Function parametrization: Difference between revisions
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The application of the technique requires that a model exists to compute the response of the measurements (''q'') to variations of the system parameters (''p''), i.e. the mapping ''q = M(p)'' is known. | The application of the technique requires that a model exists to compute the response of the measurements (''q'') to variations of the system parameters (''p''), i.e. the mapping ''q = M(p)'' is known. | ||
In doing so, all functional dependencies are parametrized (hence the name of the technique), | In doing so, all functional dependencies are parametrized (hence the name of the technique), | ||
e.g., spatially dependent functions ''f(r)'' are given in terms of an parametric expansion (such as a | e.g., spatially dependent functions ''f(r)'' are given in terms of an parametric expansion (such as a [[:Wikipedia:Polynomial|polynomial]]), and the corresponding parameters are included in the vector ''p''. | ||
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. | ||
Revision as of 15:25, 9 February 2010
Function Parametrization (FP) is a technique to provide fast (real-time) construction of system parameters from a set of diverse measurements. [1]
Method
The application of the technique requires that a model exists to compute the response of the measurements (q) to variations of the system parameters (p), i.e. the mapping q = M(p) is known. In doing so, all functional dependencies are parametrized (hence the name of the technique), e.g., spatially dependent functions f(r) are given in terms of an parametric expansion (such as a polynomial), and the corresponding parameters are included in the vector p.
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 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. [2]
Applications
Alternatives
- Bayesian data analysis [6], which allows non-Gaussian error distributions.
- Neural networks.
References
- ↑ B.J. Braams, W. Jilge, and K. Lackner, Fast determination of plasma parameters through function parametrization, Nucl. Fusion 26 (1986) 699
- ↑ 2.0 2.1 B.Ph. van Milligen, N.J. Lopes Cardozo, Function Parametrization: a fast inverse mapping method, Comp. Phys. Commun. 66 (1991) 243
- ↑ 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
- ↑ W. Schneider, P.J. McCarthy, et al., ASDEX upgrade MHD equilibria reconstruction on distributed workstations, Fusion Engineering and Design 48, Issues 1-2 (2000) 127-134
- ↑ A. Sengupta, P.J. McCarthy, 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
- ↑ R. Fischer, A. Dinklage, Integrated data analysis of fusion diagnostics by means of the Bayesian probability theory, Rev. Sci. Instrum. 75 (2004) 4237