System reliability analysis with small failure probability based on relevant vector machine and Meta-IS idea

Structural failure is a complex system problem and traditional methods face difficulties in solving system reliability problems with small failure probability. This paper proposes an efficient sampling simulation method termed SDMI, which integrates metamodel-based importance sampling (Meta-IS) with spherical decomposition (SD). SDMI transforms the failure probability into a product of spherical augmented failure probability and a correction factor. The implementation of SDMI for each component further facilitates the proposition of a system probability classification function. The integration of the relevant vector machine (RVM) leads to the proposal of a more efficient methodology, termed RVM-SDMI. The efficacy and precision of the proposed methods have been validated through four numerical examples and two engineering examples. The results demonstrate that SDMI successfully addresses the convergence challenges inherent in Meta-IS. Moreover, RVM-SDMI exhibits remarkable accuracy and computational efficiency in the system reliability analysis with small failure probabilities.