Second-order reliability methods: a review and comparative study

• Published in: Structural and multidisciplinary optimization Vol. 64; no. 6; pp. 3233 - 3263
• Main Authors: Hu, Zhangli, Mansour, Rami, Olsson, Mårten, Du, Xiaoping
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-12-2021; Springer Nature B.V
• Subjects: Accuracy; Approximation; Business metrics; Capability; Comparative studies; Computational Mathematics and Numerical Analysis; Engineering; Engineering Design; First-order reliability method; Limit states; Methods; Monte Carlo simulation; Optimization; Performance measurement; Performance metrics; Probability; Random variables; Reliability analysis; Reliability engineering; Review Paper; Robustness; Second-order reliability method; Theoretical and Applied Mechanics; Performance metrics; Accuracy; First-order reliability method; Second-order reliability method; Robustness; Capability
• ISSN: 1615-147X; 1615-1488; 1615-1488
• DOI: 10.1007/s00158-021-03013-y

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.