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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 678965, 12 pages
http://dx.doi.org/10.1155/2015/678965
Research Article

Fuzzy Wavelet Neural Network Using a Correntropy Criterion for Nonlinear System Identification

1Postgraduate Program in Electrical and Computer Engineering (PPgEEC), Federal University of Rio Grande do Norte, 59078-970 Natal, RN, Brazil
2Department of Computer Engineering, Federal University of Rio Grande do Norte, 59078-970 Natal, RN, Brazil
3Department of Elecrtical Engineering, Federal University of Rio Grande do Norte, 59078-970 Natal, RN, Brazil

Received 17 September 2014; Accepted 28 November 2014

Academic Editor: Yudong Zhang

Copyright © 2015 Leandro L. S. Linhares et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Recent researches have demonstrated that the Fuzzy Wavelet Neural Networks (FWNNs) are an efficient tool to identify nonlinear systems. In these structures, features related to fuzzy logic, wavelet functions, and neural networks are combined in an architecture similar to the Adaptive Neurofuzzy Inference Systems (ANFIS). In practical applications, the experimental data set used in the identification task often contains unknown noise and outliers, which decrease the FWNN model reliability. In order to reduce the negative effects of these erroneous measurements, this work proposes the direct use of a similarity measure based on information theory in the FWNN learning procedure. The Mean Squared Error (MSE) cost function is replaced by the Maximum Correntropy Criterion (MCC) in the traditional error backpropagation (BP) algorithm. The input-output maps of a real nonlinear system studied in this work are identified from an experimental data set corrupted by different outliers rates and additive white Gaussian noise. The results demonstrate the advantages of the proposed cost function using the MCC as compared to the MSE. This work also investigates the influence of the kernel size on the performance of the MCC in the BP algorithm, since it is the only free parameter of correntropy.