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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.

Direct localization of multiple magnetic dipoles for surface crack detection