A coupled adaptive radial-based importance sampling and single-loop Kriging surrogate model for time-dependent reliability analysis

To efficiently analyze the time-dependent reliability is still a challenge today for many applications. This paper aims at modifying the original single-loop Kriging surrogate method to make it more efficient especially for assessing the small time-dependent failure probability. The first contribution of the proposed method is that the radial-based importance sampling scheme is nested in the single-loop Kriging surrogate model-based time-dependent reliability analysis method. By the radial-based importance sampling scheme, the optimal hypersphere can be searched and the samples inside the optimal hypersphere can be removed from the candidate sampling pool. Besides, the samples outside the optimal hypersphere are divided into several sub-candidate sampling pools by the in-process hyperspheres. By decreasing the size of candidate sampling pool in each updating process of Kriging model, the training time of updating Kriging model can be reduced so that the efficiency of time-dependent reliability analysis is enhanced. The second contribution of the proposed method is that the Kriging model-based dichotomy is embedded skillfully to efficiently find the hyperspheres layer after layer until the optimal hypersphere is found. The third contribution of the proposed method is that a modified learning function is constructed from selecting the most easily identifiable failure time during the time period of interest to efficiently update the Kriging model in each sub-candidate sampling pool. Finally, the accuracy and efficiency of the proposed method are verified by three examples.