Cross-entropy based importance sampling for stochastic simulation models
Cross-entropy based importance sampling for stochastic simulation models
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DOI：
10.1016/j.ress.2019.106526
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
Q. D. Cao;Youngjun Choe
中科院分区：
文献类型：
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作者：
Q. D. Cao;Youngjun Choe
为了有效地评估系统的可靠性，基于蒙特卡罗模拟，重要抽样被广泛使用。确定性仿真模型的最优重要性抽样密度是在20世纪50年代提出的，它将输入确定性地映射到输出，并在实际中使用各种方法进行近似。对于给定输入输出为随机的随机模拟模型，最优重要抽样密度是最近才得到的。在现有的文献中，基于元模型的方法已被用来近似这个最佳密度。然而，在实践中，构建一个令人满意的元模型通常是困难或耗时的。本文提出了一种基于交叉熵的方法，它是自动的，不需要特定的领域知识。该方法使用期望最大化算法来指导混合分布模型的选择，以近似最优密度。该方法迭代地更新近似密度，以最小化其估计的差异，通过估计的交叉熵测量，从最佳密度。混合模型的复杂性控制使用交叉熵信息准则。该方法是经验验证，使用广泛的数值研究和应用的案例研究，评估风力涡轮机的可靠性，使用随机模拟模型。
To efficiently evaluate system reliability based on Monte Carlo simulation, importance sampling is used widely. The optimal importance sampling density was derived in 1950s for the deterministic simulation model, which maps an input to an output deterministically, and is approximated in practice using various methods. For the stochastic simulation model whose output is random given an input, the optimal importance sampling density was derived only recently. In the existing literature, metamodel-based approaches have been used to approximate this optimal density. However, building a satisfactory metamodel is often difficult or time-consuming in practice. This paper proposes a cross-entropy based method, which is automatic and does not require specific domain knowledge. The proposed method uses an expectation–maximization algorithm to guide the choice of a mixture distribution model for approximating the optimal density. The method iteratively updates the approximated density to minimize its estimated discrepancy, measured by estimated cross-entropy, from the optimal density. The mixture model’s complexity is controlled using the cross-entropy information criterion. The method is empirically validated using extensive numerical studies and applied to a case study of evaluating the reliability of wind turbine using a stochastic simulation model.