To alleviate the intensive computational burden of reliability analysis, a new parallel active learning reliability method is proposed from the multi-point look-ahead paradigm. First, in the framework of probability density evolution method, a global measure of epistemic uncertainty about Kriging-based failure probability estimation, referred to as the targeted integrated mean squared error (TIMSE), is defined and well proved. Then, three key ingredients are developed in the workflow of parallel active learning reliability analysis: (i) A look-ahead learning function called k-point targeted integrated mean square error reduction (k-TIMSER) is deduced in closed form, quantifying explicitly the reduction of TIMSE induced by adding a batch of k(≥1) new points in expectation. (ii) A hybrid convergence criterion is specified according to the actual reduction of TIMSE at each iteration. (iii) Both prescribed scheme and adaptive scheme are devised to identify the rational size of batch of new points added per iteration. The most distinctive feature of the proposed approach lies in that the multi-point enrichment process is fully guided by the learning function k-TIMSER itself, without resorting to additional batch selection strategies. Hence, it is much more theoretically elegant and easy to implement. The effectiveness of the proposed approach is testified on three examples, and comparisons are made against several existing reliability methods. The results show that the proposed method achieves fair superiority over other existing ones in terms of the accuracy of failure probability estimate and the number of iterations. Particularly, the advantage of the total computational time becomes very evident in the proposed method, when computationally-expensive reliability problems are considered.

中文翻译：

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并行主动学习可靠性分析：一种多点前瞻范式


为了减轻可靠性分析的密集计算负担，从多点前瞻范式中提出了一种新的并行主动学习可靠性方法。首先，在概率密度进化法的框架中，定义并充分证明了基于克里金法的失败概率估计的认识不确定性的全局度量，称为目标积分均方误差 （TIMSE）。然后，在并行主动学习可靠性分析的工作流程中开发了三个关键要素：（i） 以封闭形式推导出一种称为 k 点目标综合均方误差减少 （k-TIMSER） 的前瞻性学习函数，明确量化了通过在期望中添加一批 k（≥1） 个新点而诱导的 TIMSE 减少。（ii） 根据每次迭代时 TIMSE 的实际减少指定混合收敛标准。（iii） 设计了规定方案和自适应方案来确定每次迭代添加的新点批次的合理大小。所提出的方法最显着的特点在于，多点富集过程完全由学习函数 k-TIMSER 本身引导，而无需求助于额外的批次选择策略。因此，它在理论上更加优雅且易于实现。所提出的方法的有效性在三个例子中得到了证明，并与几种现有的可靠性方法进行了比较。结果表明，所提方法在故障概率估计精度和迭代次数方面优于其他现有方法。 特别是，当考虑计算成本高昂的可靠性问题时，总计算时间的优势在所提出的方法中变得非常明显。