A Fast Forward Model for Surface Defect Characterization in Magnetic Flux Leakage Testing

This study aims to develop a robust and computationally efficient forward model for surface defect characterization in Magnetic Flux Leakage (MFL) testing. The proposed approach extends the Magnetic Dipole Model (MDM) into a Numerical Magnetic Dipole Model (NMDM), enabling the simulation of MFL signals for complex defect geometries. A comprehensive evaluation of multiple defect cases demonstrates the model’s effectiveness. First, the NMDM achieves superior accuracy over analytical MDMs when applied to ellipsoidal defect, with the predicted radial component closely matching Finite Element Method (FEM) simulations, yielding a root mean square error (RMSE) of 3.84%. Second, for complex defects, the method maintains high precision, with RMSE values below 6% relative to FEM results. Third, for corrosion-like defects exhibiting gradual depth variations, the model retains high accuracy, achieving a RMSE of 3.94% compared to experimental data. However, for artificial defects with abrupt depth changes, the prediction error increases, reaching a maximum RMSE of 9.01%. Despite this, the method remains computationally efficient, achieving a runtime of under 1 second for predicting MFL signals at 100 field points. These results confirm that NMDM is a robust and practical approach for corrosion defect characterization, particularly when maintaining a sensor lift-off distance below 2 mm to ensure accurate defect reconstruction.