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Modélisation stochastique en grande dimension et identification en inverse aux travers de problèmes aux limites de champs de tenseurs aléatoires non gaussiens

Abstract : 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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Submitted on : Sunday, January 13, 2013 - 5:01:19 PM
Last modification on : Thursday, March 19, 2020 - 11:52:03 AM
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Christian Soize. Modélisation stochastique en grande dimension et identification en inverse aux travers de problèmes aux limites de champs de tenseurs aléatoires non gaussiens. 20ème Congrès Français de Mécanique 2011 - Colloque "Rencontre Mathématiques - Mécanique", Université de Besançon, Aug 2011, Besançon, France. pp.1-10. ⟨hal-00773380⟩

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