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Multi-step ahead nonlinear identification of Lorenz’s chaotic system using radial basis neural network with learning by clustering and particle swarm optimization

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  • Guerra, Fábio A.
  • Coelho, Leandro dos S.

Abstract

An important problem in engineering is the identification of nonlinear systems, among them radial basis function neural networks (RBF-NN) using Gaussian activation functions models, which have received particular attention due to their potential to approximate nonlinear behavior. Several design methods have been proposed for choosing the centers and spread of Gaussian functions and training the RBF-NN. The selection of RBF-NN parameters such as centers, spreads, and weights can be understood as a system identification problem. This paper presents a hybrid training approach based on clustering methods (k-means and c-means) to tune the centers of Gaussian functions used in the hidden layer of RBF-NNs. This design also uses particle swarm optimization (PSO) for centers (local clustering search method) and spread tuning, and the Penrose–Moore pseudoinverse for the adjustment of RBF-NN weight outputs. Simulations involving this RBF-NN design to identify Lorenz’s chaotic system indicate that the performance of the proposed method is superior to that of the conventional RBF-NN trained for k-means and the Penrose–Moore pseudoinverse for multi-step ahead forecasting.

Suggested Citation

  • Guerra, Fábio A. & Coelho, Leandro dos S., 2008. "Multi-step ahead nonlinear identification of Lorenz’s chaotic system using radial basis neural network with learning by clustering and particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 967-979.
  • Handle: RePEc:eee:chsofr:v:35:y:2008:i:5:p:967-979
    DOI: 10.1016/j.chaos.2006.05.077
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    References listed on IDEAS

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    1. Bai, Yanping & Jin, Zhen, 2005. "Prediction of SARS epidemic by BP neural networks with online prediction strategy," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 559-569.
    2. Fotsin, H.B. & Woafo, P., 2005. "Adaptive synchronization of a modified and uncertain chaotic Van der Pol-Duffing oscillator based on parameter identification," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1363-1371.
    3. Yang, Hong Ying & Ye, Hao & Wang, Guizeng & Khan, Junaid & Hu, Tongfu, 2006. "Fuzzy neural very-short-term load forecasting based on chaotic dynamics reconstruction," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 462-469.
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    Cited by:

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    2. Janmenjoy Nayak & Bighnaraj Naik, 2018. "A Novel Honey-Bees Mating Optimization Approach with Higher order Neural Network for Classification," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 511-548, October.
    3. Ait Maatallah, Othman & Achuthan, Ajit & Janoyan, Kerop & Marzocca, Pier, 2015. "Recursive wind speed forecasting based on Hammerstein Auto-Regressive model," Applied Energy, Elsevier, vol. 145(C), pages 191-197.
    4. Sangiorgio, Matteo & Dercole, Fabio, 2020. "Robustness of LSTM neural networks for multi-step forecasting of chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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