A Qualitative-Fuzzy Framework for Nonlinear Black-Box System Identification

Riccardo Bellazzi, Raffaella Guglielmann, and Liliana Ironi

Reasoning about a natural or man-made system often requires a model that gives an accurate quantitative description of its dynamics. Such a model may be built from observations on the system either using structural models of the underlying physics or learning an input-output relation directly from observed data. The process of modeling based on experimentation is called System Identification, and in the end, whichever approach is used, it reduces to an optimization procedure for parameter estimation. A central problem of optimization techniques deals with the choice of a good initialization. This paper presents a novel approach to nonlinear black-box system identification which combines QR methods with fuzzy logic systems: such a method aims at building a good initialization of a fuzzy identifier, so that it will converge to the input-output relation which captures the nonlinear dynamics of the system. Fuzzy inference procedures are initialized with a rule-base predefined by the human expert: when such a base is not available or poorly defined, the inference procedure becomes extremely inefficient. Our method aims at solving the problem of the construction of a meaningful rule-base: fuzzy rules are automatically generated by encoding the knowledge of the system dynamics described by the outcomes of its qualitative simulation. Both efficiency and robustness of the method is demonstrated by its application to different domains: in this paper, we consider the problem of identifying the dynamics of Thiamine (vitamin B1) and its phosphoesters in the cells of the intestine tissue.

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