基于功能/结构相似的复杂系统相似准则研究

Research on similarity criterion of complex systems based on functional and structural similarity

相似理论是一种研究试验模型与真实模型之间相似关系的方法,目前以相似三定理为基础的经典相似理论主要针对元件,对实际中大型化与复杂化的真实系统而言,相似理论的应用就受到了极大的限制.对此,本文将经典相似理论与系统论相结合,从功能与结构的角度建立了针对复杂系统的相似准则,该准则的核心是结合了功能相似与结构相似的复杂系统相似矩阵,只要原型系统与模型系统对应矩阵相等,则原型系统与模型系统相似.该准则填补了相似三定理不适用与复杂系统的理论不足,实现了将相似理论拓展并应用于大型复杂系统的目的.最后通过算例分析验证了该理论的可行性与优越性.

Similarity theory is a method studying the similarity relation of model and pro-type.At present,classical similarity theory based on the three similarity theorem is mainly aiming at components,but for the complex and large real systems in practice,similarity theory is greatly limited.To solve this problem,this paper combined similarity theory with system theory and established similarity criterion of complex systems based on functional and structural similarity.The key of this similarity criterion is the similarity matrix and the prototype system is similar to model system only if the two corresponding similarity matrices are equal.The criterion remedied the defect of the three similarity theorem and expanded the similarity theory into large complex systems.Finally,this paper verified the feasibility and superiority of this method through analysis of examples.