Model Building by Merging Submodels Using PLSR

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Abstract

PLSR (partial least squares regression) has become a basic tool for chemometrics, monitoring and modeling of processes, etc. The basic idea of PLSR is to relate two data matrices X and Y into a multivariate linear model, for analysis of the data with noisy and collinear variables. In industrial processes, sub-models of the specific units are built for monitoring and engineering process control. However, we know that these process units are not individually independent. As a result, the full model is usually desirable. In an actual process, there are thousands to ten thousands of variables being measured and conveniently recorded instantaneously. It is not practical to deal with such a large number of variables to construct a full model at time, especially they are collinear and embedded with noise. In this paper, the linear regression model merging procedure is proposed to incorporate PLSR models of subsystems into a full model. By way of this approach, the computation time and memory can thus significantly be reduced. It is quite suitable to merge the process sub-models built from PLSR into the complete one. The method could be extended to dynamic and non-linear modeling easily. Two examples for dynamic modeling and monitoring are presented for illustration. One is the dynamic modeling of a 4 × 4 linear process. Second one is the process monitoring of a double effect evaporator.

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