# A Procedure for Detecting Hidden Surface Defects in a Thin Plate by Means of Active Thermography

A Procedure for Detecting Hidden Surface Defects in a Thin Plate by Means of Active Thermography Let $$\varOmega _\epsilon$$ Ω ϵ 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 $$u^\epsilon$$ u ϵ . Here, we construct a formal explicit approximation of the damage $$\epsilon \theta$$ ϵ 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 realistic synthetic data and used in a real laboratory experiment. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Nondestructive Evaluation Springer Journals

# A Procedure for Detecting Hidden Surface Defects in a Thin Plate by Means of Active Thermography

, Volume 36 (3) – Aug 10, 2017
11 pages

/lp/springer_journal/a-procedure-for-detecting-hidden-surface-defects-in-a-thin-plate-by-bT7ug0o6mt
Publisher
Springer US
Subject
Engineering; Structural Mechanics; Characterization and Evaluation of Materials; Vibration, Dynamical Systems, Control; Classical Mechanics
ISSN
0195-9298
eISSN
1573-4862
D.O.I.
10.1007/s10921-017-0440-6
Publisher site
See Article on Publisher Site

### Abstract

Let $$\varOmega _\epsilon$$ Ω ϵ 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 $$u^\epsilon$$ u ϵ . Here, we construct a formal explicit approximation of the damage $$\epsilon \theta$$ ϵ 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 realistic synthetic data and used in a real laboratory experiment.

### Journal

Journal of Nondestructive EvaluationSpringer Journals

Published: Aug 10, 2017

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