Monotone Pieces Analysis for Qualitative Modeling
Yuhong Yan, Daniel Lemire A, Martin Brooks · NPARC · 2004
Abstract. It is a crucial task to build qualitative models of industrial applications for model-based diagnosis. A Model Abstraction proce-dure is designed to automatically transform a quantitative model into qualitative model. If the data is monotone, the behavior can be eas-ily abstracted using the corners of the bounding rectangle. Hence, many existing model abstraction approaches rely on monotonicity. But it is not a trivial problem to robustly detect monotone pieces from scattered data obtained by numerical simulation or experiments. This paper introduces an approach based on scale-dependent monotonic-ity: the notion that monotonicity can be defined relative to a scale. Real-valued functions defined on a finite set of reals e.g. simula-tion results, can be partitioned into quasi-monotone segments. The end points for the monotone segments are used as the initial set of landmarks for qualitative model abstraction. The qualitative model abstraction works as an iteratively refining process starting from the initial landmarks. The monotonicity analysis presented here can be used in constructing many other kinds of qualitative models; it is ro-bust and computationally efficient. 1