中文摘要：

针对物理系统性能仿真形成的非连续高指标微分代数模型，提出一种基于加权二部图的指标转换方法．该方法将微分代数系统表示为加权二部图，基于二部图匹配算法可以判定微分代数系统是否为高指标系统．对于高指标系统，采用文中方法可以找出需要求导的最小结构奇异方程子集，以便将高指标系统转换为低指标形式．最后，针对定结构与变结构的非连续微分代数模型给出了相应的指标分析策略．文中策略与相关算法已在基于Modelica语言的建模仿真平台MWorks上实现．

英文摘要：

For discontinuous high index differential-algebraic models （DAE） from performance simulation of physical systems, an index transformation method based on weighted bipartite graph is proposed. By representing a DAE system as a weighted bipartite graph, the proposed method can determine if the DAE system is high index by a bipartite graph matching algorithm, and for a high index DAE system, the method can locate minimal structurally singular subsets of equations which need to be differentiated in order to transform the high index DAE system into a lower index formulation. Based on the proposed method, the strategies for index analysis of discontinuous DAE models are presented. The proposed strategies and algorithms have been successfully implemented in a Modelica based modeling and simulation system, named MWorks.