A Kriging-assisted two-stage adaptive radial-based importance sampling method for random-interval hybrid reliability analysis

For uncertain structures with the coexisting random and interval inputs, effectively estimating the lower and upper bounds of failure probability is always a challenge. To address this issue, this paper first proposes a two-stage adaptive radial-based importance sampling (TARBIS) method, where two optimal spheres are sought successively in two stages to estimate the bounds of failure probability. Then, by replacing the true limit state function using the Kriging model, a Kriging-assisted TARBIS (K-TARBIS) is further developed to improve the computational efficiency. In the first stage, the training points mostly contributing to the estimation of two bounds of failure probability are identified by a system reliability theory-based U ( SYSU ) learning function to update the Kriging model. In the second stage, the Kriging model is updated only on sample points contributing to the estimation of the upper bound of failure probability. Throughout the active learning process, the Kriging model is sequentially updated in a series of small sub-candidate sample pools of TARBIS, which greatly reduces the computational cost. The accuracy and efficiency of the proposed method are demonstrated through four representative examples.