## 3 Application of Drive-by Methodology on the Railway Track Subsystem
### Rail Condition-Based Assessment
Based on a simplified 2 DOF multibody vehicle model, the authors conducted simulations of the vehicle passing at 180 km/h over a bump-type track defect. As can be seen in Figure 7, the passage of the wheel over the bump, which happens at approximately 30 s, results in energetic components which are spread along frequencies higher than those associated with the healthy track. Based on these findings, an automatic damage detection algorithm was proposed by defining a threshold for the value of the sum of all Wavelet coefficients for each time instant. This powerful time-frequency analysis technique was also used by [PERSON] et al. [51] to evaluate  
Figure 5: Squat type defect identification: (**a**) Top view of a damaged rail and (**b**) Wavelet acceleration spectrogram [46]. the bolt tightness of rail joints. The correlation between the energy content calculated from the Wavelet transform of axle box acceleration for specific frequency ranges and bolt tightness of rail joints was established employing a series of controlled experimental tests comprising different bolt tightness. Based on this, a simple algorithm was proposed that could efficiently distinguish between tight, intermediate loose, and completely loose bolts. The method was experimentally validated by axle box acceleration measured on a regular service tram with resilient wheels, which poses more challenges for these methods, given the lightness of the vehicle, low speed, and flexibility of the resilient wheels. Even so, the algorithm performed quite well in detecting the state of the rail joints. Another undesirable condition affecting the surface geometry of the rails is corrugation. This undulatory defect consists of short-length waves distributed along the top of the rail that may cause strong forces at the wheel-rail contact, as well as high noise levels [52]. [PERSON] et al. [53] proposed a machine-learning (ML) methodology to identify and characterize rail corrugation in metro lines. Firstly, a 1 DCNN was trained to identify, as well as classify, rail corrugation by its wavelength from acceleration measured at the axle  
Figure 6: Measurement setup for Squat detection: (**a**) Sensors positioning in the bogie and (**b**) detail of the accelerometer’s installation at the axle box [48]. Figure 7: Wavelet transform of vehicle acceleration: (**a**) healthy track and (**b**) damaged track [50]. boxes. Then, based on numerical simulations at different speeds and rail corrugation of different wavelengths and depths, a Kriging surrogate model (KSM) was constructed to model the relationship between vehicle speed, corrugation depth, and axle box RMS acceleration levels. From this model, the corrugation depth could then be inferred by reverse optimization through a Particle Swarm Optimization (PSO) algorithm. The method was experimentally validated and an accuracy of 99% was achieved for the fault identification and an average relative error of 6.75% for the corrugation depth estimation. [PERSON] et al. [54] investigated the use of a different ML algorithm to identify rail corrugation on heavy-haul railway lines from axle box acceleration. The acceleration signal was decomposed by the wavelet packet transform (WPT) and an adaptative short-time Fourier transform was used to compute the frequency content of the packets with the best resolution. Then a damage feature based on the mean Renyi entropy value of the packets is proposed and the classification is performed by a Support Vector Machine (SVM) ML algorithm. Experimental validation was performed on a real train and an accuracy of 93% was achieved. Taking advantage of the high acoustic emissions associated with corrugations, some authors have investigated the possibility of using embedded microphones instead of accelerometers to detect corrugations. [PERSON] et al. [55] used sound pressure levels measured by a bogie-mounted microphone (Figure 8) to detect corrugation on metro lines.