基于Kriging模型梯度解析解的改进一次二阶矩方法

doi:10.7527/S1000-6893.2018.22629

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基于Kriging模型梯度解析解的改进一次二阶矩方法

李宝玉^1,2, 张磊刚², 裘群海², 余雄庆¹

1. 南京航空航天大学航空宇航学院, 南京 210016;
2. 中国运载火箭技术研究院, 北京 100076

收稿日期:2018-08-27 修回日期:2018-09-26 出版日期:2019-05-15 发布日期:2018-10-25
通讯作者: 张磊刚 E-mail:leigang_zhang@163.com
基金资助:
军委装备发展部"十三五"装备发展领域基金（6140244010216HT15001）

An advanced first order and second moment method based on gradient analytical solution of Kriging surrogate model

LI Baoyu^1,2, ZHANG Leigang², QIU Qunhai², YU Xiongqing¹

1. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. China Academy of Launch Vehicle Technology, Beijing 100076, China

Received:2018-08-27 Revised:2018-09-26 Online:2019-05-15 Published:2018-10-25
Supported by:
Equipment Development Department "13th Five-year" Equipment Research Field Foundation of China Central Military Commission

摘要/Abstract

摘要： 改进一次二阶矩（AFOSM）法是一种基于功能函数梯度的结构可靠性分析方法，鉴于其对隐式函数的梯度较难求解，提出了一种基于Kriging模型梯度解析解的AFOSM方法，利用Kriging代理模型的解析表达式推导得到功能函数对输入变量的梯度解析解，为AFOSM中设计点的确定提供高精度的梯度信息。通过Kriging与AFOSM的结合，很好地解决了基于有限元模型的隐式情况下梯度计算量相当大、可靠性分析难的问题。数值与工程算例验证了所提Kriging梯度解析解的较高精确性，同时验证了所提基于Kriging解析解的AFOSM结构可靠性分析方法的正确性与较高精度。

关键词: 结构可靠性, Kriging代理模型, 梯度解析解, 改进一次二阶矩, 失效概率

Abstract: The Advanced First Order and Second Moment (AFOSM) method is a structural reliability analysis method based on the gradient information of performance function. Since the gradient information of the implicit function is difficult to solve, an AFOSM method based on the gradient analytical solution of Kriging surrogate model is proposed, using the analytical expression of Kriging surrogate model to obtain gradient information of the performance function with respect to input variables, and providing a high-precision gradient information for the computation of the design point in the AFOSM method. By combining Kriging and AFOSM, the problem of gradient calculation and reliability analysis in the implicit situation based on the finite element model can be better solved. Numerical and engineering examples are introduced to verify the high precision of the proposed gradient solution based on Kriging; besides, the accuracy and precision of the proposed Kriging analytical solution based AFOSM reliability analysis method are also verified.

Key words: structural reliability, Kriging surrogate model, gradient analytical solution, advanced first order and second moment, probability density

中图分类号:

V19
TB114.3

李宝玉, 张磊刚, 裘群海, 余雄庆. 基于Kriging模型梯度解析解的改进一次二阶矩方法[J]. 航空学报, 2019, 40(5): 222629-222629.

LI Baoyu, ZHANG Leigang, QIU Qunhai, YU Xiongqing. An advanced first order and second moment method based on gradient analytical solution of Kriging surrogate model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(5): 222629-222629.

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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Kriging模型梯度解析解的改进一次二阶矩方法

An advanced first order and second moment method based on gradient analytical solution of Kriging surrogate model

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