Reduced basis representation of large-scale random eigenvalue problems

Abstract

A reduced basis formulation is presented for efficient solution of large-scale random eigenvalue problems. The present formulation aims to improve the accuracy of the first-order perturbation method, and also allow the efficient computation of higher-order statistical moments of the eigenparameters. In the proposed method, the two terms of the first-order perturbation approximation for the eigenvector are used as basis vectors for Ritz analysis of the random eigenvalue problem. Since only two basis vectors are used to represent each eigenmode of interest, explicit expressions for the random eigenvalues and eigenvectors can be readily derived. A complete statistical description of the eigenvalues and eigenvectors is hence made posssible in a computationally expedient fashion. Numerical studies are presented for free and forced vibration analysis of a stochastic structural system. It is demonstrated that the reduced basis method gives significantly better results as compared to the first-order perturbation method, particularly for large stochastic variations in the random system parameters.