Assessment of Two Forward Solution Approaches in Lorentz Force Evaluation

Two different forward models for Lorentz force evaluation, the approximate forward solution (AFS) and the novel extended area approach (EAA), are evaluated using a goal function scan. A setup that contains a spherical permanent magnet and a specimen of stacked aluminum sheets with a cuboidal defect of size 12 mm x2 mm x2 mm at a depth of 2 mm is simulated by the finite-element method (FEM). Deviations between force perturbation of FEM and AFS or EAA are compared in terms of normalized root mean square errors (NRMSEs). The goal function scan yields minimal NRMSE for the correct depth with values of 6.1% for AFS and 1.7% for EAA, corresponding to the determined defect dimensions of 7 mm x 10 mm x 2 mm for AFS and 11 mm x 2 mm x 2 mm for EAA.