Adaptive Fuzzy C-Means clustering in process monitoring

Modifications are proposed and a simple strategy for updating the cluster centers is given for the adaptive and the flexible FCM algorithms, which were compared to the basic non-adaptive FCM.

Abstract

Quite often, quality control models fail because, e.g., the mean values are changing continuously. These kinds of changes, e.g., process drifts due to seasonal fluctuations, are common in an activated sludge waste-water treatment plant in Finland. Different Fuzzy C-Means (FCM) clustering algorithms were tested in order to cope with these kinds of seasonal effects. Firstly, a Principal Component Analysis (PCA) model was constructed in order to visualize the data set and reduce the dimensionality of the problem. Then, score values of the PCA were used in the FCM. The cluster centers represented the different process conditions (winter and summer seasons). Different algorithms were used to update the cluster centers or to give them some flexibility. The testing of different FCM algorithms was carried out by using a separate test set. The adaptive and the flexible FCM algorithms were compared to the basic non-adaptive FCM. For both cases, modifications are proposed and a simple strategy for updating the cluster centers is given.