THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Emiliya Dimitrova

,

Christo Boyadjiev

INCORRECT INVERSE PROBLEM SOLUTION METHOD FOR PARAMETER IDENTIFICATION OF TRANSPORT PROCESSES MODELS

ABSTRACT
A method for model parameter identification on the bases of minimization of the least square function has been proposed. An iterative regularization procedure and a numerical algorithm have been developed for incorrect (ill-posed) or essentially incorrect inverse problem solution. The method has been tested with one and two-parameter models, when the relations between objectives function and parameters are linear and non-linear. The "experimental" data for parameters identification are obtained from the model and a generator for random numbers. The effects of the initial approximations of the parameter values and the regularization parameter values have been investigated. A statistical approach has been proposed for the analysis of the model adequacy. It is demonstrated that in the cases of essential incorrectness, the least square function do not reach minima. A criterion for the incorrectness of the inverse problem was proposed.
KEYWORDS
model parameter identification, incorrect inverse problems, iterative method, regularization, model adequacy
PAPER SUBMITTED: 2005-07-09
PAPER REVISED: 2006-05-23
PAPER ACCEPTED: 2006-06-12
DOI REFERENCE: https://doi.org/10.2298/TSCI0602155D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2006, VOLUME 10, ISSUE Issue 2, PAGES [155 - 166]
REFERENCES
  1. Beck, J.V. & Aruold, K.I. (1977). Parameter Estimation in Engineering and Science. New York: J. Wiley.
  2. Beck, J.V., Blackwell, B. & St. Clair C.R. Jr. (1985). Inverse Heat Condition. Ill-posed problems. New York: J. Wiley - Interscience Publications.
  3. Glasko, V.B.(1994). Inverse Problem of Mathematical Physics, translated by Adam Bincer, AIP.
  4. Tikhonov, A.N. & Arsenin, V.I., (1986). Methods for Solutions of Incorrect Problems. Moscow: Nauka (in Russian).
  5. Tikhonov, A.N, Kal'ner, V.D. & Glasko, V.B. (1990). Mathematical Modelling of Technological Processes and Method of Inverse Problems. Moscow: Mashinostroenie (in Russian).
  6. Alifanov, O.M., Artiukhin, E.A. & Rumiantsev, C.B. (1988). Extremal Methods for Incorrect Problem Solutions. Moskow: Nauka (in Russian).
  7. Alifanov, O.M. (1994). Inverse Heat Transfer Problems. Berlin: Springer ? Verlag.
  8. Brakham, R.L. (1989). Jr. Scientific Data Analysis, Berlin: Springer-Verlag.
  9. Banks, H.T. & Kunsch, K. (1989). Estimation Techniques for Distributed Parameter Systems. Birkhauser
  10. Boyadjiev, Chr. (1993). Fundamentals of Modeling and Simulation in Chemical Engineering and Technology. Sofia: Edit. Bulg. Acad. Sci.,Inst. Chem. Eng. (in Bulgarian).
  11. Alifanov, O.M. (1974). Solution of the Inverse Heat Conduction Problems by Iterative Methods. J. Eng. Physics (Russia), 26 (4), 682-689.
  12. Alifanov, O.M. (1977). Inverse Heat Transfer Problems. J. Eng. Physics (Russia), 33 (6), 972-981.
  13. Alifanov, O.M. (1983). On the Solution Methods of the Inverse Incorrect Problems. J. Eng. Physics (Russia), 45 (5), 742-752.
  14. Alifanov, O.M. & Rumiantsev C.B. (1980). Regularization Iterative Algorithms for the Inverse Problem Solutions of the Heat Conduction. J. Eng. Physics (Russia), 39 (2), 253-252.
  15. Draper, N.R. & Smith, H. (1966). Applied Regression Analysis, New York: J. Wiley.
  16. Vuchkov, I. & Stoyanov, S. (1986). Mathematical Modelling and Optimization of Technological Objects. Sofia: Technics (in Bulgarian).
  17. Bojanov, E.S. & Vuchkov, I.N. (1973). Statistical Methods for Modelling and Optimization of Multifactor Object. Sofia: Technics (in Bulgarian).
  18. Boyadjiev, Chr. & Dimitrova, E. (2005), A iterative method for model parameter identification. 1. Incorrect problem, Computers Chem. Eng. 29 (4), 941-948.
  19. Boyadjiev, Chr. (2002), Incorrect inverse problem connected with the parameter identification of the heat and mass transfer models, Thermal Science .6 (1), 23-28.
PDF VERSION [DOWNLOAD]
Incorrect inverse problem solution method for parameter identification of transport processes models

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence