MPCA for Monitoring Emulsion Polymerization Process: Alternative Strategies for Decomposing Three-Way Data Matrices

CARLOS R. ALVAREZ; ADRIANA BRANDOLIN; MABEL SÁNCHEZ

San Francisco, E.E.U.U.

Congreso; 2006 AIChE Annual Meeting; 2006

AIChE (American Institute of Chemical Engineers)

En libro de proceedings publicado en CD (Nro págs: 16)Abstract: Batch manufacturing processes are common in chemical, pharmaceutical, bio-technical and semiconductors industries. After charging the equipment with raw materials, the operation is initiated and, the observation of the first point is obtained. This corresponds to a vector of dimension J. The evolution of the batch is then registered measuring the same J variables at time intervals 2, 3,…, until K, when the operation is finished. Hence the information of I batch runs can be grouped in a three way data matrix X (batch×variables×time).Multivariate Statistical Process Control has been successfully applied for the monitoring and diagnostic of batch process during the last decade (Nomikos and Mc Gregor (1994, 1995), Wold et al. (1998)). These applications are based on Multiway Principal Component Analysis (MPCA) and Multiway Partial Least Square (MPLS) strategies proposed by Wold et al. (1987).The unfolding method of the three-way data matrix X (batch×variable×time) plays an important role in the required effort to develop the control charts, to process data on line during monitoring and to identify the source of faults. Generally X is unfolded into a large two dimensional matrix X, such that, each vertical timeslide of X is put side by side to the right in X, starting with the slide corresponding to the first time interval.  Another arrangement has been also proposed by Wold et al. (1998) that consist in putting each vertical timeslide of X under the previous one.In the first unfolding strategy the whole batch is considered as one object. Thus each batch can be compared against a group of good batches to determine if it is a good batch or not. Since the mean trajectories of all process variables are removed, and consequently the main nonlinear and dynamic component of the data are not present any more, a PCA allows to study the systematic variation of variable trajectories about their mean trajectories. In contrast, the approach developed by Wold et al. (1998) for the vertical unfolding only removes the grand mean of the variables for all batches and times, leaving the non-linear time-varying trajectories in the data. To avoid the capture of the deterministic behaviour of the process by the first principal components, Yooet al. (2004) uses the vertical unfolding after centering and scaling the horizontal matrix X. In this way the information regarding process variability for each time is maintained.This work presents a comparative of analysis of performance between PCA techniques based on the horizontal unfolding and the vertical unfolding proposed by Yoo et al. (2004) for the modeling, on-line monitoring and fault identification stages. The study is carried out for a methyl-methacrylate emulsion polymerization reactor.