Second-order reliability methods: a review and comparative study

Abstract

Second-order reliability methods are commonly used for the computation of reliability, defined as the probability of satisfying an intended function in the presence of uncertainties. These methods can achieve highly accurate reliability predictions owing to a second-order approximation of the limit-state function around the Most Probable Point of failure. Although numerous formulations have been developed, the lack of full-scale comparative studies has led to a dubiety regarding the selection of a suitable method for a specific reliability analysis problem. In this study, the performance of commonly used second-order reliability methods is assessed based on the problem scale, curvatures at the Most Probable Point of failure, first-order reliability index, and limit-state contour. The assessment is based on three performance metrics: capability, accuracy, and robustness. The capability is a measure of the ability of a method to compute feasible probabilities, i.e., probabilities between 0 and 1. The accuracy and robustness are quantified based on the mean and standard deviation of relative errors with respect to exact reliabilities, respectively. This study not only provides a review of classical and novel second-order reliability methods, but also gives an insight on the selection of an appropriate reliability method for a given engineering application.

A probabilistic life prediction framework for vibration fatigue of turbine blade based on refined polynomial chaos expansion

“…15 Early uncertainty analyses of fatigue relied on moment methods, including first-order reliability method 16,17 and second-order reliability method. [18][19][20] To assess the steam turbine failure probability, Bagaviev and Ulbrich 21 applied the mean value method, the first moment reliability method, and the importance sampling Monte Carlo simulation (MCS) method. The results indicate a consistency in accuracy between the first-order reliability method and the MCS method.…”

“…Both the structural response and the ultimate predicted fatigue life are also random variables with a probability distribution 15 . Early uncertainty analyses of fatigue relied on moment methods, including first‐order reliability method 16,17 and second‐order reliability method 18–20 . To assess the steam turbine failure probability, Bagaviev and Ulbrich 21 applied the mean value method, the first moment reliability method, and the importance sampling Monte Carlo simulation (MCS) method.…”

Moment-independent sensitivity analysis of a fold mechanism based on an active learning kriging method

“…To increase efficiency, researchers have made some attempts. The first order reliability method (FORM) 5 and the second order reliability mothed (SORM) 6 are two representative analytical reliability methods. But they can only analysis component reliability.…”

The probabilistic model for system reliability analysis of a steel plane and spatial trusses

“…The reliability methods can be divided into two groups: considering the reliability of single elements and the reliability of the whole structural systems. In the first group one can enumerate approximation methods as: FORM (Breitung, 2015;Ditlevsen, 1987;Keshtegar and Meng,2017), SORM (Cai and Elishakoff, 1994;Hu et al, 2021) and simulation methods like: Monte Carlo (Rausch et al, 2019; Sharma, 2020; Zaeimi and Ghoddosain, 2020), Importance Sampling (Melchers, 1989;Papaioannou et al, 2018), Artificial Neural Networks (Flood, 2008;Potrzeszcz-Sut and Dudzik, 2022).…”