Efficient computing technique for reliability analysis of high-dimensional and low-failure probability problems using active learning method

In spite of recent advancements in reliability analysis, high-dimensional and low-failure probability problems remain challenging because many samples and function calls are required for an accurate result. Function calls lead to a sharp increase in computational cost in terms of time. For this reason, an active learning algorithm is proposed using Kriging metamodel, where an unsupervised algorithm is used to select training samples from random samples for the first and second iterations. Then, the metamodel is improved iteratively by enriching the concerned domain with samples near the limit state function and samples obtained from a space-filling design. Hence, rapid convergence with the minimum number of function calls occurs using this active learning algorithm. An efficient stopping criterion has been developed to avoid premature or late-mature terminations of the metamodel and to regulate the accuracy of the failure probability estimations. The efficacy of this algorithm is examined using relative error, number of function calls, and coefficient of efficiency in five examples which are based on high-dimensional and low-failure probability with random and interval variables.