基于优化Kriging模型和重要抽样法的结构可靠度混合算法

doi:10.7527/S1000-6893.2013.0235

固体力学与飞行器总体设计

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基于优化Kriging模型和重要抽样法的结构可靠度混合算法

刘瞻¹, 张建国¹, 王灿灿¹, 谭春林², 孙京³

1. 北京航空航天大学可靠性与系统工程学院, 北京 100191;
2. 中国空间技术研究院北京空间飞行器总体设计部, 北京 100094;
3. 北京卫星制造厂, 北京 100094

收稿日期:2012-07-24 修回日期:2013-01-03 出版日期:2013-06-25 发布日期:2013-01-09
通讯作者: 张建国, Tel.: 010-82338356 E-mail: zjg@buaa.edu.cn E-mail:zjg@buaa.edu.cn
作者简介:张建国男, 博士, 教授, 博士生导师。主要研究方向: 机械及机构可靠性。 Tel: 010-82338356 E-mail: zjg@buaa.edu.cn
基金资助:
国家"973"计划(2013CB733000)

Hybrid Structure Reliability Method Combining Optimized Kriging Model and Importance Sampling

LIU Zhan¹, ZHANG Jianguo¹, WANG Cancan¹, TAN Chunlin², SUN Jing³

1. School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China;
2. Beijing Institute of Spacecraft Overall Design, China Academy of Space Technology, Beijing 100094, China;
3. Beijing Satellite Manufacturer, Beijing 100094, China

Received:2012-07-24 Revised:2013-01-03 Online:2013-06-25 Published:2013-01-09
Contact: 10.7527/S1000-6893.2013.0235 E-mail:zjg@buaa.edu.cn
Supported by:
National Basic Research Program of China (2013CB733000)

摘要/Abstract

摘要：

结构可靠度分析计算通常采用多项式响应面拟合隐式极限状态函数,但对于复杂航空航天机械结构产品极限状态方程往往表现出高度非线性,此时多项式响应面的模拟精度不够就会造成计算不收敛。为了提高结构可靠度计算的精度、效率和收敛性,提出了基于优化Kriging模型和重要抽样法的结构可靠度计算方法。首先,利用人工蜂群算法对Kriging模型的参数进行优化;再用优化后的模型模拟隐式极限状态函数,结合重要抽样法不断修正抽样重心,逐步提高模拟精度以达到给定要求;最后,结合一阶矩法(FORM)/二阶矩法(SORM)经典算法求解结构可靠度。该方法提高了高度非线性隐式极限状态方程可靠度计算的精度和收敛性,并且具有较高的计算效率。

关键词: 结构可靠度, Kriging模型, 重要抽样法, 函数拟合, 人工蜂群算法, 参数优化

Abstract:

In structural reliability analysis, a polynomial function is usually used to approach the implicit limit state function. But the limit state function is likely to be implicit and highly nonlinear for complex aeronautic and astronautic structures. The calculation may not converge if the simulation of the polynomial function is not accurate enough. In order to improve the accuracy, efficiency, and convergency, a reliability method combining the approved Kriging model and importance sampling is proposed in this paper. Firstly, the parameter of Kriging model is optimized using the artificial bee colony algorithm. Then the implicit limit state function is fitted with the optimized Kriging model, and the sampling center is revised constantly by importance sampling to improve gradually the fitting accuracy. Finally, the reliability is solved combining the Kriging model and the parsing algorithm such as the first order reliability method (FORM) or second order reliability method (SORM). This method improves the accuracy and convergency of reliability calculations with highly nonlinear limit state functions, and has high computing efficiency.

Key words: structure reliability, Kriging model, importance sampling, function fitting, artificial bee colony algorithm, parameter optimization

中图分类号:

V215.7

刘瞻, 张建国, 王灿灿, 谭春林, 孙京. 基于优化Kriging模型和重要抽样法的结构可靠度混合算法[J]. 航空学报, 2013, 34(6): 1347-1355.

LIU Zhan, ZHANG Jianguo, WANG Cancan, TAN Chunlin, SUN Jing. Hybrid Structure Reliability Method Combining Optimized Kriging Model and Importance Sampling[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2013, 34(6): 1347-1355.

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E-mail：hkxb@buaa.edu.cn

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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

基于优化Kriging模型和重要抽样法的结构可靠度混合算法

Hybrid Structure Reliability Method Combining Optimized Kriging Model and Importance Sampling

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