Non-linear dynamic projection to latent structures modelling

Projection to Latent Structures (PLS) has been shown to be a powerful linear regression technique for non-dynamic problems where the data is noisy and highly correlated and where there are only a limited number of observations. However, in many real-world situations, process data exhibits both non-linear characteristics and dynamics. A number of methodologies have been proposed to integrate non-linear features within the linear PLS framework, resulting in the development of non-linear PLS algorithms. The PLS methodology has also been extended to enable the modelling of dynamic processes. The paper presents an approach for the development of non-linear dynamic PLS algorithms which incorporate polynomial or neural network functions that are fully integrated within the PLS algorithm through weight updating of the PLS inner and outer models. The modelling capabilities of these approaches are assessed through structured comparisons on a bench-mark simulation of a pH neutralisation process.