Modélisation stochastique en grande dimension et identification en inverse aux travers de problèmes aux limites de champs de tenseurs aléatoires non gaussiens
Résumé
We present the probabilistic modeling and the identification of non-Gaussian tensor-valued random fields using partial experimental data relative to a partial observation vector of the solution of a stochastic boundary value problem, the latter being a function of the tensor-valued random field which must be identified. Stochastic modeling is based on the introduction of a probabilistic model of a prior non-Gaussian tensor-valued random field and its development on the polynomial Gaussian chaos with random coefficients. The identification methodology is based on several optimization problems, the last being on the construction of a posterior probabilistic model adapted to high dimension. The methodology is illustrated through a three-dimensional linear elasticity problem for materials with a complex heterogeneous microstructure.
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