TWO-STAGE BAYESIAN INFERENCE FOR RAIL MODEL UPDATING AND CRACK DETECTION WITH ULTRASONIC GUIDED WAVE MEASUREMENTS

Abstract

Railway infrastructure is highly susceptible to fatigue-induced cracks, which, if undetected, may lead to catastrophic derailments and significant economic losses. Conventional non-destructive testing (NDT) methods effectively identify surface-level damage but often fail to detect internal or small-scale cracks. Ultrasonic Guided Waves (UGWs) offer deeper penetration and long-range detection but face challenges in mode selection, noise interference, and uncertainty quantification. To address these issues, this study proposes a two-stage Bayesian inference framework that integrates UGW measurements with deep learning–based segmentation. In the first stage, Bayesian model updating using Markov Chain Monte Carlo (MCMC) refines rail material parameters, incorporating prior knowledge and UGW data for accurate wave propagation modeling. In the second stage, a Bayesian U-Net with Monte Carlo Dropout is employed to achieve pixel-level crack segmentation while providing uncertainty-aware predictions. Experimental evaluations demonstrate that the proposed Bayesian U-Net achieves superior performance (IoU = 0.82, Dice Score = 0.88, Pixel Accuracy = 95.2%) compared to traditional U-Net and Mask R-CNN, while maintaining robustness under noisy conditions with only a 7.3% performance drop. Furthermore, the integration of segmentation into Bayesian updating reduces mean squared error from 0.042 to 0.018, highlighting the framework’s accuracy and reliability. The results confirm that combining Bayesian inference with deep learning significantly improves crack localization, uncertainty quantification, and computational efficiency, providing a practical solution for real-world rail structural health monitoring.