Finish the file about measurements. Add raw measurements to git
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<head>
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<!-- 2019-07-03 mer. 13:53 -->
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<!-- 2019-07-03 mer. 13:58 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Modal Analysis of the ID31 Micro-Station</title>
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<title>Modal Analysis of the ID31 Micro-Station</title>
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<h1 class="title">Modal Analysis of the ID31 Micro-Station</h1>
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<h1 class="title">Modal Analysis of the ID31 Micro-Station</h1>
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<p>
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<p>
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The modal analysis of the ID31 Micro-station consists of several parts:
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The goal is to experimentally extract a <b>Spatial Model</b> (mass, damping, stiffness) of the structure (shown on figure <a href="#orgf65e30f">1</a>) in order to tune the Multi-Body model.
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</p>
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<div id="orgf65e30f" class="figure">
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<p><img src="img/nass_picture.png" alt="nass_picture.png" width="500px" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Picture of the ID31 Micro-Station. (1) Granite (2) Translation Stage (3) Tilt Stage (4) Hexapod (5) Dummy Mass</p>
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</div>
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<p>
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The procedure is represented on figure <a href="#org28538ba">2</a> where we go from left to right.
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</p>
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<div id="org28538ba" class="figure">
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<p><img src="img/vibration_analysis_procedure.png" alt="vibration_analysis_procedure.png" width="400px" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Vibration Analysis Procedure</p>
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</div>
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<p>
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The steps are:
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</p>
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<ul class="org-ul">
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<li>we obtain a <b>Response Model</b> (Frequency Response Functions) from measurements (described <a href="measurement.html">here</a>)</li>
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<li>the response model is further converted into a <b>Modal Model</b> (Natural Frequencies and Mode Shapes) (described <a href="modal_extraction.html">here</a>)</li>
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<li>this is converted into a <b>Spatial Model</b> with the Mass/Damping/Stiffness matrices (described <a href="mathematical_model.html">here</a>)</li>
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</ul>
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<p>
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Theses matrices will be used to tune the Simscape (multi-body) model.
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</p>
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<p>
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The modes we want to identify are those in the frequency range between 0Hz and 150Hz.
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</p>
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<p>
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The modal analysis of the ID31 Micro-station thus consists of several parts:
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</p>
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</p>
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<ul class="org-ul">
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<ul class="org-ul">
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<li><a href="measurement.html">Frequency Response Measurements</a></li>
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<li><a href="measurement.html">Frequency Response Measurements</a></li>
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</div>
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</div>
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<div id="postamble" class="status">
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2019-07-03 mer. 13:53</p>
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<p class="date">Created: 2019-07-03 mer. 13:58</p>
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</div>
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</body>
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</body>
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#+HTML_MATHJAX: align: center tagside: right font: TeX
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#+HTML_MATHJAX: align: center tagside: right font: TeX
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:END:
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:END:
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The modal analysis of the ID31 Micro-station consists of several parts:
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The goal is to experimentally extract a *Spatial Model* (mass, damping, stiffness) of the structure (shown on figure [[fig:nass_picture]]) in order to tune the Multi-Body model.
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#+name: fig:nass_picture
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#+caption: Picture of the ID31 Micro-Station. (1) Granite (2) Translation Stage (3) Tilt Stage (4) Hexapod (5) Dummy Mass
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#+attr_html: :width 500px
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[[file:img/nass_picture.png]]
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The procedure is represented on figure [[fig:vibration_analysis_procedure]] where we go from left to right.
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#+name: fig:vibration_analysis_procedure
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#+caption: Vibration Analysis Procedure
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#+attr_html: :width 400px
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[[file:img/vibration_analysis_procedure.png]]
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The steps are:
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- we obtain a *Response Model* (Frequency Response Functions) from measurements (described [[file:measurement.org][here]])
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- the response model is further converted into a *Modal Model* (Natural Frequencies and Mode Shapes) (described [[file:modal_extraction.org][here]])
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- this is converted into a *Spatial Model* with the Mass/Damping/Stiffness matrices (described [[file:mathematical_model.org][here]])
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Theses matrices will be used to tune the Simscape (multi-body) model.
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The modes we want to identify are those in the frequency range between 0Hz and 150Hz.
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The modal analysis of the ID31 Micro-station thus consists of several parts:
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- [[file:measurement.org][Frequency Response Measurements]]
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- [[file:measurement.org][Frequency Response Measurements]]
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- [[file:modal_extraction.org][Modal Parameter Extraction]]
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- [[file:modal_extraction.org][Modal Parameter Extraction]]
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- [[file:mathematical_model.org][Derivation of Mathematical Model]]
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- [[file:mathematical_model.org][Derivation of Mathematical Model]]
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23
modal-analysis/mat/acc_pos.txt
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23 1.5500e-001 -9.0000e-002 -5.9400e-001
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22 0.0000e+000 1.8000e-001 -5.9400e-001
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21 -1.5500e-001 -9.0000e-002 -5.9400e-001
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20 8.6490e-001 -5.0600e-001 -9.5060e-001
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19 8.7500e-001 7.9900e-001 -9.5060e-001
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18 -7.3500e-001 8.1400e-001 -9.5060e-001
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17 -7.3000e-001 -5.2600e-001 -9.5060e-001
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16 2.9500e-001 -4.8100e-001 -7.8560e-001
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15 4.5000e-001 5.3400e-001 -7.8560e-001
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14 -4.8000e-001 5.3400e-001 -7.8560e-001
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13 -3.2000e-001 -4.4600e-001 -7.8560e-001
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12 4.7500e-001 -4.1900e-001 -4.2730e-001
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11 4.7500e-001 4.2400e-001 -4.2730e-001
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10 -4.6500e-001 4.0700e-001 -4.2730e-001
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9 -4.7500e-001 -4.1400e-001 -4.2730e-001
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8 3.8000e-001 -3.0000e-001 -4.1680e-001
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7 4.2000e-001 2.8000e-001 -4.1680e-001
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6 -4.2000e-001 2.8000e-001 -4.1680e-001
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5 -3.8500e-001 -3.0000e-001 -4.1680e-001
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4 6.4000e-002 -6.4000e-002 -2.9600e-001
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3 6.4000e-002 6.4000e-002 -2.9600e-001
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2 -6.4000e-002 6.4000e-002 -2.9600e-001
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1 -6.4000e-002 -6.4000e-002 -2.9600e-001
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This file was saved by N-Modal automatically.
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16:49:47, Monday, July 01, 2019
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HEADER
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Data are imported from UFF files.
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FREQVEC
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UFF
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RES_TYPE
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ACCELERATION
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COOR_SYS
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1 0 0.0000e+000 0.0000e+000 0.0000e+000 0.0000e+000 0.0000e+000 0.0000e+000 0.0000e+000 0.0000e+000 0.0000e+000 Cartesian1
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NODES
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23 1.5500e-001 -9.0000e-002 -5.9400e-001 0 bot
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22 0.0000e+000 1.8000e-001 -5.9400e-001 0 bot
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21 -1.5500e-001 -9.0000e-002 -5.9400e-001 0 bot
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20 8.6490e-001 -5.0600e-001 -9.5060e-001 0 low
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19 8.7500e-001 7.9900e-001 -9.5060e-001 0 low
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18 -7.3500e-001 8.1400e-001 -9.5060e-001 0 low
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17 -7.3000e-001 -5.2600e-001 -9.5060e-001 0 low
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16 2.9500e-001 -4.8100e-001 -7.8560e-001 0 top
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15 4.5000e-001 5.3400e-001 -7.8560e-001 0 top
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14 -4.8000e-001 5.3400e-001 -7.8560e-001 0 top
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13 -3.2000e-001 -4.4600e-001 -7.8560e-001 0 top
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12 4.7500e-001 -4.1900e-001 -4.2730e-001 0 outer
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11 4.7500e-001 4.2400e-001 -4.2730e-001 0 outer
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10 -4.6500e-001 4.0700e-001 -4.2730e-001 0 outer
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9 -4.7500e-001 -4.1400e-001 -4.2730e-001 0 outer
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8 3.8000e-001 -3.0000e-001 -4.1680e-001 0 inner
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7 4.2000e-001 2.8000e-001 -4.1680e-001 0 inner
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6 -4.2000e-001 2.8000e-001 -4.1680e-001 0 inner
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5 -3.8500e-001 -3.0000e-001 -4.1680e-001 0 inner
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4 6.4000e-002 -6.4000e-002 -2.7000e-001 0 Top
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3 6.4000e-002 6.4000e-002 -2.7000e-001 0 Top
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2 -6.4000e-002 6.4000e-002 -2.7000e-001 0 Top
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1 -6.4000e-002 -6.4000e-002 -2.7000e-001 0 Top
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SETUP
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Setup 1
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FILE
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C:\Users\lesourd\Downloads\id31_modal_analysis\uff_data\Measurement1.uff|Measurement2.uff|Measurement3.uff|Measurement4.uff|Measurement5.uff|Measurement6.uff|Measurement7.uff|Measurement8.uff|Measurement9.uff|Measurement10.uff|Measurement11.uff|Measurement12.uff|Measurement13.uff|Measurement14.uff|Measurement15.uff|Measurement16.uff|Measurement17.uff|Measurement18.uff|Measurement19.uff|Measurement20.uff|Measurement21.uff|Measurement22.uff|Measurement23.uff|Measurement24.uff
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modal-analysis/mat/meas_frf_coh_18.mat
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modal-analysis/mat/meas_frf_coh_19.mat
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modal-analysis/mat/meas_frf_coh_2.mat
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modal-analysis/mat/meas_frf_coh_2.mat
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modal-analysis/mat/meas_frf_coh_20.mat
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modal-analysis/mat/meas_frf_coh_20.mat
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modal-analysis/mat/meas_frf_coh_21.mat
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modal-analysis/mat/meas_frf_coh_22.mat
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modal-analysis/mat/meas_frf_coh_22.mat
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modal-analysis/mat/meas_frf_coh_23.mat
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modal-analysis/mat/meas_frf_coh_24.mat
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modal-analysis/mat/meas_frf_coh_24.mat
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modal-analysis/mat/meas_frf_coh_3.mat
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modal-analysis/mat/meas_frf_coh_3.mat
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modal-analysis/mat/meas_frf_coh_4.mat
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modal-analysis/mat/meas_frf_coh_4.mat
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modal-analysis/mat/meas_frf_coh_5.mat
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modal-analysis/mat/meas_frf_coh_5.mat
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modal-analysis/mat/meas_frf_coh_6.mat
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modal-analysis/mat/meas_frf_coh_6.mat
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modal-analysis/mat/meas_frf_coh_7.mat
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modal-analysis/mat/meas_frf_coh_7.mat
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modal-analysis/mat/meas_frf_coh_8.mat
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modal-analysis/mat/meas_frf_coh_8.mat
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modal-analysis/mat/meas_frf_coh_9.mat
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modal-analysis/mat/meas_frf_coh_9.mat
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modal-analysis/mat/meas_raw_1.mat
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modal-analysis/mat/meas_raw_1.mat
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modal-analysis/mat/meas_raw_10.mat
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modal-analysis/mat/meas_raw_10.mat
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modal-analysis/mat/meas_raw_11.mat
Normal file
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modal-analysis/mat/meas_raw_11.mat
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modal-analysis/mat/meas_raw_12.mat
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modal-analysis/mat/meas_raw_12.mat
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modal-analysis/mat/meas_raw_13.mat
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modal-analysis/mat/meas_raw_13.mat
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modal-analysis/mat/meas_raw_14.mat
Normal file
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modal-analysis/mat/meas_raw_14.mat
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modal-analysis/mat/meas_raw_15.mat
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modal-analysis/mat/meas_raw_15.mat
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modal-analysis/mat/meas_raw_16.mat
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modal-analysis/mat/meas_raw_16.mat
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modal-analysis/mat/meas_raw_17.mat
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modal-analysis/mat/meas_raw_17.mat
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modal-analysis/mat/meas_raw_18.mat
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modal-analysis/mat/meas_raw_18.mat
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modal-analysis/mat/meas_raw_19.mat
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modal-analysis/mat/meas_raw_19.mat
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modal-analysis/mat/meas_raw_2.mat
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modal-analysis/mat/meas_raw_2.mat
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modal-analysis/mat/meas_raw_20.mat
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modal-analysis/mat/meas_raw_20.mat
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modal-analysis/mat/meas_raw_21.mat
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modal-analysis/mat/meas_raw_21.mat
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modal-analysis/mat/meas_raw_22.mat
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modal-analysis/mat/meas_raw_22.mat
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modal-analysis/mat/meas_raw_23.mat
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modal-analysis/mat/meas_raw_23.mat
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modal-analysis/mat/meas_raw_24.mat
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modal-analysis/mat/meas_raw_24.mat
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modal-analysis/mat/meas_raw_3.mat
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modal-analysis/mat/meas_raw_3.mat
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modal-analysis/mat/meas_raw_4.mat
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modal-analysis/mat/meas_raw_4.mat
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modal-analysis/mat/meas_raw_5.mat
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modal-analysis/mat/meas_raw_5.mat
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modal-analysis/mat/meas_raw_6.mat
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modal-analysis/mat/meas_raw_6.mat
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modal-analysis/mat/meas_raw_7.mat
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modal-analysis/mat/meas_raw_7.mat
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modal-analysis/mat/meas_raw_8.mat
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modal-analysis/mat/meas_raw_8.mat
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modal-analysis/mat/meas_raw_9.mat
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modal-analysis/mat/meas_raw_9.mat
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21
modal-analysis/mat/mode_damps.txt
Normal file
21
modal-analysis/mat/mode_damps.txt
Normal file
@@ -0,0 +1,21 @@
|
|||||||
|
8.72664
|
||||||
|
11.75321
|
||||||
|
6.44322
|
||||||
|
3.60695
|
||||||
|
0.24170
|
||||||
|
2.83603
|
||||||
|
4.60472
|
||||||
|
0.64145
|
||||||
|
1.58544
|
||||||
|
3.56361
|
||||||
|
0.26865
|
||||||
|
2.86851
|
||||||
|
3.30737
|
||||||
|
3.27213
|
||||||
|
1.89158
|
||||||
|
3.02795
|
||||||
|
2.71094
|
||||||
|
0.56008
|
||||||
|
1.64638
|
||||||
|
2.17368
|
||||||
|
1.39142
|
||||||
21
modal-analysis/mat/mode_freqs.txt
Normal file
21
modal-analysis/mat/mode_freqs.txt
Normal file
@@ -0,0 +1,21 @@
|
|||||||
|
11.41275
|
||||||
|
18.51409
|
||||||
|
37.58431
|
||||||
|
39.43487
|
||||||
|
53.99524
|
||||||
|
56.14871
|
||||||
|
69.68561
|
||||||
|
71.58533
|
||||||
|
72.35341
|
||||||
|
84.92538
|
||||||
|
90.56538
|
||||||
|
91.00542
|
||||||
|
95.76079
|
||||||
|
105.43696
|
||||||
|
106.76771
|
||||||
|
112.58508
|
||||||
|
116.84928
|
||||||
|
124.13356
|
||||||
|
145.35893
|
||||||
|
150.10734
|
||||||
|
164.65885
|
||||||
21
modal-analysis/mat/mode_modal_a.txt
Normal file
21
modal-analysis/mat/mode_modal_a.txt
Normal file
@@ -0,0 +1,21 @@
|
|||||||
|
-4.50556e+003 -9.41744e+003
|
||||||
|
-1.56119e+003 -1.64408e+004
|
||||||
|
1.24918e+004 -2.00022e+004
|
||||||
|
-1.83730e+004 +8.73583e+004
|
||||||
|
-6.02120e+005 -5.53574e+004
|
||||||
|
-8.13722e+003 -4.17194e+004
|
||||||
|
9.12802e+003 -3.78264e+004
|
||||||
|
1.83523e+005 -5.45837e+005
|
||||||
|
-1.85481e+005 -8.15852e+004
|
||||||
|
-6.44647e+003 -3.91843e+004
|
||||||
|
2.02548e+005 -4.85436e+005
|
||||||
|
-1.54209e+002 -3.09920e+004
|
||||||
|
2.10759e+004 -1.47578e+004
|
||||||
|
-8.03639e+003 -7.00743e+004
|
||||||
|
1.73222e+005 +1.94075e+005
|
||||||
|
5.46351e+003 -9.46357e+003
|
||||||
|
-2.00775e+004 +5.23111e+004
|
||||||
|
-6.04037e+004 -8.70001e+004
|
||||||
|
1.50266e+004 -1.61655e+005
|
||||||
|
1.66427e+005 +1.73772e+005
|
||||||
|
-2.41033e+005 +2.81618e+005
|
||||||
21
modal-analysis/mat/mode_modal_b.txt
Normal file
21
modal-analysis/mat/mode_modal_b.txt
Normal file
@@ -0,0 +1,21 @@
|
|||||||
|
-7.00928e+005 +2.62922e+005
|
||||||
|
-1.92061e+006 -4.44325e+004
|
||||||
|
-4.52363e+006 -3.24813e+006
|
||||||
|
2.14671e+007 +5.33018e+006
|
||||||
|
-1.92744e+007 +2.04231e+008
|
||||||
|
-1.47938e+007 +2.45218e+006
|
||||||
|
-1.63606e+007 -4.75508e+006
|
||||||
|
-2.44974e+008 -8.41188e+007
|
||||||
|
-3.84216e+007 +8.37228e+007
|
||||||
|
-2.10181e+007 +2.69256e+006
|
||||||
|
-2.75921e+008 -1.15999e+008
|
||||||
|
-1.77166e+007 -4.20197e+005
|
||||||
|
-8.45524e+006 -1.29677e+007
|
||||||
|
-4.65722e+007 +3.80208e+006
|
||||||
|
1.32368e+008 -1.13721e+008
|
||||||
|
-6.57437e+006 -4.06578e+006
|
||||||
|
3.79924e+007 +1.57763e+007
|
||||||
|
-6.81189e+007 +4.67313e+007
|
||||||
|
-1.47397e+008 -1.61530e+007
|
||||||
|
1.67266e+008 -1.53366e+008
|
||||||
|
2.87859e+008 +2.53398e+008
|
||||||
1449
modal-analysis/mat/mode_shapes.txt
Normal file
1449
modal-analysis/mat/mode_shapes.txt
Normal file
File diff suppressed because it is too large
Load Diff
1600
modal-analysis/mat/modes.asc
Normal file
1600
modal-analysis/mat/modes.asc
Normal file
File diff suppressed because it is too large
Load Diff
2
modal-analysis/mat/nohup.out
Normal file
2
modal-analysis/mat/nohup.out
Normal file
@@ -0,0 +1,2 @@
|
|||||||
|
|
||||||
|
(termite:6464): GLib-WARNING **: 10:26:13.129: GChildWatchSource: Exit status of a child process was requested but ECHILD was received by waitpid(). See the documentation of g_child_watch_source_new() for possible causes.
|
||||||
@@ -7,7 +7,7 @@
|
|||||||
#+AUTHOR: Dehaeze Thomas
|
#+AUTHOR: Dehaeze Thomas
|
||||||
|
|
||||||
#+HTML_LINK_HOME: ../index.html
|
#+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/htmlize.css"/>
|
||||||
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
|
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
|
||||||
@@ -38,3 +38,25 @@
|
|||||||
#+PROPERTY: header-args:latex+ :mkdirp yes
|
#+PROPERTY: header-args:latex+ :mkdirp yes
|
||||||
#+PROPERTY: header-args:latex+ :output-dir figs
|
#+PROPERTY: header-args:latex+ :output-dir figs
|
||||||
:END:
|
:END:
|
||||||
|
|
||||||
|
* Type of Model
|
||||||
|
The model that we want to obtain is a *multi-body model*.
|
||||||
|
It is composed of several *solid bodies connected with springs and dampers*.
|
||||||
|
The solid bodies are represented with different colors on figure [[fig:nass_solidworks]].
|
||||||
|
|
||||||
|
In the simscape model, the solid bodies are:
|
||||||
|
- the granite (1 or 2 solids)
|
||||||
|
- the translation stage
|
||||||
|
- the tilt stage
|
||||||
|
- the spindle and slip-ring
|
||||||
|
- the hexapod
|
||||||
|
|
||||||
|
#+name: fig:nass_solidworks
|
||||||
|
#+caption: CAD view of the ID31 Micro-Station
|
||||||
|
#+attr_html: :width 800px
|
||||||
|
[[file:img/nass_solidworks.png]]
|
||||||
|
|
||||||
|
However, each of the DOF of the system may not be relevant for the modes present in the frequency band of interest.
|
||||||
|
For instance, the translation stage may not vibrate in the Z direction for all the modes identified. Then, we can block this DOF and this simplifies the model.
|
||||||
|
|
||||||
|
The modal identification done here will thus permit us to determine *which DOF can be neglected*.
|
||||||
|
|||||||
317
modal-analysis/matlab/modal_frf_coh.m
Normal file
317
modal-analysis/matlab/modal_frf_coh.m
Normal file
@@ -0,0 +1,317 @@
|
|||||||
|
%% Clear Workspace and Close figures
|
||||||
|
clear; close all; clc;
|
||||||
|
|
||||||
|
%% Intialize Laplace variable
|
||||||
|
s = zpk('s');
|
||||||
|
|
||||||
|
% Windowing
|
||||||
|
% Windowing is used on the force and response signals.
|
||||||
|
|
||||||
|
% A boxcar window (figure [[fig:windowing_force_signal]]) is used for the force signal as once the impact on the structure is done, the measured signal is meaningless.
|
||||||
|
% The parameters are:
|
||||||
|
% - *Start*: $3\%$
|
||||||
|
% - *Stop*: $7\%$
|
||||||
|
|
||||||
|
|
||||||
|
figure;
|
||||||
|
plot(100*[0, 0.03, 0.03, 0.07, 0.07, 1], [0, 0, 1, 1, 0, 0]);
|
||||||
|
xlabel('Time [%]'); ylabel('Amplitude');
|
||||||
|
xlim([0, 100]); ylim([0, 1]);
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:windowing_force_signal
|
||||||
|
% #+CAPTION: Window used for the force signal
|
||||||
|
% [[file:figs/windowing_force_signal.png]]
|
||||||
|
|
||||||
|
% An exponential window (figure [[fig:windowing_response_signal]]) is used for the response signal as we are measuring transient signals and most of the information is located at the beginning of the signal.
|
||||||
|
% The parameters are:
|
||||||
|
% - FlatTop:
|
||||||
|
% - *Start*: $3\%$
|
||||||
|
% - *Stop*: $2.96\%$
|
||||||
|
% - Decreasing point:
|
||||||
|
% - *X*: $60.4\%$
|
||||||
|
% - *Y*: $14.7\%$
|
||||||
|
|
||||||
|
|
||||||
|
x0 = 0.296;
|
||||||
|
xd = 0.604;
|
||||||
|
yd = 0.147;
|
||||||
|
|
||||||
|
alpha = log(yd)/(x0 - xd);
|
||||||
|
|
||||||
|
t = x0:0.01:1.01;
|
||||||
|
y = exp(-alpha*(t-x0));
|
||||||
|
|
||||||
|
figure;
|
||||||
|
plot(100*[0, 0.03, 0.03, x0, t], [0, 0, 1, 1, y]);
|
||||||
|
xlabel('Time [%]'); ylabel('Amplitude');
|
||||||
|
xlim([0, 100]); ylim([0, 1]);
|
||||||
|
|
||||||
|
% Force and Response signals
|
||||||
|
% Let's load some obtained data to look at the force and response signals.
|
||||||
|
|
||||||
|
|
||||||
|
meas1_raw = load('mat/meas_raw_1.mat');
|
||||||
|
|
||||||
|
% Raw Force Data
|
||||||
|
% The force input for the first measurement is shown on figure [[fig:raw_data_force]]. We can see 10 impacts, one zoom on one impact is shown on figure [[fig:raw_data_force_zoom]].
|
||||||
|
|
||||||
|
% The Fourier transform of the force is shown on figure [[fig:fourier_transfor_force_impact]]. This has been obtained without any windowing.
|
||||||
|
|
||||||
|
|
||||||
|
time = linspace(0, meas1_raw.Track1_X_Resolution*length(meas1_raw.Track1), length(meas1_raw.Track1));
|
||||||
|
|
||||||
|
figure;
|
||||||
|
plot(time, meas1_raw.Track1);
|
||||||
|
xlabel('Time [s]');
|
||||||
|
ylabel('Force [N]');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:raw_data_force
|
||||||
|
% #+CAPTION: Raw Force Data from Hammer Blow
|
||||||
|
% [[file:figs/raw_data_force.png]]
|
||||||
|
|
||||||
|
|
||||||
|
figure;
|
||||||
|
plot(time, meas1_raw.Track1);
|
||||||
|
xlabel('Time [s]');
|
||||||
|
ylabel('Force [N]');
|
||||||
|
xlim([22.1, 22.3]);
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:raw_data_force_zoom
|
||||||
|
% #+CAPTION: Raw Force Data from Hammer Blow - Zoom
|
||||||
|
% [[file:figs/raw_data_force_zoom.png]]
|
||||||
|
|
||||||
|
|
||||||
|
Fs = 1/meas1_raw.Track1_X_Resolution; % Sampling Frequency [Hz]
|
||||||
|
impacts = [5.9, 11.2, 16.6, 22.2, 27.3, 32.7, 38.1, 43.8, 50.4]; % Time just before the impact occurs [s]
|
||||||
|
|
||||||
|
L = 8194;
|
||||||
|
f = Fs*(0:(L/2))/L; % Frequency vector [Hz]
|
||||||
|
|
||||||
|
F_fft = zeros((8193+1)/2+1, length(impacts));
|
||||||
|
|
||||||
|
for i = 1:length(impacts)
|
||||||
|
t0 = impacts(i);
|
||||||
|
[~, i_start] = min(abs(time-t0));
|
||||||
|
i_end = i_start + 8193;
|
||||||
|
|
||||||
|
Y = fft(meas1_raw.Track1(i_start:i_end));
|
||||||
|
|
||||||
|
P2 = abs(Y/L);
|
||||||
|
P1 = P2(1:L/2+1);
|
||||||
|
P1(2:end-1) = 2*P1(2:end-1);
|
||||||
|
F_fft(:, i) = P1;
|
||||||
|
end
|
||||||
|
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
for i = 1:length(impacts)
|
||||||
|
plot(f, F_fft(:, i), '-k');
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
xlim([0, 200]);
|
||||||
|
xlabel('Frequency [Hz]'); ylabel('Force [N]');
|
||||||
|
|
||||||
|
% Raw Response Data
|
||||||
|
% The response signal for the first measurement is shown on figure [[fig:raw_data_acceleration]]. One zoom on one response is shown on figure [[fig:raw_data_acceleration_zoom]].
|
||||||
|
|
||||||
|
% The Fourier transform of the response signals is shown on figure [[fig:fourier_transform_response_signals]]. This has been obtained without any windowing.
|
||||||
|
|
||||||
|
|
||||||
|
figure;
|
||||||
|
plot(time, meas1_raw.Track2);
|
||||||
|
xlabel('Time [s]');
|
||||||
|
ylabel('Acceleration [m/s2]');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:raw_data_acceleration
|
||||||
|
% #+CAPTION: Raw Acceleration Data from Accelerometer
|
||||||
|
% [[file:figs/raw_data_acceleration.png]]
|
||||||
|
|
||||||
|
|
||||||
|
figure;
|
||||||
|
plot(time, meas1_raw.Track2);
|
||||||
|
xlabel('Time [s]');
|
||||||
|
ylabel('Acceleration [m/s2]');
|
||||||
|
xlim([22.1, 22.5]);
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:raw_data_acceleration_zoom
|
||||||
|
% #+CAPTION: Raw Acceleration Data from Accelerometer - Zoom
|
||||||
|
% [[file:figs/raw_data_acceleration_zoom.png]]
|
||||||
|
|
||||||
|
|
||||||
|
X_fft = zeros((8193+1)/2+1, length(impacts));
|
||||||
|
|
||||||
|
for i = 1:length(impacts)
|
||||||
|
t0 = impacts(i);
|
||||||
|
[~, i_start] = min(abs(time-t0));
|
||||||
|
i_end = i_start + 8193;
|
||||||
|
|
||||||
|
Y = fft(meas1_raw.Track2(i_start:i_end));
|
||||||
|
|
||||||
|
P2 = abs(Y/L);
|
||||||
|
P1 = P2(1:L/2+1);
|
||||||
|
P1(2:end-1) = 2*P1(2:end-1);
|
||||||
|
X_fft(:, i) = P1;
|
||||||
|
end
|
||||||
|
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
for i = 1:length(impacts)
|
||||||
|
plot(f, X_fft(:, i), '-k');
|
||||||
|
end
|
||||||
|
hold off;
|
||||||
|
xlim([0, 200]);
|
||||||
|
set(gca, 'Yscale', 'log');
|
||||||
|
xlabel('Frequency [Hz]'); ylabel('Acceleration [$m/s^2$]');
|
||||||
|
|
||||||
|
% Computation of one Frequency Response Function
|
||||||
|
% Now that we have obtained the Fourier transform of both the force input and the response signal, we can compute the Frequency Response Function from the force to the acceleration.
|
||||||
|
|
||||||
|
% We then compare the result obtained with the FRF computed by the modal software (figure [[fig:frf_comparison_software]]).
|
||||||
|
|
||||||
|
% The slight difference can probably be explained by the use of windows.
|
||||||
|
|
||||||
|
% In the following analysis, FRF computed from the software will be used.
|
||||||
|
|
||||||
|
|
||||||
|
meas1 = load('mat/meas_frf_coh_1.mat');
|
||||||
|
|
||||||
|
figure;
|
||||||
|
hold on;
|
||||||
|
for i = 1:length(impacts)
|
||||||
|
plot(f, X_fft(:, i)./F_fft(:, i), '-k');
|
||||||
|
end
|
||||||
|
plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_AvSpc_2_RMS_Y_Val)
|
||||||
|
hold off;
|
||||||
|
xlim([0, 200]);
|
||||||
|
set(gca, 'Yscale', 'log');
|
||||||
|
xlabel('Frequency [Hz]'); ylabel('Acceleration/Force [$m/s^2/N$]');
|
||||||
|
|
||||||
|
% Frequency Response Functions and Coherence Results
|
||||||
|
% Let's see one computed Frequency Response Function and one coherence in order to attest the quality of the measurement.
|
||||||
|
|
||||||
|
% First, we load the data.
|
||||||
|
|
||||||
|
meas1 = load('mat/meas_frf_coh_1.mat');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% And we plot on figure [[fig:frf_result_example]] the frequency response function from the force applied in the $X$ direction at the location of the accelerometer number 11 to the acceleration in the $X$ direction as measured by the first accelerometer located on the top platform of the hexapod.
|
||||||
|
|
||||||
|
% The coherence associated is shown on figure [[fig:frf_result_example]].
|
||||||
|
|
||||||
|
|
||||||
|
figure;
|
||||||
|
ax1 = subplot(2, 1, 1);
|
||||||
|
plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_AvXSpc_2_1_RMS_Y_Mod);
|
||||||
|
set(gca, 'Yscale', 'log');
|
||||||
|
set(gca, 'XTickLabel',[]);
|
||||||
|
ylabel('Magnitude');
|
||||||
|
|
||||||
|
ax2 = subplot(2, 1, 2);
|
||||||
|
plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_AvXSpc_2_1_RMS_Y_Phas);
|
||||||
|
ylim([-180, 180]);
|
||||||
|
yticks([-180, -90, 0, 90, 180]);
|
||||||
|
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||||
|
|
||||||
|
linkaxes([ax1,ax2],'x');
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% #+NAME: fig:frf_result_example
|
||||||
|
% #+CAPTION: Example of one measured FRF
|
||||||
|
% [[file:figs/frf_result_example.png]]
|
||||||
|
|
||||||
|
|
||||||
|
figure;
|
||||||
|
plot(meas1.FFT1_AvSpc_2_RMS_X_Val, meas1.FFT1_Coh_2_1_RMS_Y_Val);
|
||||||
|
xlabel('Frequency [Hz]');
|
||||||
|
ylabel('Coherence');
|
||||||
|
|
||||||
|
% Generation of a FRF matrix and a Coherence matrix from the measurements
|
||||||
|
% We want here to combine all the Frequency Response Functions measured into one big array called the *Frequency Response Matrix*.
|
||||||
|
|
||||||
|
% The frequency response matrix is an $n \times p \times q$:
|
||||||
|
% - $n$ is the number of measurements: $23 \times 3$ (23 accelerometers measuring 3 directions each)
|
||||||
|
% - $p$ is the number of excitation inputs: $3$
|
||||||
|
% - $q$ is the number of frequency points $\omega_i$
|
||||||
|
|
||||||
|
% Thus, the FRF matrix is an $69 \times 3 \times 801$ matrix.
|
||||||
|
|
||||||
|
|
||||||
|
% #+begin_important
|
||||||
|
% For each frequency point $\omega_i$, we obtain a 2D matrix:
|
||||||
|
% \begin{equation}
|
||||||
|
% \text{FRF}(\omega_i) = \begin{bmatrix}
|
||||||
|
% \frac{D_{1_x}}{F_x}(\omega_i) & \frac{D_{1_x}}{F_y}(\omega_i) & \frac{D_{1_x}}{F_z}(\omega_i) \\
|
||||||
|
% \frac{D_{1_y}}{F_x}(\omega_i) & \frac{D_{1_y}}{F_y}(\omega_i) & \frac{D_{1_y}}{F_z}(\omega_i) \\
|
||||||
|
% \frac{D_{1_z}}{F_x}(\omega_i) & \frac{D_{1_z}}{F_y}(\omega_i) & \frac{D_{1_z}}{F_z}(\omega_i) \\
|
||||||
|
% \frac{D_{2_x}}{F_x}(\omega_i) & \frac{D_{2_x}}{F_y}(\omega_i) & \frac{D_{2_x}}{F_z}(\omega_i) \\
|
||||||
|
% \vdots & \vdots & \vdots \\
|
||||||
|
% \frac{D_{23_z}}{F_x}(\omega_i) & \frac{D_{23_z}}{F_y}(\omega_i) & \frac{D_{23_z}}{F_z}(\omega_i) \\
|
||||||
|
% \end{bmatrix}
|
||||||
|
% \end{equation}
|
||||||
|
% #+end_important
|
||||||
|
|
||||||
|
% We generate such FRF matrix from the measurements using the following script.
|
||||||
|
|
||||||
|
n_meas = 24;
|
||||||
|
n_acc = 23;
|
||||||
|
|
||||||
|
dirs = 'XYZ';
|
||||||
|
|
||||||
|
% Number of Accelerometer * DOF for each acccelerometer / Number of excitation / frequency points
|
||||||
|
FRFs = zeros(3*n_acc, 3, 801);
|
||||||
|
COHs = zeros(3*n_acc, 3, 801);
|
||||||
|
|
||||||
|
% Loop through measurements
|
||||||
|
for i = 1:n_meas
|
||||||
|
% Load the measurement file
|
||||||
|
meas = load(sprintf('mat/meas_frf_coh_%i.mat', i));
|
||||||
|
|
||||||
|
% First: determine what is the exitation (direction and sign)
|
||||||
|
exc_dir = meas.FFT1_AvXSpc_2_1_RMS_RfName(end);
|
||||||
|
exc_sign = meas.FFT1_AvXSpc_2_1_RMS_RfName(end-1);
|
||||||
|
% Determine what is the correct excitation sign
|
||||||
|
exc_factor = str2num([exc_sign, '1']);
|
||||||
|
if exc_dir ~= 'Z'
|
||||||
|
exc_factor = exc_factor*(-1);
|
||||||
|
end
|
||||||
|
|
||||||
|
% Then: loop through the nine measurements and store them at the correct location
|
||||||
|
for j = 2:10
|
||||||
|
% Determine what is the accelerometer and direction
|
||||||
|
[indices_acc_i] = strfind(meas.(sprintf('FFT1_H1_%i_1_RpName', j)), '.');
|
||||||
|
acc_i = str2num(meas.(sprintf('FFT1_H1_%i_1_RpName', j))(indices_acc_i(1)+1:indices_acc_i(2)-1));
|
||||||
|
|
||||||
|
meas_dir = meas.(sprintf('FFT1_H1_%i_1_RpName', j))(end);
|
||||||
|
meas_sign = meas.(sprintf('FFT1_H1_%i_1_RpName', j))(end-1);
|
||||||
|
% Determine what is the correct measurement sign
|
||||||
|
meas_factor = str2num([meas_sign, '1']);
|
||||||
|
if meas_dir ~= 'Z'
|
||||||
|
meas_factor = meas_factor*(-1);
|
||||||
|
end
|
||||||
|
|
||||||
|
% FRFs(acc_i+n_acc*(find(dirs==meas_dir)-1), find(dirs==exc_dir), :) = exc_factor*meas_factor*meas.(sprintf('FFT1_H1_%i_1_Y_ReIm', j));
|
||||||
|
% COHs(acc_i+n_acc*(find(dirs==meas_dir)-1), find(dirs==exc_dir), :) = meas.(sprintf('FFT1_Coh_%i_1_RMS_Y_Val', j));
|
||||||
|
|
||||||
|
FRFs(find(dirs==meas_dir)+3*(acc_i-1), find(dirs==exc_dir), :) = exc_factor*meas_factor*meas.(sprintf('FFT1_H1_%i_1_Y_ReIm', j));
|
||||||
|
COHs(find(dirs==meas_dir)+3*(acc_i-1), find(dirs==exc_dir), :) = meas.(sprintf('FFT1_Coh_%i_1_RMS_Y_Val', j));
|
||||||
|
end
|
||||||
|
end
|
||||||
|
freqs = meas.FFT1_Coh_10_1_RMS_X_Val;
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
% And we save the obtained FRF matrix and Coherence matrix in a =.mat= file.
|
||||||
|
|
||||||
|
save('./mat/frf_coh_matrices.mat', 'FRFs', 'COHs', 'freqs');
|
||||||
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
Reference in New Issue
Block a user