结构建模中区域划分的代数方法

An Algebraic Method for Region Partition in Structural Modeling

针对现有结构建模区域划分方法的不足，基于将拓扑分析转化为代数分析的原理，指出区域划分的实质是要构造某种等价关系，该等价关系是元素不可分的充要条件．进而给出了充要条件定理．在此基础上提出了结构建模区域划分的代数方法．列出了代数方法的实施步骤。

The existing method for region partition in structural modeling is analyzed. It is pointed out that the basis of decision in the existing method is but the sufficient condition, not the necessary one. So the completeness of region partition in structural modeling cannot be ensured. Besides, the existing topological method is disadvantageous if it is to be implemented by computer programming. In this paper, the topological analysis is transformed into an algebraic one using the corresponding relation between the topological structure of the directed graph and the isomorphic boolean matrix, as the crux of region partition is to construct a certain equivalent relation which is the sufficient and necessary condition for the elements in the same region. A sufficient and necessary theorem is put forward after an analysis of how to construct such an equivalent relation from the reachability matrix. An algebraic method for region partition in structural modeling is then proposed. The implementation steps are listed and an example is given to demonstrate the simplicity and effectiveness of the method proposed.