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An inverse Problem in Thermal Imaging

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Computation and Control III

Part of the book series: Progress in Systems and Control Theory ((PSCT,volume 15))

Abstract

Thermal imaging is a technique which has proven quite useful for the nondestructive evaluation of materials, especially locating cracks or disbonds in structures. In thermal imaging, one applies a specified heat flux to the boundary of an object and records the resulting surface temperature as a function of time. From this information one hopes to determine the internal thermal diffusivity of the object, perhaps to locate flaws—cracks, bubbles, corrosion, etc. Some recent work on this subject is detailed in [2], [3], [4] and [7].

This research was carried out while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA, 23681, which is operated under National Aeronautics and Space Administration contracts NAS1-18605 and NAS1-19480.

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References

  1. Atkinson, K.E., A survey of numerical methods for the solution of fredholm integral equations of the second kind ,SIAM, Philadelphia, PA, 1976.

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  2. Banks, H.T. and F. Kojima, “Approximations techniques for domain identification in two-dimensional parabolic systems under boundary observations,” Proc. 20th IEEE CDC Conference, Los Angels, Dec. 9–11, (1987), pp.14411-1416.

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  3. Banks, H.T. and F. Kojima, “Boundary shape identification problems in two-dimensional domains related to thermal testing of materials,” Quart. Appl. Math., Vol. 47 (1989), pp. 273-293.

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  4. Banks, H.T., F. Kojima and W.P. Winfree, “Boundary estimation problems arising in thermal tomography,” Inverse Problems 6 (1990), pp. 897-922.

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  5. Bryan, K., “A boundary integral method for an inverse problem in thermal imaging,” ICASE report 92-38, submitted to the Journal of Mathematical Systems, Estimation and Control.

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  6. Folland, Gerald B., Introduction to partial differential equations. Princeton, NJ: Princeton University Press, 1976.

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  7. Kojima, F., “Identification of microscopic flaws arising in thermal tomography by domain decomposition method,” Proc. Computation and Control II, MSU (1990), Birkhäuser.

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  8. More’, J. “The Levenberg-Marquardt algorithm: implementation and theory,” Numerical Analysis (Edited by Watson, G.A.), pp. 105-116. Lecture Notes in Math. 630. Springer Verlag, 1977.

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© 1993 Springer Science+Business Media New York

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Bryan, K. (1993). An inverse Problem in Thermal Imaging. In: Bowers, K., Lund, J. (eds) Computation and Control III. Progress in Systems and Control Theory, vol 15. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0321-6_5

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  • DOI: https://doi.org/10.1007/978-1-4612-0321-6_5

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6706-5

  • Online ISBN: 978-1-4612-0321-6

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