Institution: | aInstitute of Technology for Development, LACTEC, Low Voltage Technology Unit, UTBT Centro Politécnico UFPR, Zip code 81531-980, Curitiba, PR, Brazil bPontifícal Catholic University of Parana, PUCPR, Production and Systems Engineering Graduate Program, LAS/PPGEPS, Imaculada Conceição, 1155, Zip code 80215-901, Curitiba, PR, Brazil |
Abstract: | An important problem in engineering is the identification of nonlinear systems, among them radial basis function neural networks (RBF-NN) using Gaussian activation functions models, which have received particular attention due to their potential to approximate nonlinear behavior. Several design methods have been proposed for choosing the centers and spread of Gaussian functions and training the RBF-NN. The selection of RBF-NN parameters such as centers, spreads, and weights can be understood as a system identification problem. This paper presents a hybrid training approach based on clustering methods (k-means and c-means) to tune the centers of Gaussian functions used in the hidden layer of RBF-NNs. This design also uses particle swarm optimization (PSO) for centers (local clustering search method) and spread tuning, and the Penrose–Moore pseudoinverse for the adjustment of RBF-NN weight outputs. Simulations involving this RBF-NN design to identify Lorenz’s chaotic system indicate that the performance of the proposed method is superior to that of the conventional RBF-NN trained for k-means and the Penrose–Moore pseudoinverse for multi-step ahead forecasting. |