Issue
Korean Journal of Chemical Engineering,
Vol.17, No.6, 696-703, 2000
Hybrid Neural Network Approach in Description and Prediction of Dynamic Behavior of Chaotic Chemical Reaction Systems
A chaotic system with available prior knowledge is identified with both the sequential hybrid neural network and the standard Artificial Neural Network (ANN). The identified models are validated with phase portrait, return map, the largest Lyapunov exponent and correlation dimension instead of using Sum of Square Errors (SSE). Interpolation and Extrapolation capability of the models ate compared. This is demonstrated for nonisothermal, irreversible, first-order, series reaction A-->B-->C in a CSTR.
[References]
  1. Abarbanel HDI, Brown R, Sidorowich JJ, Tsimring LS, Rev. Mod. Phys., 65(4), 1331, 1993
  2. Adomaitis RA, Farber RM, Hudson JL, Kevrekidis IG, Kube M, Lapedes AS, "Application of Neural Nets to System Identification and Bifurcation Analysis of Real World Experimental Data," In: Neural Networks: Biological Computers of Electronic Brains, Springer Verlag, Paris, 87, 1990
  3. Aguirre LA, Billings SA, Int. J. Bifurcation Chaos, 4(1), 109, 1994
  4. Casdagli M, Physica D, 35, 335, 1989
  5. Doedel EJ, "AUTO: Software for Continuation and Bifurcation Problems in Ordinary Differential Equations," AUTO 86 User Manual, CALTECH, 1986
  6. Farmer JD, Ott E, Yorke JA, "The Dimensions of Chaotic Attractors," Physica 7D, 153, 1983
  7. Giona M, Lentini F, Cimagalli V, Phys. Rev., A, 44, 3496, 1991
  8. Grassberger P, Procaccia I, Physica D, 9, 189, 1983
  9. Grassberger P, Schreiber T, Schaffrath C, Int. J. Bifurcation Chaos, 1(3), 521, 1991
  10. Jordan MI, Rumelhart DE, Cognitive Sci., 16, 307, 1992
  11. Kahlert C, Rossler OE, Varma A, Springer Ser. Chem. Phys., 18, 355, 1981
  12. Kim HJ, "Identification and Validation of Neural Network Models for Chaotic Chemical Reaction Systems," M.S. Thesis, Pohang University of Science and Technology, Korea, 1998
  13. Kim HJ, Chang KS, Comput. Chem. Eng., submitted, 1998
  14. Kim HJ, Lee JS, Han C, Chang KS, "Chaos and Fractals in Process Systems Engineering," Proceedings of the Forty-first Annual Meeting of the ISSS, Seoul, 1997
  15. Packard NH, Crutchfield JP, Farmer JD, Shaw RS, Phys. Rev. Lett., 45(9), 712, 1980
  16. Parker TS, Chua LO, "Practical Numerical Algorithms for Chaotic Systems," Springer-Verlag, 1989
  17. Principe JC, Rathie A, Kuo JM, Int. J. Bifurcation Chaos, 2(4), 989, 1992
  18. Psaltis D, Sideris A, Yamamura AA, IEEE Cont. Syst. Mag., 4(17), 1988
  19. Psichogios DC, Ungar LH, AIChE J., 38(10), 1499, 1992
  20. Rand DA, Young LS, "Dynamical Systems and Turbulence," Springer Verlag (Berlin), 366, 1981
  21. Roux JC, Simoyi RH, Swinney HL, "Observation of a Strange Attractor," Physica 8D, 257, 1983
  22. Rumelhart D, Hinton G, Williams R, "Learning Internal Representations by Error Propagation," Parallel Distributed Processing: Explorations in the Microstructures of Cognition: 1. Foundation, MIT Press, 1986
  23. Sauer T, Yorke JA, Casdagli M, J. Stat. Phys., 65(3-4), 579, 1991
  24. Seydel R, "From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis," Elsevier, New York, 1988
  25. Takens F, "Detecting Strange Attractors in Turbulence," in Lecture Notes in Mathematics, vol. 898 eds
  26. Thompson ML, Kramer MA, AIChE J., 40(8), 1328, 1994
  27. Wolf A, Swift JB, Swinney HL, Vastano JA, "Determining Lyapunov Exponents from a Time Series," Physica 16D, 285, 1985