Multilevel model reduction for uncertainty quantification in computational structural dynamics

Abstract : This work deals with an extension of the reduced order models (ROMs) that are classically constructed by modal analysis in linear structural dynamics of complex structures for which the computational models are assumed to be uncertain. Such an extension is based on a multilevel projection strategy consisting in introducing three reduced-order bases (ROBs) 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 prob-abilistic approach of uncertainties. It allows for affecting a specific level of uncertainties to each type of displacements associated with the corresponding vibration regime, knowing that the local elastic modes are more sensitive to uncertainties than the global elastic modes. 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.