 id="orgc36603f"><span class="section-number-2">3</span> Matlab - Data Import</h2>
<div class="outline-text-2" id="text-3">
<div class="org-src-container">
<pre class="src src-matlab">filename = <span style="color: #CC9393;">'data/data.txt'</span>;
fileID = fopen<span style="color: #DCDCCC;">(</span>filename<span style="color: #DCDCCC;">)</span>;
data = cell2mat<span style="color: #DCDCCC;">(</span>textscan<span style="color: #BFEBBF;">(</span>fileID,'<span style="color: #7F9F7F;">%f %f %f </span>%f', 'collectoutput', <span style="color: #BFEBBF;">1</span>,'headerlines',<span style="color: #BFEBBF;">1</span>));
fclose<span style="color: #D0BF8F;">(</span>fileID<span style="color: #D0BF8F;">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-orgf7ebbe2" class="outline-2">
<h2 id="orgf7ebbe2"><span class="section-number-2">4</span> Data - Plot</h2>
<div class="outline-text-2" id="text-4">
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span>=<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:data</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">end, </span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>
plot<span style="color: #DCDCCC;">(</span>data<span style="color: #BFEBBF;">(</span>data<span style="color: #D0BF8F;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #D0BF8F;">)</span> <span style="color: #7CB8BB;">==</span> <span style="color: #BFEBBF;">i</span>, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span>, data<span style="color: #BFEBBF;">(</span>data<span style="color: #D0BF8F;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #D0BF8F;">)</span> <span style="color: #7CB8BB;">==</span> <span style="color: #BFEBBF;">i</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span>, <span style="color: #CC9393;">'-k'</span><span style="color: #DCDCCC;">)</span>;
<span style="color: #F0DFAF; font-weight: bold;">end</span>
hold off;
xlabel<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Target Value </span><span style="color: #BFEBBF;">[</span><span style="color: #CC9393;">mm</span><span style="color: #BFEBBF;">]</span><span style="color: #CC9393;">'</span><span style="color: #DCDCCC;">)</span><span style="color: #CC9393;">; ylabel</span><span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Error Value </span><span style="color: #BFEBBF;">[</span><span style="color: #CC9393;">um</span><span style="color: #BFEBBF;">]</span><span style="color: #CC9393;">'</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<div id="orgd8a6bbb" class="figure">
<p><img src="figs/raw_data.png" alt="raw_data.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Time domain Data</p>
</div>
<p>
Compute mean value of each position
</p>
<div class="org-src-container">
<pre class="src src-matlab">mean_pos = zeros<span style="color: #DCDCCC;">(</span>sum<span style="color: #BFEBBF;">(</span>data<span style="color: #D0BF8F;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">==</span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span>, <span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>;
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span>=<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:sum</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">data</span><span style="color: #BFEBBF;">(</span><span style="color: #BFEBBF;">:, </span><span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #BFEBBF;">==</span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>
mean_pos<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">i</span><span style="color: #DCDCCC;">)</span> = mean<span style="color: #DCDCCC;">(</span>data<span style="color: #BFEBBF;">(</span>data<span style="color: #D0BF8F;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">2</span><span style="color: #D0BF8F;">)</span><span style="color: #7CB8BB;">==</span><span style="color: #BFEBBF;">i</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
<span style="color: #F0DFAF; font-weight: bold;">end</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span>=<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:data</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">end, </span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>
filt = data<span style="color: #DCDCCC;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span> <span style="color: #7CB8BB;">==</span> <span style="color: #BFEBBF;">i</span>;
plot<span style="color: #DCDCCC;">(</span>data<span style="color: #BFEBBF;">(</span>filt, <span style="color: #BFEBBF;">3</span><span style="color: #BFEBBF;">)</span>, data<span style="color: #BFEBBF;">(</span>filt, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span> <span style="color: #7CB8BB;">-</span> mean_pos, <span style="color: #CC9393;">'-k'</span><span style="color: #DCDCCC;">)</span>;
<span style="color: #F0DFAF; font-weight: bold;">end</span>
hold off;
xlabel<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Target Value </span><span style="color: #BFEBBF;">[</span><span style="color: #CC9393;">mm</span><span style="color: #BFEBBF;">]</span><span style="color: #CC9393;">'</span><span style="color: #DCDCCC;">)</span><span style="color: #CC9393;">; ylabel</span><span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Error Value </span><span style="color: #BFEBBF;">[</span><span style="color: #CC9393;">um</span><span style="color: #BFEBBF;">]</span><span style="color: #CC9393;">'</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<div id="org4555ce3" class="figure">
<p><img src="figs/processed_data.png" alt="processed_data.png" />
</p>
<p><span class="figure-number">Figure 2: </span>caption</p>
</div>
</div>
</div>
<div id="outline-container-orgd305b40" class="outline-2">
<h2 id="orgd305b40"><span class="section-number-2">5</span> Translate to time domain</h2>
<div class="outline-text-2" id="text-5">
<div class="org-src-container">
<pre class="src src-matlab">t = linspace<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">0</span>, <span style="color: #BFEBBF;">1</span>, length<span style="color: #BFEBBF;">(</span>data<span style="color: #D0BF8F;">(</span>data<span style="color: #93E0E3;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #93E0E3;">)</span><span style="color: #7CB8BB;">==</span><span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">4</span><span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
plot<span style="color: #DCDCCC;">(</span>t, data<span style="color: #BFEBBF;">(</span>data<span style="color: #D0BF8F;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #D0BF8F;">)</span> <span style="color: #7CB8BB;">==</span> <span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">4</span><span style="color: #BFEBBF;">)</span> <span style="color: #7CB8BB;">-</span> mean_pos, <span style="color: #CC9393;">'-k'</span><span style="color: #DCDCCC;">)</span>;
hold off;
xlabel<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Time </span><span style="color: #BFEBBF;">[</span><span style="color: #CC9393;">s</span><span style="color: #BFEBBF;">]</span><span style="color: #CC9393;">'</span><span style="color: #DCDCCC;">)</span><span style="color: #CC9393;">; ylabel</span><span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Error Value </span><span style="color: #BFEBBF;">[</span><span style="color: #CC9393;">um</span><span style="color: #BFEBBF;">]</span><span style="color: #CC9393;">'</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<div id="org1cc3634" class="figure">
<p><img src="figs/time_domain.png" alt="time_domain.png" />
</p>
<p><span class="figure-number">Figure 3: </span>caption</p>
</div>
</div>
</div>
<div id="outline-container-orgbc4466d" class="outline-2">
<h2 id="orgbc4466d"><span class="section-number-2">6</span> Compute the PSD</h2>
<div class="outline-text-2" id="text-6">
<div class="org-src-container">
<pre class="src src-matlab">n_av = <span style="color: #BFEBBF;">5</span>;
Fs = <span style="color: #BFEBBF;">1</span><span style="color: #7CB8BB;">/</span>t<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">2</span><span style="color: #DCDCCC;">)</span>;
x = data<span style="color: #DCDCCC;">(</span>data<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span> <span style="color: #7CB8BB;">==</span> <span style="color: #BFEBBF;">1</span>, <span style="color: #BFEBBF;">4</span><span style="color: #DCDCCC;">)</span> <span style="color: #7CB8BB;">-</span> mean_pos;
<span style="color: #DCDCCC;">[</span>pxx, f<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>x, hanning<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span>length<span style="color: #93E0E3;">(</span>x<span style="color: #93E0E3;">)</span><span style="color: #7CB8BB;">/</span>n_av<span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>;
pxx_t = zeros<span style="color: #DCDCCC;">(</span>length<span style="color: #BFEBBF;">(</span>pxx<span style="color: #BFEBBF;">)</span>, data<span style="color: #BFEBBF;">(</span>end, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
<span style="color: #F0DFAF; font-weight: bold;">for</span> <span style="color: #DFAF8F;">i</span>=<span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">:data</span><span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">end, </span><span style="color: #BFEBBF;">1</span><span style="color: #DCDCCC;">)</span>
x = data<span style="color: #DCDCCC;">(</span>data<span style="color: #BFEBBF;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">1</span><span style="color: #BFEBBF;">)</span> <span style="color: #7CB8BB;">==</span> <span style="color: #BFEBBF;">i</span>, <span style="color: #BFEBBF;">4</span><span style="color: #DCDCCC;">)</span> <span style="color: #7CB8BB;">-</span> mean_pos;
<span style="color: #DCDCCC;">[</span>pxx, f<span style="color: #DCDCCC;">]</span> = pwelch<span style="color: #DCDCCC;">(</span>x, hanning<span style="color: #BFEBBF;">(</span>ceil<span style="color: #D0BF8F;">(</span>length<span style="color: #93E0E3;">(</span>x<span style="color: #93E0E3;">)</span><span style="color: #7CB8BB;">/</span>n_av<span style="color: #D0BF8F;">)</span><span style="color: #BFEBBF;">)</span>, <span style="color: #BFEBBF;">[]</span>, <span style="color: #BFEBBF;">[]</span>, Fs<span style="color: #DCDCCC;">)</span>;
pxx_t<span style="color: #DCDCCC;">(</span><span style="color: #7CB8BB;">:</span>, <span style="color: #BFEBBF;">i</span><span style="color: #DCDCCC;">)</span> = pxx;
<span style="color: #F0DFAF; font-weight: bold;">end</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span style="color: #7CB8BB;">figure</span>;
hold on;
plot<span style="color: #DCDCCC;">(</span>f, mean<span style="color: #BFEBBF;">(</span>pxx_t, <span style="color: #BFEBBF;">2</span><span style="color: #BFEBBF;">)</span><span style="color: #DCDCCC;">)</span>;
hold off;
xlabel<span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">'Frequency </span><span style="color: #BFEBBF;">(</span><span style="color: #CC9393;">Hz</span><span style="color: #BFEBBF;">)</span><span style="color: #CC9393;">'</span><span style="color: #DCDCCC;">)</span>;
ylabel<span style="color: #DCDCCC;">(</span>'PSD <span style="color: #BFEBBF;">(</span>$m<span style="color: #7CB8BB;">^</span><span style="color: #BFEBBF;">2</span><span style="color: #7CB8BB;">/</span>Hz$<span style="color: #BFEBBF;">)</span>'<span style="color: #DCDCCC;">)</span>;
<span style="color: #7CB8BB;">set</span><span style="color: #DCDCCC;">(</span><span style="color: #DFAF8F;">gca</span>, <span style="color: #CC9393;">'XScale', 'log'</span><span style="color: #DCDCCC;">)</span><span style="color: #CC9393;">; set</span><span style="color: #DCDCCC;">(</span><span style="color: #CC9393;">gca, 'YScale', 'log'</span><span style="color: #DCDCCC;">)</span>;
legend<span style="color: #DCDCCC;">(</span><span style="color: #BFEBBF;">{</span><span style="color: #CC9393;">'PSD - x', 'PSD - y', 'PSD - z'</span><span style="color: #BFEBBF;">}</span><span style="color: #DCDCCC;">)</span>;
</pre>
</div>
<div id="org30d047a" class="figure">
<p><img src="figs/psd.png" alt="psd.png" />
</p>
<p><span class="figure-number">Figure 4: </span>PSD of the Z motion when scanning with Ty at 1Hz</p>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-03-15 ven. 11:43</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>