Qualitative Algebra and Graph Theory Methods for Dynamic Trend Analysis of Continuous System

Qualitative algebraic equations are the basis of qualitative simulation, which are used to express the dynamic behavior of steady-state continuous processes. When the values and operation of qualitative variables are redefined, qualitative algebraic equations can be transformed into signed direct graphs, which are frequently used to predict the trend of dynamic changes. However, it is difficult to use traditional qualitative algebra methods based on artificial trial and error to solve a complex problem for dynamic trends. An important aspect of modern qualitative algebra is to model and characterize complex systems with the corresponding computer-aided automatic reasoning. In this study, a qualitative affection equation based on multiple conditions is proposed, which enables the signed direct graphs to describe complex systems better and improves the fault diagnosis resolution. The application to an industrial case shows that the method performs well.