Nonparametric probabilistic approach of uncertainties with correlated mass and stiffness random matrices

This paper concerns the probabilistic modeling of uncertainties in structural dynamics. For real complex structures, the accurate modeling and identification of uncertainties is challenging due to the large number of involved uncertain parameters. In this context, the nonparametric probabilistic approach which consists in modeling globally the uncertainties by replacing the mass, stiffness and damping reduced matrices by random matrices is attractive since it yields a stochastic modeling for which the level of uncertainties is controlled by a small number of dispersion parameters. In its classical version, these random matrices are assumed to be independent. This assumption is valid (and proven) in absence of information concerning the dependence structure of these random matrices. In some situation, such as the presence of geometry uncertainties, this assumption is not valid any more and may yield an overestimation of the output levels of fluctuation. In this context, the present paper presents an extension of the classical nonparametric probabilistic to take into account a dependence between the random mass and stiffness matrices. This new modeling is illustrated on a beam structure for which the diameter presents spatial random fluctuations along the longitudinal direction.