Identification of Bayesian posteriors for coefficients of chaos expansions

Journal Article · Sat May 01 04:00:00 EDT 2010 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2009.12.033· OSTI ID:21333947

Ghanem, R ^[1]; Soize, C ^[2]

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1. 210 KAP Hall, University of Southern California, Los Angeles, CA 90089 (United States)
2. Universite Paris-Est, Laboratoire de Modelisation et Simulation Multi-Echelle, MSME UMR8208 CNRS, 5 bd Descartes, Champs-sur-Marne, 77454 Marne-la-Vallee, Cedex 2 (France)

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.

• OSTI ID: 21333947
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 9 Vol. 229; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
CHAOS THEORY
MAXIMUM-LIKELIHOOD FIT
POLYNOMIALS
PROBABILISTIC ESTIMATION
PROBABILITY DENSITY FUNCTIONS
RANDOMNESS
STOCHASTIC PROCESSES