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Function parametrization: Difference between revisions
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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, | The technique, developed by H. Wind for the purpose of momentum determination from spark chamber data, <ref> Wind, H. `Function Parametrization' | ||
in ``Proceedings of the 1972 CERN Computing and Data Processing School'', CERN 72--21, 1972, pp.~53--106. | in ``Proceedings of the 1972 CERN Computing and Data Processing School'', CERN 72--21, 1972, pp.~53--106. </ref> <ref>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 | in ``Formulae and Methods in Experimental Data Evaluation'',Vol. 3, European Physical Society, Geneva, 1984</ref> 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. | 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> | ||
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> | |||
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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> | |||
== Applications == | == Applications == | ||
* RTP | * RTP <ref name=RTP></ref> | ||
* TEXTOR | * 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> | ||
* ASDEX-UG | * 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> | ||
* Wendelstein 7-X | * 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> | ||
== Alternatives == | == Alternatives == | ||
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== References == | == References == | ||
<references /> | |||