Generalization and comparative studies of similarity measures for Just-in-Time modeling

Abstract

Abstract Just-in-Time (JIT) modeling has become one of the most effective data analytic approaches for nonlinear time-varying process modeling. Locally weighted partial least squares method (LW-PLS) is the most representative of the JIT modeling methods. It has been widely applied to the development of the virtual sensors that can cope with abrupt changes in process characteristic as well as nonlinearity. LW-PLS has been investigated and applied successfully in various industrial processes. The accuracy of its prediction performance is however strongly dependent on how the similarity between data is determined. Usually, the Euclidean distance or the Mahalanobis distance between input data is used to determine the similarity, but they have a clear limitation, that is, they do not take into account of the relationship between the input variables and output variables when selecting data for modeling. Other advanced methods to determine the similarities with the considerations of the relationship between input and output have also been proposed in the literature in a specific form. This work further investigates the properties of these advanced methods and proposes extensions as well as points out opportunities for further research. The comparison and effectiveness of these methods along with their generalizations are demonstrated through a numerical example and an industrial application example.