Reliability estimation using univariate dimension reduction and extended generalised lambda distribution

Abstract

This paper presents an analytical approach for structural reliability analysis without requiring the calculation of most probable point of failure. Initially, the primary statistical moments of a multi-dimensional performance function are estimated using the Univariate Dimension-Reduction (UDR) methodology based on additive decomposition of the limit state function. Through moment matching, the UDR-based estimated moments are then used to fit the parameters of Extended Generalised Lambda Distribution (EGLD), and finally the probability of failure is calculated. To evaluate the accuracy and efficiency of the UDR + EGLD approach in comparison to the traditional First-Order Reliability Method (FORM) and direct Monte Carlo Simulation (MCS), five example problems involving nonlinear limit state functions are examined. The results show that UDR + EGLD offers nearly the same level of accuracy as MCS with superior efficiency to FORM. However, UDR + EGLD appears to have tail sensitivity, which limits its application to problems with moderate levels of reliability.