基于Copula函数的并联结构系统可靠度分析

发布时间：2018-08-16 18:12

【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。
[Abstract]:Under the condition of incomplete probability information, the determination of joint distribution function of variables and its influence on the reliability of structural systems are not systematically studied. The purpose of this paper is to study the influence of Copula function, which characterizes the correlation between variables, on the reliability of structural systems. Firstly, the Copula function method of joint distribution function is introduced briefly. Secondly, the failure probability calculation method of parallel system is proposed, and the corresponding formula is deduced. Finally, several typical Copula functions are taken as examples to study the influence of Copula function types on the reliability of parallel structure systems. The results show that the type of Copula function, which characterizes the correlation between variables, has an obvious influence on the reliability of structural system, and the system failure probability calculated by different Copula functions has obvious differences, and the difference increases with the decrease of failure probability of components. When the failure region of the parallel system is located at the tail of the Copula function, the tail correlation of the Copula function has an obvious effect on the reliability of the system, and the calculated failure probability is larger than that of the Copula function without the tail correlation. The failure probability of the system increases with the increase of the correlation coefficient, and decreases with the increase of the correlation coefficient when the functional functions of the two components of the parallel system are positively correlated with each other. In addition, the failure probability calculated by the Copula function is within the upper and lower limits of the failure probability of the system, regardless of the variation of the component failure probability and the correlation coefficient between variables.
【作者单位】：武汉大学水资源与水电工程科学国家重点实验室;武汉大学水工岩石力学教育部重点实验室;新加坡国立大学土木与环境工程系;
【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)
【分类号】：TU312.3

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