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Herbert Kay

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AIJ Journal 2000 Journal Article

Semi-quantitative system identification

  • Herbert Kay
  • Bernhard Rinner
  • Benjamin Kuipers

System identification takes a space of possible models and a stream of observational data of a physical system, and attempts to identify the element of the model space that best describes the observed system. In traditional approaches, the model space is specified by a parameterized differential equation, and identification selects numerical parameter values so that simulation of the model best matches the observations. We present SQUID, a method for system identification in which the space of potential models is defined by a semi-quantitative differential equation (SQDE): qualitative and monotonic function constraints as well as numerical intervals and functional envelopes bound the set of possible models. The simulator SQSIM predicts semi-quantitative behavior descriptions from the SQDE. Identification takes place by describing the observation stream in similar semi-quantitative terms and intersecting the two descriptions to derive narrower bounds on the model space. Refinement is done by refuting impossible or implausible subsets of the model space. SQUID therefore has strengths, particularly robustness and expressive power for incomplete knowledge, that complement the properties of traditional system identification methods. We also present detailed examples, evaluation, and analysis of SQUID.

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AAAI Conference 1993 Conference Paper

Numerical Behavior Envelopes for Qualitative Models

  • Herbert Kay

Semiquantitative models combine both qualitative and quantitative knowledge within a single semiquantitative qualitative differential equation (S&DE) 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 extremad 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.

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