Random matrix models and nonparametric method for uncertainty quantification

Christian Soize (1)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

This paper deals with the fundamental mathematical tools and the associated computational aspects for constructing the stochastic models of random matrices that appear in the nonparametric method of uncertainties and in the random consti-tutive equations for multiscale stochastic modeling of heterogeneous materials. The explicit construction of ensembles of random matrices, but also the presentation of numerical tools for constructing general ensembles of random matrices are presented and can be used for high stochastic dimension. The developments presented are illustrated for the nonparametric method for multiscale stochastic mod-eling of heterogeneous linear elastic materials and for the nonparametric stochas-tic models of uncertainties in computational structural dynamics.

Mots clés: Parametric-nonparametric uncertainties; Uncertainty quantification in nonlinear structural dynamics; Random matrix; Symmetric random matrix; Positive-definite random matrix; Nonparametric uncertainty; Nonparametric method for uncertainty quantification; Random vector; Maximum entropy principle; Non-Gaussian; Generator; Random elastic medium; Uncertainty quantification in linear structural dynamics; Identification; Inverse problem; Statistical inverse problem

Domaines: Sciences de l'ingénieur [physics]; Probabilités [math.PR]; Statistiques [math.ST]

Christian Soize. Random matrix models and nonparametric method for uncertainty quantification. R. Ghanem, D. Higdon, and H. Owhadi. Handbook for Uncertainty Quantification, 1, Springer International Publishing Switzerland, pp.219-287, 2017, 978-3-319-12384-4. ⟨10.1007/978-3-319-11259-6\_5-1⟩. ⟨hal-01284669⟩