云制造环境下的演化博弈公差分配方法

A Tolerance Allocation Method Based on Evolutionary Game in Cloud Manufacturing

针对云制造环境下复杂多样的制造资源对产品装配尺寸链公差分配的影响,提出了一种基于演化博弈的公差分配方法。首先以同属一个尺寸链中的各公差单元为博弈方,综合考虑公差设计方案的质量损失和资源价格两方面,将装配质量要求和成本转换为公差单元选择制造资源后的总支付,以公差单元对资源的选择为博弈策略,建立演化博弈模型;然后,构造模型的复制动力学方程,模拟不同用户的策略适应过程;最后,运用Lyapunov第二方法证明该模型能够收敛至演化均衡,并利用分布式迭代算法进行求解。以车身前端装配总成公差分配设计为例,验证该模型及算法的可行性与有效性,实验结果表明:质量损失系数对资源选择策略无影响,但会影响总支付;所提演化博弈方法与非合作博弈方法、线性加权方法相比,可降低公差分配方案的质量损失及总支付,平均降低了28.3%~54.0%和18.2%~63.6%。将该演化博弈方法应用于装配尺寸链公差分配设计,实现了云制造环境下依据公差设计进行制造资源的选择。

A tolerance allocation method based on evolutionary game is proposed to solve the influence of complex and diverse manufacturing resources on the tolerance allocation of product assembly dimension chain in cloud manufacturing(CMfg).Firstly,all tolerance elements in the same dimension chain are taken as the game parties,and an evolutionary game model is established with the selection of manufacturing resources.The game strategy comprehensively considers the quality loss and the resource price of the tolerance design scheme,and the assembly quality requirements and cost are converted into the total payment benefit after the selection of manufacturing resources by the tolerance element.Secondly,a replication dynamics equation of the model is constructed to simulate the strategy adaptation process of different users.Finally,the Lyapunov’s second method is used to prove the convergence of the model to evolutionary equilibrium,and the distributed iterative algorithm is used to find its solution.The feasibility and effectiveness of the model and algorithm are verified by a tolerance design example of the front end assembly.Experimental results show that the quality loss coefficient has no effect on the resource selection strategy,but affects the total payment.Comparisons with the non-cooperative game method and the linear weighting method show that the proposed evolutionary game method reduces the quality loss and total payment of the tolerance allocation scheme by 28.3%to 54.0%and 18.2%to 63.6%on average,respectively.The proposed method can be applied to the tolerance allocation design of assembly dimensional chain and to realize the selection of manufacturing resources according to tolerance design in cloud manufacturing environment.