An adaptive wavelet network for function learning

In this article, a wavelet neural network (WNN) model is proposed for approximating arbitrary nonlinear functions. Our WNN model structure comes from the idea of adaptive neuro-fuzzy inference system (ANFIS) which is used for obtaining fuzzy rule base from the input–output data of an unknown function. The WNN model which is called in this study as adaptive wavelet network (AWN) consists of wavelet scaling functions in its processing units whereas in an ANFIS, mostly Gaussian-type membership functions are used for a function approximation. We present to train an AWN by a hybrid-learning method containing least square estimation (LSE) with gradient-based optimization algorithm to obtain the optimal translation and dilation parameters of our AWN for model accuracy. Simulation examples are also given to illustrate the effectiveness of the method.

[1]  Okyay Kaynak,et al.  Identification and Control of Dynamic Plants Using Fuzzy Wavelet Neural Networks , 2008, 2008 IEEE International Symposium on Intelligent Control.

[2]  Yong-Zai Lu,et al.  Fuzzy Model Identification and Self-Learning for Dynamic Systems , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[3]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[4]  J. A. Leonard,et al.  Radial basis function networks for classifying process faults , 1991, IEEE Control Systems.

[5]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[6]  Qinghua Zhang,et al.  Using wavelet network in nonparametric estimation , 1997, IEEE Trans. Neural Networks.

[7]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

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

[9]  Chulhyun Kim,et al.  Forecasting time series with genetic fuzzy predictor ensemble , 1997, IEEE Trans. Fuzzy Syst..

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

[11]  E. Mizutani,et al.  Neuro-Fuzzy and Soft Computing-A Computational Approach to Learning and Machine Intelligence [Book Review] , 1997, IEEE Transactions on Automatic Control.

[12]  P. Torkzadeh,et al.  Structural optimization with frequency constraints by genetic algorithm using wavelet radial basis function neural network , 2008 .

[13]  Robert M. Sanner,et al.  Gaussian Networks for Direct Adaptive Control , 1991, 1991 American Control Conference.

[14]  Jerry M. Mendel,et al.  Generating fuzzy rules by learning from examples , 1992, IEEE Trans. Syst. Man Cybern..

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

[16]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[18]  Shyh Hwang,et al.  An identification algorithm in fuzzy relational systems , 1996, Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium.

[19]  Héctor Pomares,et al.  Time series analysis using normalized PG-RBF network with regression weights , 2002, Neurocomputing.

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

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

[22]  Michael J. Watts,et al.  FuNN/2 - A Fuzzy Neural Network Architecture for Adaptive Learning and Knowledge Acquisition , 1997, Inf. Sci..

[23]  Chun-Yi Su,et al.  Dynamic wavelet neural network for nonlinear dynamic system identification , 2000, Proceedings of the 2000. IEEE International Conference on Control Applications. Conference Proceedings (Cat. No.00CH37162).

[24]  Peter Strobach,et al.  Linear Prediction Theory: A Mathematical Basis for Adaptive Systems , 1990 .

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

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

[27]  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..

[28]  Yoshiki Uchikawa,et al.  On fuzzy modeling using fuzzy neural networks with the back-propagation algorithm , 1992, IEEE Trans. Neural Networks.

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

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

[31]  Kwang Bo Cho,et al.  Radial basis function based adaptive fuzzy systems , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[32]  H. Surmann,et al.  Self-Organizing and Genetic Algorithms for an Automatic Design of Fuzzy Control and Decision Systems , 1993 .

[33]  R. Tong.  The evaluation of fuzzy models derived from experimental data , 1980 .

[34]  Jiwen Dong,et al.  Nonlinear System Modelling Via Optimal Design Of Neural Trees , 2004, Int. J. Neural Syst..

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

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