One-step look-ahead policy for active learning reliability analysis

Active-learning reliability analysis is essentially a problem of sequential decision making under uncertainty from the Bayesian decision-theoretic perspective. Hence, leveraging on basic principle of the one-step look-ahead policy, a novel learning function named Targeted integrated mean squared error (TIMSE) is proposed to combine polynomial-chaos Kriging and probability density evolution method for structural reliability analysis. The TIMSE makes the following three critical contributions. First, its closed-form formula is tractable, getting rid of cumbersome issues about numerical quadrature or drawing realizations of Gaussian process. Second, the TIMSE accounts for global impacts of adding a new point on any other point. Third, the TIMSE takes into account the horizon of future experimental designs, by virtue of Kriging update formulae. Besides, a hybrid convergence criterion is developed that effectively avoids two categories of premature termination. Two benchmark analytical functions and three numerical examples are investigated, and comparisons are made against several existing reliability methods. Results indicate that the TIMSE outperforms its localized version and other existing learning functions. Moreover, the proposed reliability approach is more computationally advantageous when time-consuming, complex dynamic problems are involved.