We analyze the ability of the Tikhonov regularization to retrieve different shapes of in-depth thermal conductivity profiles, usually encountered in hardened materials, from surface temperature data. Exponential, oscillating, and sigmoidal profiles are studied. By performing theoretical experiments with added white noises, the influence of the order of the Tikhonov functional and of the parameters that need to be tuned to carry out the inversion are investigated. The analysis shows that the Tikhonov regularization is very well suited to reconstruct smooth profiles but fails when the conductivity exhibits steep slopes. We check a natural alternative regularization, the total variation functional, which gives much better results for sigmoidal profiles. Accordingly, a strategy to deal with real data is proposed in which we introduce this total variation regularization. This regularization is applied to the inversion of real data corresponding to a case hardened AISI1018 steel plate, giving much better anticorrelation of the retrieved conductivity with microindentation test data than the Tikhonov regularization. The results suggest that this is a promising way to improve the reliability of local inversion methods.
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15 September 2010
Research Article|
September 20 2010
Analysis of the Tikhonov regularization to retrieve thermal conductivity depth-profiles from infrared thermography data
Estibaliz Apiñaniz;
Estibaliz Apiñaniz
1Departamento de Física Aplicada I, Escuela Técnica Superior de Ingeniería,
Universidad del País Vasco
, Alameda Urquijo s/n, 48013 Bilbao, Spain
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Arantza Mendioroz;
Arantza Mendioroz
a)
1Departamento de Física Aplicada I, Escuela Técnica Superior de Ingeniería,
Universidad del País Vasco
, Alameda Urquijo s/n, 48013 Bilbao, Spain
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Agustín Salazar;
Agustín Salazar
1Departamento de Física Aplicada I, Escuela Técnica Superior de Ingeniería,
Universidad del País Vasco
, Alameda Urquijo s/n, 48013 Bilbao, Spain
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Ricardo Celorrio
Ricardo Celorrio
2Departamento de Matemática Aplicada, EUITIZ/IUMA,
Universidad de Zaragoza
, Campus Río Ebro, Edificio Torres Quevedo, 50018 Zaragoza, Spain
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a)
Electronic mail: [email protected].
J. Appl. Phys. 108, 064905 (2010)
Article history
Received:
June 02 2010
Accepted:
July 03 2010
Citation
Estibaliz Apiñaniz, Arantza Mendioroz, Agustín Salazar, Ricardo Celorrio; Analysis of the Tikhonov regularization to retrieve thermal conductivity depth-profiles from infrared thermography data. J. Appl. Phys. 15 September 2010; 108 (6): 064905. https://doi.org/10.1063/1.3475498
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