Some aspects of probabilistic modeling, identification and propagation of uncertainties in computational mechanics

Abstract

In this paper, we present some aspects relative to the types of uncertainties, the variability of real systems, the types of probabilistic approaches and of the representations for the probabilistic models of uncertainties, the construction of the probabilistic models using the maximum entropy principle. We then present the nonparametric probabilistic approach of uncertainties for elliptic problems, for 3D continuous dynamical systems with geometrical nonlinearities induced by large displacements and for low- and mediumfrequency vibroacoustics of a complex system with experimental validations. Finally, a generalized probabilistic approach of uncertainties in computational dynamics using the random matrix theory and polynomial chaos decompositions is presented.