Detection of Magnetic Samples by Electromagnetic Tomography With PID-Controlled Iterative L₁ Regularization Method

Metal defect detection is significant for smart manufacturing, such as improving product quality, reducing production costs, and ensuring production safety. Compared to defect detection, defect imaging can obtain information on the spatial location, orientation, and distribution of defects, so as to make a quantitative judgment on the degree of damage of defects. The electromagnetic properties of metal samples are closely related to their microstructures, and the reconstruction of electromagnetic distribution can image defects. In this article, a PID-controlled L<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularized tomography method is investigated to achieve high-precision 3-D imaging of defects. Since the coupling between the conductivity and magnetic of the magnetic sample will affect the reconstruction results, the relationship between the excitation frequency and the electromagnetic properties is first analyzed in accordance with the theoretical model to select a suitable excitation frequency. Moreover, the idea of closed-loop control is applied to the L<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularization algorithm. Specifically, the L<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularization algorithm is used as the controlled object of the PID controller. In the feedback loop, the reconstructed image is mapped to the computed projected values via Dirichlet-to-Neumann. The deviation between the computed projection value and the measured value is used as an input to the controller, thus constituting the PID-controlled iterative L<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularization method. The DP steels with different defect distributions are used to verify the proposed method, and the numerical and experimental results indicate that the proposed method can eliminate artifacts and obtain high-quality defect reconstruction results. Compared with the classical imaging method, the correlation coefficients of the reconstruction errors using the proposed method are improved by 18.0% and 23.6% for complex defect distribution.