Efficient parallel reliability analysis method based on dynamic multi-center importance sampling

The reliability assessment of nonlinear systems characterized by multiple failure modes presents significant challenges, particularly in scenarios involving low failure probabilities and high computational demands. This study introduces a novel parallel reliability analysis framework that integrates an augmented radial basis function with a multi-center importance sampling algorithm (ARBF-MIS). The proposed methodology establishes an adaptive learning function through cross-validation techniques, determines the optimal number of clusters based on silhouette analysis, and implements weighted clustering of candidate points based on the predictive outcomes of the learning function, thereby achieving parallelization. Furthermore, the critical issue of low failure probability in multi-failure-zone systems is addressed by the development of a multi-center importance sampling function. Setting the centroids of weighted clustering as the center of importance sampling, and iterate the importance sampling function continuously as the accuracy of the approximate model for predicting limit states improves. The computational efficacy and practical applicability of the ARBF-MIS are validated through multiple analytical cases and a reliability analysis for a solid rocket motor.