Nearest-Neighbor Method for the Automatic Maintenance of Multivariate Statistical Soft Sensors in Batch Processing

Soft sensors based on multivariate statistical models are used very frequently for the monitoring of batch processes. From the moment of model calibration onward, the model is usually assumed to be time-invariant. Unfortunately, batch process conditions are subject to several events that make the correlation structure between batches change with respect to that of the original model. This can determine a decay of the soft sensor performance, unless periodic maintenance (i.e., updating) of the model is carried out. This article proposes a methodology for the automatic maintenance of PLS soft sensors in batch processing. Whereas the adaptation scheme usually follows chronological order in classical recursive updating, the proposed strategy defines the reference data set for model recalibration as the set of batches (nearest neighbors) that are most similar to the currently running batch. The nearest neighbors to a running batch are identified during the initial evolution of the batch following a concept of proximity in the latent space of principal components. In this way, for any new batch to be run, a model can be tailored on the running batch itself. The effectiveness of the proposed updating methodology is evaluated in two case studies related to the development of adaptive soft sensors for real-time product quality monitoring: a simulated fed-batch process for the production of penicillin and an industrial batch polymerization process for the production of a resin.