Numerical Behavior Envelopes for Qualitative Models

Semiquantitative models combine both qualitative and quantitative knowledge within a single semiquantitative qualitative differential equation (SQDE) representation. With current simulation methods, the quantitative knowledge is not exploited as fully as possible. This paper describes dynamic envelopes — a method to exploit quantitative knowledge more fully by deriving and numerically simulating an exfremal system whose solution is guaranteed to bound all solutions of the SQDE. It is shown that such systems can be determined automatically given the SQDE and an initial condition. As model precision increases, the dynamic envelope bounds become more precise than those derived by other semiquantitative inference methods. We demonstrate the utility of our method by showing how it improves the dynamic monitoring and diagnosis of a vacuum pumpdown system. “This work has taken place in the Qualitative Reasoning Group at the Artificial Intelligence Laboratory, The University of Texas at Austin. Research of the Qualitative Reasoning Group is supported in part by NSF grants IRI-8905494 and IRI-8904454, by NASA grant NAG 2-507, by the Texas Advanced Research Program under grant no. 003658175, and by the Jet Propulsion Laboratory.