Statistical Inverse Problems for Non-Gaussian Non-Stationary Stochastic Processes Defined by a Set of Realizations

Abstract

Abstract.This paper presents a method to analyze the transitory response of complex and nonlinear systems, which are excited by non-Gaussian and non-stationary random fields, by solving of a statistical inverse problem with experimental measurements. Based on a double expansion, it is particularly adapted to the modeling of stochastic processes that are only characterized by a relatively small set of independent realizations. First, an adaptation of the classical KarhunenLoève expansion is presented. Indeed, for the past fifty years, the use of reduced basis has spread to many scientific fields to condense the statistical properties of stochastic processes, and among these bases, the Karhunen-Loève basis plays a major role as it allows the minimization of the total mean square error. Secondly, the random vector, which gathers the projection coefficients of the stochastic process on this basis, is characterized using a polynomial chaos expansion approach. The dimension of this random vector being very high (around several hundreds), advanced identification techniques are introduced to allow performing relevant convergence analyses and identifications. The non-Gaussian non-stationary stochastic process is identified using the experimental measurements and consequently, constitutes a realistic stochastic modeling. The proposed method is then applied to the modeling of seismic accelerations from a measured data set.