失效模式相关的机械结构可靠性的Copula分析方法

Copula Analysis of Structural Systems Reliability with Correlated Failure Mode

分析了几种常用Copula函数及它们在相关分析上的应用特点。针对具有相关失效模式的机械结构系统,提出了利用混合Copula函数实现机械结构系统的可靠性建模方法。该方法分别以各失效模式的功能函数值为Copula分析变量,通过离差平方和准则法与MATLAB优化工具箱,利用MonteCarlo法产生的随机抽样数据估计Copula参数,实现各功能函数间的联合概率分布函数的Copula建模,从而可以利用Copula函数实现机械结构系统的可靠性分析。用工程算例验证了该理论方法的可行性。研究结果可为具有相关失效模式的机械结构系统可靠性分析提供新途径。

Several kinds of Copula functions were introduced,which were used for correlation analysis.Aiming at engineering structural systems with failure-dependence,a new method was put forward for reliability modeling by introducing mixed Copula.Copula model of joint probability distribution function was built among every limit state equations,where every limit state equation value was chosen as the analytic variables of Copula function and unknown parameters of Copula were estimated by means of the random sampling data generated by Monte Carlo simulation and using residual square sum method in MATLAB software,thereby failure probability of the machine components was got by Copula function.Finally,a practical case of Copula demonstrates the feasibility of the method,which gives a new way for the reliability analysis of structural system with correlated failure modes.