FusionWiki

Function parametrization: Difference between revisions

Page Discussion

Function parametrization (view source)

Revision as of 01:22, 24 November 2010

228 bytes added ,  24 November 2010
no edit summary
No edit summary
No edit summary
Line 1: Line 1:
=[http://ujybyqum.co.cc UNDER COSTRUCTION, PLEASE SEE THIS POST IN RESERVE COPY]=
Function Parametrization (also spelt Parameterization) or FP is a technique to provide fast (real-time) construction of system parameters from a set of diverse measurements. It consists of the numerical determination, by statistical regression on a database of simulated states, of  simple functional representations  
Function Parametrization (also spelt Parameterization) or FP is a technique to provide fast (real-time) construction of system parameters from a set of diverse measurements. It consists of the numerical determination, by statistical regression on a database of simulated states, of  simple functional representations  
of  parameters characterizing the state of a particular physical system, where the arguments of the functions are statistically independent combinations of diagnostic raw measurements of the system.  
of  parameters characterizing the state of a particular physical system, where the arguments of the functions are statistically independent combinations of diagnostic raw measurements of the system.  
The technique,  developed by H. Wind for the purpose of momentum determination from spark chamber data, <ref>   Wind, H. `Function Parametrization'
The technique,  developed by H. Wind for the purpose of momentum determination from spark chamber data, &lt;ref&gt;   Wind, H. `Function Parametrization'
in ``Proceedings of the 1972 CERN Computing and Data Processing School'', CERN 72--21, 1972, pp.~53--106. </ref> <ref>Wind, H.,  
in ``Proceedings of the 1972 CERN Computing and Data Processing School'', CERN 72--21, 1972, pp.~53--106. &lt;/ref&gt; &lt;ref&gt;Wind, H.,  
(a)`Principal component analysis and its application to track finding',  (b) `interpolation and function representation'
(a)`Principal component analysis and its application to track finding',  (b) `interpolation and function representation'
in ``Formulae and Methods in Experimental Data Evaluation'',Vol. 3, European Physical Society, Geneva, 1984</ref> was introduced by B. Braams to plasma physics,  
in ``Formulae and Methods in Experimental Data Evaluation'',Vol. 3, European Physical Society, Geneva, 1984&lt;/ref&gt; was introduced by B. Braams to plasma physics,  
where it was  first applied to the analysis of equilibrium magnetic measurements on the  
where it was  first applied to the analysis of equilibrium magnetic measurements on the  
circular cross-section ASDEX tokamak. <ref>B.J. Braams, W. Jilge, and K. Lackner, ''Fast determination of plasma parameters through function parametrization'', Nucl. Fusion '''26''' (1986) 699</ref> It was later extended to the non-circular cross-section ASDEX Upgrade tokamak<ref>[http://www.physics.ucc.ie/~pjm/people/trachtas.htm  P.J. Mc Carthy,  ''An Integrated Data Interpretation System for Tokamak Discharges'', PhD thesis, University College Cork, 1992]</ref>
circular cross-section ASDEX tokamak. &lt;ref&gt;B.J. Braams, W. Jilge, and K. Lackner, ''Fast determination of plasma parameters through function parametrization'', Nucl. Fusion '''26''' (1986) 699&lt;/ref&gt; It was later extended to the non-circular cross-section ASDEX Upgrade tokamak&lt;ref&gt;[http://www.physics.ucc.ie/~pjm/people/trachtas.htm  P.J. Mc Carthy,  ''An Integrated Data Interpretation System for Tokamak Discharges'', PhD thesis, University College Cork, 1992]&lt;/ref&gt;
and the Wendelstein 7-AS stellarator.
and the Wendelstein 7-AS stellarator.
<ref>[http://iopscience.iop.org/0029-5515/39/4/308  H.P. Callaghan, P.J. Mc Carthy, J. Geiger "Fast equilibrium interpretation on the W7-AS stellarator using Function Parameterization", Nucl. Fusion "39" (1999) 509-523.]</ref>
&lt;ref&gt;[http://iopscience.iop.org/0029-5515/39/4/308  H.P. Callaghan, P.J. Mc Carthy, J. Geiger &quot;Fast equilibrium interpretation on the W7-AS stellarator using Function Parameterization&quot;, Nucl. Fusion &quot;39&quot; (1999) 509-523.]&lt;/ref&gt;




Line 19: Line 20:


The fast reconstruction of the system parameters is obtained by computing the inverse of the mapping ''M''. To do so, the parameters ''p'' are varied over a range corresponding to the expected variation in actual experiments, the corresponding ''q'' are obtained, and the set of ''(p,q)'' data are stored in a database. This database is then subjected to a statistical analysis in order to recover the inverse of ''M''. This analysis is typically a [[:Wikipedia:Principal Component Analysis|Principal Component Analysis]]. This procedure is also amenable to a rather detailed error analysis, so that errors in the recovered parameters ''p'' for the interpretation of actual data ''q'' can be obtained.
The fast reconstruction of the system parameters is obtained by computing the inverse of the mapping ''M''. To do so, the parameters ''p'' are varied over a range corresponding to the expected variation in actual experiments, the corresponding ''q'' are obtained, and the set of ''(p,q)'' data are stored in a database. This database is then subjected to a statistical analysis in order to recover the inverse of ''M''. This analysis is typically a [[:Wikipedia:Principal Component Analysis|Principal Component Analysis]]. This procedure is also amenable to a rather detailed error analysis, so that errors in the recovered parameters ''p'' for the interpretation of actual data ''q'' can be obtained.
<ref name=RTP>B.Ph. van Milligen, N.J. Lopes Cardozo, ''Function Parametrization: a fast inverse mapping method'', Comp. Phys. Commun. '''66''' (1991) 243</ref>
&lt;ref name=RTP&gt;B.Ph. van Milligen, N.J. Lopes Cardozo, ''Function Parametrization: a fast inverse mapping method'', Comp. Phys. Commun. '''66''' (1991) 243&lt;/ref&gt;


== Applications ==
== Applications ==


* RTP <ref name=RTP></ref>
* RTP &lt;ref name=RTP&gt;&lt;/ref&gt;
* TEXTOR <ref>B.Ph. van Milligen et al., ''Application of Function Parametrization to the analysis of polarimetry and interferometry data in TEXTOR'', Nucl. Fusion '''31''' (1991) 309</ref>
* TEXTOR &lt;ref&gt;B.Ph. van Milligen et al., ''Application of Function Parametrization to the analysis of polarimetry and interferometry data in TEXTOR'', Nucl. Fusion '''31''' (1991) 309&lt;/ref&gt;
* ASDEX-UG <ref>[http://dx.doi.org/10.1016/S0920-3796(00)00109-5 W. Schneider, P.J. Mc Carthy, et al., ''ASDEX upgrade MHD equilibria reconstruction on distributed workstations'', Fusion Engineering and Design '''48''', Issues 1-2 (2000) 127-134]</ref>
* ASDEX-UG &lt;ref&gt;[http://dx.doi.org/10.1016/S0920-3796(00)00109-5 W. Schneider, P.J. Mc Carthy, et al., ''ASDEX upgrade MHD equilibria reconstruction on distributed workstations'', Fusion Engineering and Design '''48''', Issues 1-2 (2000) 127-134]&lt;/ref&gt;
* Wendelstein 7-X <ref>[http://dx.doi.org/10.1088/0029-5515/44/11/003 A. Sengupta, P.J. Mc Carthy, et al., ''Fast recovery of vacuum magnetic configuration of the W7-X stellarator using function parametrization and artificial neural networks'', Nucl. Fusion '''44''' (2004) 1176]</ref>
* Wendelstein 7-X &lt;ref&gt;[http://dx.doi.org/10.1088/0029-5515/44/11/003 A. Sengupta, P.J. Mc Carthy, et al., ''Fast recovery of vacuum magnetic configuration of the W7-X stellarator using function parametrization and artificial neural networks'', Nucl. Fusion '''44''' (2004) 1176]&lt;/ref&gt;


== Alternatives ==
== Alternatives ==
Line 34: Line 35:


== References ==
== References ==
<references />
&lt;references /&gt;
Otihizuv
24

edits

Retrieved from "http://wiki.fusenet.eu/wiki/Special:MobileDiff/2742"