Look-ahead active learning reliability analysis based on stepwise margin reduction

According to the concept of limit-state margin probability function, a new look-ahead learning function called stepwise margin reduction (SMR) is proposed for active learning reliability analysis. SMR aims to select the best next point as the one minimizing, in expectation, the integrated margin probability function when adding such a new point. The plain definition of SMR involves a double integral, and three-fold contributions are made to reducing the associated computational burden. First, the closed-form expression of inner integral is well deduced, which avoids burdensome Gaussian-Hermite quadrature or drawing simulations of Gaussian process. Second, thanks to the locality of analytical expression of inner integral, truncated-integral scheme (TIS) is devised for the outer integral to avoid serious computer memory issue. Third, the candidate pool is pruned to accelerate the selection of best next point per iteration. The efficacy of SMR-based active learning reliability method is illustrated on two analytical functions, three numerical examples and one real-world engineering problem. Results demonstrate that in SMR, the TIS performs better than the traditional limited-integral scheme. Then, in comparison with existing pointwise and look-ahead learning functions, SMR gains favorable advantage in term of both computational accuracy and efficiency.