基于自适应Kriging代理模型的交叉熵重要抽样法

doi:10.7527/S1000-6893.2019.23123

固体力学与飞行器总体设计

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基于自适应Kriging代理模型的交叉熵重要抽样法

史朝印, 吕震宙, 李璐祎, 王燕萍

西北工业大学航空学院, 西安 710072

收稿日期:2019-04-30 修回日期:2019-08-14 出版日期:2020-01-15 发布日期:2019-09-16
通讯作者: 吕震宙 E-mail:zhenzhoulu@nwpu.edu.cn
基金资助:
国家自然科学基金（11902254）；国家重大科技专项（2017-IV-0009-0046）

Cross-entropy importance sampling method based on adaptive Kriging model

SHI Zhaoyin, LYU Zhenzhou, LI Luyi, WANG Yanping

School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2019-04-30 Revised:2019-08-14 Online:2020-01-15 Published:2019-09-16
Supported by:
National Natural Science Foundation of China (11902254); National Science and Technology Major Project (2017-IV-0009-0046)

摘要/Abstract

摘要： 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。

关键词: 失效概率, 交叉熵, 重要抽样, 高斯混合模型, 自适应Kriging

Abstract: 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.

Key words: failure probability, cross-entropy, importance sampling, Gaussian mixed model, adaptive Kriging

中图分类号:

V19
TB114.3

史朝印, 吕震宙, 李璐祎, 王燕萍. 基于自适应Kriging代理模型的交叉熵重要抽样法[J]. 航空学报, 2020, 41(1): 223123-223123.

SHI Zhaoyin, LYU Zhenzhou, LI Luyi, WANG Yanping. Cross-entropy importance sampling method based on adaptive Kriging model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(1): 223123-223123.

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于自适应Kriging代理模型的交叉熵重要抽样法

Cross-entropy importance sampling method based on adaptive Kriging model

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