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An efficient surrogate-based method for computing rare failure probability

机译：一种基于代理的有​​效稀有故障概率计算方法

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摘要

In this paper, we present an efficient numerical method for evaluating rare failure probability. The method is based on a recently developed surrogate-based method from Li and Xiu [J. Li, D. Xiu, Evaluation of failure probability via surrogate models, J. Comput. Phys. 229 (2010) 8966-8980] for failure probability computation. The method by Li and Xiu is of hybrid nature, in the sense that samples of both the surrogate model and the true physical model are used, and its efficiency gain relies on using only very few samples of the true model. Here we extend the capability of the method to rare probability computation by using the idea of importance sampling (IS). In particular, we employ cross-entropy (CE) method, which is an effective method to determine the biasing distribution in IS. We demonstrate that, by combining with the CE method, a surrogate-based IS algorithm can be constructed and is highly efficient for rare failure probability computation-it incurs much reduced simulation efforts compared to the traditional CE-IS method. In many cases, the new method is capable of capturing failure probability as small as 10~(-12)~10~(-6) with only several hundreds samples.
机译：在本文中，我们提出了一种评估稀有故障概率的有效数值方法。该方法基于Li和Xiu的最新开发的基于替代的方法[J. Li D. Xiu，通过替代模型评估失效概率，J。Comput。物理229（2010）8966-8980]进行故障概率计算。 Li和Xiu的方法具有混合性质，从某种意义上说，使用了替代模型和真实物理模型的样本，并且其效率增益仅依赖于使用真实模型的极少样本。在这里，我们通过使用重要性抽样（IS）的思想将方法的功能扩展到稀有概率计算。特别是，我们采用交叉熵（CE）方法，这是确定IS中偏差分布的有效方法。我们证明，通过与CE方法相结合，可以构建基于代理的IS算法，并且该算法对罕见故障概率计算非常有效-与传统的CE-IS方法相比，它大大减少了仿真工作。在许多情况下，该新方法仅用几百个样本就能够捕获低至10〜（-12）〜10〜（-6）的故障概率。

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