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Damage Detection in Thin Plates via Time-Harmonic Infrared Thermography

  • Manuel María-Luisa Pena RapúnEmail author
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)

Abstract

Non-destructive damage detection has become a very active research topic recently. This paper is devoted to the processing of time-harmonic thermograms (color images of one side of the sample to be inspected, obtained by a thermal camera) for structural health monitoring of thin plates. Our approach is based on the evaluation of an indicator function, the so-called topological derivative, which will identify the regions inside the plate where damage is located.

Notes

Acknowledgements

The authors are supported by the Spanish Ministry of Economy and Competitiveness under the research projects MTM2014-56948-C2-1-P and TRA2016-75075-R.

References

  1. 1.
    Carpio, A., Rapún, M.L.: Solving inhomogeneous inverse problems by topological derivative methods. Inv. Probl. 24, art. 045014 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Carpio, A., Rapún, M.L.: Hybrid topological derivative and gradient-based methods for electrical impedance tomography. Inv. Probl. 28, art. 095010 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Funes, J.F., Perales, J.M., Rapún, M.-L., Vega, J.M.: Defect detection from multifrequency limited data via topological sensitivity. J. Math. Imaging Vis. 55, 19–35 (2016)CrossRefGoogle Scholar
  4. 4.
    Guzina, B.B., Bonnet, M.: Small-inclusion asymptotic of misfit functionals for inverse problems in acoustics. Inv. Probl. 22(5), 1761–1786 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Pena, M., Rapún, M.L.: Detecting damage in thin plates by processing infrared thermographic data with topological derivatives. Adv. Math. Phys. 4, 1–18 (2019)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Sokolowski, J., Zochowski, A.: On the topological derivative in shape optimization. SIAM J. Control Optim. 38, 1251–1272 (1999)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Universidad Politécnica de MadridMadridSpain

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