Non-linear projection to latent structures

Abstract

This Thesis focuses on the study of multivariate statistical regression techniques which have been used to produce non-linear empirical models of chemical processes, and on the development of a novel approach to non-linear Projection to Latent Structures regression. Empirical modelling relies on the availability of process data and sound empirical regression techniques which can handle variable collinearities, measurement noise, unknown variable and noise distributions and high data set dimensionality. Projection based techniques, such as Principal Component Analysis (PCA) and Projection to Latent Structures (PLS), have been shown to be appropriate for handling such data sets. The multivariate statistical projection based techniques of PCA and linear PLS are described in detail, highlighting the benefits which can be gained by using these approaches. However, many chemical processes exhibit severely nonlinear behaviour and non-linear regression techniques are required to develop empirical models. The derivation of an existing quadratic PLS algorithm is described in detail. The procedure for updating the model parameters which is required by the quadratic PLS algorithms is explored and modified. A new procedure for updating the model parameters is presented and is shown to perform better the existing algorithm. The two procedures have been evaluated on the basis of the performance of the corresponding quadratic PLS algorithms in modelling data generated with a strongly non-linear mathematical function and data generated with a mechanistic model of a benchmark pH neutralisation system. Finally a novel approach to non-linear PLS modelling is then presented combining the general approximation properties of sigmoid neural networks and radial basis function networks with the new weights updating procedure within the PLS framework. These algorithms are shown to outperform existing neural network PLS algorithms and the quadratic PLS approaches. The new neural network PLS algorithms have been evaluated on the basis of their performance in modelling the same data used to compare the quadratic PLS approaches.