Abstract
In this paper we examine modeling of a nonlinear system using wavelet networks. Wavelet networks are similar to neural networks for the structure and the learning approach. But training algorithms for wavelet networks require a smaller number of iterations when compared with neural networks. Also interpretation of the model with neural networks is so hard. Gaussian based mother wavelet function is used as an activation function. Wavelet networks have these parameters; dilation, translation, and weights. Wavelets are rapidly vanishing functions. For this reason heuristic procedure has been used. Selecting initial values of weights are made randomly. Then parameters are optimized during learning. To update parameters, gradient method has been applied by using momentum. Quadratic cost function is used for error minimization. Two test data have been used for the simulations. One of them is a static function and the other one is a second order nonlinear function.
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References
Zhang, Q., Benveniste, A.: Wavelet Networks. IEEE Transaction on Neural Networks 3, 889–898 (1992)
Galvao Roberto, K.H., Becerra, V.M.: Linear-Wavelet Models for System Identification. In: IFAC15th Triennial World Congress, Barcelona, Spain (2002)
Zhang, Q.: Using Wavelet Network in Non parametric Estimation. IEEE trans. Neural Networks 8, 227–236 (1997)
Thuillard, M.: Review of Wavelet Networks, Wavenets, Fuzzy Wavenets and Their Applications. In: ESIT 2000, Aachen, Germany (2000)
Polycarpou, M., Mears, M., Weaver, S.: Adaptive Wavelet Control of Nonlinear Systems. In: Proceedings of the1997 IEEE Conference on Decision and Control, pp. 3890–3895 (1997)
Pati, Y.C., Krishnaprasad, P.S.: Analysis and Synthesis of Feedforward Neural Networks Using Discrete Affine Wavelet Transformations. IEEE Trans. On Neural Networks 4, 73–85 (1993)
Oussar, Y., Rivals, I., Personnaz, L., Dreyfus, G.: Training Wavelet Networks for Nonlinear Dynamic Input Output Modeling. Elsevier neurocomputing 20, 173–188 (1998)
Oussar, Y., Dreyfus, G.: Initialization by Selection for Wavelet Network Training. Neurocomputing 34, 131–143 (2000)
Reza, A.M.: Wavelet Characteristics. White Paper, Spire Lab. UWM (1999)
Polikar R.: The wavelet tutorial (2001), http://engineering.rowan.edu/~polikar/WAVELETS
Becerikli, Y., Oysal, Y., Konar, A.F.: On a Dynamic Wavelet Network and Its Modeling Application. In: Kaynak, O., Alpaydın, E., Oja, E., Xu, L. (eds.) ICANN 2003 and ICONIP 2003. LNCS, vol. 2714, pp. 710–718. Springer, Heidelberg (2003)
Becerikli, Y.: On Three Intelligent Systems: Dynamic Neural, Fuzzy and Wavelet Networks For Training Trajectory. Neural Computing & Applications (NC&A) 13, 339–351 (2004)
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Postalcioglu, S., Becerikli, Y. (2005). Nonlinear System Modeling Using Wavelet Networks. In: Wang, J., Liao, XF., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427445_67
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DOI: https://doi.org/10.1007/11427445_67
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25913-8
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