Research On Methods For Consistency Analysis And Reduction Of Declarative Simulation Models

Mathematical modeling and simulation has become an important technology to analyze product performance. Along with advance in science and technology, modern products are increasingly complex and heterogeneous. Complex products generally are composed of subsystems from multiple engineering domains such as mechanic, electric, hydraulic, and control system components. To optimize complex products, it is necessary to integrate simulation models from several engineering domains to cooperatively simulate the total behavior of complex products. Modelica is an equation based language for physical systems modeling. The language unifies and generalizes previous modeling languages, and is appropriate to model modern complex multi-domain systems very well. The optimizer for equations is a kernel of a Modelica based modeling and simulation tool, its key issues are studied in this dissertation.The consistency of a model is the precondition for that the model can be solved. The causes of inconsistencies of simulation models are analyzed, and a consistency analysis method based on graph theoretical algorithms is proposed, which can enhance the error detecting and correcting process. The method determines whether a model is consistent or not by computing a maximum matching in the bipartite graph associated with the model. In order to find out singular components, fictitious equations are used to replace the equations generated from the connections of the component. The equations and variables, which are responsible for the inconsistencies, are reduced by singular components, and then are further reduced by the structural filtering rule and the semantic filtering rule. Finally, efficient correcting messages for the user are elaborated.The DAE system resulted from declarative model is of very large dimension, and its numerical solution requires excessively long computation times. Techniques for the symbolic manipulation of general DAE systems are presented, and used for model reduction purpose, to support efficient simulation of complex multi-domain systems. Canonical transformation rules are used to simplify and transform equations, which are represented as binary trees, into canonical forms. Some graph theoretical algorithms are employed to address the specific problems, which are elimination of trivial equations by means of substitution, and partitioning the whole DAE system into subsystems which can be solved in sequence, and reducing algebraic loops by tearing algorithm. These symbolic manipulations can considerably reduce the dimension and coupling of a DAE system to make the simulation of the DAE system be executed much more efficiently.It is numerically difficult to solve a high-index DAE system. The strategy for index analysis of DAE system is discussed, and the basic principle of index reduction is elaborated. The minimally structurally singular subset and the weighted bipartite graph are introduced, and then an index reduction algorithm based on weighted bipartite graph is developed, which can locate those subsets of the system equations which need to be differentiated. By representing equation as binary tree, a symbolic method for calculating the derivative of equation is presented. On the basis of the techniques proposed for model reduction, an index analysis method for large scale DAE system is proposed, which can improve index reduction efficiency. Finally, the consistent initialization of DAE model is discussed, the criterion for determining whether an initial condition is consistent or not is given, and the strategy for solving the initialization equation system is presented.On the basis of the above achievement, an optimizer for Modelica models has been developed, which provides technology foundation for the development of Modelica based modeling and simulation environment, and has been integrated into a hybrid modeling and simulation tool, named MWorks, for multi-domain physical system.