Qualitative Dynamic Behavior of Physical System Models with Algebraic Loops

Abstract

TRANSCEND, a system for monitoring and diagnosis of abrupt faults in complex dynamic systems, relies on system models to predict dynamic behavior in response to abrupt faults. The use of qualitative predictions of this transient behavior mitigates complexity issues and convergence problems that exist in numerical diagnosis approaches. In this framework, it is important to model the system under diagnostic scrutiny at a level of detail that relates to the bandwidth of the measurement data. Too much detail results in a model that captures very fast dynamics as continuous transients, whereas they appear as discontinuous changes in the measured signals. In many cases, abstracting away these small parameter values may result in algebraic dependencies between variables, i.e., variables affect one another instantaneously without integrating effects. Because of the compensating effects inherent in physical system behavior, a straightforward deviation propagation results in predictions that are unknown in a qualitative sense. A method is proposed that recognizes such dependencies and propagates compensating effects without introducing unnecessary conflicts by tracking the origins of compensating influences in feedback loops.