Crack Angle Estimation in Metallic Tubes by Eddy Current Testing and Gray Wolf Optimizer: A Finite Element Inverse Approach

For the failure prediction in structures, it is essential to accurately estimate the geometric parameters, especially the crack. This paper presents a numerical simulation of eddy current testing (ECT) using the finite element method (FEM) to estimate the crack angle in a 2D axisymmetric cracked tube. FEM simulation was done for different crack angles, revealing a monotonic increase in normalized impedance with increasing crack angle. The relation between the sensor impedance and crack angle was expressed by a tangential fitting function with a high coefficient of determination ( R ²  = 0.99991) and low RMSE (0.167°). The fitted function can be employed as a direct technique to estimate the angle of a hidden crack for the sensor impedance. As a supportive alternative, the gray wolf optimizer (GWO) was used to optimize the crack angle using a measured normalized impedance value. The efficiency of the proposed technique was tested across seven crack angle cases covering the full range from 0° to 90°, with both methods achieving relative errors below 1% in all cases, demonstrating the reliable behavior of the proposed approach.