Multilevel stochastic reduced-order model for the robust vibration analysis of complex structures in a broad frequency band

International audienceThis paper deals with the construction of a multilevel stochastic reduced-order model (ROM) devoted to the robust dynamical analysis of complex structures in a broad frequency band. In particular, we are interested in complex structures characterized by the presence of several structural scales (such as a stiff main body supporting flexible parts). In such a case, in addition to the usual global elastic modes (long-wavelengthmodes), numerous local elastic modes (associated with the flexible parts) appear. These local elastic modes, which are numerous in the low-frequency band already, exhibit high-frequency behavior, namely high modal density, small wavelength, and high sensitivity to uncertainty. In such a context, the low- , medium-, and highfrequency (LF, MF, HF) vibration regimes overlap. The objectives are to adapt the modeling of uncertainty to each vibration regime and, also, to deal with the unusually high dimension of the classic ROMs, which is due to the numerous local elastic modes. Thanks to a spatial filtering method of local displacements (that is based on the use of global polynomial shape functions for the kinetic energy), three successive filterings allow three families of displacements to be constructed, namely the LF-, MF-, and HF-type displacements. The filtering of the most local displacements allows the final dimension of the proposed ROM to be reduced. The multilevel reduced-order basis that is obtained yields a multilevel ROM. Using the nonparametric probabilistic approach of uncertainties with this ROM allows for obtaining a stochastic ROM for which the levels of uncertainty can be controlled independently for each type of displacements.The methodology is applied to a detailed finite element model of a car for which FRF measurements are available on a broad frequency band. Unlike a classic stochastic ROM constructed with the nonparametric approach, for which the probability law of each random reduced matrix is controlled by a unique dispersion hyperparameter, three hyperparameters are introduced for each random matrix of the multilevel stochasticROM. These stochastic ROMs are identified with respect to the measurements and are compared