Development of a Physics-Informed Doubly Fed Cross-Residual Deep Neural Network for High-Precision Magnetic Flux Leakage Defect Size Estimation

Defect depth is an essential indicator in magnetic flux leakage (MFL) detection and estimation. The quantification errors for defect depth are closely related to length and width errors, and this feature has always been used to support the operator's judgment in defect identification. However, the existing defect quantification algorithms based on shallow and deep neural networks only employed simple general network structures inspired by the field of artificial intelligence; consequently, these network structures lack the support of physical concepts and result in large quantification errors regarding defect size, especially depth. In this article, to describe and integrate the above theory into a deep neural network, we propose a physics-informed doubly fed cross-residual network (DfedResNet) suitable for MFL defect detection based on deep learning. Physics-based MFL defect quantification theory is studied and integrated into loss functions during the neural network training. DfedResNet quantifies defects in MFL data and automatically extracts deep features of defects. The experimental results show that it effectively achieves high-precision quantification of defect length, width, and depth simultaneously, especially defect depth. Moreover, it considers data from all three dimensions during network training, and use the originally measured magnetic signal data in place of recognized images to avoid defect information loss and further improve the quantification accuracy. The deep DfedResNet model proposed in this article reduces defect length and width quantification errors to within 0.3 mm and defect depth quantification errors to within 0.4% t. In addition, compared with other network structures and traditional algorithms, DfedResNet improves defect quantification accuracy by 1-2 orders of magnitude and thus achieves a high quantification performance.

Automated summary

In this study, a physics-informed doubly fed cross-residual network (DfedResNet) is proposed for MFL defect detection, integrating physics-based MFL defect quantification theory into the neural network training. DfedResNet quantifies defects with high precision, especially in defect depth, by considering data from all three dimensions during training and using original magnetic signal data instead of recognized images. The DfedResNet model significantly reduces defect quantification errors and achieves a high quantification performance compared to other network structures and traditional algorithms.