Identification of time-varying systems using multiresolution wavelet models

International Journal of Systems Science

Volumn 33, Issue 15, 2002, Pages 1217-1228

  Wei, Hua Liang ^a   Billings, S A ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; LINEAR CONTROL SYSTEMS; NONLINEAR CONTROL SYSTEMS; PARAMETER ESTIMATION;

MULTIRESOLUTION WAVELET MODELS;

TIME VARYING CONTROL SYSTEMS;

EID: 0038040955     PISSN: 00207721     EISSN: None     Source Type: Journal    
DOI: 10.1080/0020772031000081982     Document Type: Article

References (41)

1. Aguirre, L. A. and Billings, S. A., 1995, Retrieving dynamical invariants from chaotic data using NARMAX models. International Journal of Bifurcation and Chaos, 5, 449-474.
2. Billings, S. A. and Voon, W. S. F., 1983, Structure detection and model validity tests in the identification of nonlinear systems. Proceedings of the Institute of Electrical Engineerings, Part D, 130, 193-199.
3. Billings, S. A. and Voon, W. S. F., 1986, Correlation based model validity tests for nonlinear models. International Journal of Control, 44, 235-244.
4. Billings, S. A. Chen, S. and Korenberg, M. J, 1989, Identification of MIMO non-linear systems suing a forward regression orthogonal estimator. International Journal of Control, 49, 2157-2189.
5. Billings, S. A. and Chen, S., 1989, Extended model set, global data and threshold model identification of severely nonlinear systems. International Journal of Control, 50, 1897-3923.
6. Billings, S. A. and Zhu, Q. M., 1994, Nonlinear model validation using correlation tests. International Journal of Control, 60, 1107-1120.
7. Billings, S. A. and Zhu, Q. M., 1995, Model validation tests for multivariable nonlinear models including neural networks. International Journal of Control, 62, 749-766.
8. Billings, S. A. and Coca, D., 1999, Discrete wavelet models for identification and qualitative analysis of chaotic systems. International Journal of Bifurcation and Chaos, 9, 1263-1284.
9. Bouzeghoub, M. C., Ellacott, S. W., Easdown, A. and Brown M., 2000, On the identification of nonstationary linear processes. International Journal of Systems Science, 31, 273-286.
10. Cakrak, F., Loughlin, P. J., 2001, Multiple window time-varying spectral analysis. IEEE Transactions on Signal Processing, 49, 448-453.
11. Chen, S. and Billings, S. A., 1989, Representation of non-linear systems: the NARMAX model. International Journal of Control, 49, 1013-1032.
12. Chen, S., Billings, S. A. and Luo, W., 1989, Orthogonal least squares methods and their application to non-linear system identification. International Journal of Control, 50, 1873-1896.
13. Cho, Y. S., Kim, S. B. and Powers E. J., 1991, Time-varying spectral estimation using AR models with variable forgetting factors. IEEE Transactions on Signal Processing, 39, 1422-1426.
14. Chowdhury, F. N., 2000, Input-output modelling of nonlinear systems with time-varying linear models. IEEE Transactions on Automatic Control, 45, 1355-1358.
15. Chui, C. K., 1992, An Introduction to Wavelets (Boston: Academic Press).
16. Chui, C. K. and Wang, J. H., 1992, On compactly supported spline wavelets and a duality principle. Transactions of the American Mathematical Society, 330, 903-915.
17. Coca, D. and Billings, S. A., 1997, Continuous-time system identification for linear and nonlinearsystems using wavelet decomposition. International Journal of Bifurcation and Chaos, 7, 87-96.
18. Coca, D., 1996, A class of wavelet multiresolution decomposition for nonlinear system identification and signal processing. PhD thesis, University of Sheffield.
19. Cooper, R. A., 1991, System-identification of human-performance models, IEEE Transactions on Systems Man and Cybernetics, 21, 244-252.
20. Daubechies, I., 1992, Ten Lectures on Wavelets (Philadelphia: Society for Industrial and Applied Mathematics).
21. Glass, J. W. and Franchek, M. A., 1999, NARMAX modelling and robust control of internal combustion engines. International Journal of Contorl, 72, 289-304.
22. Grenier, Y., 1983, Time-dependent ARMA modelling of non-stationary signals. IEEE Transactions on Signal Processing, ASSP 31, 899-911.
23. Jang, H. K. and Kim, K. J., 1994, Identification of loudspeaker non-linearities using the NARMAX modelling technique. Journal of the Audio Engineering Society, 42, 50-59.
24. Jones, D. L. and Parks, T. W., 1992, A resolution comparison of several time-frequency representations. IEEE Transactions on Signal Processing, 40, 413-420.
25. Korenberg, M., Billings, S. A., Liu, Y. P. and McIlroy P. J., 1988, Orthogonal parameter estimation algorithm for non-linear stochastic systems. International Journal of Control, 48, 193-210.
26. Kozin, F. and Nakajima, F., 1980, The order determination problem for linear time-varying AR models. IEEE Transactions on Automatic Control, AC-25, 250-257.
27. Leontaritis, I. J. and Billings, S. A., 1985, Input-output parametric models foe non-linear systems, part I: deterministic non-linear systems; part II: stochastic non-linear systems. International Journal of Control, 41, 303-344.
28. Liu, G. P., Billings, S. A. and Kadirkamnathan, V., 2000, Nonlinear system identification using wavelet networks. International Journal of Systems Science, 31, 1531-1541.
29. Mallat, S. G., 1989, A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 674-693.
30. Niedzwiecki, M., 1988, Functional series modelling approach to identification of nonstationary stochastic systems. IEEE Transactions Automatic Control, 33, 955-961.
31. Noshiro, M., Furuya, M., Linkens, D. and Goode, K., 1993, Nonlinear identification of the PCO2 control-system in man. Computer Methods and Programs in Biomedicine, 40, 189-202.
32. Potamianos, A. and Maragos, P., 2001, Time-frequency distributions for automatic speech recognition. IEEE Transactions on Speech and Audio Processing, 9, 196-200.
33. Priestley, M. B., 1988, Non-linear and Non-stationary Time Series Analysis (London: Academic Press).
34. Radhakrishnan, T. K., Sundaram, S. and Chidambaram, M., 1999, Non-linear control of continuous bioreactors. Bioprocess Engineering, 20, 173-178.
35. Sattar, F. and Salomonsson, G., 1999, The use of a filter bank and the Wigner-Ville distribution for time-frequency representation. IEEE Transactions on Signal Processing, 47, 1776-1783.
36. Sjoberg, J., Zhang, Q. H., Ljung, L., Benveniste, A., Delyon, B., Glorennec, R. Y., Hjalmarsson, H. and Juditsky, A., 1995, Nonlinear black-box modelling in system identification: a unified overview Automatica, 31, 1691-1724.
37. Sureshbabu, N. and Farrell, J. A., 1999, Wavelet-based system identification for nonlinear control. IEEE Transactions on Automatic Control, 44, 412-417.
38. Tabrizi, M. H. N., Jamaluddin, H., Billings, S. A. and Skaggs, R. W., 1990, Use of identification techniques to develop a water-table. Prediction Model Transactions of the ASAE, 33, 1913-1918.
39. Tsatsanis, M. K. and Giannakis, G. B., 1993, Time-varying system identification and model validation using wavelets. IEEE Transactions Signal Processing, 41, 3512-3523.
40. Young, P., 1994. Time variable and state dependent modelling of nonstationary and nonlinear lime series. In T. Subba Rao (ed.), Development in Time Series Analysis (London: Chapman & Hall), pp. 375-413.
41. Zhang, Q., 1997, Using wavelet networks in nonparametric estimation. IEEE Transactions on Neural Networks, 8, 227-236.