Rare reliability analysis by beta-surfaces and Kriging model

Conducting reliability analysis for rare events poses a significant challenge in structural safety assessment and reliability-based design optimization. This paper introduces the Stratified Beta-Spheres (SBS) method to address these challenges. The approach starts by partitioning the entire support space of random input variables into sub-domains using multiple Beta-spheres, specified by the user. Truncated samples are then generated within these sub-domains both explicitly and efficiently. Using these truncated samples, the original failure probability can be estimated by summing the failure probabilities of the sub-domains. The paper also discusses and demonstrates the unbiasedness of the failure probability estimator in the proposed method. The SBS method inherits the advantages of Monte Carlo simulation (MCS) applicable to rare events and problems with multiple failure domains while maintaining ease of implementation. Additionally, the method is integrated with adaptive Gaussian process regression to perform reliability analysis for complex structures. The superiority of the proposed SBS method is validated through both numerical and engineering examples.