Efficient high dimensional model representation based method for system reliability bounds estimation for problems with mixed uncertain variables

Abstract

This paper presents an efficient uncertainty analysis method for estimating the bounds on the failure probability of structural/mechanical systems in the presence of mixed uncertain (both random and fuzzy) variables. The proposed method involves High Dimensional Model Representation (HDMR) for the limit state/performance function approximation, transformation technique to obtain the contribution of the fuzzy variables to the convolution integral and fast Fourier transform for solving the convolution integral. The limit state/performance function approximation is obtained by linear and quadratic approximations of the fi rst-order HDMR component functions at most probable point. In the proposed method, efforts are required in evaluating conditional responses at a selected input determined by sample points, as compared to full scale simulation methods. Therefore, the proposed technique estimates the failure probability accurately with signifi cantly less computational effort compared to the direct Monte Carlo simulation. The methodology developed is applicable for failure probability estimation involving any number of fuzzy variables and random variables with any kind of distribution. The accuracy and efficiency of the proposed method is demonstrated through three examples involving implicit performance functions.