Nonlinear FIR modeling via a neural net PLS approach

Abstract

This paper presents a dynamic modeling method using nonlinear finite impulse response (NFIR) models and a neural net PLS approach. Finite impulse response models have been successfully applied to dynamic matrix control as non-parametric dynamic models. These models usually have very large input dimensions which can result in a collinearity problem due to variable correlations and over-parametrilization. Linear biased statistical methods such as partial least squares have been used to circumvent these problems. This paper uses a neural net PLS (NNPLS) approach to build nonlinear FIR models which may not be suitable for a direct neural network training approach due to a large number of correlated model inputs which cause large prediction error variance. The NNPLS method is an integration of partial least squares and neural networks. By using the NNPLS method for NFIR modeling, the collinearity problem is circumvented and hence the prediction error variance is reduced. For comparison, an alternative approach using nonlinear autoregressive models with exogenous inputs (NARX) is discussed. It is found that the NNPLS-NFIR approach gives superior long-term prediction compared to the NARX approach. The superior performance of the NNPLS-NFIR approach is demonstrated on data from two industrial MIMO processes.