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Real Time Estimation in 1-Dimensional Temperature Distribution Using Modal Analysis and Observer

모드해석과 관측기를 이용한 1차원 온도분포의 실시간 예측

  • Published : 2001.02.01

Abstract

An inverse heat conduction problem(IHCP) arises when unknown heat fluxes and whole temperature field are to be found with temperature measurements of a few points. In this paper, observers are proposed as solution algorithm for the IHCP. A 1-dimensional heat transfer problem is modeled with modal analysis and state space equations. Position of the heat source is estimated through test heat inputs and the autocorrelation among a few of temperature data. The modified Bass-Gura method is used to design a state observer to estimate the intensity of heat source and the whole temperature field of a 1-dimensional body. To verify the reliability of this estimator, analytic solutions obtained from the proposed method are compared.

Keywords

References

  1. Bass, B. R. and Ott, L. J., 1980, Numerical Methods for Nonlinear Problems, Pineridge Press, Swansea, England, pp. 649-661
  2. Blum, J. and Marquardt, W., 1997, 'An Optimal solution to Inverse Heat Conduction Problems Based On Frequency-Domain Interpretation and Observers,' Numerical Heat Transfer(B), Vol. 32, pp. 453-478 https://doi.org/10.1080/10407799708915019
  3. Beck, J. V., Blackwell, B., and Clair, C. St., 1985, Inverse Heat Conduction. Ill-Posed Problems, John Wiley, New York
  4. Deuflhard, P. and Hairer, E., 1983, Numerical treatment of Inverse Problems in Differential and Integral Equations, Birkhauser, Boston
  5. Tikhonov, A. N. and Arsenin, V. Y., 1977, Solution of Ill-posed Problems, Winston, Washington, DC.
  6. Hensel, E. and Hills, R. G., 1986, 'An initial value approach to the inverse heat conduction problem,' Trans. ASME J. Heat Transfer, Vol. 108, pp. 248-256
  7. El Bagdouri, M. and Jarny, Y., 1986, 'Optimal Boundary Control of a Thermal System. Inverse Conduction Problems,' Prepr. 4th IFAC Symp.(Control of Distributed Parameter Systems), Los Angels, California
  8. Park, H. M. and Lee, J. H., 1998, 'A Method of solving Inverse Convection Problems by Means of Mode Reduction,' Chemical Engineering Science, Vol. 53, No. 9, pp. 1731-1744 https://doi.org/10.1016/S0009-2509(98)00024-4
  9. Int. J. Heat and Mass Transfer v.33 no.7 An Observer-based solution of Inverse Heat Conduction Problems Marquardt, W.;Auracher, H.
  10. Marquardt, W. and Auracher, H., 1990, 'An Observer-based solution of Inverse Heat Conduction Problems,' Int. J. Heat and Mass Transfer, Vol. 33, No. 7, pp. 1545-1562 https://doi.org/10.1016/0017-9310(90)90050-5
  11. Ji, C. C., Tuan, P. C., and Jang, H. Y., 1997, 'A Recursive Least-squares Algorithm for on-line 1-D Inverse Heat Conduction Estimation,' Int. J. Heat and Mass Transfer, Vol. 40, No. 9, pp. 2081-2096 https://doi.org/10.1016/S0017-9310(96)00289-X
  12. Tandy, D. F., Trujillo, D. M. and Busby, H. R., 1986, 'Solution of Inverse Heat Conduction Problems using an Eigenvalue Reduction Technique,' Numerical Heat Transfer, Vol. 10, pp. 597-617 https://doi.org/10.1080/10407788608913538
  13. Silva Neto, A. J. and Ozisik, M. N., 1993, 'Simultaneous Estimation of Location and Timewisevarying strength of A plane Heat Source,' Numerical Heat Transfer, Vol. 24, pp. 467-477 (in Japanese) https://doi.org/10.1080/10407789308902635
  14. Bendat, J. S., Piersol, A. G., 1991, Random Data(Analysis and Measurement Procedure) 2nd Ed. John Wiley & Sons
  15. Friedland, B., 1987, Control System Design (An Introduction to State-Space Methods), 2nd Ed. McGraw-Hill, John Wiley & Sons, Inc.