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摘   要：针对机电产品（系统）性能可靠性建模和分析困难的问题，提出一种基于非线性Gamma随机过程和混合Copula函数的元动作单元性能可靠性分析通用模型. 分析性能退化过程特点建立产品性能退化與其实现的特定功能之间的联系，利用“功能（Function）-运动（Motion）-动作（Action）”的功能运动分解方法将机电产品分解成一系列最小运动单元——元动作单元，将机电产品性能可靠性问题转化为实现特定功能的元动作单元性能可靠性问题. 非线性Gamma随机退化过程描述单元内关键零件磨损的退化过程，在此基础上，结合Copula函数考虑元动作单元内部零件和结构的依赖耦合关系，提出一种元动作单元的性能可靠性分析方法. 为了更准确地评估元动作单元的性能可靠性，采用描述相关关系更优的混合Copula函数建立元动作单元的性能可靠性分析模型，并利用改进的遗传算法，在适应度函数中加入惩罚项，实现混合Copula函数的最优参数估计，最后结合串联系统概念得到考虑内部结构依赖耦合的元动作单元的性能可靠度表达式. 以某托盘交换架分解得到的不同元动作单元为例进行分析，并通过实验对比验证了该模型的可行性和有效性.

关键词：机电产品;元动作单元;可靠性分析;随机过程;Copula函数

中图分类号：TB114.3                             文献标志码：A

Performance Reliability Analysis of Meta-action Unit Based

on Gamma Process and Hybrid Copula Function

ZHANG Genbao，ZHANG Dingfei，RAN Yan，YING Guangqi

（College of Mechanical Engineering，Chongqing University，Chongqing 400044，China）

Abstract：Motivated by the difficulty of the electromechanical product （system） performance reliability analysis and modeling， an general analysis method is developed for meta action unit performance reliability based on hybrid copula. The characteristics of performance degradation process are analyzed to establish the relationship between the product performance degradation and the realized specific functions. Using the functional motion decomposition method of "Function-Motion-Action"， the electromechanical products are decomposed into a series of meta action units via linking functions with their performance. The components performance reliability analysis model is constructed that we consider it obeys the nonlinear gamma random degradation process is used to describe the degradation process of key parts in the unit. Considering the coupling relation of meta action unit internal parts and structure， a performance reliability model of the meta action unit is constructed based on the hybrid copula function. In order to more accurately evaluate the performance reliability of meta-action unit，  the optimal Copula Functions having is selected to develop the performance reliability model of meta-action unit. The unknown parameter estimation of hybrid copula function is realized by improved genetic algorithm， which adds penalty term to fitness function. Combining the hybrid copula mathematical expression and the concept of a series system， the performance reliability expression of meta action unit considering the coupling dependence is obtained. The feasibility and effectiveness of the method are verified by an example.

Key words：electromechanical products;meta action unit;reliability analysis;random process;copula function

随着高新技术不断发展和应用，产品（或系统）的高度集成化、高度智能化和复杂性不断提高，并广泛应用于航空航天、核……