POSSIBILISTIC AND FUZZY C-MEANS CLUSTERING FOR PROCESS MONITORING IN AN ACTIVATED SLUDGE WASTE-WATER TREATMENT PLANT PEKKA TEPPOLA* AND PENTTI MINKKINEN Chemometrics Group, Laboratory of Inorganic and Analytical Chemistry, Lappeenranta University of Technology, PO Box 20, FIN-53851 Lappeenranta, Finland SUMMARY A partial least squares (PLS) regression is used to model and visualize the waste-water treatment process. The score values of PLS are submitted to both a fuzzy C-means (FCM) clustering and a possibilistic C-means (PCM) clustering. In this work, four concepts are presented. Firstly, a hidden path process modeling is illustrated. Secondly, the use of and the difference between the PCM and FCM algorithms in process monitoring are shown. The difference between these algorithms is significant and should not be disregarded, because the membership values and consequently the typicality values generated by different algorithms have different interpretations. In FCM the memberships are relative and correspond to partition information, i.e. they sum to unity. In PCM the ‘partition constraint’ has been relaxed and thus so-called typicality values are computed that are no longer relative. Instead, these values represent a degree of typicality with the class prototypes that in turn correspond to different process states. Thirdly, a couple of possible uses of permanent and temporary cluster prototypes are given. Fourthly, a recursive cluster prototype updating is documented to follow the systematic variations, i.e. the movement of seasonal attraction points. These seasonal attraction points correspond to the process mean values during different seasons. This updating is necessary because these attraction points are dynamic in nature. The updating corresponding to adjusting the process mean to correct drifting problems of the mean values. Copyright  1999 John Wiley & Sons, Ltd. KEY WORDS: activated sludge waste-water treatment plant; chemometrics; process monitoring; hidden path process modeling; PLS; PCM; FCM; recursive updating INTRODUCTION A typical activated sludge waste-water treatment plant is a biochemical process that purifies effluents from e.g. paper and pulp mills. In Finland the actual process is very often complicated by seasonal fluctuations. The process itself consists of several successive steps: equalization, primary clarification, neutralization, aeration and secondary clarification. After these sections, purified water is discharged into a water system. After the secondary clarification basin a part of the sludge is removed while another part is recycled into the aeration basin. It is important to make a distinction between two different categories of waste-water treatment plants, i.e. between municipal waste-water JOURNAL OF CHEMOMETRICS J. Chemometrics 13, 445–459 (1999) * Correspondence to: P. Teppola, Chemometrics Group, Laboratory of Inorganic and Analytical Chemistry, Lappeenranta University of Technology, PO Box 20, FIN-53851 Lappeenranta, Finland. E-mail: teppola@lut.fi Contract/grant sponsor: Southeast Finland Regional Environment Center. Contract/grant sponsor: Academy of Finland. CCC 0886–9383/99/040445–15 $17.50 Copyright  1999 John Wiley & Sons, Ltd. Received 1 July 1998 Accepted 18 March 1999