Estimation of Membership Function of Design Variables Using HDMR and FFT

This paper presents an inverse reliability analysis to determine the unknown design parameters such that prescribed reliability indices are attained in the presence of mixed uncertain variables. The proposed computational procedure involves the failure probability estimation using High Dimensional Model Representation, transformation technique to obtain the contribution of the fuzzy variables to the convolution integral, convolution using fast Fourier transform, and update of reliability index and most probable point. This is aversatile 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 three examples involving explicit/implicit performance functions.