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中文摘要：
利用核函数将产品的零部件样本映射至希尔伯特空间内,使零部件样本的差异性＂放大＂,从而提高产品模块划分过程的鲁棒性.利用粗糙集对希尔伯特空间内的零部件样本进行初步分类,获得产品的模块数量和每个模块内零部件组成的上近似集合与下近似集合.构建模块间耦合度、加工装配复杂度和变型设计复杂度3个目标函数,利用改进的非支配排序遗传算法（NSGA）进行求解进而获得最优的模块划分方案.以大型空分设备的模块划分作为实例,对该方法进行检验.数值仿真结果表明了该方法的有效性和可行性.
英文摘要：
Component samples of the product were mapped into Hilbert space by kernel function.Then the heterogeneity between different components was enlarged,which will strengthen the robustness of product module partition process.The rough set was applied to preliminarily classify the components within the Hilbert space.The number of modules,the upper approximation of modules and the lower approximation of modules were obtained.Coupling degree indices between modules,complexity degree indices of manufacturing and assembly,and complexity degree indices of variant design were constructed as object functions.The improved non-dominated sorting genetic algorithm（NSGA） was used for searching the optimal module partition solution.A large scale deep cooling air-separating equipment＇s module partition process was provided as a practical case,which illustrated the validity and feasibility of the method.
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