Ž . Chemometrics and Intelligent Laboratory Systems 41 1998 73–81 Adaptive batch monitoring using hierarchical PCA Stefan Rannar a, ) , John F. MacGregor a , Svante Wold b ¨ a Department of Chemical Engineering, McMaster UniÕersity, Hamilton, ON, Canada b Department of Organic Chemistry, Umea UniÕersity, Umea, Sweden Abstract A new approach to monitoring batch processes using the process variable trajectories is presented. It was developed to w overcome the need in the approach of Nomikos and MacGregor P. Nomikos, J.F. MacGregor, Monitoring of batch pro- Ž . cesses using multi-way principal components analysis, Am. Inst. Chem. Eng. J. 40 1994 1361–1375; P. Nomikos, J.F. Ž . MacGregor, Multivariate SPC charts for batch processes, Technometrics 37 1995 41–59; P. Nomikos, J.F. MacGregor, Ž . x Multi-way partial least squares in monitoring batch processes, Chemometrics Intell. Lab. Syst. 30 1995 97–108 for esti- mating or filling in the unknown part of the process variable trajectory deviations from the current time until the end of the Ž . batch. The approach is based on a recursive multi-block hierarchical PCArPLS method which processes the data in a se- quential and adaptive manner. The rate of adaptation is easily controlled with a parameter which controls the weighting of past data in an exponential manner. The algorithm is evaluated on industrial batch polymerization process data and is com- pared to the multi-way PCArPLS approaches of Nomikos and MacGregor. The approach may have significant benefits when monitoring multi-stage batch processes where the latent variable structure can change at several points during the batch. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Batch monitoring; Variable trajectories; Hierarchical PCA; Adaptive PCA; Multi-way PCA 1. Introduction Many chemical, pharmaceutical and biochemical products are produced in batch reactors, and many other manufacturing processes are batch in nature Ž . i.e., they have fixed start and end points . In most of these processes product quality variables are only measured after the end of each batch, often hours later in a quality control laboratory. This makes it difficult to achieve control over product quality or to monitor the progress of these batch processes. However, on- line process computers routinely collect data on the ) Corresponding author. time history of many process variables such as tem- peratures, pressures and flowrates throughout the du- ration of each batch run. Nomikos and MacGregor w x wx 1–3 and Kourti et. al. 4 have presented very pow- erful process analysis, monitoring and diagnostic procedures which utilize these process variable tra- jectory data. These procedures, based on multi-way Ž . Ž . PCA MPCA and multi-way PLS MPLS methods wx 5 , are now being widely adopted by the batch chemical industry. The methods have proven to be very powerful for analysing historical data from past production, and diagnosing operating problems. They have also proven to be very effective for the on-line monitor- ing of new batches. However, one characteristic of 0169-7439r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. Ž . PII S0169-7439 98 00024-0