Model predictive monitoring for batch processes

In the procedure to monitor a new batch using the method proposed by Nomikos and MacGregor [AIChE J. 1994, 40 (8), 1361-1375], an assumption about the unknown future samples in the batch has to be taken. This work demonstrates that using the missing data option and solving the score estimation problem with an appropriate method are equivalent to the use of an accurate adaptive forecast model for the future samples over the shrinking horizon of the remainder of the batch. The dynamic properties of the principal component analysis (PCA) model are illustrated by re-expressing the projection model as a time-varying multivariate prediction model. The benefits of using the missing data estimation option are analyzed by contrasting it with other options on the basis of (i) the accuracy of the forecast done for the unknown samples, (ii) the quality of the score estimates, and (iii) the detection performance during monitoring. Because of the tremendous structural information built into these multivariate PCA models for batch processes, the missing data option is shown to yield the best performance by all measures in predicting the future unknown part of the trajectory, even from the beginning of the batch. However, for the purpose of online detection of process faults (in process monitoring), the differences among the trajectory estimation methods appear to be much less critical because the control charts used in each case are tailored to the filling-in mechanism employed. All of the approaches appear to provide powerful charting methods for monitoring the progress of batch processes.