147
Views
31
CrossRef citations to date
0
Altmetric
Original Articles

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

&
Pages 351-366 | Received 01 Jul 2003, Accepted 12 Jan 2004, Published online: 19 Feb 2007

References

References

  • Billings , SA , Chen , S and Korenberg , MJ . 1989 . Identification of MIMO non-linear systems using a forward regression orthogonal estimator . International Journal of Control , 49 : 2157 – 2189 .
  • Billings , SA and Coca , D . 1999 . Discrete wavelet models for identification and qualitative analysis of chaotic systems . International Journal of Bifurcation and Chaos , 9 : 1263 – 1284 .
  • Billings , SA , 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 .
  • Billings SA Leontaritis IJ 1982 Parameter estimation techniques for nonlinear systems The 6th IFAC Symposium on Identification and Systems Parameter Estimation Washington, DC, USA pp. 427–432
  • Chen , S , Billings , SA , Cowan , CFN and Grant , PW . 1990 . Nonlinear system identification using radial basis functions . International Journal of Systems Science , 21 : 2513 – 2539 .
  • Chen , S , Billings , SA and Grant , PW . 1992 . Recursive hybrid algorithm for nonlinear system identification using radial basis function network . International Journal of Control , 55 : 1051 – 1070 .
  • Chen , S , Billings , SA and Luo , W . 1989 . Orthogonal least squares methods and their application to non-linear system identification . International Journal of Control , 50 : 1873 – 1896 .
  • Chen , S , Cowan , CFN and Grant , PM . 1991 . Orthogonal least-squares learning algorithm for radial basis function networks . IEEE Transactions Neural Networks , 2 : 302 – 309 .
  • Chen , ZH . 1993 . Fitting multivariate regression functions by interaction spline models . Journal of the Royal Statistical Society, Series B (Methodological) , 55 : 473 – 491 .
  • Chui CK 1992 An Introduction to Wavelets Boston Academic Press
  • Chui , CK and Wang , JH . 1992 . On compactly supported spline wavelets and a duality principle . Transactions of the American Mathematical Society , 330 : 903 – 915 .
  • Coca , D and Billings , SA . 2001 . Non-linear system identification using wavelet multiresolution models . International Journal of Control , 74 : 1718 – 1736 .
  • Daubechies I 1992 Ten Lectures on Wavelets Philadelphia PA Society for Industrial and Applied Mathematics
  • Friedman , JH . 1991 . Multivariate adaptive regression splines . The Annals of Statistics , 19 : 1 – 67 .
  • Friedman , JH and Stuetzle , W . 1981 . Projection pursuit regression . Journal of the American Statistical Association , 76 : 817 – 823 .
  • Gorban , AN . 1998 . Approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions . Applied Mathematics Letters , 11 : 45 – 49 .
  • Hastie TJ Tibshirani RJ 1990 Generalized Additive Models London Chapman & Hall
  • Haykin S 1994 Neural Networks: A Comprehensive Foundation New York Maxwell Macmillan International
  • Hong , X and Harris , CJ . 2001 . Nonlinear model structure detection using optimum experimental design and orthogonal least squares . IEEE Transactions on Neural Networks , 12 : 435 – 439 .
  • Kavli , T . 1993 . ASMOD—An algorithm for adaptive spline modelling of observational data . International Journal of Control , 58 : 947 – 967 .
  • Korenberg , M , Billings , SA , Liu , YP and McIlroy , PJ . 1988 . Orthogonal parameter estimation algorithm for non-linear stochastic systems . International Journal of Control , 48 : 193 – 210 .
  • Leontaritis , IJ and Billings , SA . 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 .
  • Liu , GP , Billings , SA and Kadirkamnathan , V . 2000 . Nonlinear system identification using wavelet networks . International Journal of Systems Science , 31 : 1531 – 1541 .
  • Mallat , SG . 1989 . A theory for multiresolution signal decomposition: the wavelet representation . IEEE Transactions on Pattern Analysis and Machine Intelligence , 11 : 674 – 693 .
  • Pearson , RK . 1995 . Nonlinear input/output modelling . Journal of Process Control , 5 : 197 – 211 .
  • Pearson RK 1999 Discrete-time Dynamic Models Oxford Oxford University Press
  • Schumaker LL 1981 Spline Functions: Basic Theory New York Wiley
  • Wang , LX and Mendel , JM . 1992 . Fuzzy basis functions, universal approximations, and orthogonal least squares learning . IEEE Transactions on Neural Networks , 3 : 807 – 814 .
  • Wei , HL and Billings , SA . 2002 . Identification of time-varying systems using multi-resolution wavelet models . International Journal of Systems Science , 33 : 1217 – 1228 .
  • Wei HL Billings SA Balikhin MA 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
  • Wei , HL , Billings , SA and Liu , J . 2004 . Term and variable selection for nonlinear system identification . International Journal of Control , 77 : 86 – 110 .
  • Zhang , Q . 1997 . Using wavelet network in nonparametric estimation . IEEE Transactions on Neural Networks , 8 : 227 – 236 .
  • Zhang , Q and Benveniste , A . 1992 . Wavelet networks . IEEE Transactions on Neural Networks , 3 : 889 – 898 .
  • Zhu , QM and Billings , SA . 1996 . Fast orthogonal identification of nonlinear stochastic models and radial basis function neural networks . International Journal of Control , 64 : 871 – 886 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.