A nonparametric model of random uncertainties in linear structural dynamics

Random uncertainties in finite element models in linear structural dynamics are usually modeled by using parametric models. This means that 1) the uncertain local parameters occurring in the global mass, damping and stiffness matrices of the finite element model have to be identified; 2) appropriate probabilistic models of these uncertain parameters have to be constructed, and 3) functions mapping the domains of uncertain parameters into the global mass, damping and stiffness matrices have to be constructed. In this paper we propose an approach for constructing a random uncertainties model of the global mass, damping and stiffness matrices of finite element models in linear structural dynamics. This nonparametric model does not require identifying the uncertain local parameters and consequently, obviates construction of functions which map the domains of uncertain local parameters into the global mass, damping and stiffness matrices of the finite element models. This nonparametric model of random uncertainties is based on direct construction of a probabilistic model of the global mass, damping and stiffness matrices, which uses only the available information constituted of the mean value of the global mass, damping and stiffness matrices. This paper describes the explicit construction of the theory of such a nonparametric model.