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

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. (c) 2022 Elsevier Masson SAS. All rights reserved.

Automated summary

Failure credibility is a measure of the safety degree of a structure under fuzzy uncertainty. The fuzzy first-order and second-moment (FFOSM) method is an efficient and accurate analytical method for solving failure credibility. This study proposes an equivalent regularization (EqRe) method to extend FFOSM to problems with irregularly and diversely distributed fuzzy inputs (Ir-FuI). The proposed E-FFOSM efficiently estimates the failure credibility of problems with Ir-FuI, inheriting the high efficiency and accuracy of classical FFOSM.