A hybrid spectral and metamodeling approach for the stochastic finite element analysis of structural dynamic systems

A novel approach for uncertainty propagation and response statistics estimation of randomly parametrized structural dynamic systems is developed in this paper. The frequency domain response of a stochastic finite element system is resolved at randomly sampled design points in the input stochastic space with an infinite series expansion using preconditioned stochastic Krylov bases. The system response is expressed in the eigenvector space of the structural system weighted with finite order rational functions of the input random variables, termed spectral functions. The higher the order of the spectral functions, the more accurate is the order of approximation of the stochastic system response. However, this increased accuracy comes at a computational cost. This cost is mitigated by using a Bayesian metamodel. The proposed approach is used to the analyze the stochastic vibration response of a corrugated panel with random elastic parameters. The results obtained with the proposed hybrid approach are compared with direct Monte Carlo simulations, which have been considered as the benchmark solution.