Monitoring batch processes with an incomplete set of variables

Abstract

Approaches to batch monitoring are mostly grounded on multiway principal component analysis (MPCA) due to the complexity of the underlying processes. Given the variety of scenarios, discussions and improvements about MPCA are found in the literature. However, there is a lack of works discussing batch monitoring in the important scenario where the set of available variables is incomplete. In fact, when some relevant variable is missing, such lack of information can substantially compromise MPCA modeling and diminish its ability to detect abnormal behaviors of future batch samples. In this paper, we present an approach to deal with that problem proposing what we call T-MPCA, a MPCA modification by using the reconstruction method based on Takens’ theorem. Through this method, some information of the missing variables can be recovered from correlating the measured variables with itself lagged in time. Besides its presentation, the efficacy of the new approach is illustrated using simulated data.