A Hybrid Data–Physics Residual Network with Class-Orthogonal Physics Heads for EMAT Lamb-Wave Fault Diagnosis on Rail-Steel Plates

Steel rails are critical components of industrial dynamic transportation systems, and their in-service fault diagnosis demands reliable discrimination of multiple defect categories under multi-mode Lamb-wave dispersion and sample-level physical-parameter drift. The rail surface is modelled by a thin metal plate instrumented with two EMAT probes (the standard laboratory surrogate for in-service rail inspection), and the proposed architecture is evaluated on this rail-equivalent plate geometry. Purely data-driven one-dimensional classifiers plateau near 80% test accuracy on a 25,000-sample simulated EMAT A-scan benchmark, while conventional physics-informed neural networks (PINNs) that inject the physical prior only at the loss-function level fail to break this ceiling. We propose a hybrid data–physics residual network, the proposed EMAT-PINN, that couples a convolutional backbone with a logit-orthogonal four-head architecture tying each defect class—hole, crack, corrosion, weld—to one simulator-derived physical quantity (reflected energy, S0/A0 ratio, arrival time, or dispersion shift) via a bias-free additive projection of the class logit. The bias-free construction guarantees that deleting or zeroing any head collapses the affected class logit to the shared baseline, so the remaining heads cannot reroute around the missing head—a structural non-replaceability that supports explainable fault diagnosis. Combined with a four-term physics regression loss (λphys=2.0), the resulting proposed EMAT-PINN attains 95.05% test accuracy at only 0.195 M parameters, with every knockout ablation dropping the model below the 80% threshold commonly referenced as a practical acceptance benchmark. This per-class mapping provides an auditable link between the model’s internal representation and the physical scattering mechanism behind each decision, directly supporting explainable fault diagnosis in industrial deployment.