Random matrix theory for modeling uncertainties in computational mechanics

This paper deals with data uncertainties and model uncertainties issues in computational mechanics. If data uncertainties can be modeled by parametric probabilistic methods, for a given mean model, a nonparametric probabilistic approach can be used for modeling model uncertainties. The first part is devoted to random matrix theory for which we summarize previous published results and for which two new ensembles of random matrices useful for the nonparametric models are introduced. In a second part, the nonparametric probabilistic approach of random uncertainties is presented for linear dynamical systems and for nonlinear dynamical systems constituted of a linear part with additional localized nonlinearities. In a third part, a new method is proposed for estimating the parameters of the nonparametric approach from experiments. Finally, examples with experimental comparisons are given.