A Hierarchical Evolutionary Algorithm for Constructing and Training Wavelet Networks

The wavelet network has been introduced as a special feed-forward neural network supported by the wavelet theory, and has become a popular tool in the approximation and forecast fields. In this paper, an evolutionary algorithm is proposed for constructing and training the wavelet network for approximation and forecast. This evolutionary algorithm utilises the hierarchical chromosome to encode the structure and parameters of the wavelet network, and combines a genetic algorithm and evolutionary programming to construct and train the network simultaneously through evolution. The numerical examples are presented to show the efficiency and potential of the proposed algorithm with respect to function approximation, sunspot time series forecast and condition forecast for a hydroturbine machine, respectively. The study also indicates that the proposed method has the potential to solve a wide range of neural network construction and training problems in a systematic and robust way.

[1]  S. Yao,et al.  Evolving wavelet neural networks for function approximation , 1996 .

[2]  Kwok-Wo Wong,et al.  On-line Successive Synthesis of Wavelet Networks , 1998, Neural Processing Letters.

[3]  Daniel Tylavsky,et al.  Prediction of top-oil temperature for transformers using neural networks , 2000 .

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

[5]  David B. Fogel,et al.  An introduction to simulated evolutionary optimization , 1994, IEEE Trans. Neural Networks.

[6]  Kwok-Wo Wong,et al.  Self-construction algorithm for synthesis of wavelet networks , 1998 .

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

[8]  Jooyoung Park,et al.  Universal Approximation Using Radial-Basis-Function Networks , 1991, Neural Computation.

[9]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[10]  Thomas Bäck,et al.  Evolutionary computation: comments on the history and current state , 1997, IEEE Trans. Evol. Comput..

[11]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[12]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[13]  Peter W. Tse,et al.  Prediction of Machine Deterioration Using Vibration Based Fault Trends and Recurrent Neural Networks , 1999 .

[14]  S. Mallat.  Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[15]  C. Chui.  Wavelets: A Tutorial in Theory and Applications , 1992 .

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

[17]  Bernard Delyon,et al.  Accuracy analysis for wavelet approximations , 1995, IEEE Trans. Neural Networks.

[18]  He Yong.  Artificial Neural Networks Design and Implementation Based on Evolutionary Computation , 2001 .

[19]  Shien-Ming Wu,et al.  Time series and system analysis with applications , 1983 .

[20]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[21]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.