二维联合概率密度函数构造方法及结构并联系统可靠度分析  

BIVARIATE DISTRIBUTION CONSTRUCTION METHOD AND ITS APPLICATION TO STRUCTURAL PARALLEL SYSTEM RELIABILITY ANALYSIS

作　　者：李典庆[1,2] 吴帅兵[3] 周创兵[1,2] 方国光[4] 

机构地区：[1]武汉大学水资源与水电工程科学国家重点实验室,武汉430072 [2]武汉大学水工岩石力学教育部重点实验室,武汉430072 [3]南昌工程学院水利与生态工程学院,南昌330099 [4]新加坡国立大学土木与环境工程系,新加坡117576

出　　处：《工程力学》2013年第3期37-45,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(51225903;51028901);高等学校全国优秀博士学位论文作者专项资金项目(2007B50)

摘　　要：该文目的在于研究二维联合概率密度函数构造方法对结构系统可靠度的影响规律。首先简要介绍了2种构造联合分布函数的近似方法:基于Pearson相关系数的近似方法 P和基于Spearman相关系数的近似方法 S。提出了基于直接积分方法的并联系统失效概率计算方法。算例结果表明2种近似方法计算的系统失效概率误差取决于系统失效概率的大小、功能函数的形式以及功能函数间相关程度。系统失效概率越小,近似方法计算的系统失效概率误差越大。当系统失效概率小于10 3量级时,近似方法计算的系统失效概率误差较大,工程应用中应该引起足够的重视。功能函数间负相关时近似方法的误差明显大于功能函数间正相关时的误差。此外,系统失效概率误差并不是随着功能函数间相关性的增加而单调增加。This paper aims to study the errors of the method P and method S. Firstly, method P and method S as well as the exact method are presented. Thereafter, the formulae for system probability of failure based on direct integration are derived. Finally, an illustrative example is investigated to demonstrate the errors associated with the two methods. The results indicate that the errors in system probabilities of failure for the two methods highly depend on the level of system probability of failure, the performance function underlying the system and the degree of correlation. Such errors increase greatly with the decreasing of system probabilities of failure. When the target system probability of failure is above 1.0x 10-3, the errors in the system probabilities of failure obtained from the two methods are significant, implying that the two approximate methods should be used carefully. The errors in system probability of failure for negative correlated performance functions are significantly higher thanthose for positive correlated performance functions. The maximum error in the system probability of failure may not be associated with a large correlation. It can happen at an intermediate correlation.

关 键 词：联合分布函数 Pearson相关系数 Spearman相关系数 系统失效概率 功能函数 

分 类 号：TU318[建筑科学—结构工程]