Reference: Vescovi, M.; Farquhar, A.; & Iwasaki, Y. Numerical Interval Simulation: Bounding Behaviors of Non-Monotonic Systems. 1994.
Abstract: Models of complex physical systems often cannot be defined precisely, either because of lack of knowledge or because the system parameters change over time according to unknown phenomena. Such systems can be represented by semi-quantitative models that combine both qualitative and quantitative knowledge. Previous semi-quantitative methods do not fully exploit the quantitative knowledge and produce only weak predictions across time intervals. The more recent dynamic envelope method produces much better predictions by deriving and numerically simulating an "external system," whose solution bounds all solutions of the semi-quantitative model. However, the dynamic envelope method derives such extremal sytems only for systems of monotonic relations. This paper present Numerical Interval Simulation, a method that can simulate systems involving any continuous, nonmonontonic functions. We present a successful application of NIS to predict the behavior of a complex industrial process at CST Companhia Siderurgica de Tubarao, a Brazilian-Japanese steel company located in Brazil.
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