Abstract
In this study, we investigated modeling performances of two popular nonlinear system identification methods, namely fuzzy modeling and Volterra series. In literature a general approach to nonlinear structure modeling does not exist, therefore both fuzzy models and Volterra series are interesting and widely used as they can approximate a large class of nonlinear functions. In fuzzy modeling, a dynamic system is modeled using a set of fuzzy membership functions and rules. The fuzzy model parameters are trained using optimization techniques. In Volterra series approach, the dynamic system is modeled using a set of kernel functions that represent the first and higher order convolutions. The kernel functions are typically estimated using an orthogonal expansion technique using a set of suitable basis functions such as Laguerre. We compared the modeling performance of these approaches on a hypothetical test system whose kernels or structure is known priori and observed that the Volterra modeling based on Laguerre basis expansion of kernels offers better performance.
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References
Westwick, D.T., Kearney, R.E.: Identification of Nonlinear Physiological Systems. IEEE Biomedical Engineering Book Series, IEEE Press/Wiley, (2003)
Asyali, M.H., Juusola, M.: Use of the Meixner functions in estimation of Volterra kernels of nonlinear systems with delay. IEEE Transactions on Biomedical Engineering, 52(2), 229–237 (2005)
Sjoberg, J., Zhang, Q., Ljung, L., et al.: Nonlinear black-box modeling in system identification: a unified overview. Automatica, 31(12), 1691–1724 (1995)
Marmarelis, V.Z.: Identification of nonlinear biological system using Laguerre expansions of kernels. Ann. Biomed. Eng., 21(6), 573–589 (1993)
Lee, C.C.: Fuzzy logic in control systems: fuzzy logic control parts I and II. IEEE Transactions on System, Man, and Cybernetics, 20(2), 404–435 (1990)
Leu, Y.G., Lee, T.T., Wang, W.Y.: Online tuning of fuzzy-neural network for adaptive control of nonlinear dynamical systems. IEEE Trans. on System, Man and Cybernetics, 27(6), 1034–1043 (1997)
Wang, L.X.: Adaptive Fuzzy Systems and Control: Design and Stability Analysis. PTR Prentice Hall Inc., Englewood Cliffs (NJ) (1994)
Wang, L.X.: A Course in Fuzzy Systems and Control. Prentice Hall Inc., Upper Saddle River (NJ) (1997)
Karatepe, E., Alci, M.: A new approach to fuzzy-wavelet system modeling. International Journal of Approximate Reasoning, 40(3), 302–322 (2005)
Barron, A., Rissanen, J., Yu, B.: The minimum description length principle in coding and modeling. IEEE Trans. Information Theory, 44(6), 2743–2760 (1998)
Rissanen, J.: Universal coding, information, prediction, and estimation. IEEE Trans. Information Theory, 30, 629–636 (1984)
Lagarias, J.C., Reeds, J.A., Wright, M. H., Wright, P.E.: Convergence properties of the Nelder-Meads Simplex method in low dimensions. SIAM Journal of Optimization, 9, 112–147 (1998)
Schetzen, M.: The Volterra and Wiener Theory of the Nonlinear Systems. Wiley and Sons, New York (1980)
Chon, K.H., Holstein-Rathlou, N.-H., Marsh, D.J., Marmarelis, V.Z.: Comparative Nonlinear Modeling of Renal Autoregulation in Rats: Volterra Approach Versus Artificial Neural Networks. IEEE Transactions On Neural Networks, 9(3), 430–435 (1998)
Stegmayer, G.: Neural-based Identification for Nonlinear Dynamic Systems, CIMSA 2005-Proc. of IEEE International Conference on Computational Intelligence for Measurement Systems and Applications (Giardini Naxos, Italy), ISBN 0-7803-9026-1, (2005)
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Asyali, M.H., Alci, M. (2007). Comparison of fuzzy and Volterra series nonlinear system modeling approaches. In: TaÅŸ, K., Tenreiro Machado, J.A., Baleanu, D. (eds) Mathematical Methods in Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5678-9_29
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DOI: https://doi.org/10.1007/978-1-4020-5678-9_29
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