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

- Journal title : Transactions of the Korean Society of Mechanical Engineers B
- Volume 25, Issue 2, 2001, pp.195-201
- Publisher : The Korean Society of Mechanical Engineers
- DOI : 10.22634/KSME-B.2001.25.2.195

Title & Authors

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

An, Jung-Yong; Park, Yeong-Min; Jeong, Seong-Jong;

An, Jung-Yong; Park, Yeong-Min; Jeong, Seong-Jong;

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

Inverse Heat Problem;Model Analysis;Observer;State Space Equation;Temperature Field;

Language

Korean

Cited by

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

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

9.

Int. J. Heat and Mass Transfer, 1990.
vol.33. 7,
pp.1545-1562

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

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

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

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)

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.