Multicut-High Dimensional Model Representation for Structural Reliability Bounds Estimation Under Mixed Uncertainties

In reliability analysis of structural systems involving both aleatory and epistemic uncertainties, in conjunction with multiple design points, every configuration of the interval variables is to be explored to determine the bounds on reliability. To reduce the computational cost involved, this article presents a novel uncertain analysis method for estimating the bounds on reliability of structural systems involving multiple design points in the presence of mixed uncertain (both random and fuzzy) variables. The proposed method involves Multicut-High Dimensional Model Representation (MHDMR) technique for the limit state/performance function approximation, the 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 function approximation is obtained by linear and quadratic approximations of the first-order HDMR component functions at the most probable point. In the proposed method, efforts are required in evaluating conditional responses at a selected input determined by the sample points, as compared to full-scale simulation methods. Therefore, the proposed technique estimates the failure probability accurately with significantly less computational effort compared to the direct Monte Carlo simulation. The methodology developed is applicable for structural reliability 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 four examples involving explicit/implicit performance functions.