This article presents a new method of estimation of thermophysical parameters using the hybrid Monte Carlo (HMC) algorithm that synergistically combines the advantages of a Markov chain Monte Carlo (MCMC) method and molecular dynamics. The advantages of this technique over the conventional MCMC are elucidated by considering the multiparameter estimation in heat transfer. Four situations were analyzed. The first two involve a two- and a three-parameters estimation in a lumped capacitance model, third involves estimation in a distributed system, and the fourth involves estimation in a fin system. The goal is to establish the potency and usefulness of the HMC method for a wide class of engineering problems.
Issue Section:
Heat and Mass Transfer
References
1.
Vairaktaris
, E.
, 2010
, “Inverse Problems in Geomechanics
,” Eur. J. Environ. Civ. Eng.
, 14
(8–9
), pp. 1155
–1166
.2.
Kroon
, M.
, and Holzapfel
, G. A.
, 2007
, “A Model for Saccular Cerebral Aneurysm Growth by Collagen Fibre Remodelling
,” J. Theor. Biol.
, 247
(4
), pp. 775
–787
.3.
Issartel
, J.-P.
, Sharan
, M.
, and Modani
, M.
, 2007
, “An Inversion Technique to Retrieve the Source of a Tracer With an Application to Synthetic Satellite Measurements
,” Proc. R. Soc. London Ser. A
, 463
(2087
), pp. 2863
–2886
.4.
Balaji
, C.
, Konda Reddy
, B.
, and Herwig
, H.
, 2013
, “Incorporating Engineering Intuition for Parameter Estimation in Thermal Sciences
,” Heat Mass Transfer
, 49
(12
), pp. 1771
–1785
.5.
Gnanasekaran
, N.
, and Balaji
, C.
, 2011
, “A Bayesian Approach for the Simultaneous Estimation of Surface Heat Transfer Coefficient and Thermal Conductivity From Steady State Experiments on Fins
,” Int. J. Heat Mass Transfer
, 54
(13–14
), pp. 3060
–3068
.6.
Link
, W. A.
, Cam
, E.
, Nichols
, J. D.
, and Cooch
, E. G.
, 2002
, “Of Bugs and Birds: Markov Chain Monte Carlo for Hierarchical Modeling in Wildlife Research
,” J. Wildl. Manage.
, 66
(2
), pp. 277
–291
.7.
Sun
, L.
, Wang
, Q.
, and Zhan
, H.
, 2013
, “Likelihood of the Power Spectrum in Cosmological Parameter Estimation
,” Astrophys. J.
, 777
(1
), pp. 1
–6
.8.
Orlande
, H. R. B.
, Dulikravich
, G. S.
, and Colaco
, M. J.
, 2008
, “Application of Bayesian Filters to Heat Conduction Problem
,” International Conference on Engineering Optimization (EngOpt
), Rio de Janeiro, Brazil, June 1–5, pp. 1
–12
.9.
Orlande
, H. R. B.
, 2012
, “Inverse Problems in Heat Transfer: New Trends on Solution Methodologies and Applications
,” ASME J. Heat Transfer
, 134
(3), pp. 1
–13
.10.
Howell
, J. R.
, Ezekoye
, O. A.
, and Morales
, J. C.
, 2000
, “Inverse Design Model for Radiative Heat Transfer
,” ASME J. Heat Transfer
, 122
(3
), pp. 492
–502
.11.
Addepalli
, B.
, Sikorski
, K.
, Pardyjak
, E. R.
, and Zhdanov
, M. S.
, 2011
, “Source Characterization of Atmospheric Releases Using Stochastic Search and Regularized Gradient Optimization
,” Inverse Probl. Sci. Eng.
, 19
(8
), pp. 1097
–1124
.12.
Parthasarathy
, S.
, and Balaji
, C.
, 2008
, “Estimation of Parameters in Multi-Mode Heat Transfer Problems Using Bayesian Inference—Effect of Noise and a Priori
,” Int. J. Heat Mass Transfer
, 51
(9
), pp. 2313
–2334
.13.
Metropolis
, N.
, Rosenbluth
, A. W.
, Rosenbluth
, M. N.
, Teller
, A. H.
, and Teller
, E.
, 1953
, “Equation of State Calculations by Fast Computing Machines
,” J. Chem. Phys.
, 21
(6
), pp. 1087
–1092
.14.
Duane
, S.
, Kennedy
, A. D.
, Pendleton
, B. J.
, and Roweth
, D.
, 1987
, “Hybrid Monte Carlo
,” Phys. Lett. B
, 195
(2
), pp. 216
–222
.15.
Cheung
, S. H.
, and Beck
, J. L.
, 2009
, “Bayesian Model Updating Using Hybrid Monte Carlo Simulation With Application to Structural Dynamic Models With Many Uncertain Parameters
,” J. Eng. Mech.
, 135
(4
), pp. 243
–255
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