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首页> 外文期刊>Methodology and computing in applied probability >Rare Event Probability Estimation in the Presence of Epistemic Uncertainty on Input Probability Distribution Parameters
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Rare Event Probability Estimation in the Presence of Epistemic Uncertainty on Input Probability Distribution Parameters

机译：输入概率分布参数存在认知不确定性的稀有事件概率估计

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摘要

The accurate estimation of rare event probabilities is a crucial problem in engineering to characterize the reliability of complex systems. Several methods such as Importance Sampling or Importance Splitting have been proposed to perform the estimation of such events more accurately (i.e., with a lower variance) than crude Monte Carlo method. However, these methods assume that the probability distributions of the input variables are exactly defined (e.g., mean and covariance matrix perfectly known if the input variables are defined through Gaussian laws) and are not able to determine the impact of a change in the input distribution parameters on the probability of interest. The problem considered in this paper is the propagation of the input distribution parameter uncertainty defined by intervals to the rare event probability. This problem induces intricate optimization and numerous probability estimations in order to determine the upper and lower bounds of the probability estimate. The calculation of these bounds is often numerically intractable for rare event probability (say 10(-5)), due to the high computational cost required. A new methodology is proposed to solve this problem with a reduced simulation budget, using the adaptive Importance Sampling. To this end, a method for estimating the Importance Sampling optimal auxiliary distribution is proposed, based on preceding Importance Sampling estimations. Furthermore, a Kriging-based adaptive Importance Sampling is used in order to minimize the number of evaluations of the computationally expensive simulation code. To determine the bounds of the probability estimate, an evolutionary algorithm is employed. This algorithm has been selected to deal with noisy problems since the Importance Sampling probability estimate is a random variable. The efficiency of the proposed approach, in terms of accuracy of the found results and computational cost, is assessed on academic and engineering test cases.
机译：罕见事件概率的准确估计是工程中表征复杂系统可靠性的关键问题。已经提出了诸如重要性采样或重要性分裂之类的几种方法，以比粗蒙特卡洛方法更准确地（即，具有更低的方差）执行这种事件的估计。但是，这些方法假设输入变量的概率分布是精确定义的（例如，如果输入变量是通过高斯定律定义的，均值和协方差矩阵就可以完全了解），并且无法确定输入分布变化的影响感兴趣概率的参数。本文考虑的问题是由间隔定义的输入分布参数不确定性向稀有事件概率的传播。为了确定概率估计的上限和下限，此问题引起了复杂的优化和大量的概率估计。由于极高的计算成本，对于极少数事件概率（例如10（-5）），这些界限的计算通常在数值上难以处理。提出了一种新的方法，通过使用自适应重要性采样以减少的仿真预算来解决此问题。为此，基于先前的重要性采样估计，提出了一种估计重要性采样最佳辅助分布的方法。此外，使用基于克里格的自适应重要性采样来最小化计算上昂贵的仿真代码的评估次数。为了确定概率估计的范围，采用了进化算法。由于重要性采样概率估计是随机变量，因此已选择此算法来处理嘈杂的问题。在研究结果的准确性和计算成本方面，对学术和工程测试案例评估了所提出方法的效率。

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