REAK：基于误差率的自适应克里金可靠性分析
REAK: Reliability analysis through Error rate-based Adaptive Kriging
摘要：
随着各个领域的模型变得越来越复杂，相关的计算需求也在显著增加。这些系统的可靠性分析时，故障概率很小，是非常具有挑战性的，需要大量的昂贵的模拟。为了应对这一挑战，本文介绍了通过基于误差率的自适应克里格（REAK）的可靠性分析。本文采用基于Lindeberg条件的中心极限定理的一个推广，导出了具有错误符号估计的设计样本数的分布，从而确定了失效概率估计的最大误差率。该误差率使得能够在用于设计样本的战略生成的自适应方案的每个阶段最佳地建立有效采样区域。此外，它有助于设置一个目标精度的故障概率估计，这是用来作为停止标准的可靠性分析。这些功能一起可以显着减少对复杂的，计算要求高的模型的调用数量。应用REAK的四个例子与不同程度的非线性和尺寸。结果表明，REAK是能够减少高达50%的计算需求相比，国家的最先进的自适应克里格与蒙特卡罗模拟（AK-MCS）和改进的顺序克里格可靠性分析（ISKRA）的方法。
英文摘要：
As models in various fields are becoming more complex, associated computational demands have been increasing significantly. Reliability analysis for these systems when failure probabilities are small is significantly challenging, requiring a large number of costly simulations. To address this challenge, this paper introduces Reliability analysis through Error rate-based Adaptive Kriging (REAK). An extension of the Central Limit Theorem based on Lindeberg condition is adopted here to derive the distribution of the number of design samples with wrong sign estimate and subsequently determine the maximum error rate for failure probability estimates. This error rate enables optimal establishment of effective sampling regions at each stage of an adaptive scheme for strategic generation of design samples. Moreover, it facilitates setting a target accuracy for failure probability estimation, which is used as stopping criterion for reliability analysis. These capabilities together can significantly reduce the number of calls to sophisticated, computationally demanding models. The application of REAK for four examples with varying extent of nonlinearity and dimension is presented. Results indicate that REAK is able to reduce the computational demand by as high as 50% compared to state-of-the-art methods of Adaptive Kriging with Monte Carlo Simulation (AK-MCS) and Improved Sequential Kriging Reliability Analysis (ISKRA).
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