摘要
不完备概率信息条件下变量联合分布函数的确定及其对结构系统可靠度的影响还缺少系统地研究,该文目的在于研究表征变量间相关性的Copula函数对结构系统可靠度的影响规律。首先,简要介绍了变量联合分布函数构造的Copula函数方法。其次,提出了并联系统失效概率计算方法,并推导了相应的计算公式。最后以几种典型Copula函数为例研究了Copula函数类型对结构并联系统可靠度的影响规律。结果表明:表征变量间相关性的Copula函数类型对结构系统可靠度具有明显的影响,不同Copula函数计算的系统失效概率存在明显的差别,这种差别随构件失效概率的减小而增大。当并联系统的失效区域位于Copula函数尾部时,Copula函数的尾部相关性对系统可靠度有明显的影响,计算的失效概率比没有尾部相关性的Copula函数的失效概率大。当组成并联系统的两构件功能函数间正相关时,系统失效概率随相关系数的增大而增加;当构件功能函数间负相关时,系统失效概率随相关系数的增大而减小。此外,无论构件失效概率和变量间相关系数如何变化,Copula函数计算的失效概率都位于系统失效概率的上下限内。
Structural system reliability can not be determined uniquely based on incomplete probability information of correlated variables.This paper aims to investigate the effect of copula choice on system reliability when probability information is incomplete.First,the method for constructing the joint probability distribution of correlated variables using copulas is introduced.Thereafter,a parallel system reliability model is formulated and the formulae for calculating the system probability of failure are derived.Finally,several typical copulas are selected to model the dependence structure between correlated variables.A parallel system with two components is presented to demonstrate the effect of copula choice on system reliability.The results indicate that the copula choice has a significant effect on the system reliability.The system probabilities of failure produced by different copulas can differ considerably,and the level of difference increases with decreasing component probability of failure.Tail dependence has a significant impact on the system probability of failure.When tail dependence associated with a specified copula falls in a failure domain,the resulting system probability of failure will rise.The system probability of failure increases with increasing dependence between variables for positively correlated component performance functions,while it decreases with increasing correlation between variables for negatively correlated component performance functions.In addition,the system probabilities of failure associated with different copulas will be restricted within the upper bound and lower bound underlying the parallel system probability of failure for any given component probability of failure and correlation coefficient between variables.
出处
《工程力学》
EI
CSCD
北大核心
2014年第8期32-40,共9页
Engineering Mechanics
基金
国家杰出青年科学基金项目(51225903)
国家自然科学基金项目(51329901)
高等学校博士学科点专项科研基金项目(20120141110009)
关键词
联合概率分布函数
不完备概率信息
相关性
COPULA
系统失效概率
joint probability distribution function
incomplete probability information
correlation
copula
system probability of failure
