Multilevel model reduction for uncertainty quantification in computational structural dynamics

This work deals with an extension of the reducedorder models (ROMs) that are classically constructed by modal analysis in linear structural dynamics for which the computational models are assumed to be uncertain. It is based on a multilevel projection strategy consisting in introducing three reduced-order bases that are obtained by using a spatial filtering methodology of local displacements. This filtering involves global shape functions for the kinetic energy. The proposed multilevel stochastic ROM is constructed by using the nonparametric probabilistic approach of uncertainties. It allows for affecting a specific level of uncertainties to each type of displacements associated with the corresponding vibration regime. The proposed methodology is applied to the computational model of an automobile structure, for which the multilevel stochastic ROM is identified with respect to experimental measurements. This identification is performed by solving a statistical inverse problem.