Determination of the Magnetic Permeability, Electrical Conductivity, and Thickness of Ferrite Metallic Plates Using a Multifrequency Electromagnetic Sensing System

In this paper, an inverse method was developed which can, in principle, reconstruct arbitrary permeability, conductivity, thickness, and lift-off with a multifrequency electromagnetic sensor from inductance spectroscopic measurements. Both the finite-element method and the Dodd and Deeds formulation are used to solve the forward problem during the inversion process. For the inverse solution, a modified Newton-Raphson method was used to adjust each set of parameters (permeability, conductivity, thickness, and lift-off) to fit inductances (measured or simulated) in a least-squared sense because of its known convergence properties. The approximate Jacobian matrix (sensitivity matrix) for each set of the parameter is obtained by the perturbation method. Results from an industrial-scale multifrequency sensor are presented including the effects of noise. The results are verified with measurements and simulations of selected cases. The findings are significant because they show for the first time that the inductance spectra can be inverted in practice to determine the key values (permeability, conductivity, thickness, and lift-off) with a relative error of less than 5% during the thermal processing of metallic plates.