(302p) Mpca for Monitoring Emulsion Polymerization Process: Alternative Strategies for Decomposing Three-Way Data Matrices

Batch processes are devoted to the production of low-volume, high-value products as polymers obtained by emulsion polymerization. Batch to batch variations arise from errors in charging raw materials, their impurity concentrations, variations in refrigerant temperature, etc., that are difficult to be taken into account by the control system. Small variations in operating conditions may degrade the product quality if the problem is not detected and corrected, thus Multivariate Statistical Control techniques are developed for on-line monitoring and fault diagnosis of batch processes.

Multiway Principal Component Analysis (MPCA) was developed by Nomikos and Mc Gregor (1994) as an extension of the classic Principal Component Analysis (PCA) to batch processes data. Furthermore, the same authors (Nomikos and Mc Gregor, 1995) proposed Multiway Partial Least Square (MPLS) for monitoring purposes if product quality data are available.

The unfolding way of the three-way data matrix X(batch×variables×time) play 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. Consequently different unfolding strategies are proposed. Generally X is unfolded into a large two dimensional matrix X, such that, each vertical time-slide of X is put side by side to the right in X, starting with the slice corresponding to the first time interval (Westerhuis at.al, 1999). Another arrangement has been proposed by Wold et. al. (1998) that consist in putting each vertical time-slide 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.

For on-line monitoring, the incomplete set of measurements should be augmented with predicted data to create a data set that spans the entire batch. Some drawbacks arise: the computational effort to develop the control charts and to check the test statistic during on-line monitoring increase and, the predicted value of future measurements may have a significant effect on statistic calculation.

If the statistic tests indicate the process is out of control, the contribution plots are analysed to identify the source of faults. Only the contribution plot for that time is considered, but the statistic values depend on the whole set of measurements (the real observations and the estimated ones).

In contrast, the second arrangement only removes the grand mean of the variables for all batches and times, leaving the non linear time-varying trajectories in the data. Then the first principal components capture the deterministic behaviour of the process instead its random variability. As one batch is not considered as an object, the post analysis of the reference set of data can not be performed. This representation allows to use biplots for fault identification and the estimation of future observations is avoided.

In this work an exhaustive comparative analysis is performed between the previous unfolding strategies for the modelling, on-line monitoring and fault identification stages. Furthermore a different processing of the data set is proposed to avoid the first principal components capture the deterministic behaviour of the process. In this way the information regarding process variability for each time is maintained. This study is performed for on-line monitoring and fault diagnosis of a styrene emulsion polymerization reactor.

References Nomitos, P.; MacGregor, J. F., 1994. Monitoring Batch Processes Using Multiway Principal Component Análisis, AIChe Journal, 40, 8, 1361-1375. Nomitos, P.; MacGregor, J. F., 1995. Multiway Partial Least Squares in Monitoring Batch Processes, Chemometrics & Intelligent Laboratory Systems, 30, 97-108. Westerhuis J. A., Kourti T., MacGregor, J. F., 1999. Comparing Alternative Approahes for Multivariate Statistical Analysis of Batch Process Data, Journal of Chemometrics, 13, 397-413. Wold, S.; Kettaneh, H.; Friden, H.; Holmberg, A., 1998. Modelling and Diagnosis of Batch Processes and Analogous Kinetics Experiments, Chemometrics & Intelligent Laboratory Systems, 44, 331-340.