• A non-uniform magnetic charge distribution model is established to overcome the limitations of the conventional uniform charge assumption in MFL testing. • The physical mechanism of MFL signal propagation induced by spatially varying magnetic charge density is revealed. • A quantitative signal propagation model is derived, explicitly linking magnetic charge non-uniformity to signal amplitude and spatial distortion. • The proposed model enables quantitative interpretation of MFL signal deformation under realistic magnetization conditions. • Experimental and numerical results validate the superior accuracy of the proposed model compared with traditional uniform-magnetic charge based approaches. As the world's predominant in-line inspection technique, magnetic flux leakage (MFL) provides essential support for the operational integrity of long-distance oil and gas pipelines. However, the propagation mechanism of MFL signals within pipeline walls remains insufficiently understood, and current quantitative models for inner and outer wall defects require further improvement. To address this gap, this paper proposes a quantitative MFL signal model based on a non-uniform magnetic charge model (NUMCM). By introducing a demagnetization factor (DF), the model enables quantitative characterization of outer wall defects and reveals the attenuation behavior of their MFL signals. Using this model, the magnetic field intensity (MFI) distributions of triaxial MFL signals for both inner and outer wall defects were derived, and the attenuation mechanism of outer wall defect signals was analyzed. To validate the proposed model, a pull-through test was conducted using a Φ508 mm MFL inspection tool. The results indicate that as defect depth increases, the peak MFL signal amplitudes for both inner and outer wall defects grow exponentially. The MFL signals from outer wall defects exhibit significant attenuation compared to those from inner wall defects. The detection error for defect depth is within ±0.3 mm, confirming the model's effectiveness in supporting quantitative MFL analysis for pipeline inner and outer wall defects.
Shi et al. (Sun,) studied this question.