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Maximum likelihood estimation of stochastic chaos representations from experimental data
Author(s) -
Desceliers Christophe,
Ghanem Roger,
Soize Christian
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1576
Subject(s) - polynomial chaos , random field , mathematics , inverse problem , realization (probability) , discretization , displacement field , basis (linear algebra) , displacement (psychology) , boundary (topology) , boundary value problem , representation (politics) , field (mathematics) , probabilistic logic , stochastic process , mathematical optimization , finite element method , mathematical analysis , geometry , monte carlo method , statistics , psychology , law , psychotherapist , thermodynamics , physics , politics , political science , pure mathematics
This paper deals with the identification of probabilistic models of the random coefficients in stochastic boundary value problems (SBVP). The data used in the identification correspond to measurements of the displacement field along the boundary of domains subjected to specified external forcing. Starting with a particular mathematical model for the mechanical behaviour of the specimen, the unknown field to be identified is projected on an adapted functional basis such as that provided by a finite element discretization. For each set of measurements of the displacement field along the boundary, an inverse problem is formulated to calculate the corresponding optimal realization of the coefficients of the unknown random field on the adapted basis. Realizations of these coefficients are then used, in conjunction with the maximum likelihood principle, to set‐up and solve an optimization problem for the estimation of the coefficients in a polynomial chaos representation of the parameters of the SBVP. Copyright © 2005 John Wiley & Sons, Ltd.