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Mathematical Problems in Engineering
Volume 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.

Linked References

  1. X. Lu, K. L. V. Iyer, K. Mukherjee, and N. C. Kar, “A dual purpose triangular neural network based module for monitoring and protection in Bi-directional off-board level-3 charging of EV/PHEV,” IEEE Transactions on Smart Grid, vol. 3, no. 4, pp. 1670–1678, 2012. View at Publisher · View at Google Scholar · View at Scopus
  2. Z. Tian and M. J. Zuo, “Health condition prediction of gears using a recurrent neural network approach,” IEEE Transactions on Reliability, vol. 59, no. 4, pp. 700–705, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. Y.-Y. Lin, J.-Y. Chang, and C.-T. Lin, “Identification and prediction of dynamic systems using an interactively recurrent self-evolving fuzzy neural network,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 2, pp. 310–321, 2013. View at Publisher · View at Google Scholar · View at Scopus
  4. Z. Shao, Y. Zhan, and Y. Guo, “Fuzzy neural network-based model reference adaptive inverse control for induction machines,” in Proceedings of the International Conference on Applied Superconductivity and Electromagnetic Devices (ASEMD '09), pp. 56–59, Chengdu, China, 2009.
  5. S. Yilmaz and Y. Oysal, “Fuzzy wavelet neural network models for prediction and identification of dynamical systems,” IEEE Transactions on Neural Networks, vol. 21, no. 10, pp. 1599–1609, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. R. H. Abiyev and O. Kaynak, “Fuzzy wavelet neural networks for identification and control of dynamic plants—a novel structure and a comparative study,” IEEE Transactions on Industrial Electronics, vol. 55, no. 8, pp. 3133–3140, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. R. J. Bessa, V. Miranda, and J. Gama, “Entropy and correntropy against minimum square error in offline and online three-day ahead wind power forecasting,” IEEE Transactions on Power Systems, vol. 24, no. 4, pp. 1657–1666, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. H. Qu, W. Ma, J. Zhao, and T. Wang, “Prediction method for network traffic based on maximum correntropy criterion,” China Communications, vol. 10, no. 1, pp. 134–145, 2013. View at Publisher · View at Google Scholar · View at Scopus
  9. O. Nelles, Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models, Springer, Berlin, Germany, 2001.
  10. S. Haykin, Neural Networks: A Comprehensive Foundation, Prentice-Hall, Upper Saddle River, NJ, USA, 1999.
  11. Y. Zhang and L. Wu, “Crop classification by forward neural network with adaptive chaotic particle swarm optimization,” Sensors, vol. 11, no. 5, pp. 4721–4743, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. Y. Zhang, S. Wang, G. Ji, and P. Phillips, “Fruit classification using computer vision and feedforward neural network,” Journal of Food Engineering, vol. 143, pp. 167–177, 2014. View at Google Scholar
  13. K. S. Narendra and K. Parthasarathy, “Identification and control of dynamical systems using neural networks,” IEEE Transactions on Neural Networks, vol. 1, no. 1, pp. 4–27, 1990. View at Publisher · View at Google Scholar · View at Scopus
  14. A. Banakar and M. F. Azeem, “Identification and prediction of nonlinear dynamical plants using TSK and wavelet neuro-fuzzy models,” in Proceedings of the 3rd IEEE Conference on Intelligent Systems, pp. 617–620, London, UK, September 2006. View at Publisher · View at Google Scholar
  15. T. Kara and I. Eker, “Experimental nonlinear identification of a two mass system,” in Proceedings of the IEEE Conference on Control Applications (CCA '03), vol. 1, pp. 66–71, Istanbul, Turkey, 2003. View at Publisher · View at Google Scholar
  16. M. O. Efe, “A comparison of ANFIS, MLP and SVM in identification of chemical processes,” in Proceedings of the IEEE Control Applications & Intelligent Control, pp. 689–694, St. Petersburg, Russia, 2009.
  17. X. Xue, J. Lu, and W. Xiang, “Nonlinear system identification with modified differential evolution and RBF networks,” in Proceedings of the 5th IEEE International Conference on Advanced Computational Intelligence ( ICACI '12), pp. 332–335, Nanjing, China, October 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. Q. Zhang and A. Benveniste, “Wavelet networks,” IEEE Transactions on Neural Networks, vol. 3, no. 6, pp. 889–898, 1992. View at Publisher · View at Google Scholar · View at Scopus
  19. S. A. Billings and H.-L. Wei, “A new class of wavelet networks for nonlinear system identification,” IEEE Transactions on Neural Networks, vol. 16, no. 4, pp. 862–874, 2005. View at Publisher · View at Google Scholar · View at Scopus
  20. F.-J. Lin, P.-H. Shen, and Y.-S. Kung, “Adaptive wavelet neural network control for linear synchronous motor servo drive,” IEEE Transactions on Magnetics, vol. 41, no. 12, pp. 4401–4412, 2005. View at Publisher · View at Google Scholar · View at Scopus
  21. J.-S. R. Jang, “ANFIS: adaptive-network-based fuzzy inference system,” IEEE Transactions on Systems, Man and Cybernetics, vol. 23, no. 3, pp. 665–685, 1993. View at Publisher · View at Google Scholar · View at Scopus
  22. L. Zhao, J.-P. Zhang, J. Yang, and Y. Chu, “Software reliability growth model based on fuzzy wavelet neural network,” in Proceedings of the 2nd International Conference on Future Computer and Communication (ICFCC '10), pp. V1664–V1668, IEEE, Wuhan, China, May 2010. View at Publisher · View at Google Scholar · View at Scopus
  23. J.-R. Song and H.-B. Shi, “Dynamic system modeling based on wavelet recurrent fuzzy neural network,” in Proceedings of the 7th International Conference on Natural Computation (ICNC '11), vol. 2, pp. 766–770, Shanghai, China, July 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. C. H. Lu, “Wavelet fuzzy neural networks for identification and predictive control of dynamic systems,” IEEE Transactions on Industrial Electronics, vol. 58, no. 7, pp. 3046–3058, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. D. W. C. Ho, P.-A. Zhang, and J. Xu, “Fuzzy wavelet networks for function learning,” IEEE Transactions on Fuzzy Systems, vol. 9, no. 1, pp. 200–211, 2001. View at Publisher · View at Google Scholar · View at Scopus
  26. A. Ebadat, N. Noroozi, A. A. Safavi, and S. H. Mousavi, “New fuzzy wavelet network for modeling and control: the modeling approach,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 3385–3396, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. S. H. Mousavi, N. Noroozi, A. . Safavi, and A. Ebadat, “Modeling and control of nonlinear systems using novel fuzzy wavelet networks: the output adaptive control approach,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 9, pp. 3798–3814, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. S. Ganjefar and M. Tofighi, “A fuzzy wavelet neural network stabilizer design using genetic algorithm for multi-machine systems,” Przegląd Elektrotechniczny, vol. 89, no. 5, pp. 19–25, 2013. View at Google Scholar · View at Scopus
  29. L. L. S. Linhares, J. M. Araújo Jr., F. M. U. Araújo, and T. Yoneyama, “A nonlinear system identification approach based on fuzzy wavelet neural network,” Journal of Intelligent and Fuzzy Systems, 2014. View at Publisher · View at Google Scholar
  30. Y. Liu and J. Chen, “Correntropy-based kernel learning for nonlinear system identification with unknown noise: an industrial case study,” in Proceedings of the 10th IFAC Symposium on Dynamics and Control of Process Systems (DYCOPS '13), vol. 10, pp. 361–366, Mumbai, India, December 2013. View at Publisher · View at Google Scholar · View at Scopus
  31. J. C. Munoz and J. Chen, “Removal of the effects of outliers in batch process data through maximum correntropy estimator,” Chemometrics and Intelligent Laboratory Systems, vol. 111, no. 1, pp. 53–58, 2012. View at Publisher · View at Google Scholar · View at Scopus
  32. T. Söderström, “System identification for the errors-in-variables problem,” Transactions of the Institute of Measurement and Control, vol. 34, no. 7, pp. 780–792, 2012. View at Publisher · View at Google Scholar · View at Scopus
  33. S. Khatibisepehr and B. Huang, “Dealing with irregular data in soft sensors: Bayesian method and comparative study,” Industrial and Engineering Chemistry Research, vol. 47, no. 22, pp. 8713–8723, 2008. View at Publisher · View at Google Scholar · View at Scopus
  34. C. M. Bishop, Neural Networks for Pattern Recognition, Oxford University Press, Oxford, UK, 1995. View at MathSciNet
  35. V. Miranda, C. Cerqueira, and C. Monteiro, “Training a FIS with epso under an entropy criterion for wind power prediction,” in Proceedings of the International Conference on Probabilistic Methods Applied to Power Systems (PMAPS '06), pp. 1–8, Stockholm, Sweden, 2006.
  36. I. Santamaría, P. P. Pokharel, and J. C. Principe, “Generalized correlation function: definition, properties, and application to blind equalization,” IEEE Transactions on Signal Processing, vol. 54, no. 6, pp. 2187–2197, 2006. View at Publisher · View at Google Scholar · View at Scopus
  37. S. Zhao, B. Chen, and J. C. Principe, “Kernel adaptive filtering with maximum correntropy criterion,” in Proceedings of the International Joint Conference on Neural Network (IJCNN '11), pp. 2012–2017, San Jose, Calif, USA, August 2011. View at Publisher · View at Google Scholar · View at Scopus
  38. J. C. Principe, Information Theoretic Learning: Rényi's Entropy and Kernel Perspectives, Springer, 2010.
  39. A. I. Fontes, A. D. M. Martins, L. F. Silveira, and J. Principe, “Performance evaluation of the correntropy coefficient in automatic modulation classification,” Expert Systems with Applications, vol. 42, no. 1, pp. 1–8, 2014. View at Publisher · View at Google Scholar
  40. A. I. R. Fontes, P. T. V. Souza, A. D. D. Neto, A. M. Martins, and L. F. Q. Silveira, “Classification system of pathological voices using correntropy,” Mathematical Problems in Engineering, vol. 2014, Article ID 924786, 7 pages, 2014. View at Publisher · View at Google Scholar
  41. R. He, B.-G. Hu, W.-S. Zheng, and X.-W. Kong, “Robust principal component analysis based on maximum correntropy criterion,” IEEE Transactions on Image Processing, vol. 20, no. 6, pp. 1485–1494, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  42. Y. Liu and J. Chen, “Correntropy-based kernel learning for nonlinear system identification with unknown noise: an industrial case study,” in Proceedings of the 10th IFAC Symposium on Dynamics and Control of Process Systems, pp. 361–366, December 2013. View at Publisher · View at Google Scholar · View at Scopus
  43. W. Liu, P. P. Pokharel, and J. C. Principe, “Correntropy: properties and applications in non-Gaussian signal processing,” IEEE Transactions on Signal Processing, vol. 55, no. 11, pp. 5286–5298, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  44. S. Zhao, B. Chen, and J. C. Principe, “An adaptive kernel width update for correntropy,” in Proceedings of the International Joint Conference on Neural Networks (IJCNN '12), pp. 1–5, Brisbane, Australia, 2012. View at Publisher · View at Google Scholar
  45. M. C. Jones, J. S. Marron, and S. J. Sheather, “A brief survey of bandwidth selection for density estimation,” Journal of the American Statistical Association, vol. 91, no. 433, pp. 401–407, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  46. B. W. Silverman, Density Estimation for Statistics and Data Analysis, vol. 3, CRC Press, New York, NY, USA, 1986. View at MathSciNet
  47. A. W. Bowman, “An alternative method of cross-validation for the smoothing of density estimates,” Biometrika, vol. 71, no. 2, pp. 353–360, 1984. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  48. D. W. Scott and G. R. Terrell, “Biased and unbiased cross-validation in density estimation,” Journal of the American Statistical Association, vol. 82, no. 400, pp. 1131–1146, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  49. N. Terzija and H. McCann, “Wavelet-based image reconstruction for hard-field tomography with severely limited data,” IEEE Sensors Journal, vol. 11, no. 9, pp. 1885–1893, 2011. View at Publisher · View at Google Scholar · View at Scopus
  50. A. Bouzida, O. Touhami, R. Ibtiouen, A. Belouchrani, M. Fadel, and A. Rezzoug, “Fault diagnosis in industrial induction machines through discrete wavelet transform,” IEEE Transactions on Industrial Electronics, vol. 58, no. 9, pp. 4385–4395, 2011. View at Publisher · View at Google Scholar · View at Scopus
  51. J. Gao, Z. Leng, Y. Qin, Z. Ma, and X. Liu, “Short-term traffic flow forecasting model based on wavelet neural network,” in Proceedings of the 25th Chinese Control and Decision Conference (CCDC '13), pp. 5081–5084, Guiyang, China, May 2013. View at Publisher · View at Google Scholar · View at Scopus
  52. J. J. Cordova, W. Yu, and X. Li, “Haar wavelet neural networks for nonlinear system identification,” in Proceedings of the 6th IEEE Multi-Conference on Systems and Control (MSC '12), pp. 276–281, Dubrovnik, Croatia, October 2012. View at Publisher · View at Google Scholar · View at Scopus
  53. R. K. Galvão, V. M. Becerra, J. M. Calado, and P. M. Silva, “Linear-wavelet networks,” International Journal of Applied Mathematics and Computer Science, vol. 14, no. 2, pp. 221–232, 2004. View at Google Scholar · View at MathSciNet
  54. M. Davanipoor, M. Zekri, and F. Sheikholeslam, “Fuzzy wavelet neural network with an accelerated hybrid learning algorithm,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 3, pp. 463–470, 2012. View at Publisher · View at Google Scholar · View at Scopus
  55. V. V. J. Rajapandian and N. Gunaseeli, “Modified standard back propagation algorithm with optimum initialization for feed forward neural networks,” International Journal of Imaging Science and Engineering, vol. 1, no. 3, pp. 86–89, 2007. View at Google Scholar
  56. T. Kathirvalavakumar and P. Thangavel, “A modified backpropagation training algorithm for feedforward neural networks,” Neural Processing Letters, vol. 23, no. 2, pp. 111–119, 2006. View at Publisher · View at Google Scholar · View at Scopus
  57. S. Abid, R. Fnaicch, and M. Najim, “A fast feedforward training algorithm using a modified form of the standard backpropagation algorithm,” IEEE Transactions on Neural Networks, vol. 12, no. 2, pp. 424–430, 2001. View at Publisher · View at Google Scholar · View at Scopus
  58. M. Davanipoor, M. Zekri, and F. Sheikholeslam, “The preference of fuzzy wavelet neural network to ANFIS in identification of nonlinear dynamic plants with fast local variation,” in Proceedings of the 18th Iranian Conference on Electrical Engineering (ICEE '10), pp. 605–609, Isfahan, Iran, May 2010. View at Publisher · View at Google Scholar · View at Scopus
  59. E. Soria, J. D. Martin, and P. J. G. Lisboa, “Classical training methods,” in Metaheuristic Procedures for Training Neural Networks, E. Alba and R. Marti, Eds., pp. 25–32, Springer, New York, NY, USA, 2006. View at Google Scholar
  60. A. Singh and J. C. Príncipe, “Information theoretic learning with adaptive kernels,” Signal Processing, vol. 91, no. 2, pp. 203–213, 2011. View at Publisher · View at Google Scholar · View at Scopus
  61. C. A. G. Fonseca, Estrutura ANFIS Modificada para identificação e Controle de Plantas com Ampla Faixa de Operação e não Linearidade Acentuada [Ph.D. thesis], Universidade Federal do Rio Grande do Norte (UFRN), Natal, Brazil, 2012.
  62. J. M. de Araújo Jr., J. M. P. de Menezes, A. A. M. de Albuquerque, O. D. M. Almeida, and F. M. U. de Araújo, “Assessment and certification of neonatal incubator sensors through an inferential neural network,” Sensors, vol. 13, no. 11, pp. 15613–15632, 2013. View at Publisher · View at Google Scholar · View at Scopus