A novel nonlinear functional expansion based PLS (FEPLS) and its soft sensor application

•An effective nonlinear FEPLS model is proposed.•Function expansion is adopted to effectively expand the input space to high nonlinear space.•A good model is found between the expanded inputs and the outputs by using PLS.•FEPLS model is easy to construct and is applied to modeling complex chemical processes.•FEPLS could achieve good prediction performance.

A novel robust nonlinear partial least square model is proposed to handle the nonlinearity and collinearity problems of process data. The proposed model integrates a nonlinear functional link artificial neural network (FLANN) with a traditional partial least square (PLS). There are two parts in the proposed model: a nonlinear mapping part and a linear regression part. In the nonlinear mapping part, the input space is effectively extended to nonlinear space through the functional expansion block of FLANN. The PLS regression (PLSR) is adopted in the linear part. Thus, a novel robust nonlinear PLS integrated with functional expansion (FEPLS) is built. The proposed FEPLS model is very easy to construct. First, a traditional FLANN is selected. Second, the input space is expanded to nonlinear space using the functional expansion block. Third, the collinearity among the expanded variables and the expected outputs is eliminated by extracting input latent variables and output latent variables through PLS projection, respectively. Finally, an optimal regression model between the expanded variables and the expected outputs is established by using PLSR. To evaluate the performance of the proposed model, case studies of modeling two complex chemical processes are provided. Four more models of FLANN, extreme learning machine based PLS (ELM-PLS), kernel PLS (KPLS), and PLSR are also developed for comparisons. Simulation results illustrated that the proposed FEPLS model could improve the prediction performance.