Full Article - Open Access.

Idioma principal

A COMPARISON OF THE ITERATIVE REGULARIZATION TECHNIQUE AND OF THE MARKOV CHAIN MONTE CARLO METHOD: ESTIMATION OF THE SOURCE TERM IN A THREE-DIMENSIONAL HEAT CONDUCTION PROBLEM

Reis, Luiz Augusto D.; Orlande, Helcio R. B.; Lesnic, Daniel;

Full Article:

This work aims at the comparison between a classical regularization technique and a method within the Bayesian framework, as applied to the solution of an inverse heat con-duction problem. The two solution approaches compared are Alifanov''s iterative regulariza-tion technique and the Markov chain Monte Carlo method. The inverse problem examined in this work deals with the estimation of a transient source term in a heat conduction problem.

Full Article:

Palavras-chave: Inverse Problem, Alifanov''s iterative regularization technique, Conjugate Gradi-ent Method with Adjoint Problem, Markov chain Monte Carlo method, Heat Conduction.,

Palavras-chave:

DOI: 10.5151/meceng-wccm2012-18836

Referências bibliográficas
  • [1] Alifanov, O. M., “Inverse Heat Transfer Problems”. Springer-Verlag, New York, 1994.
  • [2] Alifanov, O. M., Mikhailov, V. V., “Solution of the nonlinear inverse thermal conduction problem by the iteration method”. J. Eng. Phys., v.35, pp. 1501-1506, 1978.
  • [3] Alifanov, O. M., “Solution of an inverse problem of heat conduction by iteration method”. J. Eng. Phys., v. 26, pp. 471-476, 1974.
  • [4] Beck, J. V., Arnold, K. J., “Parameter Estimation in Engineering and Science”. New York, Wiley Publ., 1977.
  • [5] Beck, J. V., Blackwell, B., St. Clair, C. R., “Inverse Heat Conduction: Ill-Posed Prob-lems”. New York, Wiley Interscience, 198
  • [6] Gamerman, D., Lopes, H.F., “Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference”. Chapman Andamp; Hall/CRC, 2nd edition, Boca Raton, Florida, USA, 200
  • [7] “IMSL Library”, 10 ed., NBC Bldg., 7500 Ballaire Blvd., Houston, Texas, 198
  • [8] Kaipo, J., Fox, C., “The Bayesian Framework for Inverse Problems in Heat Transfer”. Heat Transfer Eng., v. 32, pp. 718-753, 2011.
  • [9] Kaipio, J., Somersalo, E., “Statistical and Computational Inverse Problems”. Applied Mathematical Sciences 160, Springer-Verlag, 2004.
  • [10] Orlande, Helcio R. B., Colaço, Marcelo J., “Comparison of different versions of the Conjugate Gradient Method of Function Estimation”. Numerical Heat Transfer, Part A, v. 36, pp. 229-249, 1999.
  • [11] Orlande, H. R. B., Fudym, F., Maillet, D., Cotta, R., “Thermal Measurements and In-verse Techniques”. CRC Press, Boca Raton, Florida, USA, 20
  • [12] Orlande, H. R. B., “Inverse Problems in Heat Transfer: New Trends in Solution Meth-odologies and Applications”. ASME Journal of Heat Transfer, v. 134, 2012, doi: 10.1115/1.4005131.
  • [13] Özisik, M. N., “Heat Conduction”. Second Edition, New York, John Wiley Andamp; Sons, 1993.
  • [14] Ösizik, M. N., Orlande, H. R. B., “Inverse Heat Transfer: Fundamentals and Applica-tions”. New York, Taylor Andamp; Francis, 2000.
  • [15] Reis, Luiz Augusto Diogo, “Source Function Estimation in a Three-Dimensional Heat Conduction Problem”. Rio de Janeiro, COPPE / UFRJ, M.Sc., Mechanical Engineering, 2007.
  • [16] Tikhonov, A. N., Arsenin, V. Y., “Solution of Ill-Posed Problems”. Wiston Andamp; Sons, Washington, DC, 1977.
  • [17] Wang, Jiazheng, Silva Neto, Antônio J., Moura Neto, Francisco D. e Su, Jian, “Function estimation with Alifanov’s iterative regularization method in linear and nonlinear heat conduction problems”. Applied Mathematical Modelling, v. 26, pp. 1093-1111, 2002.
Como citar:

Reis, Luiz Augusto D.; Orlande, Helcio R. B.; Lesnic, Daniel; "A COMPARISON OF THE ITERATIVE REGULARIZATION TECHNIQUE AND OF THE MARKOV CHAIN MONTE CARLO METHOD: ESTIMATION OF THE SOURCE TERM IN A THREE-DIMENSIONAL HEAT CONDUCTION PROBLEM", p. 2375-2393 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18836

últimos 30 dias | último ano | desde a publicação


downloads


visualizações


indexações