A review and assessment of importance sampling methods for reliability analysis
Citation
Tabandeh, A., Jia, G., Gardoni, P. (2022). A review and assessment of importance sampling methods for reliability analysis. Structural Safety, 97: 102216. Link to paper
Abstract
This paper reviews the mathematical foundation of the importance sampling technique and discusses two general classes of methods to construct the importance sampling density (or probability measure) for reliability analysis. The paper has three distinct contributions. First, the paper explains the mathematical foundation of the importance sampling (IS) technique. The paper presents failure probability estimators, their statistical properties, and computational complexity. Second, the paper explains two classes of IS methods, called density and limit-state approximation methods. Third, the paper explores the performances of the IS methods through benchmark numerical examples. The paper also discusses the challenges and future directions of the IS methods.