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可靠度的影响还缺少系统地研究。为此,提出了基于Copula函数的变量联合概率分布函数构造方法,并分析了不同Copula函数类型对结构可靠度的影响规律。首先,简要介绍了基于Copula函数的变量联合分布函数构造方法。其次,提出了构件失效概率计算的直接积分方法。最后以构件可靠度问题为例研究了Copula函数的类型对结构可靠度的影响规律。结果表明:不完备概率信息条件下构件可靠度是不唯一的,表征变量间相关性的Copula函数类型对构件可靠度具有明显的影响,不同Copula函数计算的构件失效概率存在明显的差别,这种差别随构件可靠指标的增大(或失效概率的减小)而增大。Copula函数尾部相关性对结构可靠度具有重要的影响。当功能函数的失效区域位于Copula函数尾部时,计算的失效概率明显比没有尾部相关性的Copula函数的失效概率大。基于功能函数的均值和标准差计算的可靠指标不能反映Copula函数的类型对结构可靠度的影响,而基于功能函数实际分布求得的失效概率则可以有效反映不同Copula函数对结构可靠度的影响。
The method for constructing the joint probability distribution of correlated variables based on incomplete probability information and its effect on component reliability has not been studied systematically. This paper aims to propose a method for modeling bivariate distribution using copulas and investigate the effect of a copula choice on component reliability. First, the method for constructing the joint probability distribution of correlated variables using copulas is briefly introduced. Thereafter, the formulae for the component probability of failure using direct integration are derived. Finally, an example of reliability analysis with linear performance functions is presented to demonstrate the effect of a copula choice on component reliability. The results indicate that component reliability cannot be determined uniquely with given marginal distributions and covariance.Copula choice has a significant effect on the component reliability. The probabilities of failure produced by different copulas differ considerably. Such a difference increases with the increase of reliability indexes or the decrease of failure probability. Tail dependence can result in a significant impact on the probability of failure. When tail dependence associated with a specified copula exists in a failure domain, the resulting probability of failure will become larger. The reliability index defined by the mean and standard deviation of a performance function cannot capture the difference among various copulas, while the probability of failure based on the actual distribution of a performance function can effectively accounts for the difference underlying various copulas.
出处
《工程力学》
EI
CSCD
北大核心
2013年第12期8-17,42,共11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
51079112)
关键词
联合分布函数
不完备概率信息
相关性
COPULA
失效概率
joint probability distribution function
incomplete probability information
correlation
Copula
probability of failure
