Multi-phase principal component analysis for batch processes modelling

Projection to latent structures based methods have been widely used for process monitoring and many extensions to batch processes have been reported. When data from a process includes nearly non-correlated groups of variables (for example, in a batch process, because of their distance in time), it can be advantageous to model theses groups separately. Additionally, traditional methods have an important drawback: they can only model linear combinations of variables. When a batch process shows non-linear dynamics in its variation around the average trajectory, linear models obtain poor performance. Traditionally, in process modelling, two solutions for non-linearity have been implemented: non-linear models and local linear models. In this paper, an algorithm for the detection of phases during the batch processing, where the behavior of the process can be well approximated by a linear local model, is presented.