Modeling experimental data with Polynomials Chaos

Emeline Gayrard (1) , Cédric Chauvière (1) , Pierre Bonnet (2) , Hacène Djellout (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 IP - Institut Pascal

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.

Mots clés: Chaos expansions; experimental data modeling; numerical methods

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Emeline Gayrard, Cédric Chauvière, Pierre Bonnet, Hacène Djellout. Modeling experimental data with Polynomials Chaos. Probability in the Engineering and Informational Sciences, 2018, Probability in the Engineering and Informational Sciences, 34 (1), pp.14-26. ⟨10.1017/S026996481800030X⟩. ⟨hal-01899730⟩