Lift-off variation causes errors in eddy current measurement of nonmagnetic plates as well as magnetic plates. For nonmagnetic plates, previous work has been carried out to address the issue. In this paper, we follow a similar strategy, but try to reduce the lift-off effect on another index-zerocrossing frequency for magnetic plates. This modified index, termed as the compensated zero-crossing frequency, can be obtained from the measured multifrequency inductance spectral data using the algorithm we developed in this paper. Since the zero-crossing frequency can be compensated, the permeability of magnetic plates can finally be predicted by deriving the relation between the permeability and zero-crossing frequency from Dodd and Deeds method. We have derived the method through mathematical manipulation and verified it by both simulation and experimental data. The permeability error caused by liftoff can be reduced within 7.5%.

In this paper, an inverse method was developed which can, in principle, reconstruct arbitrary permeability, conductivity, thickness, and lift-off with a multi-frequency electromagnetic sensor from inductance spectroscopic measurements.Both the finite element method and the Dodd & 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 multi-frequency 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.

Ti t l eTextil e-b a s e d c a p a ci tiv e s e n s o r fo r p hy sic al r e h a bilit a tio n via s u rf a c e t o p olo gic al m o dific a tio n

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Lift-off of sensor affects the prediction of electromagnetic properties for both ferrous and non-ferrous steel plates. In this paper, we developed a strategy to address this issue for ferrous plates. With increased lift-off, the phase of the measured impedance for steel plates reduces. Meanwhile, the magnitude of the impedance signal decreases. Based on these facts, a phase compensation algorithm is developed which corrects the phase change due to lift-off considering the magnitude of the impedance signal. Further, a new magnetic permeability prediction technique is presented, which has been validated by analytical and measured results. With this new technique, the error in permeability prediction is less than 2% within the range of lift-offs tested.

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