Efficient augmented radial basis function for reliability analysis with dynamic importance sampling

Conducting reliability analysis on complex systems, particularly those characterized by minimal failure probabilities and computationally intensive models, presents significant challenges. This article introduces a reliability analysis method combining the adaptive augmented radial basis function and the dynamic importance sampling (ARBF-DIS) algorithm. This method improves the generalization capacity of the augmented radial basis function at both local and global scales through the application of an anisotropic technique and orthogonal conditions. By using efficient cross-validation, the methodology facilitates the training of the metamodel, enabling it to provide predictive variance essential for constructing an adaptive sampling learning function. A key aspect of this approach is its capability to address the issue of low failure probabilities through dynamic importance sampling, which involves calculating an optimal importance sampling function derived from the current metamodel. The effectiveness and precision of the ARBF-DIS method are demonstrated through two analytical examples and a solid rocket motor reliability problem.