论文标题
贝叶斯改进的跨熵方法用于网络可靠性评估
Bayesian improved cross entropy method for network reliability assessment
论文作者
论文摘要
我们提出了改进的横熵方法（ICE）方法的修改，以提高其用于网络可靠性评估的性能。 ICE方法通过参数分布模型进行了从标称密度到最佳重要性采样（IS）密度的过渡，该参数分布模型的横向熵与最佳的交叉熵被最小化。冰法的效率和准确性在很大程度上受参数模型的选择影响。在具有独立多国家组件的系统的可靠性的背景下，参数家族的明显选择是分类分布。当用标准冰更新此分布模型时，分配给某个类别的概率通常会收敛到0，因为在自适应采样过程中缺乏该类别的样品出现，导致较差的是具有强偏见的估计值。为了解决这个问题，我们提出了一种算法，称为贝叶斯改进的横熵方法（BICE）。因此，使用后验预测分布来更新参数模型，而不是原始ICE方法中采用的加权最大似然估计方法。一组数字示例说明了所提出方法的效率和准确性。
We propose a modification of the improved cross entropy (iCE) method to enhance its performance for network reliability assessment. The iCE method performs a transition from the nominal density to the optimal importance sampling (IS) density via a parametric distribution model whose cross entropy with the optimal IS is minimized. The efficiency and accuracy of the iCE method are largely influenced by the choice of the parametric model. In the context of reliability of systems with independent multi-state components, the obvious choice of the parametric family is the categorical distribution. When updating this distribution model with standard iCE, the probability assigned to a certain category often converges to 0 due to lack of occurrence of samples from this category during the adaptive sampling process, resulting in a poor IS estima tor with a strong negative bias. To circumvent this issue, we propose an algorithm termed Bayesian improved cross entropy method (BiCE). Thereby, the posterior predictive distribution is employed to update the parametric model instead of the weighted maximum likelihood estimation approach employed in the original iCE method. A set of numerical examples illustrate the efficiency and accuracy of the proposed method.
