Possibilistic and fuzzy C‐means clustering for process monitoring in an activated sludge waste‐water treatment plant

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.