The Transactions of the Korean Institute of Electrical Engineers D (대한전기학회논문지:시스템및제어부문D)

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지

Optimization of Polynomial Neural Networks: An Evolutionary Approach

다항식 뉴럴 네트워크의 최적화: 진화론적 방법

  • 김동원 (고려대학교 공과대학 전기공학과) ;
  • 박귀태 (고려대학교 공과대학 전기공학과)
  • Published : 2003.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

Evolutionary design related to the optimal design of Polynomial Neural Networks (PNNs) structure for model identification of complex and nonlinear system is studied in this paper. The PNN structure is consisted of layers and nodes like conventional neural networks but is not fixed and can be changable according to the system environments. three types of polynomials such as linear, quadratic, and modified quadratic is used in each node that is connected with various kinds of multi-variable inputs. Inputs and order of polynomials in each node are very important element for the performance of model. In most cases these factors are decided by the background information and trial and error of designer. For the high reliability and good performance of the PNN, the factors must be decided according to a logical and systematic way. In the paper evolutionary algorithm is applied to choose the optimal input variables and order. Evolutionary (genetic) algorithm is a random search optimization technique. The evolved PNN with optimally chosen input variables and order is not fixed in advance but becomes fully optimized automatically during the identification process. Gas furnace and pH neutralization processes are used in conventional PNN version are modeled. It shows that the designed PNN architecture with evolutionary structure optimization can produce the model with higher accuracy than previous PNN and other works.

Keywords

References

  1. K. J. Astrom and P. Eykhoff, 'System identification-a survey,' Automatica, Vol. 7, pp. 123-162, 1971 https://doi.org/10.1016/0005-1098(71)90059-8
  2. A. G. Ivakhnenko, 'Polynomial theory of complex systems', IEEE Trans. Syst., Man, Cybern., Vol. SMC-1, No.1, pp. 364-378, 1971
  3. A. G. Ivakhnenko and N. A. Ivakhnenko, 'Long-term prediction by GMDH algorithms using the unbiased criterion and the balance-of-variables criterion,' Sov. Automat. Contr., Vol. 7, pp. 40-45, 1974
  4. A. G. Ivakhnenko, and N. A. Ivakhnenko, 'Long-term prediction by GMDH algorithms using the unbiased criterion and the balance-of-variables criterion, part 2,' Sov. Automat. Contr., Vol. 8, pp. 24-38, 1975
  5. A. G. Ivakhnenko, V. N. Vysotskiy, and N. A. Ivakhnenko, 'Principal version of the minimum bias criterion for a model and an investigation of their noise immunity:' Sov. Automat. Contr., Vol. 11, pp. 27-45, 1978
  6. A. G. Ivakhnenko, G. I. Krotov, and N. A. Ivakhnenko, Identification of the mathematical model of a complex system by the self-organization method, in Theoretical Systems Ecology: Aduances and Case Studies, E. Halfon, Ed. New York: Academic, 1970, ch. 13
  7. S. J. Farlow, Self-Organizing Methods in Modeling, GMDH Type-Algorithms, New York: Marcel Dekker, 1984
  8. S. Barada, and H. Singh, 'Generating Optimal Adaptive Fuzzy-Neural Models of Dynamical Systems with Applications to Control,' IEEE Trans. Syst., Man, Cybern, part C, Vol. 28, No.3, pp. 371-391, 1998 https://doi.org/10.1109/5326.704574
  9. 오성권, 김동원, 박병준, '다항식 뉴럴네트워크 구조의 최적 설계에 관한 연구', Trans. KIEE, Vol. 49D, No. 3, pp. 145-156, 2000
  10. 김동원, '자기구성 다항식 뉴럴네트워크의 진화론적 설계', Master's thesis, Dept. Control Instrum., Wonkwang Univ., 2002
  11. J.H. Holland, 'Adaptation in Natural and Artificial Systems', The Univesity of Michigan Press, Ann Arbor, M.I., 1975
  12. C.T. Lin, C.P. Jou, and C.J. Lin, 'GA-based reinforecement learning for neural networks', International Journal of System Science, Vol. 29, No. 3, pp. 233-247, 1998 https://doi.org/10.1080/00207729808929517
  13. A. Homaifar and E. McCormick, 'Simulaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms', IEEE Trans. Fuzzy Syst., Vol. 3, pp. 129-139, 1995 https://doi.org/10.1109/91.388168
  14. G.E.P. Box and F.M. Jenkins, 'Time Series Analysis : Forecasting and Control', 2nd ed. Holden-day, 1976
  15. F.G. Shinskey, 'pH and pION Control in Process and Waste Streams', Wiley, New York, 1973
  16. 장병탁, '유전 알고리즘이론 및 응용', 전자공학회지, 제22권, 제11호, 1995
  17. Sung-Kwun Oh, Dong-Won Kim, Byoung- jun Park, and Hyung-Soo Hwang, 'Advanced Polynomial Neural Networks Architecture with New Adaptive Nodes', Trans. on Control, Automation and Systems Engineering, Vol. 3, No.1, pp. 43-50, 2001
  18. J. Nie, AP. Loh, C.C. Hang, 'Modeling pH neutralization processes using fuzzy-neural approaches', Fuzzy Sets Syst, Vol. 78, pp. 5-22, 1996 https://doi.org/10.1016/0165-0114(95)00118-2
  19. M. Sugeno and T. Yasukawa, 'A fuzzy-logic-based approach to qualitative modeling', IEEE Trans. Fuzzy Syst., Vol. I, No.1, pp. 7-31, 1993 https://doi.org/10.1109/TFUZZ.1993.390281
  20. W. Pedrycz, 'An identification algorithm in fuzzy relational system', Fuzzy Sets Syst., Vol. 13, pp.I53-167, 1984 https://doi.org/10.1016/0165-0114(84)90015-0
  21. J. Leski, and E. Czogala, 'A new artificial neural networks based fuzzy inference system with moving consequents in if-then rules and selected applications', Fuzzy Sets Syst., Vol. 108, 289-297, 1999 https://doi.org/10.1016/S0165-0114(97)00314-X
  22. S.J. Kang, C.H. Woo, H.S. Hwang, and K.B. Woo, Evolutionary Design of Fuzzy Rule Base for Nonlinear System Modeling and Control, IEEE Trans. Fuzzy Syst., Vol. 8, No.1, Feb., 2000 https://doi.org/10.1109/91.824766
  23. E. Kim, H. Lee, M. Park, M. Park, 'A simple identified Sugeno-type fuzzy model via double clustering,' Inf. Sci., Vol. 110, pp. 25-39, 1998 https://doi.org/10.1016/S0020-0255(97)10083-4
  24. Y. Lin, G.A Cunningham Ill, 'A new approach to fuzzy-neural modeling', IEEE Trans. Fuzzy Syst., Vol. 3, No.2, pp. 190-197, 1995 https://doi.org/10.1109/91.388173
  25. D. W. Kim, G. T. Park, 'A Design of EA-based Self-Organizing Polynomial Neural Networks using Evolutionary Algorithm for Nonlinear System Modeling', IEEE Trans. Syst. Man Cybern: Part B- Cybern. (submitted)
  26. S. K. Oh and W. Pedrycz, 'Fuzzy identification by means of auto-tuning algorithm and its application to nonlinear systems,' Fuzzy Sets and Systems, vol. 115, no. 2, pp. 205-230, 2000 https://doi.org/10.1016/S0165-0114(98)00174-2