USING FUZZY CLUSTERING WITH ELLIPSOIDAL UNITS IN NEURAL NETWORKS FOR ROBUST FAULT CLASSIFICATION

The limitations of standard backpropagation networks on issues such as the robustness of fault classification and speed of network training have been pointed in recent investigations. Kavuri and Venkatasubramanian demonstrated that a network using ellipsoidal activation functions is a better choice for fault classification problems and that it has certain advantages over the standard backpropagation and radial basis function approaches. Ellipsoidal activation functions generate ellipsoids in the space of the network inputs. Since a mixture of ellipsoids form asymmetric bounded decision regions, they are better suited for fault diagnosis problems where the fault classes are bounded and arbitrarily shaped. Furthermore, ellipsoids indirectly use a distance measure, thus avoiding unintuitive and arbitrary classification of unspecified regions in the measurement space. In this paper, we address issues concerning the generation of ellipsoids, such as the number, location and size of these ellipsoids. The backpropagation algorithm does not guarantee the proper determination of the ellipsoids as it runs into local minima problems, attributable mainly to poor choices of initial network weights. To avoid this and related problems, we have developed a two-stage algorithm. In the first stage, a fuzzy clustering algorithm is used to determine the number of hidden nodes and the initial estimates for the hidden layer weights. The algorithm is demonstrated to determine a minimal number of hidden nodes. The algorithm also avoids having to determine the number of hidden nodes a priori. In the second stage, network weights are tuned to minimize RMS error in classification. Backpropagation is used in this stage for fine-tuning of ellipsoids initialized by the fuzzy clustering algorithm. The performance of the proposed approach on typical classification problems is presented.