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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
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.
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.
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DOI: 10.5151/meceng-wccm2012-18836
Referências bibliográficas
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- [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, 1985.
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- [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, 2011.
- [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 23580828,
DOI 10.5151/meceng-wccm2012-18836
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TY - CONF T1 - 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 JO - Blucher Mechanical Engineering Proceedings VL - 1 IS - 1 SP - 2375 EP - 2393 PY - 2014 T2 - 10th World Congress on Computational Mechanics AU - , , SN - 23580828 DO - http://dx.doi.org/10.5151/meceng-wccm2012-18836 UR - www.proceedings.blucher.com.br/article-details/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-9169 KW - ER -
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@article{Reis20144,
title="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",
journal="Blucher Mechanical Engineering Proceedings",
volume="1",
number="1",
pages="2375 - 2393",
year="2014",
note="",
issn="23580828",
doi="http://dx.doi.org/10.5151/meceng-wccm2012-18836",
url="www.proceedings.blucher.com.br/article-details/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-9169",
author="Luiz Augusto D. Reis", "Helcio R. B. Orlande", "Daniel Lesnic",
keywords="",
}
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Luiz Augusto D. Reis, Helcio R. B. Orlande, Daniel Lesnic, 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, Blucher Mechanical Engineering Proceedings, Volume 1, 2014, Pages 2375-2393, ISSN 23580828, http://dx.doi.org/10.5151/meceng-wccm2012-18836 (www.proceedings.blucher.com.br/article-details/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-9169) Palavras-chave:: ;