Inverse structural reliability analysis under mixed uncertainties using high dimensional model representation and fast Fourier transform

This paper presents a novel solution procedure for inverse reliability problems with implicit response functions without requiring the derivatives of the response functions with respect to the uncertain variables, that can be used to determine the unknown design parameters such that prescribed reliability indices are attained in the presence of mixed uncertain (both random and fuzzy) variables. The proposed computational procedure involves three steps: (i) probability of failure calculation using 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, (ii) reliability index update, and (iii) most probable point MPP update. The limit state function approximation is obtained by linear and quadratic approximations of the first-order HDMR component functions at most probable point. This is a versatile method that can solve even highly nonlinear problems or the problems with multiple parameters. The methodology developed is applicable for inverse reliability analysis 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.