Physics-guided machine learning for ultrasonic crack-depth quantification in laboratory rail specimens using laser ultrasonics

Abstract

Accurate quantification of crack depth is essential for ensuring the structural integrity and operational safety of railway infrastructure. Conventional ultrasonic inspection techniques primarily focus on defect detection and often require baseline measurements or expert interpretation, limiting their suitability for autonomous structural health monitoring. This study proposes a physics-guided machine learning (ML) framework for baseline-free ultrasonic crack-depth quantification in rail-track structures using ultrasonic guided-wave and data-driven regression models. Rayleigh-wave ultrasonic signals were acquired from 13 rail specimens, comprising three healthy specimens and ten specimens with crack depths ranging from 2 to 20 mm. Each specimen was tested 25 times, resulting in a database of 325 ultrasonic measurements. After signal preprocessing, nine physics-guided damage-sensitive features, including amplitude, energy, attenuation, arrival time, and wavelet-based descriptors, were extracted to characterize crack-induced changes in wave propagation. Four regression algorithms, namely Gradient Boosted Regression Trees (GBRT-LSBoost), Random Forest (RF), Support Vector Regression (SVR), and Gaussian Process Regression (GPR), were evaluated using independent test data and specimen-wise, grouped cross-validation. Model interpretability and robustness were further assessed through feature importance, permutation importance, feature ablation, correlation analysis, and uncertainty quantification. The results show that amplitude and attenuation-based features are the most influential predictors of crack depth, whereas time-of-flight and several wavelet features contribute marginally. Among the four nonlinear ML models, Random Forest achieved the best independent-test performance (R² = 0.961, RMSE = 1.610 mm), closely followed by GBRT-LSBoost (R² = 0.960, RMSE = 1.623 mm) which could be suitable for field deployment under complex and dynamic conditions. Notably, a peak-amplitude-only linear regression baseline achieved lower error (R² = 0.995, RMSE = 0.563 mm), demonstrating the strong approximately linear relationship between transmitted Rayleigh-wave amplitude and prescribed crack depth under the controlled laboratory conditions. The results demonstrate the feasibility of the proposed feature-level physics-guided regression framework under controlled laboratory conditions, while further validation using a larger number of independent specimens and naturally occurring service cracks is required before field deployment.

Keywords

Physics-guided machine learning / Ultrasonic guided waves / Rail-track structural health monitoring / Crack-depth quantification / Rayleigh wave ultrasonics / Non-destructive testing

References

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