Nonlinear PLS Integrated with Error-Based LSSVM and Its Application to NOx Modeling

Abstract

This article presents a novel nonlinear partial least-squares (PLS) method to address a nonlinear problem with input collinearity in an industrial process. The proposed method integrates an inner least-squares support vector machine (LSSVM) function with an outer linear PLS framework. First, the input and output latent variables are extracted to eliminate the collinearity through PLS projection, and then LSSVM is used to construct nonlinear relation between each pair of latent variables. Moreover, a weight-updating procedure is incorporated to enhance the accuracy of prediction. Then, training and predicting algorithms based on modified nonlinear iterative partial least-squares (NIPALS) steps are also described in detail. The performance of the new method is also investigated with a benchmark data set. Finally, this approach is applied to a real industrial process to predict the NO x emissions of a coal-fired boiler. The root-mean-square errors (RMSEs) on the training and testing data decreased to only 12.6632 and 37.6609, respectively. Compared with the original linear PLS and other kinds of nonlinear PLS methods, a reduction of approximately 40.8―47.4% in the prediction errors is attained. The results reveal that the new approach is capable of modeling the nonlinear relation of NO x emissions with other process parameters and improving the prediction performance.