复杂系统结构建模分析

Analysis of structural modeling for complex systems

结构模型描述的是系统的结构性态,它是从系统的概念模型过渡到定量分析的中介。在结构建模方法中,由Warfield提出并发展的解释结构建模(ISM)应用最为广泛。针对现有ISM的拓扑分析方法的不足,阐明适于复杂系统结构建模的代数分析途径的优越性,围绕复杂系统结构建模的几个重要问题剖析概念本质,进行原理性分析。首先对结构建模进行了概要论述,给出了有关概念的定义。针对现有ISM方法对复杂系统进行结构建模时所采用拓扑分析方法的欠缺,即求解大规模问题存在的“组合爆炸”和迭代操作存在的不完备性,提出将现有ISM的拓扑分析方法进一步转化为代数分析方法,以便计算机实施处理。进而讨论了系统骨架矩阵的求解问题,通过给出求骨架矩阵的代数表达式来实现骨架矩阵的代数求法。最后借助系统结构建模分析,着重讨论ISM中涉及到的几种矩阵以及它们之间的相互关系,澄清认识,结果表明邻接矩阵不仅表示的是元素之间的所有直接关系,而且还表示了元素之间的部分间接关系;在邻接矩阵的基础上求出可达矩阵,实质上是要找到系统元素之间的所有间接关系。

The structural model describes both structure and performance of a system,and it offers an intermediary from the conceptual model to the quantitative analysis.Interpretive Structural Modeling(ISM)proposed by Warfield is the most widely used structural modeling method.In view of the shortcomings of topological analysis method in the existing ISM,this paper clarifies the superiority of algebraic analysis methods for structural modeling of complex systems and dissects the concepts and principles surrounding several vital issues in structural modeling of complex systems.Firstly,the structure modeling is briefly presented and the definitions of related concepts are provided.To solve the deficiency of the topology analysis methods used in the existing ISM,i.e.,the“combinatorial explosion”and incompleteness of iterative operations in solving large-scale problems,this paper proposes a novel approach in which the ISM topology analysis methods are replaced by algebraic analysis methods to facilitate computer processing.Then,the issue of solving the system’s skeleton matrix is discussed,and the algebraic method of obtaining the skeleton matrix is given by providing an algebraic expression of the skeleton matrix.Finally,with the help of structural modeling analysis,several matrices in ISM and their interrelationships are discussed intensively to clarify some essential understandings of ISM.The results show that the adjacency matrix not only represents all the direct relationship but also represents part of the indirect relationship among elements.The essence of solving the reachability matrix from the adjacency matrix is to find all the indirect relationship among the system elements.