A theoretically-consistent parallel enrichment strategy for Bayesian active learning reliability analysis

Abstract

Although parallel active learning reliability analysis is promising and has been widely studied, there remains an open question regarding how to achieve better theoretical consistency and avoid reliance on empirical practices heavily. A new parallel Bayesian active learning reliability method is developed in this study. First, in Bayesian failure probability estimation, a metric called integrated probability of misclassification (IPM) is defined from the upper bound of mean absolute deviation of failure probability. Then, a multi-point learning function called $k$-point integrated probability of misclassification reduction ($k$-IPMR) is proposed to guide the selection of a batch of $k(\ge 1)$ new samples that maximize the expected reduction of IPM. To further reduce the computational overhead, the fast $k$-IPMR-guided parallel Bayesian active learning reliability analysis is conducted through four key workarounds. (i) The $k$-IPMR is substituted by its theoretically analogous but computationally cheaper variant. (ii) A stepwise maximization of $k$-IPMR is deployed to replace the cumbersome direct maximization approach. (iii) The number of new samples added per iteration is identified in an adaptive manner. (iv) A hybrid convergence criterion is specified according to the actual reduction of IPM at each iteration. Owing to the core role of IPM, we fuse the three major ingredients, i.e., Bayesian inference of failure probability, multi-point enrichment process, and convergence criterion, in a theoretically consistent way. The performance of the proposed method is testified on four examples of varying complexity. The results indicate that the proposed approach needs a fewer number of iterations than those existing ones and thus is more computationally efficient, particularly when dealing with time-intensive complex reliability problems.