Advertisement

Real-Time Identification and Forecasting of Chaotic Time Series Using Hybrid Systems of Computational Intelligence

  • Yevgeniy Bodyanskiy
  • Vitaliy Kolodyazhniy
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 187)

Abstract

In this chapter, the problems of identification, modeling, and forecasting of chaotic signals are discussed. These problems are solved with the use of the conventional techniques of computational intelligence as radial basis neural networks and learning neuro-fuzzy architectures, as well as novel hybrid structures based on the Kolmogorov’s superposition theorem and using the neo-fuzzy neurons as elementary processing units. The need for the solution of the forecasting problem in real time poses higher requirements to the processing speed, so the considered hybrid structures can be trained with the proposed algorithms having high convergence rate and providing a compromise between the smoothing and tracking properties during the processing of nonstationary noisy signals.

Keywords

Membership Function Fuzzy System Fuzzy Rule Radial Basis Function Network Hurst Exponent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M.C. Mackey, L. Glass: Science 197, 287–289 (1977)Google Scholar
  2. 2.
    F.C. Moon: Chaotic Vibrations (Wiley, New York, 1987)Google Scholar
  3. 3.
    M.C. Mackey, L. Glass: From Clocks to Chaos. The Rhythms of Life (Princeton University Press, Princeton, NJ, 1988)Google Scholar
  4. 4.
    P. Berge, Y. Pomeau, C. Vidal: L’ordre dans le Chaos (Hermann, Paris, 1988)Google Scholar
  5. 5.
    B.B. Mandelbrot: Die fraktale Geometrie der Natur (Birkhaeuser Verlag, Basel, 1991)Google Scholar
  6. 6.
    E. Ott: Chaos in Dynamical Systems (Cambridge University Press, New York, 1993)Google Scholar
  7. 7.
    R.M. Crownower: Introduction to Fractals and Chaos (Jones and Bartlett Publishers, Boston, 1995)Google Scholar
  8. 8.
    H.I. Abarbanel, T.W. Frison, L.S Tsimring: IEEE Signal Process. Mag. N3, 49–65 (1998)CrossRefGoogle Scholar
  9. 9.
    D.A. White, D.A. Sofge (eds): Handbook of Intelligent Control Neural, Fuzzy, and Adaptive Approaches (Van Nostrand Reinhold, New York, 1992)Google Scholar
  10. 10.
    S. Abe: Neural Networks and Fuzzy Systems: Theory and Applications (Kluwer Academic Publishers, Boston, 1997)Google Scholar
  11. 11.
    Da. Ruan (ed): Intelligent Hybrid Systems: Fuzzy Logic, Neural Networks, and Genetic Algorithms (Kluwer Academic Publishers, Boston, 1997)Google Scholar
  12. 12.
    Yu. Osana, M. Hagiwara: Successive learning in heteroassociative memories using chaotic neural networks. In: Proc. IEEE Int. Joint Conf. on Neural Networks “IJCNN’98,” Anchorage, Alaska, 1998, pp 1107–1112Google Scholar
  13. 13.
    S. Haykin: Neural Networks. A Comprehensive Foundation (Prentice Hall, Upper Saddle River, NJ, 1999)Google Scholar
  14. 14.
    I. Rojas, J. Gonzalez, A. Canas, A.F Diaz, F.J. Rojas, M. Rodriguez: Int. J. Neural Syst. 10(N5), 353–364 (2000)Google Scholar
  15. 15.
    L. Ljung: System Identification—Theory for the User. 2nd edn (Prentice Hall, Upper Saddle River, NJ, 1999)Google Scholar
  16. 16.
    R. Isermann: Digitale Regelsysteme (Springer, Berlin Heidelberg New York, 1988)Google Scholar
  17. 17.
    T. Kohonen: Self-Organizing Maps (Springer, Berlin Heidelberg New York, 1995)Google Scholar
  18. 18.
    E.S. Chang, S. Chen, B. Mulgrew: IEEE Trans. Neural Networks 7, 190–194 (1996)CrossRefGoogle Scholar
  19. 19.
    S.A. Billings, X. Hong: Neural Networks 11, 479–493 (1998)CrossRefGoogle Scholar
  20. 20.
    O. Nelles, S. Ernst, R. Isermann: Automatisierungstechnik 6, 251–262 (1997)Google Scholar
  21. 21.
    Ye. Bodyanskiy, O. Chaplanov, V. Kolodyazhniy: Adaptive quadratic radial basis function network for time series forecasting. In: Proc. 10th East-West Fuzzy Colloquim, Zittau, Germany, 2002, pp 164–172Google Scholar
  22. 22.
    J. Platt: Neural Comput. 3, 213–225 (1991)MathSciNetGoogle Scholar
  23. 23.
    Ye. Bodyanskiy, V. Kolodyazhniy, A. Stephan: An adaptive learning algorithm for a neuro-fuzzy network. In: Computational Intelligence. Theory and Applications, ed by B. Reusch. Lecture Notes in Computer Science, vol 2206 (Springer, Berlin Heidelberg New York, 2001), pp 68–75Google Scholar
  24. 24.
    J.-S.R. Jang, C.-T. Sun: IEEE Trans. Fuzzy Syst. 4, 156–159 (1993)Google Scholar
  25. 25.
    S. Chiu: J. Intelligent Fuzzy Syst. 2, 267–278 (1994)MathSciNetGoogle Scholar
  26. 26.
    S. Horikawa, T. Furuhashi, Y. Uchikawa: IEEE Trans. Neural Networks 3, 801–860 (1992)CrossRefGoogle Scholar
  27. 27.
    J.-S. R. Jang, C.-T. Sun, E. Mizutani: Neuro-Fuzzy and Soft Computing—A Computational Approach to Learning and Machine Intelligence (Prentice Hall, Upper Saddle River, NJ, 1997)Google Scholar
  28. 28.
    C.-T. Lin, C.S.G. Lee: IEEE Trans. on Comput. 40, 1320–1336 (1991)CrossRefMathSciNetGoogle Scholar
  29. 29.
    J.-S. R. Jang: IEEE Trans. Syst. Man, Cybern. 23, 665–685 (1993)CrossRefGoogle Scholar
  30. 30.
    J.-S. R. Jang: Neuro-Fuzzy Modeling: Architectures, Analyses, and Applications, Ph.D. Dissertation, EECS Department, University of California at Berkeley (1992)Google Scholar
  31. 31.
    C.-F. Juang, C.-T. Lin: IEEE Trans. Fuzzy Syst. 6, 12–32 (1998)CrossRefGoogle Scholar
  32. 32.
    D.E. Rumelhart, G.R. Hinton, R.J. Williams: Learning internal representation by error propagation. In: Parallel Distributed Processing, ed by D.E. Rumelhart, J.L. McClelland (MIT Press, Cambridge, MA, 1986), pp 318–364Google Scholar
  33. 33.
    L.-X. Wang, J.M. Mendel: Back-propagation fuzzy systems as nonlinear dynamic system identifiers. In: Proc. 1st IEEE Int. Conf. on Fuzzy Systems, 1992, pp 1409–1416Google Scholar
  34. 34.
    B. Kosko: Fuzzy systems as universal approximators. In: Proc. 1st IEEE Int. Conf. on Fuzzy Systems, San Diego, CA, 1992, pp 1153–1162Google Scholar
  35. 35.
    V. Kreinovich, G.C. Mouzouris, H.T. Nguyen: Fuzzy rule based modeling as a universal approximation tool. In: Fuzzy Systems: Modeling and Control, ed by H.T. Nguyen, M. Sugeno (Kluwer Academic Publishers, Boston, 1998), pp 135–195Google Scholar
  36. 36.
    L.-X. Wang: Fuzzy systems are universal approximators. In: Proc. 1st IEEE Int. Conf. Fuzzy Systems, San Diego, CA, 1992), pp 1163–1170Google Scholar
  37. 37.
    T. Takagi, M. Sugeno: IEEE Trans. Syst., Man, Cybern. 15, 116–132 (1985)Google Scholar
  38. 38.
    H. Ying: IEEE Trans. Fuzzy Syst. 6, 582–587 (1998)CrossRefGoogle Scholar
  39. 39.
    H. Ying: IEEE Trans. Syst., Man, Cybern. 28, 515–520 (1998)CrossRefGoogle Scholar
  40. 40.
    L.A. Zadeh: Fuzzy Sets, Inf. Control 8, 338–353 (1965)zbMATHMathSciNetGoogle Scholar
  41. 41.
    L.H. Tsoukalas, R.E. Uhrig: Fuzzy and Neural Approaches in Engineering (Wiley-Interscience, New York, 1997)Google Scholar
  42. 42.
    J.C. Bezdek: Pattern Recognition with Fuzzy Objective Function Algorithms (Plenum, New York, 1981)Google Scholar
  43. 43.
    B. Fritzke: Incremental neuro-fuzzy systems. In: Proc. SPIE’s Optical Science, Engineering and Instrumentation’ 97: Applications of Fuzzy Logic Technology IV, San Diego, CA, 1997Google Scholar
  44. 44.
    Q. Song, N. Kasabov: Dynamic evolving neural-fuzzy inference system (DENFIS): On-line learning and application for time-series prediction. In: Proc. 6th Int. Conf. on Soft Computing, Iizuka, Fukuoka, Japan, 2000, pp 696–701Google Scholar
  45. 45.
    A.J. Shepherd: Second-Order Methods for Neural Networks: Fast and Reliable Training Methods for Multi-Layer Perceptrons (Springer-Verlag, London, 1997)Google Scholar
  46. 46.
    H. Hartley: Technometrics 3, 269–280 (1961)zbMATHMathSciNetGoogle Scholar
  47. 47.
    D.W. Marquardt: SIAM J. Appl. Math. 11, 431–441 (1963)CrossRefzbMATHMathSciNetGoogle Scholar
  48. 48.
    P. Otto, Ye. Bodyanskiy, V. Kolodyazhniy: Integrated Computer-Aided Eng. 10, 399–409 (2003)Google Scholar
  49. 49.
    B. Widrow, M.E. Hoff: IRE Western Electric Show and Convention Record Part 4, 96–104 (1960)Google Scholar
  50. 50.
    D. Nauck, R. Kruse: A neuro-fuzzy approach to obtain interpretable fuzzy systems for function approximation. In: Proc. IEEE Int. Conf. on Fuzzy Systems, 1998, pp 1106–1111Google Scholar
  51. 51.
    D. Nauck: A fuzzy perceptron as a generic model for neuro-fuzzy approaches. In: Proc. 2nd German GI-Workshop Fuzzy-Systeme’94, Munich, Germany, 1994Google Scholar
  52. 52.
    T. Yamakawa, E. Uchino, T. Miki, H. Kusanagi: A neo-fuzzy neuron and its applications to system identification and prediction of the system behavior. In: Proc. 2nd Int. Conf. on Fuzzy Logic and Neural Networks “IIZUKA-92,” Iizuka, Japan, 1992, pp 477–483Google Scholar
  53. 53.
    T. Miki, T. Yamakawa: Analog implementation of neo-fuzzy neuron and its on-board learning. In: Computational Intelligence and Applications, ed by N.E. Mastorakis (WSES Press, Piraeus, 1999), pp 144–149Google Scholar
  54. 54.
    A.N. Kolmogorov: Dokl. Akad. Nauk SSSR 114, 953–956 (1957)zbMATHMathSciNetGoogle Scholar
  55. 55.
    R. Hecht-Nielsen: Kolmogorov’s mapping neural network existence theorem. In: Proc. IEEE Int. Conf. on Neural Networks, San Diego, CA, 1987, vol 3, pp 11–14Google Scholar
  56. 56.
    D.A. Sprecher: Neural Networks 9, 765–772 (1996)CrossRefGoogle Scholar
  57. 57.
    D.A. Sprecher: Neural Networks 10, 447–457 (1997)CrossRefGoogle Scholar
  58. 58.
    B. Igelnik, N. Parikh: IEEE Trans. Neural Networks 14, 725–733 (2003)CrossRefGoogle Scholar
  59. 59.
    Y. Yam, H.T. Nguyen, V. Kreinovich: Multi-resolution techniques in the rules-based intelligent control systems: A universal approximation result. In: Proc. 14th IEEE Int. Symp. on Intelligent Control/Intelligent Systems and Semiotics ISIC/ISAS’99, Cambridge, MA, Sept. 15–17, 1999, pp 213–218Google Scholar
  60. 60.
    A. Lopez-Gomez, S. Yoshida, K. Hirota: Int. J. Fuzzy Syst. 4, 690–695 (2002)MathSciNetGoogle Scholar
  61. 61.
    V. Kolodyazhniy, Ye. Bodyanskiy: Universal approximators employing neo-fuzzy neurons. In: Proc. 8th Fuzzy Days, Dortmund, Germany, 2004 [CD-ROM]Google Scholar
  62. 62.
    V. Kolodyazhniy, Ye. Bodyanskiy: Fuzzy neural networks with Kolmogorov’s structure. In: Proc. 11th East-West Fuzzy Colloquium, Zittau, Germany, 2004, pp 139–146Google Scholar
  63. 63.
    V. Kolodyazhniy, Ye. Bodyanskiy: Fuzzy Kolmogorov’s network. In: Proc. 8th Int. Conf. Knowledge-Based Intelligent Information and Engineering Systems International (KES 2004), Wellington, New Zealand, 2004, pp 764–771Google Scholar
  64. 64.
    A. Albert: Regression and the Moore-Penrose Pseudoinverse (Academic, New York, 1972)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yevgeniy Bodyanskiy
  • Vitaliy Kolodyazhniy

There are no affiliations available

Personalised recommendations