Translating third-order data analysis methods to chemical batch processes

Measurements collected from batch processes naturally produce a third-order or three-dimensional data form. The same structure also results when multiple samples are measured using hyphenated analysis techniques such as liquid chromatography with diode array detection. Analysis of third-order data by principal components analysis (PCA) is achieved by a nonunique rearrangement that produces a two-dimensional array. This preferentially models only one of the three orders present. In contrast, methods such as parallel factor analysis (PARAFAC) apply a particular decomposition that accounts for all three orders explicitly. The results from either approach should be related if data are to be interpreted reliably for applications to batch processes such as on-line monitoring and control. This work compares these two approaches from an applied point of view. To accomplish this objective, exemplary methods are selected from each type of analysis, parallel factor analysis (PARAFAC) and multiway principal components analysis (MPCA). These are employed to analyze data obtained during the manufacture of a condensation polymer in an industrial batch reactor.