Efficient reliability analysis based on adaptive sequential sampling design and cross-validation

Surrogate-models have proven to be an effective strategy for structural systems with expensive-to-evaluate simulations and are very useful for structural reliability analysis. Many kriging model based adaptive sequential sampling methods have been developed recently for efficient reliability analysis. In this paper, a new learning function based on cross-validation is proposed as the guideline to adaptively select new training points at each iteration for reliability analysis. The epistemic uncertainty of the surrogate models and the effects of the aleatory uncertainty of the random variables are considered simultaneously in the proposed new learning function. Three goals can be achieved using the proposed new learning function, i.e., most of the selected new training sample points (1) are selected from the desired regions to improve computational efficiency; (2) reside around the limit-sate functions and in the regions with high reliability sensitivity; and (3) tend to be far away from existing training points in the current design to avoid the clustering problem. The proposed learning function is partly linked to the probability of failure. The proposed method is easy to code and understand as well as implement. Five numerical examples are finally used to validate the accuracy and efficiency as well as applicability of the proposed method.