Semi-quantitative system identification Original Research Article

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.