A Study on the Optimal Design of Polynomial Neural Networks Structure

다항식 뉴럴네트워크 구조의 최적 설계에 관한 연구

  • O, Seong-Gwon (Dept.of Electrical Electronics Engineering, Wonkwang University) ;
  • Kim, Dong-Won (Dept.of Electrical Electronics Engineering, Wonkwang University) ;
  • Park, Byeong-Jun (Dept.of Electrical Electronics Engineering, Wonkwang University)
  • Published : 2000.03.01

Abstract

In this paper, we propose a new methodology which includes the optimal design procedure of Polynomial Neural Networks(PNN) structure for model identification of complex and nonlinear system. The proposed PNN algorithm is based on GMDA(Group Method of Data handling) method and its structure is similar to Neural Networks. But the structure of PNN is not fixed like in conventional Neural Networks and can be generated. The each node of PNN structure uses several types of high-order polynomial such as linear, quadratic and cubic, and is connected as various kinds of multi-variable inputs. In other words, the PNN uses high-order polynomial as extended type besides quadratic polynomial used in GMDH, and the number of input of its node in each layer depends on that of variables used in the polynomial. The design procedure to obtain an optimal model structure utilizing PNN algorithm is shown in each stage. The study is illustrated with the aid of pH neutralization process data besides representative time series data for gas furnace process used widely for performance comparison, and shows that the proposed PNN algorithm can produce the model with higher accuracy than previous other works. And performance index related to approximation and prediction capabilities of model is evaluated and also discussed.

Keywords

References

  1. A. G. Ivahnenko, 'The group method of data handling; a rival of method of stochastic approximation', Soviet Automatic Control, 1-3, pp. 43-55, 1968
  2. Hideo Tanaka, Katsunori and Hisao Ishibuchi, 'GMDH by If-Then Rules with Certainty Factors', Fifth IFSA World Conference, pp. 802-805, 1993
  3. I. Hayashi and H. Tanaka, 'The Fuzzy GMDH algorithm by possibility models and its application', Fuzzy Sets and Systems, 36, pp. 245-258, 1990 https://doi.org/10.1016/0165-0114(90)90182-6
  4. H. R. Madala and A. G. Ivakhnenko, Inductive Learning Algorithms for Complex Systems Modeling, CRC Press, London, 1994
  5. G. E. P. Box and F. M. Jenkins, Time Series Analysis : Forecasting and Control, 2nd ed. Holden-day, 1976
  6. A. G. Ivakhnenko, G. A. Ivakhenko, andJ. A. Muller, 'self-organization of Neural Networks with Active Neurons', published in pattern Recognition and Image Anlysis, Vol. 4, No.2, pp. 185-196
  7. R. M. Tong, 'The evaluation of fuzzy models derived from experimental data', Fuzzy Sets and Systems, Vol. 13, pp. 1-12, 1980 https://doi.org/10.1016/0165-0114(80)90059-7
  8. M. Sugeno and T. Yasukawa, 'Linguistic Modeling Based on Numerical Data', IFSA'91 Brussels, Computer, Management & Systems Science, pp. 264-267, 1991
  9. C. W. Xu, and Y. Zailu, 'Fuzzy model identification self-learning for dynamic system,' IEEE Trans on Systems, Man, Cybernetics, Vol. SMC-17, No.4, pp. 683-689, 1987 https://doi.org/10.1109/TSMC.1987.289361
  10. W. Pedrycz, 'An identification algorithm in fuzzy relational system', Fuzzy Sets Syst, Vol. 13, pp. 153-167, 1984
  11. S. S. Kim, 'A Neuro-fuzzy Approach to Integration and Control of Industrial Processes: Part I', 한국 퍼지 및 지능 시스템 학회 논문집 제 8권 제6호, pp. 58-69, 1998
  12. S. K. Oh, B. J. Park, C. S. Park, The Transaction of The Korean Institute of Electrical Engineers(KIEE), Vol. 48, No. 10, Oct., 1999
  13. C. S. Park, S. K. Oh, and W. Pedrycz, 'Fuzzy Identification by means of Auto - Tuning Algorithm and Weighting Factor', The Third Asian Fuzzy Systems Symposium(AFSS), pp. 701-706, 1998
  14. S. K. Oh, and W. Pedrycz, 'Identification of Fuzzy Systems by means of an Auto-Tuning Algorithm and Its Application to Nonlinear Systems', Fuzzy Sets and Syst, 2000.(To appear)
  15. 오성권, 노석범, 황형수, '퍼지 GMDH 모델과 하수처리공정에의 응용,' 한국 퍼지 및 지능 시스템 학회 추계학술대회 논문집 제 5권 제 2호, pp. 153-158, 1995년 11월
  16. E. T. Kim, M. K. Park, S. H. Ji, M. Park, 'A New Approach to Fuzzy Modeling', IEEE Trans. on Fuzzy Systems, Vol. 5, No.3, pp. 328-337, 1997
  17. 김동원, 박병준, 오성권, 김현기, '확장된 GMDH 알고리즘에 의한 비선형 시스템의 동정', 대한전기학회 추계학술대회 논문집B, pp. 827-829, 1999년 11월
  18. 林 勳, 'GMDH', 日本 フアジイ 學會誌, Vol.7, No.2, pp.270-274, 1995
  19. 橫出 勝則, 田中 英夫, 'GMDHの 多層構造の 用いた 確信度付きの フアジイ if-then ル-ル', 日本 フアジイ學會誌, Vol. 7, No.1, pp. 131-141, 1995
  20. F. G. Shinskey, 'pH and pION Control in Process and Waste Streams', (Wiley, New York, 1973)
  21. R. C. Hall, D. E. Seberg, 'Modeling and Self-Tuning Control of a Multivariable pH Neutralization Process', Proc. ACC, pp. 1822-1827, 1989
  22. T. J. McAvoy, E. Hsu and S. Lowenthal, 'Dynamics of pH in controlled stirred tank reactor', lnd. Engrg. Chem. Process Des. Develop. 11(1972), pp. 68-70
  23. J. Nie, A. P. Loh, C. C. Hang, 'Modeling pH neutralization processes using fuzzy-neural approaches', Fuzzy Sets and Systems, pp. 5-22, 78 (1996) https://doi.org/10.1016/0165-0114(95)00118-2
  24. R. S. Sang, S. K. Oh, T. C. Ahn and K. Hur, 'A Fuzzy Model on the PNN Structure', The Third Asian Fuzzy Systems Symposium(AFSS), pp. 83-86, June, 18-21, 1998
  25. 오성권, 퍼지모델 및 제어이론과 프로그램, 기다리 출판사, 1999년 3월