Controlling chaotic convection using neural nets - Theory and experiments

Neural Networks

Volumn 11, Issue 3, 1998, Pages 557-569

  Yuen, Po Ki ^a   Bau, Haim H ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Chaos; Control; Flow; Neural networks; Thermal convection; Thermosyphons

Indexed keywords

CHAOS THEORY; MATHEMATICAL MODELS; PATTERN RECOGNITION; PERFORMANCE; TIME SERIES ANALYSIS;

LOGISTIC EQUATION; LORENZ EQUATION; THERMOSYPHONS;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; CHAOTIC DYNAMICS; CONTROL SYSTEM; FLOW; PRIORITY JOURNAL; PROCESS CONTROL; THERMODYNAMICS;

EID: 0142080784     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-6080(98)00006-9     Document Type: Article

References (38)

1. Albano A.M., Passamante A., Hediger T., Farrell M.E. Using neural nets to look for chaos. Physica D. 58:1992;1-9.
2. Bau H.H., Torrance K.E. Transient and steady behavior of an open, symmetrically-heated, free convection loop. Int. J. Heat Mass Transfer. 24:1981;597-609.
3. Bau, H.H., Wang, Y.-Z., 1991. Chaos: a Heat Transfer Perspective. In Tien, C.L. (Ed.), Annual Reviews in Heat Transfer, IV. Hemisphere, Washington, D.C., pp. 1-50.
4. Choi H., Moin P., Kim J. Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mechanics. 262:1994;75-110.
5. Ehrhard P., Müller U. Dynamical behavior of natural convection in a single-phase loop. J. Fluid Mechanics. 217:1990;487-518.
6. Gad-el-Hak M. Interactive control of turbulent boundary layers: a futuristic overview. AIAA J. 32:1994;1753-1765.
7. Gorman M., Widmann P.J., Robbins K.A. Chaotic flow regimes in a convection loop. Physical Review Letters. 52:1984;2241-2244.
8. Gorman M., Widmann P.J., Robbins K.A. Nonlinear dynamics of a convection loop: a quantitative comparison of experiment with theory. Physica. 19D:1986;255-267.
9. Hart J.E. A new analysis of the closed loop thermosyphon. Int. J. Heat Mass Transfer. 27:1984;125-136.
10. Hart J.E. A note on the loop thermosyphon with mixed boundary conditions. Int. J. Heat Mass Transfer. 28:1985;939-947.
11. Hu H.H., Bau H.H. Feedback control to delay or advance linear loss of stability in planar Poiseuille flow. Proceedings Royal Society A. 447:1994;299-312.
12. Jacobson, S.A., Reynolds, W.C., 1995. An experimental investigation towards the active control of turbulent boundary layers. Report No TF-64, Thermosciences Division, Department of Mechanical Engineering, Stanford University, Stanford, CA.
13. Lapedes, A., Farber, R., 1987. Los Alamos National Laboratory Technical Report No. LAUR-87-2662.
14. Lorenz E.N. Deterministic nonperiodic flow. J. of the Atmospheric Sciences. 20:1963;130-141.
15. e serie, tome IV, 125-128.
16. Moin P., Bewley T. Feedback control of turbulence. App. Mechanics Review. 47:1994;S3-S13.
17. Moore, K.L., 1993. Iterative Learning Control for Deterministic Systems. Springer, London.
18. Navone H.D., Ceccatto H.A. Learning chaotic dynamics by neural networks. Chaos, Solitons and Fractals. 6:1995;382-387.
19. Omatu, S., Khalid, M., Yusof, R., 1996. Neuro-Control and its Applications. Springer, London.
20. Psaltis, D., Sideris, A., Yamamura, A., 1987. Neural controllers. In Proc. of IEEE 1st International Conference on Neural Networks, 4, pp. 551-558, San Diego, USA.
21. Robbins K.A. A new approach to subcritical instability and turbulent transitions in a simple dynamo. Math. Proc. Camb. Phil. Soc. 82:1977;309-325.
22. Rumelhart, D.E., McClelland, J.L., PDP Research Group (1986), 1988. Parallel Distributed Processing: Explorations in the Microstructure of Cognition, 1, a Bradford Book. MIT Press, Cambridge, MA.
23. Rumelhart, D.E., Hinton, G.E., Williams, R.J., 1986. Learning internal representations by error propagation. In Rumelhart, D.E., McClelland, J.L. (Eds.), Parallel Distributed Processing: Explorations in the Microstructure of Cognition, 1. MIT Press, Cambridge, MA, pp. 318-362.
24. Saerens, M., Soquet, A., 1991. Neural controller based on back-propagation algorithm. IEE Proc.-F, 138, 1, 55-62 (reprint from Artificial Neural Networks: Concepts and Control Applications, 1992, by V. Rao Vemuri, IEE Computer Society Press, pp. 484-491).
25. Singer J., Wang Y.-Z., Bau H.H. Controlling a chaotic system. Physical Review Letters. 66:1991;1123-1126.
26. Singer J., Bau H.H. Active control of convection. Physics of Fluids A. 3:1991;2859-2865.
27. Sparrow, C., 1982. The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Springer, New York.
28. Tang, J., 1996. Active control of Rayleigh-Bénard convection. Ph.D. thesis, University of Pennsylvania.
29. Tang J., Bau H.H. Stabilization of the no-motion state in Rayleigh-Bénard convection through the use of feedback control. Physical Review Letters. 70:1993;1795-1798.
30. Tang J., Bau H.H. Feedback control stabilization of the no-motion state of a fluid confined in a horizontal, porous layer heated from below. J. Fluid Mechanics. 257:1993;485-505.
31. Tang J., Bau H.H. Stabilization of the no-motion state in the Rayleigh-Bénard problem. Proceedings Royal Society A. 447:1994;587-607.
32. Tang J., Bau H.H. Stabilization of the no-motion state of a horizontal fluid layer heated from below with Joule heating. Trans. ASME-J. Heat Transfer. 117:1995;329-333.
33. Tang, J., Bau, H.H., 1997. Experiments on the stabilization of the no-motion state of a fluid layer heated from below and cooled from above. J. Fluid Mechanics (to appear).
34. Wang Y.-Z., Singer J., Bau H.H. Controlling chaos in a thermal convection loop. J. Fluid Mechanics. 237:1992;479-498.
35. Widmann P.J., Gorman M., Robbins K.A. Nonlinear dynamics of a convection loop II: chaos in laminar and turbulent flows. Physica D. 36:1989;157-166.
36. Yorke A., Yorke E.D., Mallet-Paret J. Lorenz-like chaos in partial differential equation. Physica. 24D:1987;279-291.
37. Yuen, P.K., 1997. Dynamics and control of flow in a thermal convection loop. Ph.D. thesis, University of Pennsylvania.
38. Yuen P.K., Bau H.H. Rendering a subcritical Hopf bifurcation supercritical. J. Fluid Mechanics. 317:1996;91-109.