基于自适应Kriging代理模型的交叉熵重要抽样法

对于复杂失效域和小失效概率耦合的可靠性分析问题，本文提出了一种交叉熵重要抽样（CE-IS）方法结合自适应Kriging （AK）代理模型的求解方法（CE-IS-AK）。所提方法基于交叉熵原理，用混合高斯模型逐步逼近最优重要抽样密度函数，并采用AK模型协助逼近过程中混合高斯模型的参数的更新，从而提高了CE-IS方法的计算效率。另外，本文还改进了CE-IS方法的收敛准则，避免了方法的冗余迭代，扩大了方法的适用范围。由于在CE-IS方法中引入了AK模型，因此，本文方法所构建的重要抽样函数在保证精度的基础上提高了效率。相较于AK-MCS方法，本文方法中引入了重要抽样的思想，因此在Kriging训练点数目基本相同的情况下，大幅缩减小失效概率计算时样本池规模，并且由于利用了混合高斯模型，因而对多失效域具有较好的适用性。算例分析也证明了本文所提方法的优越性。

Cross-entropy importance sampling method based on adaptive Kriging model

To solve the reliability analysis of the coupling of complex failure domain and small failure probability, an improved method shortened as CE-IS-AK is proposed by combining Cross-Entropy Importance Sampling (CE-IS) with the Adaptive Kriging (AK) model on the existing CE-IS. In the proposed CE-IS-AK, the Gaussian mixed model suitable for complex failure domain is used to approximate the optimal Importance Sampling Density Function (IS-DF), and in the approximation process, the AK model is used to iteratively update the parameters of the Gaussian mixed model, so the efficiency of CE-IS is improved by the modification. In addition, the convergence criterion of the existing CE-IS is improved by CE-IS-AK for avoiding redundant iterations and expanding the applicability of the existing CE-IS. Since the AK model is nested into the CE-IS, the efficiency of constructing IS-DF is improved by the CE-IS-AK while ensuring the accuracy. Compared with the widely applicable AK based on Monte Carlo Simulation (AK-MCS), the size of the candidate sample pool for training AK in the CE-IS-AK is greatly reduced due to the variance-reduced strategy of IS in the case of that the number of training samples keeps almost equivalent, and the introduction of the Gaussian mixed model makes the proposed CE-IS-AK applicable for the multiple complex failure domain. The presented examples demonstrate the superiority of the CE-IS-AK.