https://cstwiki.wtb.tue.nl/index.php?title=Viotar/Model&feed=atom&action=historyViotar/Model - Revision history2024-03-19T11:10:10ZRevision history for this page on the wikiMediaWiki 1.39.5https://cstwiki.wtb.tue.nl/index.php?title=Viotar/Model&diff=484&oldid=prevS070790 at 14:31, 25 January 20112011-01-25T14:31:56Z<p></p>
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</table>S070790https://cstwiki.wtb.tue.nl/index.php?title=Viotar/Model&diff=460&oldid=prevS070790 at 19:55, 24 January 20112011-01-24T19:55:40Z<p></p>
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</table>S070790https://cstwiki.wtb.tue.nl/index.php?title=Viotar/Model&diff=375&oldid=prevS071253: /* Analysis with the new model */2011-01-03T20:32:21Z<p><span dir="auto"><span class="autocomment">Analysis with the new model</span></span></p>
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</table>S071253https://cstwiki.wtb.tue.nl/index.php?title=Viotar/Model&diff=374&oldid=prevS071253: /* Analysis with the new model */2011-01-03T20:31:50Z<p><span dir="auto"><span class="autocomment">Analysis with the new model</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Region of Helmholtz motion in parameter space====</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Region of Helmholtz motion in parameter space====</div></td></tr>
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</table>S071253https://cstwiki.wtb.tue.nl/index.php?title=Viotar/Model&diff=373&oldid=prevS071253: /* Analysis with the new model */2011-01-03T20:31:28Z<p><span dir="auto"><span class="autocomment">Analysis with the new model</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:31, 3 January 2011</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>With the right model a Helmholtz vibration can be generated. This vibration can be analysed afterwards using matlab. The model itself recognises if the generated vibration is a Helmholtz vibration or a noisy type of vibration. We took a Helmholtz vibration, which looks like the left figure below, and made an m-file that generates a fourier transformation of that vibration. The powerspectrum that was generated is shown in the right figure below. These type of figures will be very important later on as we will see in the chapter 'Software Design (Quantifying the signal we want to see)'.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>With the right model a Helmholtz vibration can be generated. This vibration can be analysed afterwards using matlab. The model itself recognises if the generated vibration is a Helmholtz vibration or a noisy type of vibration. We took a Helmholtz vibration, which looks like the left figure below, and made an m-file that generates a fourier transformation of that vibration. The powerspectrum that was generated is shown in the right figure below. These type of figures will be very important later on as we will see in the chapter 'Software Design (Quantifying the signal we want to see)'.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[File:HEL.PNG|frame|border|<del style="font-weight: bold; text-decoration: none;">left</del>|Figure 7: Helmholtz vibration and it's powerspectrum]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[File:HEL.PNG|frame|border|<ins style="font-weight: bold; text-decoration: none;">center</ins>|Figure 7: Helmholtz vibration and it's powerspectrum]]</div></td></tr>
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</table>S071253https://cstwiki.wtb.tue.nl/index.php?title=Viotar/Model&diff=372&oldid=prevS071253: /* Adapting the model for the controller */2011-01-03T20:23:28Z<p><span dir="auto"><span class="autocomment">Adapting the model for the controller</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== Adapting the model for the controller ====</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==== Adapting the model for the controller ====</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The model is a practical instrument for designing a controller. This gives the ability to design a controller without actually having the real prototype. Besides the advantage that both the prototype and the controller can be designed simultaneously, it also has the advantage that the influence of a certain input on the output can be checked very easily. This will also become clear in the chapter 'Software Design (Quantifying the signal we want to see)'. The model as we received from mr. Woodhouse, contains a loop to generate vibrations for varying β, bowing speed and force. To make the model suitable for the controller, we adapted it and removed the loop. The simulation model is a function that has bowing speed and force as input variables, while β is kept constant. We run this function file in simulink, where the input parameters can be changed on the fly. Every time step, the function is called, which calculates the new location of the simulated bowing point. This gives the ability to construct a controller which adapts the input variables for the function every time step. In this way, the model simulates the response of the guitar to certain input variables.</ins></div></td></tr>
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</table>S071253https://cstwiki.wtb.tue.nl/index.php?title=Viotar/Model&diff=371&oldid=prevS071253: /* New computer model */2011-01-03T19:49:08Z<p><span dir="auto"><span class="autocomment">New computer model</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===New computer model===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===New computer model===</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Since the model we made did not satisfy the fact that frequency should not depend on bowing speed and force, we contacted an expert for help. This expert, J. Woodhouse from the Cambridge University, has done several studies about the behaviour of a bowed string. He helped us a lot by sending a model he made years ago for recognizing Helmholtz vibration. He also used this model to define the Helmholtz region as a function of bowing speed, applied force and β. We adapted and used this model for our controller and to do analysis of Helmholtz vibrations.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Analysis with the new model====</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====Analysis with the new model====</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[File:Helmholtzregionmodpath.png|frame|Border|center|Figure 8: The green path indicates the ideal modulation path.]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[File:Helmholtzregionmodpath.png|frame|Border|center|Figure 8: The green path indicates the ideal modulation path.]]</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
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</table>S071253https://cstwiki.wtb.tue.nl/index.php?title=Viotar/Model&diff=370&oldid=prevS071253: /* Model */2011-01-03T19:22:02Z<p><span dir="auto"><span class="autocomment">Model</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:22, 3 January 2011</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This problem is most probably caused by another problem, being the stiffness of the string. This stiffness plays an important role in the vibration of the string as it adds another force to force equation.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This problem is most probably caused by another problem, being the stiffness of the string. This stiffness plays an important role in the vibration of the string as it adds another force to force equation.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===Analysis with <del style="font-weight: bold; text-decoration: none;">het </del>model===</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===New computer model===</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">=</ins>===Analysis with <ins style="font-weight: bold; text-decoration: none;">the new </ins>model<ins style="font-weight: bold; text-decoration: none;">=</ins>===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>With the right model a Helmholtz vibration can be generated. This vibration can be analysed afterwards using matlab. The model itself recognises if the generated vibration is a Helmholtz vibration or a noisy type of vibration. We took a Helmholtz vibration, which looks like the left figure below, and made an m-file that generates a fourier transformation of that vibration. The powerspectrum that was generated is shown in the right figure below. These type of figures will be very important later on as we will see in the chapter 'Software Design (Quantifying the signal we want to see)'.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>With the right model a Helmholtz vibration can be generated. This vibration can be analysed afterwards using matlab. The model itself recognises if the generated vibration is a Helmholtz vibration or a noisy type of vibration. We took a Helmholtz vibration, which looks like the left figure below, and made an m-file that generates a fourier transformation of that vibration. The powerspectrum that was generated is shown in the right figure below. These type of figures will be very important later on as we will see in the chapter 'Software Design (Quantifying the signal we want to see)'.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===Region of Helmholtz motion in parameter space===</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">=</ins>===Region of Helmholtz motion in parameter space<ins style="font-weight: bold; text-decoration: none;">=</ins>===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The model has been run for a 20x20 grid of bowing speeds and bow forces. This has yielded the plot of Figure 7.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The model has been run for a 20x20 grid of bowing speeds and bow forces. This has yielded the plot of Figure 7.</div></td></tr>
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</table>S071253https://cstwiki.wtb.tue.nl/index.php?title=Viotar/Model&diff=369&oldid=prevS071253: /* Region of Helmholtz motion in parameter space */2011-01-03T18:05:58Z<p><span dir="auto"><span class="autocomment">Region of Helmholtz motion in parameter space</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:05, 3 January 2011</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Region of Helmholtz motion in parameter space===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Region of Helmholtz motion in parameter space===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The model has been run for a 20x20 grid of bowing speeds and bow forces. This has yielded the plot of Figure <del style="font-weight: bold; text-decoration: none;">1</del>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The model has been run for a 20x20 grid of bowing speeds and bow forces. This has yielded the plot of Figure <ins style="font-weight: bold; text-decoration: none;">7</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[File:Helmholtzregion.png|frame|Border|center|Figure <del style="font-weight: bold; text-decoration: none;">1</del>: Model-generated plot. Where there’s blue, there’s no Helmholtz motion. The other colors indicate note flattening effect. The darker red, the bigger the flattening.]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[File:Helmholtzregion.png|frame|Border|center|Figure <ins style="font-weight: bold; text-decoration: none;">7</ins>: Model-generated plot. Where there’s blue, there’s no Helmholtz motion. The other colors indicate note flattening effect. The darker red, the bigger the flattening.]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>It’s interesting that there are exceptions to the main trend in the figure, that is, the “holes” in the Helmholtz region and the occurrences of Helmholtz outside the main region. This is strange because in a mathematical model, unlike in “reality”, there’s no noise or chaos. Probably, the reason why the results may be unpredictable is that these are not steady-state results, so there may still be startup phenomena. A way we may solve it in the future is to use “perfect transients”, in which Helmholtz motion is obtained within one period by following a certain acceleration path for the bow speed. Restrain should also be kept regarding the accuracy of the algorithm that “recognizes” if there is a Helmholtz vibration or not.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>It’s interesting that there are exceptions to the main trend in the figure, that is, the “holes” in the Helmholtz region and the occurrences of Helmholtz outside the main region. This is strange because in a mathematical model, unlike in “reality”, there’s no noise or chaos. Probably, the reason why the results may be unpredictable is that these are not steady-state results, so there may still be startup phenomena. A way we may solve it in the future is to use “perfect transients”, in which Helmholtz motion is obtained within one period by following a certain acceleration path for the bow speed. Restrain should also be kept regarding the accuracy of the algorithm that “recognizes” if there is a Helmholtz vibration or not.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Despite the inaccuracies, there is already valuable info in this plot. It becomes very clear “where” in the parameter space you want to be, as the lower part of the Helmholtz region has the smallest note flattening. When modulating the note intensity, the ideal path that should be taken would be somewhat like the green line drawn in Figure <del style="font-weight: bold; text-decoration: none;">2</del>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Despite the inaccuracies, there is already valuable info in this plot. It becomes very clear “where” in the parameter space you want to be, as the lower part of the Helmholtz region has the smallest note flattening. When modulating the note intensity, the ideal path that should be taken would be somewhat like the green line drawn in Figure <ins style="font-weight: bold; text-decoration: none;">8</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[File:Helmholtzregionmodpath.png|frame|Border|center|Figure <del style="font-weight: bold; text-decoration: none;">2</del>: The green path indicates the ideal modulation path.]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[File:Helmholtzregionmodpath.png|frame|Border|center|Figure <ins style="font-weight: bold; text-decoration: none;">8</ins>: The green path indicates the ideal modulation path.]]</div></td></tr>
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</table>S071253https://cstwiki.wtb.tue.nl/index.php?title=Viotar/Model&diff=368&oldid=prevS071253: /* Model */2011-01-03T18:05:24Z<p><span dir="auto"><span class="autocomment">Model</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:05, 3 January 2011</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l91">Line 91:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the simple friction curve model, like it is presented in figure 3, it is assumed that the friction force only depends on the relative force between the string and the bow. However, experiments have proved that the true situation is not quite as simple as that. The dotted line in figure 4 shows the relation between string velocity and friction coefficient as described by the model above. The continuous line shows the real situation, which has been measured experimentally. From this figure it can be concluded that the classical approach is quite unprecise.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In the simple friction curve model, like it is presented in figure 3, it is assumed that the friction force only depends on the relative force between the string and the bow. However, experiments have proved that the true situation is not quite as simple as that. The dotted line in figure 4 shows the relation between string velocity and friction coefficient as described by the model above. The continuous line shows the real situation, which has been measured experimentally. From this figure it can be concluded that the classical approach is quite unprecise.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>====<del style="font-weight: bold; text-decoration: none;">Verklaringen voor fouten </del>in <del style="font-weight: bold; text-decoration: none;">het frictiemodel</del>====</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>====<ins style="font-weight: bold; text-decoration: none;">Explanations for errors </ins>in <ins style="font-weight: bold; text-decoration: none;">the friction model</ins>====</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>One of the reasons for this, is that the temperature of the interaction area is of very high importance. This is because of the melting temperature of the rosin. When the relative speed is low, the contact area cools down due to conductance in the string and bow. This causes the friction coefficient to increase. When more 'slip' behaviour occurs, this causes the temperature to raise and therefor the friction coefficient tot decrease rapidly.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>One of the reasons for this, is that the temperature of the interaction area is of very high importance. This is because of the melting temperature of the rosin. When the relative speed is low, the contact area cools down due to conductance in the string and bow. This causes the friction coefficient to increase. When more 'slip' behaviour occurs, this causes the temperature to raise and therefor the friction coefficient tot decrease rapidly.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>However, experiments proved that the simple representation of the friction curve model is precise enough to simulate what the influence of changing the bowing speed and force is, on the occurence of a Helmholtz vibration. For our computer model we will use the friction curve, like it is presented in figure 3 which will satisfy.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>However, experiments proved that the simple representation of the friction curve model is precise enough to simulate what the influence of changing the bowing speed and force is, on the occurence of a Helmholtz vibration. For our computer model we will use the friction curve, like it is presented in figure 3 which will satisfy.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>===<del style="font-weight: bold; text-decoration: none;">Computermodel</del>===</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>===<ins style="font-weight: bold; text-decoration: none;">Computer model</ins>===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>====<del style="font-weight: bold; text-decoration: none;">Variabelen</del>====</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>====<ins style="font-weight: bold; text-decoration: none;">Variabels</ins>====</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">There are 3 variables that can be set in this model. These are the bowing speed v<sub>b</sub>, bowing force f<sub>b</sub> and a factor that indicates the distance between the bow and the bridge and the bow, in relation to the length of the string (β).</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Er zijn 3 waarden in te stellen in het model. Dit zijn de snelheid van de boog (vb), de druk die met de boog op de snaar uitgeoefend wordt (Fb) en als laatste een factor die de afstand tussen de boog en de kam ten opzichte van de lengte van de snaar aangeeft (beta).</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">====Working of the program====</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">====Werking van het programma====</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[File:Gauss.PNG|frame| Border|right| Figure 6: Symmetric Gauss curve]]</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">[[File:Gauss</del>.<del style="font-weight: bold; text-decoration: none;">PNG|frame| Border|right| Figuur 6: De symmetrische Gauss-kromme</del>.<del style="font-weight: bold; text-decoration: none;">]]</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In the computer program, the simulation is devided into n intervals of size dt</ins>. <ins style="font-weight: bold; text-decoration: none;">The program runs through a loop for every time step dt. Using the known values (from earlier time steps)for position of the string, velocity of the string and applied force on the bow, new values for these quantities are calculated. Important is that the speed at which an applied force moves through the string, is known. With this structure it is always possible to calculate the new values on time i, using the values from the past. To illustrate the working of the program, one loop will be run through in the following part</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">In het programma wordt het simulatiegebied opgedeeld in n intervallen, met een grootte dt. Het programma doorloopt voor elke tijdstap dt een loop waarin met behulp van bekende waarden voor de positie, kracht en snelheid uit het verleden de nieuwe waarden voor deze grootheden bepaald kunnen worden. Van belang hierbij is dat de snelheid waarmee een op de snaar uitgeoefende kracht zich door de snaar beweegt bekend is. Zo kan er op tijdstip i altijd terug gekeken worden in de geschiedenis welke krachten uit het verleden op tijdstip i teruggekaatst zijn en dus weer van invloed zijn op de beweging van het gesimuleerde punt. Om de exacte werking van het model te illustreren, zal hieronder de loop van één tijdstap doorlopen worden. Het model zelf is ook bijgevoegd. (Let op! Het model is nog niet werkend of voorzien van commentaar).</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The string will be evaluated at position </ins>x <ins style="font-weight: bold; text-decoration: none;">on time </ins>i. <ins style="font-weight: bold; text-decoration: none;">Vibrations caused at position </ins>x, <ins style="font-weight: bold; text-decoration: none;">will move along the string to the ends</ins>, <ins style="font-weight: bold; text-decoration: none;">where the vibrations are reflected to position </ins>x. <ins style="font-weight: bold; text-decoration: none;">On time i, the time is calculated at which the vibrations that arrive on time </ins>i <ins style="font-weight: bold; text-decoration: none;">where caused on position </ins>x. <ins style="font-weight: bold; text-decoration: none;">So, this </ins>is <ins style="font-weight: bold; text-decoration: none;">a moment </ins>in <ins style="font-weight: bold; text-decoration: none;">the past</ins>. <ins style="font-weight: bold; text-decoration: none;">Beacause the travelling time of the waves </ins>is <ins style="font-weight: bold; text-decoration: none;">usually not a multiple of </ins>dt, <ins style="font-weight: bold; text-decoration: none;">the real time should most of the time be interpolated between two values</ins>. <ins style="font-weight: bold; text-decoration: none;">Beacuse </ins>of <ins style="font-weight: bold; text-decoration: none;">the fact that vibrations that are nearly at position </ins>x <ins style="font-weight: bold; text-decoration: none;">are also important for the movement of position </ins>x, <ins style="font-weight: bold; text-decoration: none;">also these vibrations are taken into account</ins>. <ins style="font-weight: bold; text-decoration: none;">Using a symmetric </ins>Gauss <ins style="font-weight: bold; text-decoration: none;">curve </ins>(<ins style="font-weight: bold; text-decoration: none;">figure </ins>6)<ins style="font-weight: bold; text-decoration: none;">, the influence of these vibrations is calculated and added to the vibration that has exactly returned on time </ins>i. <ins style="font-weight: bold; text-decoration: none;">All these vibrations together are forces that influence the vibration (velocity) of position x. Using the friction curve model, this resulting force can be converted to a new string velocity. This gives the string velocity </ins>v<ins style="font-weight: bold; text-decoration: none;"><sub></ins>i<ins style="font-weight: bold; text-decoration: none;"></sub> on time </ins>i. </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">De snaar wordt bekeken op positie </del>x <del style="font-weight: bold; text-decoration: none;">op tijdstip </del>i. <del style="font-weight: bold; text-decoration: none;">Trillingen die op positie </del>x <del style="font-weight: bold; text-decoration: none;">veroorzaakt worden</del>, <del style="font-weight: bold; text-decoration: none;">gaan via de snaar naar de uiteinden van de snaar</del>, <del style="font-weight: bold; text-decoration: none;">van waar ze teruggekaatst worden naar positie </del>x. <del style="font-weight: bold; text-decoration: none;">Op tijdstip </del>i <del style="font-weight: bold; text-decoration: none;">wordt eerst uitgerekend op welk tijdstip de trillingen die op dat moment terugkomen op positie </del>x <del style="font-weight: bold; text-decoration: none;">uitgezonden werden</del>. <del style="font-weight: bold; text-decoration: none;">Dit </del>is <del style="font-weight: bold; text-decoration: none;">dus een tijdstip </del>in <del style="font-weight: bold; text-decoration: none;">het verleden</del>. <del style="font-weight: bold; text-decoration: none;">Aangezien de snelheid waarmee de golf zich voortplant geen meervoud </del>is <del style="font-weight: bold; text-decoration: none;">van </del>dt, <del style="font-weight: bold; text-decoration: none;">zal er meestal geïnterpoleerd moeten worden tussen twee tijdstippen</del>. <del style="font-weight: bold; text-decoration: none;">Omdat trillingen die nog niet helemaal teruggekeerd zijn, </del>of <del style="font-weight: bold; text-decoration: none;">juist alweer voorbij positie </del>x <del style="font-weight: bold; text-decoration: none;">zijn ook invloed hebben op de beweging op positie </del>x, <del style="font-weight: bold; text-decoration: none;">wordt er ook rekening gehouden met deze trillingen</del>. <del style="font-weight: bold; text-decoration: none;">Met behulp van een symmetrische </del>Gauss<del style="font-weight: bold; text-decoration: none;">-kromme </del>(<del style="font-weight: bold; text-decoration: none;">zie figuur </del>6) <del style="font-weight: bold; text-decoration: none;">wordt de invloed van deze trillingen uitgerekend en opgeteld bij de trilling die precies op tijdstip </del>i <del style="font-weight: bold; text-decoration: none;">is teruggekeerd</del>. <del style="font-weight: bold; text-decoration: none;">Al deze trillingen zijn in feite krachten die van invloed zijn op de snaarsnelheid </del>v <del style="font-weight: bold; text-decoration: none;">op tijdstip </del>i<del style="font-weight: bold; text-decoration: none;">. Met behulp van het frictiemodel kunnen de resulterende kracht omgezet worden in een nieuwe snaarsnelheid. Dit is dus de snaarsnelheid vi op tijdstip </del>i.</div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">When this loop is run through for all time steps, there is a vector v which contains the string velocity for every time i. The position of point x can easily be calculated using this vector by integrating over the time steps dt.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">When the complete vibration of the string is known (postion as a function of time), a powerspectrum can be made using fourier transformation. This gives the amplitude ratios in the frequency domain.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Als deze loop voor alle tijdstappen doorlopen </del>is, is <del style="font-weight: bold; text-decoration: none;">er dus een vector v gemaakt met daarin voor elke tijdstap i de bijbehorende snelheid vi</del>. <del style="font-weight: bold; text-decoration: none;">Uit deze snelheidsvector kan eenvoudig de positievector u bepaald worden door middel van integratie over alle tijdstappen dt</del>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">====Problems====</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The biggest problem so far, is that the frequency of the vibration seems to be depending on the bowing speed and force. In reality this is not the case, and </ins>is <ins style="font-weight: bold; text-decoration: none;">the frequency only depending on the length and the width of the string. Varying the bowing speed and force</ins>, <ins style="font-weight: bold; text-decoration: none;">only changes the amplitude and therefor the loudness of the vibration in reality.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">This problem </ins>is <ins style="font-weight: bold; text-decoration: none;">most probably caused by another problem, being the stiffness of the string</ins>. <ins style="font-weight: bold; text-decoration: none;">This stiffness plays an important role in the vibration of the string as it adds another force to force equation</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Als de complete trilling van de snaar bekend is (positie als functie van de tijd), kan door een fouriertransformatie toe te passen een powerspectrum gemaakt worden waarin de amplitude verhoudingen te zien zijn in </del>het <del style="font-weight: bold; text-decoration: none;">frequentiedomein.</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">===Analysis with </ins>het <ins style="font-weight: bold; text-decoration: none;">model===</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">====Problemen====</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">With the right model a Helmholtz vibration can be generated. This vibration can be analysed afterwards using matlab. The model itself recognises if the generated vibration is a Helmholtz vibration or a noisy type of vibration. We took a Helmholtz vibration, which looks like the left figure below, and made an m-file that generates a fourier transformation of that vibration. The powerspectrum that was generated is shown in the right figure below. These type of figures will be very important later on as we will see in the chapter 'Software Design (Quantifying the signal we want to see)'.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Het grootste probleem tot nu toe is dat de frequentie van de snaartrilling steeds afhankelijk blijkt te zijn van de strijksnelheid en –druk. In de werkelijkheid is dit niet het geval en wordt de frequentie slechts beïnvloed door de lengte van de snaar. Met het variëren van de strijksnelheid en –druk wordt in werkelijkheid alleen de amplitude en dus de luidheid van de trilling beïnvloed.</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[File:HEL.PNG|frame|border|left|<ins style="font-weight: bold; text-decoration: none;">Figure 7</ins>: <ins style="font-weight: bold; text-decoration: none;">Helmholtz vibration and it's powerspectrum</ins>]]</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Dit probleem wordt waarschijnlijk veroorzaakt door een ander probleem. Namelijk het modelleren van de snaarstijfheid, dus welke kracht de snaarstijfheid genereert als functie van de tijd. Hiervoor moet nog een oplossing gevonden worden.</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">===Analyses met het model===</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Met behulp van het werkende model kan een Helmholtz trilling gegenereerd worden. Deze trilling kan daarna geanalyseerd worden met behulp van matlab. Het model herkent een trilling en kan deze klassificeren in een aantal groepen. Uit alle gemodeleerde trillingen is een zuivere Helmholttrilling gepakt, deze ziet er uit als in de linker plot hier onder. Daarna is er een m-file gemaakt die een Fourier transformatie uitvoerd op deze trilling en een frequentiedomein plot. Dit frequentiedomein is weergegeven in de rechter plot hieronder.</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[File:HEL.PNG|frame|border|left|<del style="font-weight: bold; text-decoration: none;">Figuur X</del>: <del style="font-weight: bold; text-decoration: none;">Helmholtztrilling met bijbehorend frequentiespectrum.</del>]]</div></td><td colspan="2" class="diff-side-added"></td></tr>
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</table>S071253