Research Of Symbolic Manipulation Technique On Multi-Domain Declarative Models

Computer aided modeling and simulation has progressively become a significant meansto analyze the product performance. As complex mechatronic product generally composedof subsystems from different domains such as mechanic, electric, hydraulic, and controlsystem, the entire analysis naturally leads to multi-domain modeling and simulation.Modelica, an equation-based declarative physical modeling language, is well suited for themodeling and simulation of modern complex multi-domain engineering systems. Howeverdeclarative models are solved as computational procedures. The internal declarative flattenequation system of an Modelica model should be transformed to sorted sub-equationsequences firstly, and later be converted into a set of procedures to be executed by thecomputational engine. Symbolic manipulation technologies in this transform process arestudied in this dissertation.Expression manipulation is the foundation of the entire symbolic manipulation. Basedon binary trees representation of equation, the equation expressions which are formallyflexible and unrestricted are standardized and simplified by canonical transformation rulesto easily extract the structure restriction information; the count of function calls andnon-linear equation part is reduced by function inline to improve the solving speed;symbolic differentiation and partial differentiation is implemented to support the differentialoperation and index reduction of DAE system, moreover the means of solving theexpression differentiation with regard to any variable is presented.The DAE system resulted from declarative physical model is of very large dimensionwhich may contain thousands of variables and equations, and cannot solve directly. Basedon the Bipartite Graph description of DAE system, firstly, the redundancy problem isanalyzed, then the dimension and coupling is reduced by means of alias elimination whichcombined the algebraic elimination method with the characteristics of DAE system;secondly，the concise Bipartite Graph description making use of the structure restrictioninformation is studied to improve the efficiency of space utility and symbolic manipulation.