REIF: A novel active-learning function toward adaptive Kriging surrogate models for structural reliability analysis

Structural reliability analysis is typically evaluated based on a multivariate function that describes underlying failure mechanisms of a structural system. It is necessary for a surrogate model to mimic the true performance function as the brute-force Monte-Carlo simulation is computationally intensive for rare failure probabilities. To this end, the paper presents an effective active-learning based Kriging method for structural reliability analysis. The reliability-based expected improvement function (REIF) is first derived based on the folded-normal distribution. To account for the modulating effect of the joint probability density function of input random variables on the scattering geometry of candidate samples, an improvement of the REIF active-learning function, i.e., the REIF2 is further presented. Then, the low-discrepancy samples and adaptively truncated sampling regions are combined together to initiate efficient active-learning iterations. The truncated sampling region is directly related to a structural failure probability result, rather than subjectively fixed by an analyst. Numerical validity of the proposed active-learning functions in conjunction with adaptively truncated sampling region and low-discrepancy samples is demonstrated by several structural reliability examples in the literature.