Structural Analysis of Process Models Using Their Representation Graph

Abstract

A graph-theoretical method for the structural analysis of dynamic lumped process models described by differential and algebraic equations (DAEs) is applied in this paper in order to determine the most important solvability properties (degree of freedom, structural solvability, model decomposition, dynamic degree of freedom, differential index, e.g.) of these models by using the so-called dynamic representation graph. The structure of the dynamic representation graph is suitable for the determination of the mentioned solvability properties. The most common methods in the modelling practice for the construction of models of complex systems are the union of submodels and hierarchical modelling. Our goal is to investigate the effect of the model union to the solvability properties, especially to the differential index. We show how the representation graph of a complex model can be built up from the representation graphs of submodels. The effect of the structure of submodels and their joining points to the structure of the complex graph and the conclusions drawn from the complex graph structure to the solvability properties are also investigated. The representation graph of the complex model can be easily built up from the representation graphs of the simple models according to the linking of the technological subsystems. If one of the submodels has greater than one differential index then the under and overspecified subgraphs referring to this higher index can be found in the representation graph of the complex model, too. The change in the relative position of the underspecified and the overspecified subgraphs has an effect to the value of differential index. If these subgraphs move further from their original positions the value of the differential index increases. If their relative positions do not change during the built up process then the value of the differential index of the complex system is equal to the value of the differential index of the subsystem having the higher value.