Multi-Frequency Model Reduction for Uncertainty Quantification in Computational Vibroacoustics of Automobiles

This paper deals with the vibroacoustics of complex systems over a broad frequency band of analysis. The considered system is composed of a complex structure coupled with an internal acoustic cavity. The vibroacoustics model is represented by the usual global-displacements elastic modes associated with the main part, and by local elastic modes, associated with the preponderant vibrations of the flexible sub-parts. The main difficulty of the vibroacoustics analysis of complex system is the interweaving of the global displacements with the local displacements, which introduces an overlap of the usual three frequency domains (LF, MF and HF). A reduced-order computational vibroacoustic model constructed with a classical modal analysis is introduced. Nevertheless, the dimension of such reduced-order model (ROM) is still high when the frequency band of analysis overlaps for each frequency domain. A multi-level reduced-order model for the structure is constructed over the LF, MF, and HF bands. The strategy is based on a multi-level projection consisting in introducing three reduced-order bases that are obtained by using a filtering methodology of local displacements. To filter out the local displacements we introduce a set of global shape functions. In addition, a classical ROM using acoustic modes is implemented for the acoustic cavity. Then, the coupling between the multi-level reduced order model and the acoustic reduced-order model is presented. A nonparametric probabilistic modeling is then proposed to take into account the model uncertainties induced by modeling errors that increase with the frequency. The proposed approach is applied to a car.