Structural reliability analysis based on fuzzy random uncertainty

To address the fuzzy random uncertainty in structural reliability analysis, a novel method for obtaining the membership function of fuzzy reliability is proposed on the two orders four central moments (TOFM) method based on envelope distribution. At each cut level, the envelope distribution is first constructed, which is a new expression to describe the bound of the fuzzy random variable distribution. The central moments of the bound distribution are determined by generating samples from the envelope distribution, and they are used to calculate the central moments of the limit state function based on the first two orders of the Taylor expansion. Thereafter, the modern approximation method is used to approximate the polynomial expression for the limit state function probability density function (PDF) by considering the central moments as constraint conditions. Thus, the reliability boundaries can be calculated under the considered cut level, and the membership function of the fuzzy reliability is subsequently obtained. Three examples are evaluated to demonstrate the efficiency and accuracy of the proposed method. Moreover, a comparison is made between the proposed method, Monte Carlo simulation (MCS) method, and fuzzy first-order reliability method (FFORM). The results show the superiority of the proposed method, which is feasible for the analysis of structural reliability with fuzzy randomness.