An improved reliability analysis approach based on combined FORM and Beta-spherical importance sampling in critical region

The reliability analysis of structural systems is generally difficult when limit state function (LSF) is implicitly defined especially by black-box models in engineering. To balance analysis efficiency and accuracy, an improved approach named BIS-FC is proposed in this paper based on the Beta-spherical importance sampling (BIS) framework with the innovative concept of critical region defined by combination with First Order Reliability Method (FORM). The critical region is defined by the hyper-tangent plane of LSF at the Most Probable Point (MPP) and its parallel hyperplanes according to the convex or concave features of LSF, wherein the samples are of both high occurrence probability and high misjudgment risk due to the linearization assumption of FORM. BIS-FC only conducts LSF analysis for the BIS samples located in the critical region, and the other samples are directly identified as safe or failure according to the linearized hyperplanes. Thus large computational cost can be saved compared to the original BIS, and meanwhile, the analysis accuracy can be greatly enhanced compared to FORM. An iterative process is proposed to properly define the critical region, based on which reliability is analyzed sequentially until the stopping criteria for desired estimation error level and stable convergence are satisfied. The algorithms of BIS-FC for both single and multiple MPP situations are developed and testified with six numerical examples and one satellite structural engineering problem. The results demonstrate the effectiveness of BIS-FC regarding good balance between efficiency and accuracy.