A combined projection-outline-based active learning Kriging and adaptive importance sampling method for hybrid reliability analysis with small failure probabilities

Abstract

In this paper, the adaptive importance sampling (AIS) method is extended for hybrid reliability analysis under random and interval variables (HRA-RI) with small failure probabilities. In AIS, the design space is divided into random and interval variable subspaces. In random variable subspace, Markov Chain Monte Carlo (MCMC) is employed to generate samples which populate the failure regions. Then based on these samples, two kernel sampling density functions are established for estimations of the lower and upper bounds of failure probability. To improve the computational efficiency of AIS in cases with time-consuming performance functions, a combination method of projection-outline-based active learning Kriging and AIS, termed as POALK-AIS, is proposed in this paper. In this method, design of experiments is sequentially updated for the construction of Kriging metamodel with focus on the approximation accuracy of the projection outlines on the limit-state surface. During the procedure of POALK-AIS, multiple groups of sample points simulated by AIS are used to calculate the upper and lower bounds of failure probability. The accuracy, efficiency and robustness of POALK-AIS for HRA-RI with small failure probabilities are verified by five test examples.