Multi-way partial least squares

Very often in DCS-operated batch polymer reactors the primary process variables such as pressure, temperature, level, and flow (Section 12.2.1-12.2.4) are recorded during the batch as well as the quality variables at the end of the batch. However, it may be very difficult to obtain a kinetic model of the polymerization process due to the complexity of the reaction mechanism, which is frequently encountered in the batch manufacture of specialty polymers. In this case it is possible to use advanced statistical techniques such as multi-way principal component analysis (PCA) and multi-way partial least squares (PLS), along with an historical database of past successful batches to construct an empirical model of the batch [8, 58, 59]. This empirical model is used to monitor the evolution of future batch runs. Subsequent unusual events in the future can be detected during the course of the batch by referencing the measured process behavior against this incorrective action during the batch in order to bring it on aim. 

P. Nomikos, j. F. MacGregor, Multi-way partial least squares in monitoring batch processes , Chemometrics and Intelligent Laboratory Systems, 1995, 30, 97. 

The similarity between a Tucker 1 model of a three-way array X and a PCA model of a two-way array X has already been mentioned in Section 4.1. This similarity is the basis for the most popular three-way regression model, the Tucker 1-PLS model. In the literature this regression method has also been called three-way partial least squares regression [Wold et al. 1987]. This name should be avoided for the Tucker 1 version specifically, because it gives rise to much confusion as to what is multi-way methodology. Even though the Tuckerl version of three-way partial least squares regression is indeed one way to implement a three-way method, it is actually the model that assumes the least three-way structure in the data. 

In particular, Partial Least Square Regression (PLS) and multi-way method, such as N-PLS, were applied to study the relationships between the volatile fractions, sampled and characterised by using head space solid phase micro extraction (HS-SPME)/GC techniques, and the sensory attributes obtained by expert panellists [65,66]. 

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