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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Direct localization of multiple magnetic dipoles for surface crack detection

T. Nara1 / S. Ando2

1Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan. Email:

2Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan. Email:

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 15, Issue 4, Pages 403–418, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2007.022, June 2007

Publication History

Published Online:
2007-06-27

This paper presents a novel, direct method for detecting surface cracks in a magnetic plate. In the leakage magnetic field method, a crack is modeled as being full of magnetic dipoles aligned along the crack, which is to be reconstructed from measurement of the leaked field. First, we introduce a source model of an equivalent magnetic dipole (EMD) whose location and moment coincide with the centroid of a crack and total moment distributed along the crack, respectively. Then, under the multiple EMDs model, using the multipole expansion of the leakage field, we derive algebraic equations relating the EMD parameters to data. They are formulated as a so-called 'moment problem' so that the centroid positions are reconstructed as generalized eigenvalues of Hankel matrices consisting of the multipole moments. The advantage of our method is that it requires neither initial values of the EMD parameters nor computing forward solution iteratively so that the essential parameters of the cracks are obtained by quite simple, algebraic computation. Numerical simulations show validity of our method under noisy condition.

Key Words: Crack detection,; leakage magnetic flux,; direct method.

Citing Articles

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[1]
Takaaki Nara
Inverse Problems, 2012, Volume 28, Number 2, Page 025008
[2]
Takaaki Nara
Journal of Physics: Conference Series, 2008, Volume 135, Page 012076
[3]
Takaaki Nara and Shigeru Ando
Inverse Problems, 2010, Volume 26, Number 1, Page 015011
[4]
Takaaki Nara
Inverse Problems, 2008, Volume 24, Number 2, Page 025010

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