2MSME - Laboratoire de Modélisation et Simulation Multi Echelle (Université Paris-Est, 5 Bd Descartes, 77454 Marne-la-Vallée, Cedex 2
Université Paris-Est Créteil Val de Marne (UPEC) Faculté des Sciences et Technologie - Equipe de Biomécanique
61 avenue du général de Gaulle 94010 Créteil Cedex - France)
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.
https://hal-upec-upem.archives-ouvertes.fr/hal-00684317
Contributor : Christian Soize <>
Submitted on : Sunday, April 1, 2012 - 2:31:53 PM Last modification on : Thursday, March 19, 2020 - 11:52:03 AM Long-term archiving on: : Monday, November 26, 2012 - 12:30:15 PM
M. Arnst, R. Ghanem, Christian Soize. Identification of Bayesian posteriors for coefficients of chaos expansions. Journal of Computational Physics, Elsevier, 2010, 229 (9), pp.3134-3154. ⟨10.1016/j.jcp.2009.12.033⟩. ⟨hal-00684317⟩