Modelling of spectroscopic batch process data using grey models to incorporate external information

In both analytical and process chemistry, one common aim is to build models describing measured data. In cases where additional information about the chemical system is available, this can be incorporated into the model with the aim of improving model fit and interpretability. A model which consists of a ‘hard’ or ‘white’ part describing known sources of variation and a ‘soft’ or' black' part describing unknown sources of variation is called a ‘grey’ model. In this paper the use of a grey model is demonstrated using data from a first-order chemical batch reaction monitored by UV-vis spectroscopy. The resultant three-way data matrix is modelled using a Tucker3 structure, and external information about the spectroscopically active compounds is incorporated in the form of constraints on the model parameters with additional restrictions on the Tucker3 core matrix. The grey model is then used to analyse new batches. Different approaches to building grey models are described and some of their properties discussed.