Identification of Bayesian posteriors for coefficients of chaos expansions

M. Arnst; R. Ghanem; C. Soize

hal-00684317, version 1

Identification of Bayesian posteriors for coefficients of chaos expansions

M. Arnst ( Author to contact preferably ) ¹, R. Ghanem () ¹, C. Soize (, ) ²

Journal of Computational Physics 229, 9 (2010) Pages: 3134-3154

Abstract: This article is concerned with the identification of probabilistic characterizations of random variables and fields from experimental data. The data used for the identification consist of measurements of several realizations of the uncertain quantities that must be characterized. The random variables and fields are approximated by a polynomial chaos expansion, and the coefficients of this expansion are viewed as unknown parameters to be identified. It is shown how the Bayesian paradigm can be applied to formulate and solve the inverse problem. The estimated polynomial chaos coefficients are hereby themselves characterized as random variables whose probability density function is the Bayesian posterior. This allows to quantify the impact of missing experimental information on the accuracy of the identified coefficients, as well as on subsequent predictions. An illustration in stochastic aeroelastic stability analysis is provided to demonstrate the proposed methodology.

1: Department of aerospace and mechanical engineering (USC)
University of Southern California
2: Laboratoire de Modélisation et Simulation Multi Echelle (MSME)
Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8208

hal-00684317, version 1
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From: Christian Soize <>
Submitted on: Sunday, 1 April 2012 14:31:53
Updated on: Thursday, 14 March 2013 17:38:18

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DOI: 10.1016/j.jcp.2009.12.033

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%% hal-00684317, version 1
%% http://hal-upec-upem.archives-ouvertes.fr/hal-00684317
@article{arnst:hal-00684317,
    hal_id = {hal-00684317},
    url = {http://hal-upec-upem.archives-ouvertes.fr/hal-00684317},
    title = {{Identification of Bayesian posteriors for coefficients of chaos expansions}},
    author = {Arnst, M. and Ghanem, R. and Soize, C.},
    abstract = {{This article is concerned with the identification of probabilistic characterizations of random variables and fields from experimental data. The data used for the identification consist of measurements of several realizations of the uncertain quantities that must be characterized. The random variables and fields are approximated by a polynomial chaos expansion, and the coefficients of this expansion are viewed as unknown parameters to be identified. It is shown how the Bayesian paradigm can be applied to formulate and solve the inverse problem. The estimated polynomial chaos coefficients are hereby themselves characterized as random variables whose probability density function is the Bayesian posterior. This allows to quantify the impact of missing experimental information on the accuracy of the identified coefficients, as well as on subsequent predictions. An illustration in stochastic aeroelastic stability analysis is provided to demonstrate the proposed methodology.}},
    keywords = {Uncertainty quantification; Inverse statistical problem; Bayesian, Bayes method; Maximum likelihood; Polynomial chaos; Random uncertainties; Random fields;},
    language = {English},
    affiliation = {Department of aerospace and mechanical engineering - USC , Laboratoire de Mod{\'e}lisation et Simulation Multi Echelle - MSME},
    pages = {Pages: 3134-3154},
    journal = {Journal of Computational Physics},
    volume = {229},
    number = {9 },
    audience = {international },
    doi = {10.1016/j.jcp.2009.12.033 },
    year = {2010},
    pdf = {http://hal-upec-upem.archives-ouvertes.fr/hal-00684317/PDF/publi-2010-JCP-229\_9\_3134-3154-arnst-ghanem-soize-preprint.pdf},
}