Single voxel approach for Lorentz force evaluation

Abstract

Purpose

Lorentz force evaluation is a non-destructive evaluation method for conducting specimens. The movement of a specimen relative to a permanent magnet leads to Lorentz forces that are perturbed in the presence of a defect. This defect response signal (DRS) is used for defect reconstruction. To solve a linear inverse problem for defect reconstruction, an accurate and fast forward computation method is required. As existing forward methods are either too slow or too inaccurate, the purpose of this paper is to propose the single voxel approach (SVA) as a novel method.

Design/methodology/approach

In SVA, the DRS is computed as a superposition of DRSs from single defect voxels, which are calculated in advance, by applying the boundary element source method. This research uses a setup of an isotropic conducting specimen, a spherical permanent magnet and defects of different shapes at different depths. With the help of simulations, this study compares the SVA to the previously proposed approximate forward solution (AFS) and the extended area approach (EAA) using the normalized root mean square error (NRMSE). Simulated data using the finite element method serve as the reference solution.

Findings

SVA shows across all simulations NRMSE values <2.5 per cent compared to <8 per cent for EAA and <12 per cent for AFS.

Originality/value

The superposition principle of SVA allows for the application of linear inverse methods for defect reconstruction while providing sufficient accuracy of the forward method.

Citation

Dölker, E.-M., Petković, B., Schmidt, R., Ziolkowski, M., Brauer, H. and Haueisen, J. (2019), "Single voxel approach for Lorentz force evaluation", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 38 No. 3, pp. 943-952. https://doi.org/10.1108/COMPEL-09-2018-0354