Keywords: structural reliability bounds, random variables, fuzzy variables, high dimensional model representation, HDMR, fast Fourier transform, FFT, convolution integral, bounds estimation, mixed uncertainties, failure probability, Monte Carlo simulation, structural reliability estimation, structural engineering
High dimensional model representation for structural reliability bounds estimation under mixed uncertainties
This paper presents an efficient uncertain analysis method for estimating the bounds on the reliability of structural systems in the presence of mixed uncertain variables. The proposed method involves high dimensional model representation (HDMR) for the limit state 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. 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 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 numerical examples.