Efficient uncertainty analysis method for structures with hybrid uncertainty based on reduced-order model

Abstract

An efficient uncertainty analysis method is proposed in this paper for structures with hybrid random and interval variables by using the idea of reduced-order model. In the proposed method, proper orthogonal decomposition (POD) is firstly employed to extract the optimal orthogonal bases, which are the most characteristic structure functions, from the hybrid uncertainty space based on a set of selected full hybrid uncertainty analysis. Due to the existence of the hybrid uncertainty, the truncated orthogonal bases of the POD are functions of the random variables with unknown coefficients being functions of the interval variables. Kriging model is then used to approximate these unknown coefficients to improve the computational efficiency. Combined with the model reduction ability of POD and the efficiency of the Kriging model, the proposed method provides an efficient reduced-order model for full uncertainty propagation of hybrid random and interval uncertainty. Furthermore, due to the complete decoupling of the random and interval effect, the proposed method avoids repeated random uncertainty analysis at each realization of the interval variables, and significantly improves the efficiency of hybrid uncertainty analysis. Two test examples demonstrate that the proposed method significantly reduces the computational cost that arise due to high-dimensional random and interval variables, while demonstrating a similar accuracy for predicting the response bounds as the full-order hybrid uncertainty analysis.