A Fuzzy Wavelet Neural Network Model for System Identification

In this paper, a fuzzy wavelet neural network model is proposed for system identification problems. The proposed model is obtained from the traditional Takagi-Sugeno-Kang (TSK) fuzzy system by replacing the consequent part of fuzzy rules with wavelet basis functions that have time-frequency localization properties. We use a radial function of Mexican Hat wavelet in the consequent part of each rule. A fast gradient algorithm based on quasi-Newton methods is used to obtain the optimal values for unknown parameters of the model. Simulation results of some benchmark problems in the literature are also given to illustrate the effectiveness of the model.

[1]  David E. Rumelhart,et al.  Predicting the Future: a Connectionist Approach , 1990, Int. J. Neural Syst..

[2]  Qinghua Zhang,et al.  Wavelet networks , 1992, IEEE Trans. Neural Networks.

[3]  H. Tong,et al.  Threshold Autoregression, Limit Cycles and Cyclical Data , 1980 .

[4]  Yusuf Oysal,et al.  Fuzzy Wavelet Neural Network Models for Prediction and Identification of Dynamical Systems , 2010, IEEE Transactions on Neural Networks.

[5]  Madhusudan Singh,et al.  New fuzzy wavelet neural networks for system identification and control , 2005, Appl. Soft Comput..

[6]  Philip E. Gill,et al.  Practical optimization , 1981 .

[7]  Kumpati S. Narendra,et al.  Neural Networks In Dynamical Systems , 1990, Other Conferences.

[8]  Daniel W. C. Ho,et al.  Fuzzy wavelet networks for function learning , 2001, IEEE Trans. Fuzzy Syst..

[9]  Sheng Chen,et al.  Orthogonal least squares methods and their application to non-linear system identification , 1989 .

[10]  P. S. Sastry,et al.  Memory neuron networks for identification and control of dynamical systems , 1994, IEEE Trans. Neural Networks.

[11]  Jiwen Dong,et al.  Time-series prediction using a local linear wavelet neural network , 2006, Neurocomputing.

[12]  Chia-Feng Juang,et al.  A recurrent self-organizing neural fuzzy inference network , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[13]  Jeffrey L. Elman,et al.  Finding Structure in Time , 1990, Cogn. Sci..

[14]  Donald E. Waagen,et al.  Evolving recurrent perceptrons for time-series modeling , 1994, IEEE Trans. Neural Networks.

[15]  Nikola K. Kasabov,et al.  HyFIS: adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems , 1999, Neural Networks.

[16]  Okyay Kaynak,et al.  Fuzzy Wavelet Neural Networks for Identification and Control of Dynamic Plants—A Novel Structure and a Comparative Study , 2008, IEEE Transactions on Industrial Electronics.

[17]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

[18]  Mahdi Jalili-Kharaajoo,et al.  Nonlinear System Identification Using ANFIS Based on Emotional Learning , 2004 .

[19]  O. Nelles.  Nonlinear System Identification , 2001 .

[20]  O. Nelles.  Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models , 2000 .

[21]  Chia-Feng Juang,et al.  A TSK-type recurrent fuzzy network for dynamic systems processing by neural network and genetic algorithms , 2002, IEEE Trans. Fuzzy Syst..

[22]  Jun Zhang,et al.  Wavelet neural networks for function learning , 1995, IEEE Trans. Signal Process..

[23]  Maryam Zekri,et al.  Adaptive fuzzy wavelet network control design for nonlinear systems , 2008, Fuzzy Sets Syst..

[24]  D. D. Bruns,et al.  WaveARX neural network development for system identification using a systematic design synthesis , 1995 .

[25]  Bijan Fazlollahi,et al.  Evolutionary algorithm-based learning of fuzzy neural networks. Part 2: Recurrent fuzzy neural networks , 2009, Fuzzy Sets Syst..

[26]  Lars Kai Hansen,et al.  On design and evaluation of tapped-delay neural network architectures , 1993, IEEE International Conference on Neural Networks.

[27]  Stephen A. Billings,et al.  A new class of wavelet networks for nonlinear system identification , 2005, IEEE Transactions on Neural Networks.

[28]  Engin Karatepe,et al.  A new approach to fuzzy wavelet system modeling , 2005, Int. J. Approx. Reason..