A unified wavelet-based modelling framework for non-linear system identification: The WANARX model structure

International Journal of Control

Volumn 77, Issue 4, 2004, Pages 351-366

  Wei, H L ^a   Billings, S A ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DATA REDUCTION; ERROR ANALYSIS; MATHEMATICAL MODELS; MULTIVARIABLE CONTROL SYSTEMS; POLYNOMIALS; PROBLEM SOLVING; REGRESSION ANALYSIS; THEOREM PROVING;

ANALYSIS OF VARIANCE (ANOVA); ERROR REDUCTION RATIO (ERR); KOLMOGOROV THEOREM;

NONLINEAR SYSTEMS;

EID: 2342418631     PISSN: 00207179     EISSN: None     Source Type: Journal    
DOI: 10.1080/0020717042000197622     Document Type: Article

References (34)

1. BILLINGS, S. A., CHEN, S., and KORENBERG, M. J., 1989, Identification of MIMO non-linear systems using a forward regression orthogonal estimator. International Journal of Control, 49, 2157-2189.
2. 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.
3. BILLINGS, S. A., KORENBERG, M., and CHEN, S., 1988, Identification of nonlinear output-affine systems using an orthogonal least-squares algorithm. International Journal of Systems Science, 19, 1559-1568.
4. BILLINGS, S. A., and LEONTARITIS, I. J., 1982, Parameter estimation techniques for nonlinear systems. The 6th IFAC Symposium on Identification and Systems Parameter Estimation, Washington, DC, USA, pp. 427-432.
5. CHEN, S., BILLINGS, S. A., COWAN, C. F. N., and GRANT, P. W., 1990, Nonlinear system identification using radial basis functions. International Journal of Systems Science, 21, 2513-2539.
6. CHEN, S., BILLINGS, S. A., and GRANT, P. W., 1992, Recursive hybrid algorithm for nonlinear system identification using radial basis function network. International Journal of Control, 55, 1051-1070.
7. 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.
8. CHEN, S., COWAN, C. F. N., and GRANT, P. M., 1991, Orthogonal least-squares learning algorithm for radial basis function networks. IEEE Transactions Neural Networks, 2, 302-309.
9. CHEN, Z. H., 1993, Fitting multivariate regression functions by interaction spline models. Journal of the Royal Statistical Society, Series B (Methodological), 55, 473-491.
10. CHUI, C. K., 1992, An Introduction to Wavelets (Boston: Academic Press).
11. 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.
12. COCA, D., and BILLINGS, S. A., 2001, Non-linear system identification using wavelet multiresolution models. International Journal of Control, 74, 1718-1736.
13. DAUBECHIES, I., 1992, Ten Lectures on Wavelets (Philadelphia, PA: Society for Industrial and Applied Mathematics).
14. FRIEDMAN, J. H., 1991, Multivariate adaptive regression splines. The Annals of Statistics, 19, 1-67.
15. FRIEDMAN, J. H., and STUETZLE, W., 1981, Projection pursuit regression. Journal of the American Statistical Association, 76, 817-823.
16. GORBAN, A. N., 1998, Approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their super-positions. Applied Mathematics Letters, 11, 45-49.
17. HASTIE, T. J., and TIBSHIRANI, R. J., 1990, Generalized Additive Models (London: Chapman & Hall).
18. HAYKIN, S., 1994, Neural Networks: A Comprehensive Foundation (New York: Maxwell Macmillan International).
19. HONG, X., and HARRIS, C. J., 2001, Nonlinear model structure detection using optimum experimental design and orthogonal least squares. IEEE Transactions on Neural Networks, 12, 435-439.
20. KAVLI, T., 1993, ASMOD - An algorithm for adaptive spline modelling of observational data. International Journal of Control, 58, 947-967.
21. 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.
22. LEONTARITIS, I. J., and BILLINGS, S. A., 1985, Input-output parametric models for non-linear systems (part I: deterministic non-linear systems; part II: stochastic non-linear systems). International Journal of Control, 41, 303-344.
23. LIU, G. P., BILLINGS, S. A., and KADIRKAMNATHAN, V., 2000, Nonlinear system identification using wavelet networks. International Journal of Systems Science, 31, 1531-1541.
24. MALLAT, S. G., 1989, A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 674-693.
25. PEARSON, R. K., 1995, Nonlinear input/output modelling, Journal of Process Control, 5, 197-211.
26. PEARSON, R. K., 1999, Discrete-time Dynamic Models (Oxford: Oxford University Press).
27. SCHUMAKER, L. L., 1981, Spline Functions: Basic Theory (New York: Wiley).
28. WANG, L. X., and MENDEL, J. M., 1992, Fuzzy basis functions, universal approximations, and orthogonal least squares learning. IEEE Transactions on Neural Networks, 3, 807-814.
29. WEI, H. L., and BILLINGS, S. A., 2002, Identification of time-varying systems using multi-resolution wavelet models. International Journal of Systems Science, 33, 1217-1228.
30. WEI, H. L., BILLINGS, S. A., and BALIKHIN, M. A., 2003, Wavelet-based nonparametric models for nonlinear input-output system identification. In Proceedings of Annual Conference of Chinese Automation and Computer Society in the United Kingdom, 20-25, Beijing, P.R. China, Sep., 2002.
31. WEI, H. L., BILLINGS, S. A., and LIU, J., 2004, Term and variable selection for nonlinear system identification. International Journal of Control, 77, 86-110.
32. ZHANG, Q., 1997, Using wavelet network in nonparametric estimation. IEEE Transactions on Neural Networks, 8, 227-236.
33. ZHANG, Q., and BENVENISTE, A., 1992, Wavelet networks. IEEE Transactions on Neural Networks, 3, 889-898.
34. ZHU, Q. M., and BILLINGS, S. A., 1996, Fast orthogonal identification of nonlinear stochastic models and radial basis function neural networks. International Journal of Control, 64, 871-886.