An active learning method combining MRBF model and dimension-reduction importance sampling for reliability analysis with high dimensionality and very small failure probability

Multiple surrogate models suffer from the curse of dimensionality and Radial basis function (RBF) model is particularly well-suited for approximating of high-dimensional performance functions. Additionally, by leveraging matrix operations, the prediction time of RBF model can be significantly reduced. However, when the failure probability becomes extremely small, the prediction time of matrix-operation RBF (MRBF) model is also prohibitive. To address the challenges posed by both high dimensionality and very small failure probability, we propose an active learning method that fuses the MRBF model with a novel importance sampling method—iCE-m*. iCE-m* is a cross-entropy importance sampling embedded dimensionality reduction mechanism. Firstly, we define the instrumental density series of iCE-m* based on the prediction information of MRBF, which fuels iCE-m* to generate candidate samples covering the region near the limit state surface. Then, we propose a new learning function that measures the coefficient of variation of the square of the performance function, which helps identify the optimal training points near the limit state surface. The performance of the proposed method is demonstrated through five high-dimensional problems. Compared with state-of-the-art methods, the proposed method is highly competitive in terms of both function evaluations and computation time.