Fuzzy qualitative simulation and diagnosis of continuous dynamic systems

Abstract

The theory of Fuzzy Sets and the development of Qualitative Reasoning have had similar motivations: coping with complexity in reasoning about the behaviour of physical systems. The first part of this thesis presents a synthesis of these techniques to provide a fuzzy qualitative simulation algorithm, named FuSim, that offers significant advantages over existing qualitative simulation methods. It allows a more detailed description of system variables, through an arbitrary, but finite, discretisation of the quantity space which, in turn, allows a more detailed description of functional relationships in that both strength and sign information can be represented. It also enables ordering information on rates of change to be used to compute temporal information on the state and the possible state transitions. These result in a considerable reduction in the number of spurious behaviours generated during the simulation and in a mechanism for producing temporal durations associated with each qualitative state. Both of these properties are crucial to practical utilisation of qualitative simulation.

In the second part of the thesis, a synchronous iterative diagnostic framework for continuous dynamic systems, called SID, is described that utilises FuSim to model and simulate the physical system to be diagnosed. In particular, techniques for the synchronous tracking of the evolution of the system between equilibria are established. A discrepancy metric that allows for the continuous degradation from normal to faulty behaviour to be monitored is given. Furthermore, a method for identifying faults through iterative search against modelling dimensions is proposed. This provides explicit feedback from detected discrepancies to model adjustments, thereby reducing the sensitivity to modelling errors and allowing approximate fault models to be used.