Diagnosis of Impurity Levels in a Copolymerization Process Shijin Lou, Thomas A. Duever,* Hector M. Budman Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada Fax: þ1 519 746-4979; E-mail: tduever@uwaterloo.ca Received: October 22, 2004; Accepted: February 21, 2005; DOI: 10.1002/mats.200400074 Keywords: copolymerization process; fault diagnosis; impurity diagnosis; optimal experimental design (OED); projection pursuit regression; system observability analysis 1. Introduction In industrial manufacturing processes, the economic ope- ration of the polymerization reactor usually requires that unreacted species be recovered and recycled back into the process. Associated with the recycle of solvent and un- reacted monomers is the recycle of reactive impurities, which are usually traces of inhibitors or oxygen. Almost all types of polymerization are sensitive to such reactive impurities. The studies of Penlidis et al. [1] show that impurities in an emulsion polymerization system rapidly consume reactive free radicals, thus preventing particle generation and decreasing the growth of polymer particles already present in the emulsion. If the concentration of reactive impurities is not large enough to consume a sub- stantial amount of the initiator radicals, then after the impu- rities have been consumed the polymerization can proceed in a normal fashion but the end-point of the batch may need Summary: This work investigates a fault diagnosis problem in the copolymerization process of styrene and methyl meth- acrylate (STY/MMA). Two topics are discussed in this paper: the system observability and optimal experimental design (OED) to reduce fault misclassification. Lack of observa- bility has been found to be one of the major causes of mis- classification in fault diagnosis, which is not remediable by any means other than including the right measurements necessary for the observability. In this work, the system observability has been studied through simulation analysis. Then, two new experimental design methods are proposed to train the projection pursuit regression (PPR) algorithm for fault diagnosis purpose. The new design methods, referred to as Gaussian probability design and Fuzzy boundary design, are compared to a conventional factorial design, to evaluate their performance for the problem under study. The Gaussian probability design is based on the calculation of the probabi- lity of an experimental data point near a class boundary belonging to a specific class. The Fuzzy boundary design is based on a bootstrapping technique used in part for the learning process in developing neural network models. It investigates the insufficiency of training data based on the identification of class boundaries by a group of models, such as PPR models. Both Gaussian probability design and Fuzzy boundary design methods automatically search for the spar- seness of the training data, and provide guidelines to include pairs of training data on two sides of a class boundary in the areas where the data density is the lowest. The proposed design methods outperform a conventional factorial design by reducing the fault misclassification more effectively with the same amount of additional training data. Testing data in the process measurement space of temper- ature vs. conversion. Macromol. Theory Simul. 2005, 14, 181–196 DOI: 10.1002/mats.200400074 ß 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Full Paper 181