## 3 Application of Drive-by Methodology on the Railway Track Subsystem
### Track Irregularities Assessment  
Track irregularities are characterized by deviations from the ideal rail profile (Figure 2). Typically, these are evaluated in terms of longitudinal level (vertical), lateral alignment, gauge, cross-level, and twist and are strongly correlated with vibrations on the vehicles, having, therefore, a significant influence on their running safety [27,28]. Due to this fact, the level of irregularities of a railway track is an indication of its quality. Usually, these are evaluated by specialized inspection vehicles; however, there has been a growing interest in low-cost alternatives through drive-by methodologies. In one of the pioneering works in this field, [PERSON] et al. [30] investigated the vertical track irregularity assessment through a set of gyroscopic sensors embedded in railway vehicles. The authors derived analytical expressions correlating the pitch rate of the bogie and axle box vertical acceleration to the track curvature. Grounded on these formulations, a methodology for the vertical irregularity estimation based on a bogie-mounted gyroscope was formulated. The proposed system was installed in an operational train and the results obtained were compared with those derived from acceleration measurements. Good results were achieved for wavelengths greater than 8 m for different vehicle speeds when compared to reference values derived from accelerometers. The irregularities with wavelengths shorter than 8 m could not be accurately estimated by the bogie gyroscopes due to the geometric and dynamic filtering of the bogie and suspensions. Despite leading to less accurate results when compared to accelerometers, the use of the gyroscope has the advantage of being more simple, robust, and capable of providing information over a larger speed range, especially for low speeds, where the low signal-to-noise ratio makes the use of acceleration signals unfeasible. A similar approach, but involving lateral irregularities, was proposed by [PERSON] et al. [31] using a gyroscope to assess the bogie yaw rate and derive  
Figure 2: Types of track irregularities [29]. lateral track irregularities. Just as for the case involving vertical dynamics, the formulation for lateral irregularities proved to be accurate and work better for a large speed range compared to the use of accelerometers. Taking a different approach, which relies on more complex modeling of the dynamic behavior of the vehicle and its interaction with the track, [PERSON] et al. [32] assessed vertical track irregularities based on the Frequency Response Function (FRF) between track irregularities and vehicle dynamic responses. This FRF was obtained by taking the Fourier transform of the time domain dynamic equilibrium equations of the train-track interaction system. Then, from the frequency spectra of vehicle acceleration and the application of the inverse FRF, the irregularities in the frequency domain were obtained and converted to the spatial domain by the inverse Fourier transform and vehicle speed. The method was experimentally validated and, in general, reasonably good results were obtained. However, some difficulties were encountered in accurately representing the peaks, mostly due to measurement errors, such as low-frequency components and phase shifts, as well as variations in vehicle speed. Instead of using a frequency domain formulation, [PERSON] et al. [33] proposed the use of a state space model in conjunction with a Kalman filter to estimate track vertical irregularities and a 10 m-chord versine (perpendicular distance from the chord to the curve). The method was numerically and experimentally validated and reasonably good overall results were obtained for the track geometry, except for the larger wavelength components. On the other hand, the 10 m-chord versine was estimated with very good accuracy both numerically and experimentally. A similar approach using Kalman filters was also applied by [PERSON] et al. [25] in which very precise results were obtained numerically; however, there was no experimental validation.