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.

Eddy current testing (ECT) is an effective technique for evaluating depth of metal surface defects. However, in practice, evaluation primarily relies on the experience of an operator and is often carried out by manual inspection. In this article, we address the challenges of automatic depth evaluation of metal surface defects by virtual of state-of-the-art deep learning (DL) techniques. The main contributions are threefold. First, a highly integrated portable ECT device is developed, taking the advantage of an advanced field-programmable gate array (Zynq-7020 system on chip) and provides fast data acquisition and in-phase/quadrature demodulation. Second, a dataset, termed metal defects of different depths by ECT (MDDECT), is constructed using the ECT device by human operators and made openly available. It contains 48000 scans from 18 defects of different depths and liftoffs. Third, the depth evaluation problem is formulated as a time series classification problem, and various state-of-the-art 1-D residual convolutional neural networks are trained and evaluated on the MDDECT dataset. A 38-layer 1-D ResNeXt achieves an accuracy of 93.58% in discriminating the surface defects in a stainless steel sheet with depths from 0.3 to 2.0 mm in the resolution of 0.1 mm. In addition, the results show that the trained ResNeXt1D-38 model is immune to liftoff signals.

Metallic plates are widely used in a variety of industrial applications, from which conductivity is a key parameter related to the quality of metals. In order to accurately measure the conductivity, this article proposes a novel eddy current method based on sweep-frequency strategy. First, a simplified theoretical model for conductivity measurement is derived from the classical Dodd and Deeds analytical solution. Based on the analytical solution, the real and imaginary parts of the mutual inductance signal have an intersection in the frequency domain. According to mathematical derivation, the corresponding frequency (crossover frequency) of the intersection is inversely proportional to the conductivity of the sample. Moreover, the liftoff compensation method is proposed to reduce the effect of liftoff variation. Experiments have been carried out for samples with different conductivities, ranging from 0.5 to 58 MS/m, to verify the proposed method. The results show that the average error of the conductivity estimation with the proposed approach can be controlled within 1.1%, and the liftoff compensation method can significantly reduce the conductivity estimation error.