## 3 Application of Drive-by Methodology on the Railway Track Subsystem
### Rail Supporting Components' Condition-Based Assessment  
Differently from previous works, which are related more to rail defects, [PERSON] et al. [PERSON] et al. (2019) developed a drive-by methodology for detecting damages to the track's interlayers through the assessment of variations in the global track stiffness. The authors used the Cross-entropy optimization algorithm to infer the stiffness profile, which minimizes the differences between a measured and a simulated bogie acceleration response. The methodology was tested for a simplified 2D half-bogie vehicle model and a 2D single-layer model. Good results were obtained for reasonably high speeds (120 km/h) under various levels of measurement noise and uncertainties in vehicle properties. [PERSON] et al. [PERSON] et al. (2019) studied the behavior of the natural frequencies of the train track interaction system and analytically demonstrated that, as the vehicle moves along the track, the natural frequencies of the system vary in a well-defined periodic way. However, in the case of a damaged rail-supporting element, this regular behavior is changed and a noticeable shift in the natural frequencies is verified. Based on these findings, a damage index calculated from this frequency shift was proposed for detecting stiffness reductions on track supporting elements. The proposed index was validated through numerical simulations employing very simplified 2D models and reduced-scale experiments. During  
Figure 8: Bogie sound pressure level measuring system ([PERSON] et al., 2019). Figure 9: Classification accuracy for a broken rail as a function of: (**a**) position error standard deviation, (**b**) vehicle damping ratio, and (**c**) vehicle natural frequency ([PERSON] et al., 2019). these validations, promising results were obtained; however, the performance of the method in dealing with more complex situations, inherent to practical applications, still needs to be checked. [PERSON] et al. [61] investigated the use of the Instantaneous Amplitude Squared (IAS), derived from the Hilbert transform of the wheel-rail contact response, as a feature for identifying damage at the track foundation. Through a sensitivity analysis, the authors concluded that the driving frequency, which is the frequency component directly proportional to the vehicle speed, has an amplitude greatly influenced by foundation damage. Based on this conclusion, the contact response was calculated from the driving frequency component by a back calculation procedure based on vehicle dynamic responses. The performance of the IAS was evaluated for the simplified vehicle and track models, presented in Figure 10, in which all the components of the foundation were modeled by one spring layer. The influence of several field factors was investigated and it was concluded that the accuracy of the method is reduced by high levels of irregularities and also by both very high and very low speeds, with the authors obtaining better performance at 150 km/h. The use of the IAS as a damage feature was also explored by [PERSON] et al. [62], who applied the method not only for foundation but also for rail damage detection. The authors also investigated the influence of other factors besides those evaluated by [PERSON] et al. [61] and were able to conclude that the damping of the vehicle suspension is unfavorable to the accuracy of the method, while the mass is beneficial. This same feature was also used by [PERSON] et al. [58] in a more challenging situation involving a track section over a viaduct. Even for this case, the IAS was shown to be sensitive to damage at the tracks interlayer. With a different approach, but still based on contact point response, [PERSON] et el. [63] proposed the use of variations in the first rail frequency as a feature for foundation damage. To avoid undesirable influence from vehicle-related frequencies, the FFT of the contact response was used for the rail frequency assessment.