An adaptive parallel learning dependent Kriging model for small failure probability problems

Estimating the small failure probability of highly reliable structures, such as those used in aerospace, is challenging because of the large computational cost. In this paper, a new reliability analysis method that combines the improved dependent Kriging method and adaptive importance sampling for a small failure probability has been proposed. A Kriging model is constructed in each iteration, which avoids the complexity and time-consuming simulation. A new strategy for parallel learning is proposed to allow parallel computing and further reduce the overall computational time. The proposed method comprises the following strategies: (1) The importance sampling function is constructed adaptively to gradually approximate the optimal importance sampling function. (2) The learning function considers both the correlation among samples and the uncertainty contribution of samples to failure probability, with the ability to select multiple samples at each iteration to refine the Kriging model. (3) The stopping criterion is dependent on the expectation of the failure probability and converges at a fast rate. The proposed method can be applied to a system with a small failure probability, multiple failure regions, high nonlinearity, and implicit functions. The efficiency and accuracy of the proposed method are demonstrated using four numerical examples and are compared with those of five competitive reported methods.