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MODELING EXPERIMENTAL DATA WITH POLYNOMIALS CHAOS

Published online by Cambridge University Press:  14 August 2018

Emeline Gayrard ,
Cédric Chauvière ,
Hacène Djellout  and
Pierre Bonnet
Emeline Gayrard
Affiliation:
Laboratoire de Mathématiques Blaise Pascal (LMBP), CNRS UMR 6620 Université Clermont Auvergne, Campus Universitaire des Cézeaux, 3 place Vasarely, TSA 60026/CS 60026, 63 178 Aubière Cedex, France E-mail: Emeline.Gayrard@uca.fr
Cédric Chauvière
Affiliation:
Laboratoire de Mathématiques Blaise Pascal (LMBP), CNRS UMR 6620 Université Clermont Auvergne, Campus Universitaire des Cézeaux, 3 place Vasarely, TSA 60026/CS 60026, 63 178 Aubière Cedex, France E-mail: Cedric.Chauviere@uca.fr
Hacène Djellout
Affiliation:
Laboratoire de Mathématiques Blaise Pascal (LMBP), CNRS UMR 6620 Université Clermont Auvergne, Campus Universitaire des Cézeaux, 3 place Vasarely, TSA 60026/CS 60026, 63 178 Aubière Cedex, France E-mail: Hacene.Djellout@uca.fr
Pierre Bonnet
Affiliation:
Institut Pascal, CNRS UMR 6602 Université Clermont Auvergne, Campus Universitaire des Cézeaux, 4 Avenue Blaise Pascal, TSA 60026/CS 60026, 63178 Aubière Cedex, France E-mail: pierre.bonnet@univ-bpclermont.fr
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Abstract

Given a raw data sample, the purpose of this paper is to design a numerical procedure to model this sample under the form of polynomial chaos expansion. The coefficients of the polynomial are computed as the solution to a constrained optimization problem. The procedure is first validated on samples coming from a known distribution and it is then applied to raw experimental data of unknown distribution. Numerical experiments show that only five coefficients of the Chaos expansions are required to get an accurate representation of a sample.

Keywords

Chaos expansionsexperimental data modelingnumerical methods
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 1 , January 2020 , pp. 14 - 26
Copyright
Copyright © Cambridge University Press 2018 

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