Maximum likelihood estimation of stochastic chaos representations from experimental data

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.