Computers and Chemical Engineering 28 (2004) 1837–1847 Fault detection of batch processes using multiway kernel principal component analysis Jong-Min Lee a , ChangKyoo Yoo b,1 , In-Beum Lee a,∗ a Department of Chemical Engineering, Pohang University of Science and Technology, San 31 Hyoja-Dong, Pohang 790-784, South Korea b BIOMATH, Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure Links 653, B-9000 Gent, Belgium Received 14 April 2003; received in revised form 24 February 2004; accepted 24 February 2004 Available online 27 March 2004 Abstract Batch processes are very important in most industries and are used to produce high-quality materials, which causes their monitoring and control to emerge as essential techniques. Several multivariate statistical analyses, including multiway principal component analysis (MPCA), have been developed for the monitoring and fault detection of batch process. In this paper, a new batch monitoring method using multiway kernel principal component analysis (MKPCA) is proposed. Three-way batch data of normal batch process are unfolded batch-wise, and then KPCA is used to capture the nonlinear characteristics within normal batch processes. The proposed monitoring method was applied to fault detection in the simulation benchmark of fed-batch penicillin production. In both off-line analysis and on-line batch monitoring, the proposed approach can effectively capture the nonlinear relationships among process variables. In on-line monitoring, MKPCA can detect significant deviation which may cause a lower quality of final products. MPCA, however, has a limit to detect faults. © 2004 Elsevier Ltd. All rights reserved. Keywords: Batch monitoring; Fault detection; Process monitoring; Kernel principal component analysis (KPCA); Multiway kernel principal component analysis (MKPCA); Principal component analysis (PCA) 1. Introduction Nowadays, the increasing emphasis on producing high- quality materials has caused batch process to emerge as an important process in polymer, pharmaceutical, semi- conductor, and biochemical industries. However in most cases, existing batch processes show large variations in their prescribed processing trajectory. Small changes in operating conditions during critical periods may impact the final prod- uct quality and yield as well. Furthermore, produced quality variables, the key indicators of process performance, are of- ten examined off-line in a laboratory (Chen & Liu, 2002). If the produced quality variables do not satisfy a specified cri- terion, we cannot recognize what the causes were and when they occurred in the past batch process. In the past case, the nonconforming products would be useless, and another ∗ Corresponding author. Tel.: +82-54-279-2274; fax: +82-54-279-3499. E-mail addresses: iblee@postech.ac.kr, pporook@postech.ac.kr (I.-B. Lee). 1 Tel.: +32-9-264-6196; fax: +32-9-264-6220. batch process would be carried out without any corrective action. As a result, the cost of processing increases and the subsequent competitive price decreases. Therefore, on-line monitoring and diagnosis of batch processes is needed to de- tect faults that can be either corrected prior to completion of the batch or removed in subsequent batches. Early detection of faults and taking corrective action to recover the batch by on-line monitoring before the completion of the batch can prevent the manufacture of nonconforming batches. Several techniques using multivariate statistical analysis have been developed for the monitoring and fault detection of batch process. Nomikos and MacGregor (1994, 1995) have extended the multivariate statistical process control (SPC) methods of principal component analysis (PCA) to batch processes, where the method is called multiway PCA (MPCA). These approaches allow the monitoring of a batch process to be achieved once a model has been developed from nominal or good batch operations. This simple and powerful method led to many papers related to the application of MPCA to industrial batch monitoring (Gallagher & Wise, 1996; Gregersen & Jørgensen, 1999; Kosanovich, Dahl, & Piovoso, 1996; Lennox, Montague, 0098-1354/$ – see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2004.02.036