This paper deals with the solution of an inverse heat conduction problem, aiming at the identification of the interface thermal contact conductance, which can be directly associated to the quality of the adhesion between layers of multilayered composite materials. The inverse problem is solved within the Bayesian framework, with a Markov chain Monte Carlo method. A total variation prior is used for the spatially distributed contact conductance. The feasibility of the approach is evaluated with simulated temperature measurements for cases with contact failures of different sizes.
Issue Section:
Conduction
References
1.
Gay
, F.
, Hoa
, S.
, and Tsai
, S.
, 2003
, Composite Materials Design and Application
, CRC Press
, Boca Raton, FL
.2.
Beck
, J. V.
, Blackwell
, B.
, and St. Clair
, C. R.
, 1985
, Inverse Heat Conduction: Ill-Posed Problems
, Wiley Interscience
, New York
.3.
Tikhonov
, A. N.
, and Arsenin
, V. Y.
, 1977
, Solution of Ill-Posed Problems
, Winston & Sons
, Washington, DC
.4.
Beck
, J. V.
, and Arnold
, K. J.
, 1977
, Parameter Estimation in Engineering and Science
, Wiley Interscience
, New York
.5.
Alifanov
, O. M.
, 1994
, Inverse Heat Transfer Problems
, Springer-Verlag
, New York
.6.
Woodbury
, K.
, 2002
, Inverse Engineering Handbook
, CRC Press
, Boca Raton, FL
.7.
Kaipio
, J.
, and Somersalo
, E.
, 2004
, “Statistical and Computational Inverse Problems
,” Applied Mathematical Sciences, Vol. 160
, Springer-Verlag
, New York
.8.
Ozisik
, M. N.
, and Orlande
, H. R. B.
, 2000
, Inverse Heat Transfer: Fundamentals and Applications
, Taylor and Francis
, New York
.9.
Tan
, S.
, Fox
, C.
, and Nicholls
, G.
, 2006
, Inverse Problems (Course Notes for Physics, Vol. 707), University of Auckland
, Auckland, New Zealand
.10.
Orlande
, H.
, Fudym
, F.
, Maillet
, D.
, and Cotta
, R.
, 2011
, Thermal Measurements and Inverse Techniques
, CRC Press
, Boca Raton, FL
.11.
Cotta
, R. M.
, 1990
, “Hybrid Numerical-Analytical Approach to Nonlinear Diffusion Problems
,” Numer. Heat Transfer, Part B
, 127
, pp. 217
–226
.10.1080/1040779900896174012.
Cotta
, R. M.
, 1993
, Integral Transforms in Computational Heat and Fluid Flow
, CRC Press
, Boca Raton, FL
.13.
Cotta
, R. M.
, 1984
, “Benchmark Results in Computational Heat and Fluid Flow: The Integral Transform Method
,” Int J. Heat Mass Transfer
, 37
(Suppl 1
), pp. 381
–394
.10.1016/0017-9310(94)90038-814.
Cotta
, R. M.
, and Mikhailov
, M. D.
, 1997
, Heat Conduction: Lumped Analysis, Integral Transforms, Symbolic Computation
, Wiley-Interscience
, New York
.15.
Cotta
, R. M.
, 1998
, The Integral Transform Method in Thermal and Fluids Sciences and Engineering
, Begell House
, New York
.16.
Cotta
, R.
, and Mikhailov
, M.
, 2006
, “Hybrid Methods and Symbolic Computations
,” Handbook of Numerical Heat Transfer
, 2nd ed., W. J.
Minkowycz
, E. M.
Sparrow
, and J. Y.
Murthy
, eds., John Wiley
, New York
, pp. 493
–522
, Chap. 16.17.
Pletcher
, R.
, and Anderson
, D.
, 1997
, Computational Fluid Mechanics and Heat Transfer
, Taylor & Francis
, Washington, DC
.18.
Orlande
, H. R. B.
, Kolehmainen
, V.
, and Kaipio
, J. P.
, 2007
, “Reconstruction of Thermal Parameters Using a Tomographic Approach
,” Int. J. Heat Mass Transfer
, 50
, pp. 5150
–5160
.10.1016/j.ijheatmasstransfer.2007.07.01519.
Emery
, A. F.
, 2007
, “Estimating Deterministic Parameters by Bayesian Inference With Emphasis on Estimating the Uncertainty of the Parameters
,” Proceedings of the Inverse Problem, Design and Optimization Symposium
, Miami Beach, FL
, Vol. I
, pp. 266
–272
.20.
Mota
, C.
, Orlande
, H.
, De Carvalho
, M.
, Kolehmainen
, V.
, and Kaipio
, J.
, 2010
, “Bayesian Estimation of Temperature-Dependent Thermophysical Properties and Transient Boundary Heat Flux
,” Heat Transfer Eng.
, 31
, pp. 570
–580
.10.1080/0145763090342563521.
Naveira-Cotta
, C.
, Orlande
, H.
, and Cotta
, R.
, 2010
, “Integral Transforms and Bayesian Inference in the Identification of Variable Thermal Conductivity in Two-Phase Dispersed Systems
,” Numer. Heat Transfer, Part B
, 57
, pp. 173
–202
.10.1080/1040779100368510622.
Naveira-Cotta
, C.
, Cotta
, R.
, and Orlande
, H.
, 2010
, “Inverse Analysis of Forced Convection in Micro-Channels With Slip Flow via Integral Transforms and Bayesian Inference
,” Int. J. Therm. Sci.
, 49
, pp. 879
–888
.10.1016/j.ijthermalsci.2009.12.00923.
Massard
, H.
, Fudym
, O.
, Orlande
, H. R. B.
, and Batsale
, J. C.
, 2010
, “Nodal Predictive Error Model and Bayesian Approach for Thermal Diffusivity and Heat Source Mapping
,” Comptes Rendus Mécanique
, 338
, pp. 434
–449
.10.1016/j.crme.2010.07.01524.
Orlande
, H.
, Colaço
, M.
, and Dulikravich
, G.
, 2008
, “Approximation of the Likelihood Function in the Bayesian Technique for the Solution of Inverse Problems
,” Inverse Prob. Sci. Eng.
, 16
, pp. 677
–692
.10.1080/1741597080223167725.
Kaipio
, J.
, and Fox
, C.
, 2011
, “The Bayesian Framework for Inverse Problems in Heat Transfer
,” Heat Transfer Eng.
, 32
, pp. 718
–753
.10.1080/01457632.2011.52513726.
Abreu
, L.
, Orlande
, H. R. B.
, Naveira-Cotta
, C. P.
, Quaresma
, J. N. N.
, and Cotta
, R. M.
, 2011
, “Identification of Contact Failures in Multi-Layered Composites
,” Proceedings of the ASME
2011 International Design Engineering Technical Conference and Computers and Information in Engineering Conference IDETC/CIE 2011, Washington, DC, Aug. 29–31, Paper No. DETC2011–47511.10.1115/DETC2011-4751127.
Rudin
, L. I.
, Osher
, S.
, and Fatemi
, E.
, 1992
, “Nonlinear Total Variation Based Noise Removal Algorithms
,” Physica D
, 60
, pp. 259
–268
.10.1016/0167-2789(92)90242-F28.
Ozisik
, M. N.
, 1993
, Heat Conduction
, McGraw-Hill
, New York
.29.
Nissinen
, A.
, Heikkinen
, L.
, and Kapio
, J.
, 2008
, “The Bayesian Approximation Error Approach for Electrical Impedance Tomography—Experimental Results
,” Meas. Sci. Technol.
, 19
, p. 015501
.10.1088/0957-0233/19/1/01550130.
Nissinen
, A.
, Heikkinen
, L.
, Kolehmainen
, V.
, and Kapio
, J.
, 2009
, “Compensation of Errors Due to the Discretization, Domain Truncation and Unknown Contact Impedances in Electrical Impedance Tomography
,” Meas. Sci. Technol.
, 20
, p. 105504
.10.1088/0957-0233/20/10/10550431.
Nissinen
, A.
, Kolehmainen
, V.
, and Kapio
, J.
, 2011
, “Compensation of Modeling Errors Due to the Unknown Domain Boundary in Electrical Impedance Tomography
,” IEEE Trans. Med. Imaging
, 30
, pp. 231
–242
.10.1109/TMI.2010.207371632.
Kolehmainen
, V.
, Tarvainen
, T.
, Arridge
, S. R.
, and Kaipio
, J. P.
, 2011
, “Marginalization of Uninteresting Distributed Parameters in Inverse Problems—Application to Diffuse Optical Tomography
,” Int. J. Uncertainty Quantif.
, 1
, pp. 1
–17
.10.1615/Int.J.UncertaintyQuantification.v1.i1.10Copyright © 2014 by ASME
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