Quantitative evaluation of defect parameters in magnetic flux leakage testing based on an improved magnetic dipole model and convolutional neural networks

Abstract

Acquiring low-cost magnetic flux leakage (MFL) signals while accurately inverting defect geometric parameters remains a significant challenge in magnetic flux leakage non-destructive testing. To address this issue, this paper proposes a simulation-driven defect inversion framework, termed the Simulation-Driven Magnetic Dipole Convolutional Neural Network (SDMD-CNN), which integrates an improved magnetic dipole model with convolutional neural networks. By incorporating Gaussian convolution into the conventional magnetic dipole model, a high-fidelity simulated dataset consisting of 2500 sets of parameterized MFL signals with accurately labeled defect widths and depths is constructed. A one-dimensional convolutional neural network is designed to learn the nonlinear mapping between MFL signals and defect geometric parameters, enabling reliable prediction of defect width and depth on an independent test dataset. The proposed method achieves coefficients of determination of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.9837</mml:mn> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.9960</mml:mn> </mml:math> for width and depth estimation, respectively, and demonstrates strong robustness under severe noise conditions with a signal-to-noise ratio of −5 dB. Experimental validation further shows that, without training on real defect samples, the proposed model attains an average relative error below 6% when applied to actual measurements, indicating strong simulation-to-reality transferability. These results demonstrate that the proposed approach provides an effective solution for quantitative defect inversion in MFL testing and offers a low-cost strategy for constructing labeled training data.