Insight into the Eddy-current Reflection Coefficient of Plates and Pipes

The forward model of eddy-current testing can predict the measurement signals, provided the known measurement conditions and physical properties of test pieces. In the analytical forward model, the test pieces are characterised by the reflection coefficient, which describes the reflection characteristics of test pieces regarding incident electromagnetic waves and determines the phase of eddy-current signals. The reflection coefficient is calculated analytically with boundary conditions, which is sophisticated for analysing complex geometries. In this study, the analytical model of plate and pipe testing using second-order vector potential is investigated. It is found that the numerical reflection coefficient can be obtained from the source electromagnetic field in air and counterparts in the presence of test pieces. In numerical simulations, the numerical reflection coefficient is compared with the analytical reflection coefficient for plate and pipe in a 2-D axisymmetric model. In the 3-D model, the calculated numerical reflection coefficient corresponds to the dimensions of the measured plate and pipe with defects. In both 2-D and 3-D models, the phase of coil inductance from the numerical reflection coefficient aligns with the finite-element solutions. It is validated that the reflection coefficient is a characteristic of test pieces independent of the source field.