Skip to main content
SpringerLink
Log in

Reconstruction of heat transfer coefficients using the approach of stage-by-stage suboptimal optimization and Huber-Tikhonov filtering of input data

  • Published:
Automatic Control and Computer Sciences Aims and scope Submit manuscript

Abstract

The problem of the identification of time-dependent heat transfer coefficients in the initial-boundary-value problem for the nonlinear heat conduction equation is studied. An approach is proposed based on the stage-by-stage suboptimal optimization of the cost functional and input data filtering using the Huber-Tikhonov functional. Results are presented for the numerical modeling of the identification problem in conditions of both standard noisy data and noise emissions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Beck, J.V., Blackwell, B., and St. Clair, Jr., C.R., Inverse Heat Conduction: Ill-Posed Problems, New York: Wiley, 1985.

    MATH  Google Scholar 

  2. Ozisik, M.N. and Orlande, H.R.B., Inverse Heat Transfer: Fundamentals and Applications, New York: Tailor and Francis, 2000.

    Google Scholar 

  3. Alifanov, O.M., Inverse Heat Transfer Problems, Berlin: Springer-Verlag, 1994.

    Book  MATH  Google Scholar 

  4. Xiong, X.T., Liu, X.H., Yan, Y.M., and Guo, H.B., A numerical method for identifying heat transfer coefficient, Appl. Mathem. Model., 2010, vol. 34, no. 7, pp. 1930–1938.

    Article  MATH  MathSciNet  Google Scholar 

  5. Borukhov, V.T., Kostyukova, O.I., and Kurdina, M.A., Tracking of the preset program of weighted temperatures and reconstruction of heat transfer coefficients, J. Eng. Phys. Thermophys., 2010, vol. 83, no. 3, pp. 622–631.

    Article  Google Scholar 

  6. Borukhov, V.T. and Kostyukova, O.I., Identification of time-dependent coefficients of heat transfer by the method of suboptimal stage-by-stage optimization, Int. J. Heat and Mass Transfer, 2013, vol. 59, pp. 286–294.

    Article  Google Scholar 

  7. Borukhov, V.T., Zayats, G.M., Stetsenko, V.Yu., and Konovalov, R.B., Determination of heat transfer coefficients during solidification of casting in a jet crystallizer, J. Eng. Phys. Thermophys., 2012, vol. 85, no. 1, pp. 195–202.

    Article  Google Scholar 

  8. Alifanov, O.M., Identifikatsiya protsessov teploobmena letatel’nykh apparatov (vvedenie v teoriyu obratnykh zadach) (Identification of Heat Transfer Processes of Aircrafts (Introduction to the Theory of Inverse Problems)), Moscow: Mashinostroenie, 1979.

    Google Scholar 

  9. Eppler, K. and Troltzsch, F., Fast solution of optimal control problems in the selective cooling of steel, Z. Angew. Math. Mech., 2001, vol. 81, pp. 447–456.

    Google Scholar 

  10. Huber, P.J., Robust estimation of a location parameter, Annals Math. Stat., 1964, vol. 35, no. 1, pp. 73–101.

    Article  MATH  Google Scholar 

  11. Tikhonov, A.N. and Arseninv, E.A., Solution of Ill-Posed Problems, Washington: Winston, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Belarussian National Academy of Sciences, ul. Surganova 11, 220072, Minsk, Belarus

    V. T. Borukhov & O. I. Kostyukova

Authors
  1. V. T. Borukhov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. I. Kostyukova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. T. Borukhov.

Additional information

Original Russian Text © V.T. Borukhov, O.I. Kostyukova, 2013, published in Avtomatika i Vychislitel’naya Tekhnika, 2013, No. 6, pp. 5–17.

About this article

Cite this article

Borukhov, V.T., Kostyukova, O.I. Reconstruction of heat transfer coefficients using the approach of stage-by-stage suboptimal optimization and Huber-Tikhonov filtering of input data. Aut. Control Comp. Sci. 47, 289–299 (2013). https://doi.org/10.3103/S0146411613060047

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0146411613060047

Keywords

Search

Navigation