Skip to main content
Springer Nature Link
Log in

RETRACTED ARTICLE: Nonlinear dynamic systems identification based on dynamic wavelet neural units

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

This article was retracted on 01 February 2011

This article was retracted on 01 February 2011

Abstract

In this paper, a dynamic wavelet network (DWN) is proposed and applied to identify black box models of the process. The well-known delta-rule is extended to the dynamic delta-rule in order to optimize wavelet network parameters. A chemical process was chosen as a realistic nonlinear system to demonstrate the identification performance. A comparison was made between the approach presented in this paper and dynamic multi layer perceptron neural networks.

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

Access this article

Log in via an institution

Subscribe and save

Springer+
from $39.99 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Explore related subjects

Discover the latest articles, books and news in related subjects, suggested using machine learning.

References

  1. Narendra KS, Parthasarathy K (1990) Identification and control of dynamical systems using neural networks. IEEE Trans Neural Netw 1(1):4–27

    Article  Google Scholar 

  2. Nerrand O, Roussel-Ragot P, Personnaz L, Dreyfus G (1993) Neural networks and nonlinear adaptive filtering: unifying concepts and new algorithms. Neural Comput 5(2):165–199

    Article  Google Scholar 

  3. Levin AU (1992) Neural networks in dynamical systems; a system theoretic approach. Ph.D. Thesis, Yale University, New Haven

  4. Rivals I, Personnaz L (1996) Black box modeling with state-space neural networks. In: Zbikowski R, Hunt KJ (eds) Neural adaptive control technology I. World Scientific, Singapore, pp 237–264

    Google Scholar 

  5. Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Control Signals Syst 2:303–314

    Article  MathSciNet  MATH  Google Scholar 

  6. Al Seyab RK, Cao Y (2008) Nonlinear system identification for predictive control using continuous time recurrent neural networks and automatic differentiation. J Process Control 18(6):568–581

    Article  Google Scholar 

  7. Hornik K, Stinchcombe M, White H, Auer P (1994) Degree of approximation results for feedforward networks approximating unknown mappings and their derivatives. Neural Comput 6(6):1262–1275

    Article  MATH  Google Scholar 

  8. Fang Y, Chow TWS (2006) Wavelets based neural network for function approximation, advances in neural networks, book chapter. Springer, Heidelberg, pp 80–85

  9. Gao X (2002) A comparative research on wavelet neural networks. In: Proceedings of the 9th international conference on neural information processing, vol 4, pp 1699–1703, 18–22 Nov 2002

  10. Zhang Q, Benveniste A (1992) Wavelet Networks. IEEE Trans Neural Netw 3(6):889–898

    Article  Google Scholar 

  11. Pati YC, Krishnaprasad PS (1993) Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations. IEEE Trans Neural Netw 4:73–85

    Article  Google Scholar 

  12. Hong J (1992) Identification of stable systems by wavelet transform and artificial neural networks. Ph.D. dissertation, University Pittsburgh, PA

  13. Bakshi BR, Stephanopoulos G (1993) Wave-net: a multi resolution hierarchical neural network with localized learning. Am Inst Chem Eng J 39:57–81

    Google Scholar 

  14. Tsatsanis MK, Giannakis GB (1993) Time-varying system identification and model validation using wavelets. IEEE Trans Signal Process 41:3512–3523

    Article  MATH  Google Scholar 

  15. Kreinovich V, Sirisaengtaksin O, Cabrera S (1994) Wavelet neural networks are asymptotically optimal approximators for functions of one variable. In: Proceedings/IEEE international conference neural networks, Orlando, FL, pp 299–304

  16. Delyon B, Juditsky A, Benveniste A (1995) Accuracy analysis for wavelet approximations. IEEE Trans Neural Netw 6:332–348

    Article  Google Scholar 

  17. Gubta MM, Jin L, Homma N (2003) Static and dynamic neural networks: from fundamentals to advanced theory. Wiley-IEEE Press, New York

    Book  Google Scholar 

  18. Ayoubi M (1994) Nonlinear dynamic systems identification with dynamic neural networks for fault diagnosis in technical protests. In: IEEE international conference systems man and Cyberntics SMC’94 USA, pp 2120–2125

  19. Abiyev RH (2003) Fuzzy wavelet neural network for control of dynamic plants. Int J Comput Intell 1(2):139–143

    Google Scholar 

  20. Widrow B, Holt M (1960) Adaptive switching circuits. IRE WESCON convention record. New York, pp 96–104

  21. Henson M, Seborg D (1990) Input-output linearization of general nonlinear processes AIChE J 1753–1757

  22. Lightbody G, Irwin G (1997) Nonlinear control structures based on embedded neural system models. IEEE Trans Neural Netw 8:553–567

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Faculty of Sciences, University M’hamed Bougara, Boumerdès, Algeria

    L. Saad Saoud

  2. Department of Electronic, Faculty of Engineering, University Ferhat Abbas, Sétif, Algeria

    A. Khellaf

Authors
  1. L. Saad Saoud
    View author publications

    Search author on:PubMed Google Scholar

  2. A. Khellaf
    View author publications

    Search author on:PubMed Google Scholar

Corresponding author

Correspondence to L. Saad Saoud.

Additional information

This article has been retracted due to plagiarism.

An erratum to this article can be found at http://dx.doi.org/10.1007/s00521-011-0520-y

About this article

Cite this article

Saad Saoud, L., Khellaf, A. RETRACTED ARTICLE: Nonlinear dynamic systems identification based on dynamic wavelet neural units. Neural Comput & Applic 19, 997–1002 (2010). https://doi.org/10.1007/s00521-010-0438-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-010-0438-9

Keywords