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Wavelet networks for nonlinear system modeling

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Abstract

This study presents a nonlinear systems and function learning by using wavelet network. Wavelet networks are as neural network for training and structural approach. But, training algorithms of wavelet networks is required a smaller number of iterations when the compared with neural networks. Gaussian-based mother wavelet function is used as an activation function. Wavelet networks have three main parameters; dilation, translation, and connection parameters (weights). Initial values of these parameters are randomly selected. They are optimized during training (learning) phase. Because of random selection of all initial values, it may not be suitable for process modeling. Because wavelet functions are rapidly vanishing functions. For this reason heuristic procedure has been used. In this study serial-parallel identification model has been applied to system modeling. This structure does not utilize feedback. Real system outputs have been exercised for prediction of the future system outputs. So that stability and approximation of the network is guaranteed. Gradient methods have been applied for parameters updating with momentum term. Quadratic cost function is used for error minimization. Three example problems have been examined in the simulation. They are static nonlinear functions and discrete dynamic nonlinear system.

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References

  1. Becerikli Y (2004) On three intelligent systems: dynamic neural, fuzzy and wavelet networks for training trajectory. Neural Comput Appl 13(4):339–351

    Google Scholar 

  2. Becerikli Y, Oysal Y, Konar AF (2003) On a dynamic wavelet network and its modeling application. Lect Notes Comput Sci (LNCS) 2714:710–718

    Google Scholar 

  3. Galvao KH, Becerra VM (2002) Linear-wavelet models for system identification. IFAC 15th Triennial World Congress, Barcelona, Spain

  4. Gutés A, Céspedes F, Cartas R, Alegret S, del Valle M, Gutierrez JM, Muñoz R (2006) Multivariate calibration model from overlapping voltammetric signals employing wavelet neural networks. Chemometrics Intell Lab Syst 83(2):169–179

    Article  Google Scholar 

  5. He Y, Chu F, Zhong B (2002) A hierarchical evolutionary algorithm for constructing and training wavelet networks. Neural Comput Appl 10:357–366

    Article  MATH  Google Scholar 

  6. Ho DWC, Zhang P-A, Xu J (2001) Fuzzy wavelet networks for function learning. IEEE Transact Fuzzy Syst 9(1):200–211

    Article  Google Scholar 

  7. Lin Y, Wang F-Y (2005) Modular structure of fuzzy system modeling using wavelet networks. In: IEEE, networking, sensing and control proceedings, Tucson, Arizona, USA, 19–22 March 2005 pp 671–676

  8. Narendra KS, Parthasaraty K (1990) Identification and control of dynamical system using neural networks. IEEE Transact Neural Netw 1(1):4–27

    Article  Google Scholar 

  9. Oussar Y, Dreyfus G (2000) Initialization by selection for wavelet network training. Neurocomputing 34:131–143

    Article  MATH  Google Scholar 

  10. Oussar Y, Rivals I, Personnaz L, Dreyfus G (1998) Training wavelet networks for nonlinear dynamic input ouput modeling. Neurocomputing 20:173–188

    Article  MATH  Google Scholar 

  11. Özkurt N, Savacı FA (2006) The implementation of nonlinear dynamical systems with wavelet network. Int J Electron Commun (AEÜ) 60:338–344

    Article  Google Scholar 

  12. Pati YC, Krishnaprasad PS (1993) Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations. IEEE Trans Neural Netw 4(1):73–85

    Article  Google Scholar 

  13. Polikar R (January 12, 2001) The wavelet tutorial. http://engineering.rowan.edu/∼polikar/WAVELETS

  14. Polycarpou M, Mears M, Weaver S (1997) Adaptive wavelet control of nonlinear systems. In: Proceedings of the 1997 IEEE conference on decision and control, pp 3890–3895

  15. Postalcıoğlu S, Erkan K, Bolat DE (2005) Comparison of wavenet and neuralnet for system modeling. Lect Notes Artif Intell 3682:100–107

    Google Scholar 

  16. Reza AM (October 19, 1999) Wavelet characteristics. White Paper, Spire Lab., UWM

  17. Shi D, Chen F, Ng GS, Gao J (2006) The construction of wavelet network for speech signal processing. Neural Comput Appl 11(34):217–222

    MATH  Google Scholar 

  18. Thuillard M (2000) Review of wavelet networks, wavenets, fuzzy wavenets and their applications. ESIT 2000, Aachen, Germany, 14–15 September 2000

  19. Zhang Q (1997) Using wavelet network in nonparametric estimation. IEEE Trans Neural Netw 8(2):227–236

    Article  Google Scholar 

  20. Zhang Q, Benveniste A (1992) Wavelet networks. IEEE Trans Neural Netw 3(6):889–898

    Article  Google Scholar 

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Correspondence to Yasar Becerikli.

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Postalcioglu, S., Becerikli, Y. Wavelet networks for nonlinear system modeling. Neural Comput & Applic 16, 433–441 (2007). https://doi.org/10.1007/s00521-006-0069-3

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  • DOI: https://doi.org/10.1007/s00521-006-0069-3

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