Analyzing the permeability distribution of multilayered specimens using pulsed eddy-current testing with multi-scale 1D-ResNet

The mechanical properties of steel are determined by its microstructure, which is closely related to its permeability profile. In thermal processing, layered structures are formed in steel and different layers have different mechanical and magnetic properties. Therefore, it is crucial to propose a practical method to monitor the change of permeability profile along the depth, which can indicate the evolution of the microstructure of steel during thermal processing, such as hot rolling. This paper presents a method for determining the layered structure and permeability profile of the steel by using pulsed eddy current testing (PECT), which offers better penetration ability. An analytical model has been deduced for calculating the time-domain pulsed eddy current (PEC) response from a Hall sensor of a triple-layer conductor system based on the inverse Laplace transform. It is found the Tau ($\tau$) curve is closely related to the permeability profile of the conductor. For the inverse solution, the Simultaneous Iterative Reconstruction Technique (SIRT) is utilized to determine the permeability profile of the multilayered specimens from the measured response. The approximate Jacobian matrix (sensitivity matrix) is obtained by the perturbation method based on the Tau curve. However, the permeability profile suffers from smoothing effect and sharp features are lost. Deep learning (DL) algorithm based on the Multi-Scale 1D-ResNet model is therefore introduced to address this issue. Numerical simulations and experiments have been performed to evaluate the proposed method for permeability profile estimation with various materials and thicknesses. The DL method can achieve an accurate estimation of the plate permeability profile with a relative error under 5%.