• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2018, Vol. 54 ›› Issue (16): 178-185.doi: 10.3901/JME.2018.16.178

• 交叉与前沿 • 上一篇    下一篇

基于Copula函数的失效概率灵敏度分解方法

王攀1, 张磊刚2, 吕震宙1,3, 程蕾2, 岳珠峰1   

  1. 1. 西北工业大学飞行器可靠性工程研究所 西安 710129;
    2. 中国运载火箭技术研究院 北京 100076;
    3. 西北工业大学航空学院 西安 710129
  • 收稿日期:2017-08-12 修回日期:2018-03-20 出版日期:2018-08-20 发布日期:2018-08-20
  • 通讯作者: 王攀(通信作者),男,1988年出生,博士,副教授。主要研究方向为飞行器结构设计和结构可靠性工程。E-mail:panwang@nwpu.edu.cn
  • 基金资助:
    国家自然科学基金(11602197)、陕西省自然科学基金(2017JQ5041)、中央高校基本业务费(3102018ZY014)和航天科学技术基金资助项目。

Sensitivity Decomposition Approach of Failure Probability Based on Copula Function

WANG Pan1, ZHANG Leigang2, LÜ Zhenzhou1,3, CHENG Lei2, YUE Zhufeng1   

  1. 1. Institute of Aircraft Reliability Engineering, Northwestern Polytechnical University, Xi'an 710129;
    2. China Academey of Launch Vehicle Technology, Beijing 100076;
    3. School of Aeronautics, Northwestern Polytechnical University, Xi'an 710129
  • Received:2017-08-12 Revised:2018-03-20 Online:2018-08-20 Published:2018-08-20

摘要: 针对工程结构中输入变量存在相关性的失效概率灵敏度分析问题,通过引入Copula函数对输入变量联合概率分布进行描述,可将失效概率灵敏度分解为独立灵敏度和相关灵敏度。针对失效概率灵敏度的计算问题,可将失效概率的偏导数计算转化为边缘概率分布函数和Copula密度函数的核函数计算。通过对常用的概率分布以及Copula函数进行推导,可以得到其核函数的解析表达,进而直接用于失效概率灵敏度的计算。通过数值算例和工程算例对所提算法的合理性进行了验证。

关键词: Copula, 核函数, 灵敏度, 失效概率, 相关性

Abstract: For the sensitivity analysis of failure probability with dependent input variables, by introducing the Copula function to describe the joint probability distribution of input variables, the sensitivity of failure probability can be decomposed into independent sensitivity and dependent sensitivity. Then for the computation of the sensitivity of failure probability, the derivative of failure probability can be transformed into the kernel function of marginal distributions and Copula functions. While for the common probability distributions and Copula functions, their kernel functions can be derived analytically, which is directly used to the computation of sensitivity of failure probability. The numerical examples and engineering practice are employed to validate the rationality of the proposed method.

Key words: copula, dependent, failure probability, kernel function, sensitivity

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