Wavelet based non-parametric NARX models for nonlinear input-output system identification

International Journal of Systems Science

Volumn 37, Issue 15, 2006, Pages 1089-1096

  Wei, H L ^a   Billings, S A ^a   Balikhin, M A ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Additive models; NARX model; Non parametric; Nonlinear system identification; Wavelets

Indexed keywords

LEAST SQUARES APPROXIMATIONS; NONLINEAR SYSTEMS; REGRESSION ANALYSIS; WAVELET ANALYSIS;

ADDITIVE MODELS; MULTIRESOLUTION EXPANSIONS; NONLINEAR SYSTEM IDENTIFICATION; ORTHOGONAL FORWARD REGRESSION (OFR) APPROACH;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 33750295196     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720600903011     Document Type: Article

References (29)

1. S.A. Billings and S. Chen, "The determination of multivariable nonlinear models for dynamic systems using neural networks", in Neural Network Systems Techniques and Applications CT. Leondes, Ed., San Diego: Academic Press, 1998, pp. 231-278.
2. S.A. Billings, S. Chen and M.J. Korenberg, "Identification of MIMO non-linear systems using a forward regression orthogonal estimator", Int. J. Control, 49, pp. 2157-2189, 1989.
3. S.A. Billings and. D. Coca, "Discrete wavelet models for identification and qualitative analysis of chaotic systems", Int. J. Bifurcation and Chaos, 9, pp. 1263-1284, 1999.
4. S.A. Billings and H.L. Wei, "A new class of wavelet networks for nonlinear system identification", IEEE Trans. Neural Networks, 16, pp. 862-874, 2005.
5. S. Chen, S.A. Billings and W. Luo, "Orthogonal least squares methods and their application to non-linear system identification", Int. J. Control, 50, pp. 1873-1896, 1989.
6. S. Chen, S.A. Billings, C.F.N. Cowan and. P.W. Grant, "Nonlinear system identification using radial basis functions", Int. J. Systems Sci., 21, pp. 2513-2539, 1990.
7. S. Chen, S.A. Billings and P.W. Grant, "Recursive hybrid algorithm for nonlinear system identification using radial basis function network", Int. J. Control., 55, pp. 1051-1070, 1992.
8. S. Chen, X. Hong and C.J. Harris, "Sparse kernel density construction using orthogonal forward regression with, leave-one-out test score and local regularization", IEEE Trans. Sys. Man Cybern. Part B, 34, pp. 1708-1717, 2004.
9. C.K. Chui, An Introduction to Wavelets, Boston: Academic Press, 1992, pp. 1-266.
10. J.H. Friedman, and W. Stuetzle, "Projection pursuit regression", J. American Statistical Association, 76, pp. 817-823, 1981.
11. J.H. Friedman, "Multivariate adaptive regression splines", Ann. Statistics, 19, pp. 1-67, 1991.
12. C.J. Harris, X. Hong and Q. Gan, Adaptive Modelling, Estimation and Fusion from Data: A. Neurofuzzy Approach, Berlin, London: Springer-Verlag, 2002, pp. 1-323.
13. T.J. Hastie and R.J. Tibshirani, Generalized additive models, London: Chapman & Hall, 1990, pp. 1-335.
14. S. Haykin, Neural networks: a comprehensive foundation, New York: Maxwell Macmillan International, 1994, pp. 156-317 and 732-789.
15. X.D. He and H. Asada, "A new method for identifying orders of input-output models for nonlinear dynamic Systems",
16. in Proceedings of the American Control Conference, San Francisco, pp. 2520-2523, June 1993.
17. X. Hong, M. Brown, S. Chen and C.J. Harris, "Sparse model identification using orthogonal forward regression with basis pursuit and D-optimality", IEE Proc. Control Theory and Applications, 151, pp. 491-498, 2004.
18. I.J. Leontaritis and S.A. Billings, "Input-output parametric models for non-linear systems", Int. J. Control, 41, pp. 303-344, 1985.
19. G. Li, C. Rosenthal and H. Rabitz, "High dimensional model representation", J. Physical Chemistry, 105, pp. 7765-7777, 2001.
20. G.P. Liu, Nonlinear Identification and Control: A Neural Network Approach, London: Springer, 2001, pp. 1-210.
21. G.G. Lorentz, M. Golitschek and Y. Makovoz, Constructive approximation, New York: Springer, 1996, pp. 1-649.
22. S.G. Mallat, "A theory for multiresolution signal decomposition: the wavelet representation", IEEE Trans. Pattern Anal. Machine Intell., 11, pp. 674-693, 1989.
23. K.P. Pearson, "Nonlinear input/output modelling", J. Process Control, 5, pp. 197-211, 1995.
24. R. Savit and M. Green, "Time series and dependent variables", Physica D, 50, pp. 95-116, 1991.
25. G. Schwarz, "Estimating the dimension of a model", The Annals of Statistics, 6, pp. 461-464, 1978.
26. C.J. Stone, "Additive regression and other nonparametric models", The Annals of Statistics, 13, pp. 689-795, 1985.
27. H. L. Wei, S.A. Billings and J. Liu, "Term and variable selection for nonlinear system, identification", Int. J. Control, 77, pp. 86-110, 2004.
28. H. L. Wei and S.A. Billings, "A. unified wavelet-based modelling framework for nonlinear system, identification: the WANARX model structure", Int. J. Control, 11, pp. 351-366, 2004.
29. Q.H. Zhang, "Using wavelet network, in nonparametric estimation", IEEE Trans. Neural Networks, 8, pp. 227-236, 1997.