Extended fuzzy first-order and second-moment method based on equivalent regularization for estimating failure credibility

Abstract

Failure credibility can quantify safety degree of structure under fuzzy uncertainty, and fuzzy first-order and second-moment (FFOSM) method is an efficiently and accurately analytical method for solving failure credibility. However, classical FFOSM is only suitable for problem with regularly and identically distributed fuzzy input (Re-FuI). To extend FFOSM to problem with irregularly and diversely distributed fuzzy input (Ir-FuI), an equivalent regularization (EqRe) for Ir-FuI is proposed by use of property that failure credibility only depends on fuzzy design point (FDP). By ensuring that credibility distribution and membership functions of equivalent Re-FuI are separately equal to those of Ir-FuI at FDP, the proposed EqRe transforms Ir-FuI into equivalent Re-FuI. Then the extended FFOSM (E-FFOSM) is established to efficiently estimate failure credibility of problem with Ir-FuI, in which equivalent Re-FuI with respect to Ir-FuI is obtained by EqRe at each iterative FDP. The proposed E-FFOSM inherits the high efficiency and high accuracy of classical FFOSM, and avoids the limitation inapplicable to problem with Ir-FuI. Four examples are used to verify the feasibility and accuracy of the E-FFOSM.