Defect detection of metallic samples by electromagnetic tomography using closed-loop fuzzy PID-controlled iterative Landweber method

Electromagnetic tomography (EMT) uses the mutual inductance of the coil to visualise the conductivity distribution of interesting regions. Since the conductivity of defects and metal samples are different, the metal samples with defects can be treated as binary-valued material distributions. This paper investigates the closed-loop fuzzy proportional, integral and derivative (PID)-controlled iterative Landweber method. The whole method includes fuzzy PID controller, the Landweber reconstruction method, and the Dirichlet-to-Neumann map. Specifically, the differential signal between the mutual inductance of the coil and the feedback signal is used as the input of the fuzzy PID controller. The fuzzy controller can automatically adjust three parameters (${K_p}$Kp, ${K_i}$Ki and ${K_d}$Kd) of PID controller. Subsequently, the output of the PID controller can serve as the input of the Landweber algorithm to reconstruct the distribution of conductivity. Furthermore, the Dirichlet-to-Neumann map is used to calculate the mutual inductance, acting as the feedback signal based on the reconstruction conductivity distribution. Finally, both the numerical simulation and experiments are applied to verify the proposed method. The results indicate that the proposed method can reconstruct the image with a clear edge, and the average correlation coefficient can reach 0.792.