Bilinear modelling of batch processes. Part I: theoretical discussion

When studying the principal component analysis (PCA) or partial least squares (PLS) modelling of batch process data, one realizes that there is a wide range of approaches. In many cases, new modelling approaches are presented just because they work properly for a particular application, for example, on‐line monitoring and a given number of processes. A clear understanding of why these approaches perform successfully and which are the advantages and disadvantages in front of the others is seldom supplied. Why does modelling after batch‐wise unfolding capture changing dynamics? What are the consequences of variable‐wise unfolding? Is there any best unfolding method? When should several models for a single process be used? In this paper, it is shown how these and other related questions can be answered by properly analyzing the dynamic covariance structures of the various approaches.