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Mathematical Problems in Engineering
Volume 2010, Article ID 163420, 21 pages
Research Article

Nondestructive Testing of Metallic Cables Based on a Homogenized Model and Global Measurements

1Research Group for Numerical Analysis and Mathematical Modelling, Department of Mathematical Analysis, Galglaan 2, 9000 Gent, Belgium
2Department of Electrical Energy, Systems and Automation, Ghent University, Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium
3Department of Electrotechnology, Faculty of Applied Engineering Sciences, University College Ghent, Schoonmeersstraat 52, 9000 Gent, Belgium

Received 16 July 2010; Revised 21 October 2010; Accepted 21 December 2010

Academic Editor: Dane Quinn

Copyright © 2010 Valdemar Melicher and Peter Sergeant. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a simple, quick, and cost-effective method for nondestructive eddy-current testing of metallic cables. Inclusions in the cross section of the cable are detected on the basis of certain global data: hysteresis loop measurements for different frequencies. We detect air-gap inclusions inside the cross section using a homogenized model. The problem, which can be understood as an inverse spectral problem, is posed in two dimensions. We consider its reduction to one dimension. The identifiability is studied. We obtain a uniqueness result for a single inclusion in 1D by two measurements for sufficiently low frequency. We study the sensibility of the inverse problem numerically. A study case with real data is performed to confirm the usefulness.