A novel approach for structural system reliability evaluation using decoupled first-order reliability method and equivalent extreme-value event

The first-order reliability method (FORM) has been widely used in system reliability evaluation. However, calculating system reliability of structures with hundreds of components by FORM poses significant challenges. These difficulties arise because it requires determining multivariate normal integrals, which is generally impractical due to the high dimension of these integrals. Additionally, explicit expressions for the limit state functions (LSFs) of components cannot be generally obtained, leading to substantial computational costs for determining the gradients of LSFs. To address these issues, a novel approach called the equivalent extreme- value event-based decoupled FORM (EEVE-DFORM) is proposed. In EEVE-DFORM, the high-dimensional normal integrals are reduced to one-dimensional integrals of extreme value distributions according to the principle of equivalent extreme-value event (EEVE), and extreme value distributions are derived using the probability density evolution method (PDEM). In conjunction with a Galerkin-type stochastic finite element method (GSFEM), a decoupled FORM, where reliability computation is decoupled with finite element analysis, is developed to calculate the reliability of components with implicit LSFs. Five numerical examples are investigated to demonstrate the efficacy of the proposed methodology. The results indicate that the system reliability of series, parallel, and general structural systems can be accurately and efficiently determined using the proposed method, even when dealing with hundreds of components.