Electromagnetic Parameter and Thickness Estimation Using Pulsed Eddy Current and Physics-Informed Transformer Networks

Pulsed eddy current (PEC) has been widely employed in the metal industry for estimating the electromagnetic parameter and thickness of steel plates, owing to its unique advantages, such as rapid response, strong penetration ability, and richer information, in time domain and frequency domain. The slope of the last phase signal on a logarithmic scale is a crucial indicator in PEC testing. A simplified analytical expression for estimating the slope of the last phase signal is presented for the first time in this article. The slope can be computed based on the thickness, electrical conductivity, and magnetic permeability of the tested specimen. The simultaneous nonlinear mapping from measured signals to the thickness, electrical conductivity, and magnetic permeability of the tested specimen is constructed by the deep learning model based on the Transformer network, which is physics-informed through the deriveD simplified analytical expression, incorporating the last phase signal slope on a logarithmic scale to enhance test accuracy and speed. Numerical simulations and experiments were conducted to assess the proposed method for estimating electromagnetic parameters and thickness across different plate materials. The method provides real-time, accurate parameters estimation of the steel plate, and all estimated parameters have a relative error below 3%.