论文标题
通过一维投影而没有梯度估计的高维概率估算的高维概率估算的跨凝结法的改进
Improvement of the cross-entropy method in high dimension for failure probability estimation through a one-dimensional projection without gradient estimation
论文作者
论文摘要
极少数事件概率估计是可靠性分析中的重要主题。已经开发出随机方法（例如重要性抽样）来估计这种概率，但它们通常在高维度中失败。在本文中，我们提出了一种新的基于跨透明的重要性抽样算法，以改善高维度中的罕见事件概率估计。我们专注于使用高斯辅助分布的跨凝结法，我们建议仅在一维子空间中更新高斯协方差矩阵。为此，主要思想是考虑样本平均值向量跨越的一维子空间中的投影，这给出了方差估计的影响力。与基本的跨透明算法相比，这种方法不需要任何其他模拟预算，我们在不同的数值测试用例上表明，它在高维度上大大提高了其性能。
Rare event probability estimation is an important topic in reliability analysis. Stochastic methods, such as importance sampling, have been developed to estimate such probabilities but they often fail in high dimension. In this paper, we propose a new cross-entropy-based importance sampling algorithm to improve rare event probability estimation in high dimension. We focus on the cross-entropy method with Gaussian auxiliary distributions and we suggest to update the Gaussian covariance matrix only in a one-dimensional subspace. For that purpose, the main idea is to consider the projection in the one-dimensional subspace spanned by the sample mean vector, which gives an influential direction for the variance estimation. This approach does not require any additional simulation budget compared to the basic cross-entropy algorithm and we show on different numerical test cases that it greatly improves its performance in high dimension.
