ion, Soundness, and Incompleteness Once the abstraction relations from ODEs to QDEs, and from continuously differentiable functions to qualitative behaviors, are carefully defined 1 , the mathematical results are relatively straight-forward. We can view an ordinary differential equation solver as a theorem-prover for theorems of a special form: DiffEqs ` ODE State(t 0 ) ! Beh: (1) A qualitative simulation algorithm can also be viewed as a special-purpose theorem-prover: QSIM ` QDE QState(t 0 ) ! or(QBeh 1 ; : : : QBeh n ): (2) The soundness theorem says that when QSIM proves a theorem of form (2), it is true: that is, for any ODE described by the QDE, and State(t 0 ) described by QState(t 0 ), the solution Beh to the ODE is described by one of the qualitative behaviors, QBeh 1 ; : : : QBeh n . The constraint filtering algorithm makes the proof very simple: all possible real transitions from one qualitative state to the next are proposed, and only impossible ones are filtered out...

This article describes a method for monitoring and diagnosis of process systems based on three foundational technologies: semi-quantitative simulation, measurement interpretation (tracking), and model-based diagnosis. Compared to existing methods based on fixed-threshold alarms, fault dictionaries, decision trees, and expert systems, several advantages accrue: ffl the physical system is represented in a semi-quantitative model which, unlike a pure numeric model, predicts all possible behaviors that are consistent with the incomplete/imprecise knowledge of the system's devices and processes, ensuring, for example, that a hazardous-but-infrequent behavior will not be overlooked; ffl imprecise knowledge of parameter values and functional relationships (both linear and non-linear) can be expressed in the semi-quantitative model and used during simulation, producing a valid range for each variable; ffl incremental simulation of the model in step with incoming sensor readings, with subseq...

One of the major factors hindering the use of qualitative simulation techniques to reason about the behavior of complex dynamical systems is intractable branching due to a phenomenon called chatter. This paper presents two general abstraction techniques that solve the problem of chatter. Eliminating the problem of chatter significantly extends the range of models that can be tractably simulated using qualitative simulation. Chatter occurs when a variable's direction of change is constrained only by continuity within a region of the state space. This results in intractable, potentially infinite branching within the behavioral description due to irrelevant distinctions in the direction of change. While a number of techniques have been proposed to eliminate chatter, none of them provide a general solution that can eliminate all instances of chatter. Chatter box abstraction and dynamic chatter abstraction provide two such solutions to this problem. Both solutions eliminate chatter by abs...

This dissertation presents the design, the prototype implementation and the experimental evaluation of a scalable multiprocessor for qualitative simulation. The main objective of this work is to improve the running time of the qualitative simulator QSim. In qualitative simulation, physical systems are modeled on a higher level of abstraction than in other simulation paradigms, like in continuous simulation. A major strength of qualitative simulation is that it can represent and reason with incomplete knowledge - qualitative simulation requires neither a complete structural description nor a fully specified initial state. All physically possible behaviors consistent with this incomplete description are predicted by qualitative simulation. In engineering, qualitative simulation is mainly applied in monitoring and diagnosis. QSim is the most prominent algorithm for qualitative simulation. QSim is implemented in Lisp and executed on general-purpose computers. A drawback of current QSim...

Incomplete information is present in many engineering domains, hindering traditional and non--traditional simulation techniques. This paper describes SQPC (semi--quantitative physics compiler), an implemented approach to modelling and simulation that can predict the behavior of incompletely specified systems, such as those that arise in the water control domain. SQPC is the first system that unifies compositional modeling techniques with semi--quantitative representations. We describe SQPC's foundations, QSIM and QPC, and how it extends them. We demonstrate SQPC using several examples from the water supply domain. This technical report (UDMI--RT--03--94) is an extended version of [Farquhar and Brajnik, 1994]. Semi--Quantitative Physics Compiler: where are we now and where are we going? Giorgio Brajnik Dipartimento di Matematica e Informatica, Universit`a di Udine Udine -- Italy June 20, 1994 Abstract Incomplete information is present in many engineering domains, hindering tradi...