Data Science For Batch Processes – Jose M Gonzalez – Martinez

In case the batches have unequal duration, all vectors 퐲new 푖 have the same starting and ending values, but a different number of intermediate values depending on their batch length 퐾푖. Once the PLS model is fitted, the resulting OWU scores 퐓퐴, along with some multivariate statis- tics for each batch, are readjusted by linear interpolation (the so-called TLEC-based method) using the 퐲new 푖 maturity index vector, as outlined in Figure 4.6.

This read- justment permits the new OWU scores (denoted as ˆ퐓퐴) to be used for process mon- itoring and subsequent multivariate analysis at the batch level. A drawback of the observation level in real-time monitoring of new batches is that the OWU scores and the multivariate statistics cannot be aligned until the completion of the batch. Hence, there is no guarantee that the control charts on the OWU stage show aligned results, and therefore, monitoring may be misleading.

Furthermore, it is worth mentioning that the application of the synchronization procedure integrated in the OWU-TBWU approach (the TLEC-based method) may be completely inappropriate due to the underlying assumptions that are rarely fulfilled in batch processes: (i) linear process pace, (ii) all batches are completed and all the key process events defining the process evolution throughout the batch run are present in all batches, and (iii) batches with equal duration are considered as synchronized. If batch data do not meet these assumptions, the process evolution in the trajectories of the process variables will differ batch-to-batch.

Hence, the appli- cation of methods based on latent structures for process understanding and moni- toring is not recommended. 4.2.3 Dynamic Time Warping DTW is a technique originating in speech recognition, aimed at matching similar events between signals.

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