2017
DOI: 10.1007/s10921-017-0440-6
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A Procedure for Detecting Hidden Surface Defects in a Thin Plate by Means of Active Thermography

Abstract: Let Ω be a metallic plate whose top inaccessible surface has been damaged by some chemical or mechanical agent. We heat the opposite side and collect a sequence of temperature maps u . Here, we construct a formal explicit approximation of the damage θ by solving a nonlinear inverse problem for the heat equation in three steps: (i) smoothing of temperature maps, (ii) domain derivative of the temperature, (iii) thin plate approximation of the model and perturbation theory.Our inversion formula is tested with rea… Show more

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Cited by 10 publications
(5 citation statements)
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“…The nondestructive structure testing technologies must be developed and improved from qualitative to quantitative approaches. 6,7 Combinations of intelligent optimization algorithms (e.g., genetic algorithms, artificial bee colony algorithms) and numerical methods have been widely applied for the quantitative detection of structural flaws. [8][9][10][11][12][13][14][15][16][17][18][19] Initially, the measured static responses (i.e., static displacement and strain) were used to construct the objective function in these studies.…”
Section: Introductionmentioning
confidence: 99%
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“…The nondestructive structure testing technologies must be developed and improved from qualitative to quantitative approaches. 6,7 Combinations of intelligent optimization algorithms (e.g., genetic algorithms, artificial bee colony algorithms) and numerical methods have been widely applied for the quantitative detection of structural flaws. [8][9][10][11][12][13][14][15][16][17][18][19] Initially, the measured static responses (i.e., static displacement and strain) were used to construct the objective function in these studies.…”
Section: Introductionmentioning
confidence: 99%
“…Following the development of certain technologies, engineers have afforded greater attention to the locations, sizes, and shapes of flaws. The nondestructive structure testing technologies must be developed and improved from qualitative to quantitative approaches 6,7 …”
Section: Introductionmentioning
confidence: 99%
“…The present work deals with A recent effective approach to the solution of this problem, based on Reciprocity Functional technique, is described in [4]. Here, a perturbative tool like Thin Plate Approximation (TPA)(see for example [5]) is used in alternative (see section 5). The idea of using TPA comes from the general assumption (see [3] Sect 9.2.1) that thermography is effective in detection of subsurface anomalies.…”
Section: Introductionmentioning
confidence: 99%
“…In non-destructive tests, the most used form of active thermography involving an external source of heat is flash thermography, also known as stepped thermography (PT). In PT, a heat step is applied to the surface of the sample and its thermal response is monitored during the cooling phase [9]- [11]. Different geometries, as well as internal discontinuities (e.g.…”
Section: Introductionmentioning
confidence: 99%