基于邻接面复杂网络的产品功能形状特征提取和应用研究

The study of function form feature extraction and its application in function-structure mapping is of great significance for non-configurable product design. There are many shortcomings in the objectivity of function feature definitions, hierarchical function-structure mapping, computational complexity, etc. in the current literatures. The project will start from the large-scale 3D CAD model data, and analyze the ontology of product function, structure and other design elements to build the ontology-based evolutionary mechanism of adjacent surface complex network. By the parameters and clusters of complex network, the strong objective function features are extracted, as well as hierarchical relationships, causal relationships, and evolutionary laws among features are grasped. Thus, the tree function and structure models are established based on function features, and the hierarchical functions and structures are matched by tree isomorphism. The innovations are the following. 1) The nature of product function and structure can be revealed, and the objectivity of function features be achieved by analyzing the evolutionary of 3D CAD models with ontology and complex network theories. 2) The causality and hierarchical relationships among functions and structures, which are more conducive to product design, are discovered by pruning complex networks into Bayesian networks and trees. 3) The computational complexity can be reduced while sovling the matching problem of hierarchical functions and structures by designing function-structure mapping with tree isomorphism.

提取功能形状特征并应用于功构映射的研究对于非配置型产品设计有着重要意义。 目前文献在功能特征定义的客观性、层次化功构映射、计算复杂度等方面，仍存在改进的余地。 本课题拟从大规模三维CAD模型数据入手，分析产品结构、功能等设计要素的本体，构建基于本体的面邻接复杂网络的演化机制；根据复杂网络的参数和聚类，提取客观性强的功能形状特征，掌握特征的层次关系、因果关系和进化规律；以功能特征为基础建立树形功能结构模型，通过树同构方法解决层次化的功能结构匹配问题。 创新之处：1）通过本体和复杂网络等理论解析三维CAD模型的演化，能够揭示产品功能结构的本质，确保功能特征的客观性；2）把复杂网络修剪为贝叶斯网络和树，能够发现更有设计意义的功构间因果关系和层次关系；3）通过树同构算法设计功构映射，在降低计算复杂度的同时，能够解决层次化功构匹配问题。

项目从三维CAD模型数据分解入手，基于四方面理论对三维模型的形状结构进行了分析，建立了若干形状特征模型：分解重构及语义本体、小波分解、微分几何、视觉图像及形觉认知。然后构建了基于形状本体的树、子图、模板的演化模式，揭示三维模型形状和语义的层次关系、相关关系和因果关系，通过偶图匹配、树同构等比较算法解决检索分类、设计重用、三维重建、2D/3D匹配等技术问题。此外，我们进一步拓宽应用范围，将其推广到诸如创新设计、社会计算等领域。