Adaptive Kriging coupled with importance sampling strategies for time-variant hybrid reliability analysis

For the time-variant hybrid reliability problem under random and interval uncertainties, the upper bound of time-variant failure probability, as a conservative index to quantify the safety level of the structure, is highly concerned. To efficiently estimate it, the adaptive Kriging respectively combined with design point based importance sampling and meta-model based one are proposed. The first algorithm firstly searches the design point of the hybrid problem, on which the candidate random samples are generated by shifting the sampling center from mean value to design point. Then, the Kriging model is iteratively trained and the hybrid problem is solved by the well-trained Kriging model. The second algorithm firstly utilizes the Kriging-based importance sampling to approximate the quasi-optimal importance sampling samples and estimate the augmented upper bound of time-variant failure probability. After that, the Kriging model is further updated based on these importance samples to estimate the correction factor, on which the hybrid failure probability is calculated by the product of augmented upper bound of time-variant failure probability and correction factor. Meanwhile, an improved learning function is presented to efficiently train an accurate Kriging model. The proposed methods integrate the merits of adaptive Kriging and importance sampling, which can conduct the hybrid reliability analysis by as little as possible computational cost. The presented examples show the feasibility of the proposed methods.