Dual TDOA representation learning with physics-informed regularization for 3D acoustic emission localization in concrete

Accurate three-dimensional (3D) acoustic emission (AE) source localization is fundamental to structural health monitoring (SHM) and damage characterization in concrete structures. However, achieving high-precision localization remains challenging due to the inherent heterogeneity of concrete, complex boundary reflections, and the high cost of obtaining large-scale labeled datasets. This study proposes a novel physics-guided deep learning framework, termed Dual TDOA+PIR, which integrates dual Time Difference of Arrival (TDOA) representations with physics-informed regularization (PIR) for 3D AE localization in concrete prisms. Here, the physical knowledge is incorporated through algebraic and geometric constraints derived from the wave-propagation model, rather than by solving the underlying wave equation. The framework features: (1) a dual-representation strategy that fuses explicit raw TDOA features with Transformer-derived global dependencies from multi-threshold sequences; and (2) a physics-informed regularization scheme that imposes TDOA-consistency and geometric propagation constraints to ensure physical consistency under sparse data conditions. Experimental validation on a 100 × 400 × 100  mm concrete prism demonstrates that the proposed approach achieves a Mean Absolute Error (MAE) of 4.88 mm with an optimal physics weight ( λ = 10 − 5 ). This represents a 56.35% improvement over the K-nearest neighbors baseline (11.18 mm) and a 37.11% improvement over the non-physics-constrained dual-representation model (7.76 mm). Ablation studies further reveal that: (1) three-threshold TDOA extraction optimizes the balance between feature richness and generalization; (2) physics constraints substantially enhance Z-axis (depth) localization by 56.28%; and (3) the framework maintains high robustness across various physics-weight settings. This methodology provides a robust and high-precision solution for real-time monitoring of internal damage in concrete structures.