Domain derivative approach to active infrared thermography

Bison, P.; Ceseri, Maurizio; Fasino, Dario; Inglese, Gabriele

doi:10.1080/17415977.2010.492511

Cited by 9 publications

(5 citation statements)

References 15 publications

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“…It comes from straightforward calculations (reported in detail in [9]) and linearity arguments that the function w ≡ u (∀ > 0) fulfills the following IBVP in Ω 0 × (0, T ]…”

Section: Main Results In 2d: Explicit Approximation Of the Damagementioning

confidence: 99%

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

Inglese¹,

Olmi

2017

J Nondestruct Eval

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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 realistic synthetic data and used in a real laboratory experiment.

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“…It comes from straightforward calculations (reported in detail in [9]) and linearity arguments that the function w ≡ u (∀ > 0) fulfills the following IBVP in Ω 0 × (0, T ]…”

Section: Main Results In 2d: Explicit Approximation Of the Damagementioning

confidence: 99%

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

Inglese¹,

Olmi

2017

J Nondestruct Eval

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“…Then, we introduce the directional (Gateaux) derivative u θ (0; x, z, t) of u σ at 0. This calculation is detailed in [1]. The function u θ (0; x, z, t) is defined in 0 and in our special construction, is the Domain Derivative of u σ (see [2]).…”

Section: Modelling 21 Domain Derivative and Linearizationmentioning

confidence: 99%

Thin plate approximation in active infrared thermography

Inglese

Clarelli

2014

Inverse Problems in Science and Engineering

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In this work, we find and test a new approximated formula (based on the thin plate approximation), for recovering small, unknown damages on the inaccessible surface of a thin conducting (aluminium) plate. We solve this inverse problem from a controlled heat flux and a sequence of temperature maps on the accessible front boundary of our sample. We heat the front boundary by means of a sinusoidal flux. In the meanwhile, we take a sequence of temperature maps of the same side by means of an infrared camera. This procedure is called active infrared thermography. The solution of the heat equation on the accessible boundary of the damaged sample simulates the collection of data. We use domain derivative to linearize the boundary value problem for heat equation. Then, Fourier analysis on the periodic component of solutions leads us to an elliptic BVP. Finally, we apply perturbation theory in order to find out an approximation of the damage. Numerical tests obtained with synthetic data are encouraging. The solution of the heat equation on the accessible boundary of the damaged sample simulates the collection of data by means of the infrared camera. We use domain derivative to linearize the BVP for heat equation. Then, Fourier analysis on the periodic component of solutions leads us to an elliptic BVP. Finally, we apply the perturbation theory in a 2 (a is the thickness of our sample) in order to find out an approximation of the damage. Numerical tests obtained with synthetic data are encouraging.

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“…It means, in practice, that a given temperature distribution on the surface S B is 'compatible' with several shapes and scale parameters. A solution of the inverse problem can be obtained by a semi-explicit formula [12] or applying a suitable regularization strategy to treat illposedness using genetic algorithms, artificial neural networks, or other techniques to minimize an appropriate cost function ( [7,13,14,15] to cite only a few examples).…”

Section: Details Of the Mathematical Modelmentioning

confidence: 99%

Measurement of the external parameters in quantitative active thermography

Olmi

Inglese²

2017

Meas. Sci. Technol.

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Infrared thermography is widely used in non-destructive testing and in the non-destructive evaluation of subsurface defects in several materials. The detection and reconstruction (location and shape) of a defect inside a material from thermal data requires the solution of an inverse heat conduction problem. Here the problem is tackled by the thin-plate approximation of the investigated domain. A number of physical quantities must be known for the reconstruction procedure to be successful: some relating to the material (thermal conductivity, heat capacity, density), usually known, and others relating to the heating process. This paper proposes procedures for accurately measuring the latter, whose importance is often not given due consideration. Those procedures allow us to accurately measure the heat flux distribution produced by the sources on the heated surface, and the heat exchange coefficient at the remaining surfaces, and are easily applicable in ‘on field’ situations.

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Domain derivative approach to active infrared thermography

Cited by 9 publications

References 15 publications

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

Thin plate approximation in active infrared thermography

Measurement of the external parameters in quantitative active thermography

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