Skip to main content

Training of Neural Network Wiener Models with Recursive Prediction Error Algorithm

  • Conference paper
Neural Networks and Soft Computing

Part of the book series: Advances in Soft Computing ((AINSC,volume 19))

  • 496 Accesses

Abstract

Identification of the Wiener system consisting of a linear dynamics in series with a static nonlinearity is considered. A recursive prediction error training algorithm for a recurrent neural network Wiener model is proposed. The gradient of the model output w.r.t. parameters of its linear part is computed with the sensitivity method. The proposed algorithm has superior convergence properties in comparison with gradient methods such as the sensitivity method or the truncated backpropagation through time. Its performance is illustrated with a simulated example of a pneumatic valve.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Billings S. A, Fakhouri S. Y. (1982) Identification of systems containing linear dynamic and static nonlinear elements. Automatica. 10, 15–26.

    Article  MathSciNet  Google Scholar 

  2. Janczak A. (2001) On identification of Wiener systems based on a modified serial-parallel model. Proc. ECC’01, Porto, Portugal. 1852–1857.

    Google Scholar 

  3. Kalafatis A. D., Wang L., Cluett W. R. (1997) Identification of Wiener-type nonlinear systems in a noisy environment. Int. J. Control. 66, 923–941.

    Article  MathSciNet  MATH  Google Scholar 

  4. Marciak C., Latawiec K., Rojek R., Oliveira G. H. C. (2001) Adaptive least-squares parameter estimation of OBF-based Wiener models. Proc. 7th IEEE Conf. MMAR’2001, Migdzyzdroje, Poland. 965–969.

    Google Scholar 

  5. Pearson R. K., Pottmann M. (2000) Gray-box identification of block-oriented nonlinear models. J. Process Control. 10, 301–315.

    Article  Google Scholar 

  6. Greblicki W. (1994) Nonparametric identification of Wiener systems by orthogonal series. IEEE Trans Automat. Contr. 39, 2077–2086.

    Article  MathSciNet  MATH  Google Scholar 

  7. Greblicki W. (1997) Nonparametric approach to Wiener system identification. IEEE Trans. Circuits Syst. I. 44, 538–545.

    MathSciNet  Google Scholar 

  8. Wigren T. (1993) Recursive prediction error identification algorithm using the nonlinear Wiener model. Automatica. 29, 1011–1025.

    Article  MathSciNet  MATH  Google Scholar 

  9. Wigren T. (1994) Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model. IEEE Trans. Automat. Contr. 39, 2191 2206.

    Google Scholar 

  10. Al-Duwaish H., Karim M. N., Chandrasekar V. (1996) Use of multilayer feed-forward neural networks in identification and control of Wiener model. IEE Proc. Control Theory Appl. 143, 255–258.

    Article  MATH  Google Scholar 

  11. Janczak A. (1995) Identification of a class of nonlinear systems using neural networks. Proc. 2nd Int. Symp. MMAR’95, Migdzyzdroje, Poland. 697–702.

    Google Scholar 

  12. Janczak A. (1997) Identification of Wiener models using recurrent neural networks. Proc. 4th Int. Symp. MMAR’97, Migdzyzdroje, Poland. 727–732.

    Google Scholar 

  13. Janczak A. (1998) Recurrent neural network models for identification of Wiener systems. Proc. CESA’98 IMACS Multiconference, Nabeul-Hammamet, Tunisia. 965–970.

    Google Scholar 

  14. Billings S. A, Jamaluddin H B., Chen S. (1992) Properties of neural networks with application to modelling non-linear dynamical systems. Int. J. Control. 55, 193–224.

    Google Scholar 

  15. Chen S., Billings S. A. (1992) Neural networks for nonlinear dynamic system modellinig. Int. J. Control. 56, 319–346.

    Article  MathSciNet  MATH  Google Scholar 

  16. Norgaard M., Ravn O., Poulsen N. K., Hansen L. K. (2000) Neural Networks for Modelling and Control. Springer, London.

    Book  Google Scholar 

  17. Kaminsky P. G, Bryson A. E., Schmidt S. F. (1971) Discrete square root filtering: A survey of current techniques. IEEE Trans. Autaomat. Control. AC-16, 727–735.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Janczak, A. (2003). Training of Neural Network Wiener Models with Recursive Prediction Error Algorithm. In: Rutkowski, L., Kacprzyk, J. (eds) Neural Networks and Soft Computing. Advances in Soft Computing, vol 19. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1902-1_107

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-1902-1_107

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-0005-0

  • Online ISBN: 978-3-7908-1902-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics