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Identification of non-linear systems by using wavelet expansions

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper addresses the problem of identification of nonlinear characteristics of systems from a class of complex block-oriented dynamic systems. Non-linearities are recovered from the noisy input-output measurements. Wavelet functions with compact supports (Daubechies wavelets) are used in the identification algorithms. Convergence of the algorithms is shown and the asymptotic convergence rates (true for a number of measurements tending to infinity) are given. These theoretical results are supplemented by a set of numerical experiments in which performance of the algorithms is additionally tested for small and moderate number of measurements.
Rocznik
Strony
47--66
Opis fizyczny
Bibliogr. 37 poz.
Twórcy
autor
  • Institute of Engineering Cybernetics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, 50-370 Wrocław, Poland
  • Institute of Engineering Cybernetics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, 50-370 Wrocław, Poland
Bibliografia
  • [1] Akay M.: Wavelets in biomedical engineering, Annals of Biomedical Engineering, 1995, Vol.23, pp.531-542.
  • [2] Białasiewicz J. T.: Falki i aproksymacje, Wydawnictwa Naukowo-Techniczne, Warszawa, 2000 (in Polish).
  • [3] Billings S. A.: Identification of non-linear systems-а survey, 1980, Proceedings IEE, Vol.127, pp.272-285.
  • [4] Billings S. A., Fakhouri S. Y.: Identification of systems containing linear dynamic and static non-linear elements, 1982, Automatica, Vol.18, pp. 15-26.
  • [5] Daubechies I.: Ten Lectures on Wavelets, Philadelphia, SIAM Edition, 1992.
  • [6] Eskinat E., Johnson S. H., Luyben W. L.: Use of Hammerstein models in identification of non-linear systems, American Institute of Chemical Engineers Journal, 1991, Vol.37, pp.255-268.
  • [7] Greblicki W.: Nonparametric orthogonal series identification of Hammerstein systems, International Journal of Systems Science, 1991, Vol.20, pp.2355-2367.
  • [8] Greblicki W.: Nonparametric identification of Wiener systems, IEEE Transactions on Information Theory, 1992, Vol.38, pp.1487-1493.
  • [9] Greblicki W.: Nonparametric approach to Wiener system identification, IEEE Transactions on Circuits and Systems - 1: Fundamental Theory and Applications, 1997, Vol.44, pp.538-545.
  • [10] Greblicki W., Hasiewicz Z.: Wavelet identification of Wiener systems, Proceedings of 4th International Conference MMAR-1997, 1997, Międzyzdroje, Poland, pp.323-328.
  • [11] Greblicki W., Pawlak M.: Fourier and Hermite series estimates of regression function, Annals of The Institute of Statistical Mathematics, 1985, Vol.37, pp.443-455.
  • [12] Greblicki W., Pawlak M.: Identification of discrete Hammerstein system using kernel regression estimates, IEEE Transactions on Automatic Control, 1986, Vol.31, pp.74-77.
  • [13] Greblicki W., Pawlak M.: Cascade nonlinear system identification by nonparametric method, International Journal of Systems Science, 1994, Vol.25, pp. 129-153.
  • [14] Greblicki W., Śliwiński P.: Orthogonal series algorithms to identify Hammerstein systems. Proceedings of 7th IEEE International Conference MMAR-2001, 2001, pp.1009-1014, Międzyzdroje, Poland.
  • [15] Haal C. F., Hall E. L.: A non-linear model for the spatial characteristics of the human vision system, IEEE Transactions on Systems, Man, and Cybernetics, 1977, Vol.7, pp.161-170.
  • [16] Hasiewicz Z.: Hammerstein system identification by the Haar multiresolution approximation, International Journal of Adaptive Control and Signal Processing, 1999, Vol.13, pp.691-717.
  • [17] Hasiewicz Z.: Modular neural networks for non-linearity recovering by the Haar approximation, Neural Networks, 2000, Vol.13, pp.l 107-1133.
  • [18] Hasiewicz Z.: Non-parametric estimation of non-linearity in a cascade time series system by multiscale approximation, Signal Processing, 2001, Vol.81, pp.791-807.
  • [19] Hasiewicz Z., Greblicki W.: Non-linearity recovering with the help of wavelets, Proceedings of European Conference ECC'99, 1999, [available on CD-ROM], Karlsruhe, Germany.
  • [20] Hasiewicz Z., Śliwiński P.: Non-linearity recovering by wavelets of compact support, Proceedings of the 1st International Conference ICSES-2000, 2000, Vol.l, pp.213-218, Ustroń, Poland.
  • [21] Hasiewicz Z., Śliwiński P.: Linear and thresholded wavelet estimates in system identification, Proceedings of 7th IEEE International Conference MMAR-2001, 2001, pp.1015-1020, Międzyzdroje, Poland.
  • [22] Hasiewicz Z., Śliwiński P.: Identification of Non-Linear Characteristics for a Class of Block-Oriented Complex Systems via Daubechies Wavelet-Based Models, 2000, submitted to International Journal of Systems Science.
  • [23] Hardie W., Kerkyacharian G., Picard D., Tsybakov A.: Wavelets, Approximation, and Statistical Applications, Springer, New York, 1998.
  • [24] Huebner W. P., Saidel G. M., Leigh R. J.: Nonlinear parameter estimation applied to a model of smooth pursuit of eye movements, 1990, Biological Cybernetics, Vol.62, pp.265-273.
  • [25] Kelly S., Kon M., Raphael L.: Pointwise convergence of wavelet expansions, Bull. Amer. Math. Soc, 1994, Vol.30, pp.87-94,
  • [26] Mallat S. G.: A Wavelet Tour of Signal Processing, San Diego, Academic Press, 1998
  • [27] Miller J. H., Thomas J. B.: Detectors for discrete-time signals in non-gaussian noise, IEEE Transactions on Information Theory, 1972, Vo. 18, pp.241-250.
  • [28] Ogden R. T.: Essential Wavelets for Statistical Applications and Data Analysis, Birkhâuser, Boston, 1997.
  • [29] Pawlak M., Hasiewicz Z.: Non-linear system identification by the Haar multiresolution analysis, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1998, Vol.45, pp.945-961.
  • [30] Pawlak M., Hasiewicz Z.: Non-parametric system identification of non-linear block-oriented systems by multi-scale expansions, Proceedings of European Conference ECC'99, 1999, [available on CD-ROM], Karlsruhe, Germany.
  • [31] Skoczowski S.: Identification and control of electroheating processes, Proceeding of XIII National Conference KKA’99, 1999, pp.323-331.
  • [32] Stone R.: Optimal rates of convergence for nonparametric regression, Annals of Statistics, 1980, Vol.8, pp.1348-1360.
  • [33] Śliwiński P.: Non-linear system identification using wavelet algorithms, Doctor Dissertation, Institute of Engineering Cybernetics, Wroclaw University of Technology, Wroclaw, 2000.
  • [34] Śliwiński P.: Fast wavelet algorithm for non-linear system identification. Proceedings of 6th International Conference MMAR-2000, 2000, pp.945-950, Międzyzdroje, Poland.
  • [35] Śliwiński P.: A wavelet-based non-parametric algorithm for Hammerstein system identification. Proceedings of 7th IEEE International Conference MMAR-2001, 2001, pp.971-976, Międzyzdroje, Poland.
  • [36] Wojtaszczyk P.: A Mathematical Introduction to Wavelets, Cambridge University Press, Cambridge, 1997 (also available in Polish: Teoria falek. Wydawnictwo Naukowe PWN, Warszawa 2000).
  • [37] Zi-Qiang L.: A nonparametric polynomial identification algorithm for the Hammerstein system, IEEE Transactions on Automatic Control, 1997, Vol.42, pp.1435-1441.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD7-0028-0003
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