Abstract
Infrared thermography is a useful imaging technique for analyzing the thermomechanical behaviour of materials. It allows, under certain conditions, surface temperature monitoring and, via a diffusion model, estimation of heat sources induced by dissipative and/or thermally coupled deformation mechanisms. However, the noisy and discrete character of thermal data, the regularizing effect of heat diffusion and heat exchanges with the surroundings complicate the passage from temperature to heat source. The aim of this paper is to show that the prior use of reduced-basis projection of thermal data improves the signal-to-noise ratio before estimating the heat source distributions. The reduced basis is generated by proper orthogonal decomposition (POD) of physically-admissible thermal fields. These fields are solutions of ideal diffusion problems related to a set of putative heat sources. preprocessing is applied to different direct methods (finite differences, spectral solution, local least-squares fitting) already used in the past. The gain of this preprocessing is determined using a numerical penalizing benchmark test. The methods are finally compared using data extracted from a dynamic cyclic test on a pure copper specimen.
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References
Bathias C, Paris P (2005) Gigacycle fatigue in mechanical practice. Marcel Dekker
Batsale C, Chrysochoos A, Pron H, Wattrisse B (2013) Thermomechanical analysis of material behaviors, chap. 16 Measurements and Identification in Solid Mechanics. ISBN 978-1-84821-294-7
Berkoz G, Holmes P, Lumley JL (1993) The proper orthogonal decomposition in the analysis of turbulent flows. Annu Rev Fluid Mech 25:539–575
Berthel B, Chrysochoos A, Wattrisse B, Galtier A (2008) Infrared image processing for the calorimetric analysis of fatigue phenomena. Exp Mech 48(1):79–90
Boulanger T, Chrysochoos A, Mabru C, Galtier A (2004) Calorimetric analysis of dissipative and thermoelastic effects associated with the fatigue behavior of steels. Int J Fatigue 26(3):221–229
Carlberg K, Cortial J, Amsallem D, Zahr M, Farhat C (2011) The gnat nonlinear model reduction method and its application to fluid dynamics problems. In: 6th AIAA theoretical fluid mechanics conference. Honolulu pp 2011–3112
Chaturantabut S, Sorensen DC (2010) Nonlinear model reduction via discrete empirical interpolation. In: Proceedings of the 48h IEEE conference on decision and control CDC held jointly with 2009, 28th Chinese control conference, vol 32. IEEE, pp 2737–2764
Chrysochoos A (1995) Analyse du comportement thermomécanique des matériaux par thermographie infrarouge. In: Eyrolles (ed) Photomécanique vol 95, pp 203–211
Chrysochoos A (2012) Infrared thermography applied to the analysis of material behavior: a brief overview. Qirt J 9(2):193–208
Chrysochoos A, Louche H (2000) An infrared image processing to analyse the calorific effects accompanying strain localisation. Int J Eng Sci 38:1759–1788
Chrysochoos A, Wattrisse B, Muracciole JM, El Kaim YE (2009) Fields of stored energy associated with localized necking of steel. J Mech Mater Struct 4(2):245–262
Dauvergne JL, Del Barrio E (2010) Toward a simulation-free pod approach for low-dimensional description of phase-change problems. Int J Therm Sci 49(8):1369–1382
del Barrio EP, Dauvergne JL (2011) Karhunen-Loève decomposition for data, noise, and model reduction in inverse problems. Taylor & Francis Group, New York, pp 507–539
Doudard C, Calloch S, Hild F, Roux S (2010) Identification of heat source fields from infrared thermography: determination of ’self-heating’ in a dual-phase steel by using a dog bone sample. Mech Mater 42(1):55–62
Everson R, Sirovich L (1995) Karhunen-loeve procedure for gappy data. J Opt Soc Am A 12:1657–1664
Fudym O, Batsale J, Battaglia J (2013) Thermophysical properties mapping in semi-infinite longitudinally cracked plates by temperature image processing. Inverse Prob Eng 15(2):163–176
Fudym O, Batsale J, Leconte D (2002) A seminumerical approach for heat diffusion in heterogeneous media, one extension of the analytical quadrupole method. Numer Heat Trans Part B 42:325–348
Galbally D, Fidkowski K, Willcox K, Ghattas O (2010) Non-linear model reduction for uncertainty quantification in large-scale inverse problems. Int J Numer Methods Eng 81(12):1581–1608
Holmes P, Lumley J, Berkoz G (1996) Turbulence, coherent structures, dynamical systems and symmetry. Cambridge Monographs on Mechanics. Cambridge University Press
Hotteling H (1946) Analysis of complex statistical variables into principal components. Ann Acad Sci Fenn A1(37):3–79
Karhunen K (1946) Uber lineare methoden in der wahrscheinlichkeitsrechnung. Ann Acad Sci Fenn A1(37):3–79
Loève MM (1955) Probability theory. Princeton
Lumley JL (1967) The structure of inhomogeneous turbulence. In: Yaglom T (ed) Atmospheric turbulence and radio wave propagation. Nauka Press, Moscow, pp 166–178
Nayroles B, Bouc R, Caumon H, Chezeaux JC, Giacometti E (1981) Infrared telethermography and structures mechanics. Int J Eng Sci 19(7):929–947
Park HM, Lee JH (1998) A method of solving inverse convection problems by means of mode reduction. Chem End Sci 53:1731–1744
Poncelet M, Witz JF, Pron H, Wattrisse B (2011) A study of irfpa camera measurement errors: radiometric artefacts. Qirt J 8:3–20
Ryckelynck D (2005) A priori hypereduction method: an adaptive approach. J Comput Phys 202(N1):346–366
Ryckelynck D (2009) Hyper-reduction of mechanical models involving internal variables. Int J Numer Methods Eng 77(1):75–89. doi:10.1002/nme.2406
Wang C, Blanche A, Wagner D, Chrysochoos A, Bathias C (2014) Dissipative and microstructural effects associated with fatigue crack initiation on an armco iron. Int J Fatigue 58:152–157
Willcox K (2006) Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition. Comput Fluids 35(2):208–226
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Ranc, N., Blanche, A., Ryckelynck, D. et al. POD Preprocessing of IR Thermal Data to Assess Heat Source Distributions. Exp Mech 55, 725–739 (2015). https://doi.org/10.1007/s11340-014-9858-2
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DOI: https://doi.org/10.1007/s11340-014-9858-2