肖艳秋　杨先超　崔光珍　夏琼佩　周坤　张福东　夏苑菲

摘要：针对复杂机械产品系统维数高、单元数量大所引起的多维度强耦合设计制造难题，提出了一种基于谱聚类算法的模块划分方法.该方法基于功能-流-结构分解法实现了对产品的层次化分解，应用模糊数学定义特征元素之间的相关性，在此基础上构建了基于数值型设计结构矩阵的产品零部件关联关系模型，通过引入谱聚类算法将零部件聚类问题转化为图的最优划分问题，构建了基于模块内平均内聚度和模块间平均耦合度的模块划分评价指标，进而实现了产品的模块划分.实例验证结果表明，该方法能有效降低复杂机械产品设计和制造的复杂度，是科学有效的.

Abstract：Aiming at the multi-dimensional and strong coupling problem of design and manufacturing caused by the high dimensionality of systems and large number of units of complex mechanical products，a module partition method based on spectral clustering algorithm was proposed.The hierarchical decomposition of products was realized based on the function-flow-structure decomposition method，and fuzzy mathematics was used to define the correlation between feature elements.On this basis，the association relation model of product parts based on numerical design structure matrix was constructed.By introducing the spectral clustering algorithm， the component clustering problem was transformed into the optimal division problem of the graph， and the eva-luation index of module division based on the average cohesion within the module and the average coupling between the modules was constructed to realize the module division of the products. The results of the examples showed that the method could effectively reduce the complexity of the design and manufacturing of complex mechanical products， and the method was scientifically effective.

0 引言

在全面推進实施制造强国的发展战略中，复杂机械产品的设计与制造能力是我国综合实力的重要体现之一[1].由于复杂机械产品存在多主体、多层次、多变量，单元之间多耦合、强关联等属性，造成复杂机械产品设计周期长、制造工艺复杂、转运安装难等问题.模块化设计方法设计的模块具有独立性、灵活性等特点，能有效降低系统复杂性，缩短设计与制造时间，因此被广泛应用于复杂机械产品的设计与制造过程.

模块划分作为模块化设计的关键环节，在学术界得到了广泛研究.R.B.Stone等[2]提出了主流、分支流和转换-传递函数链3种启发式方法，实现了产品初始模块的识别和划分.罗石林等[3]运用模糊……