# A Feasibility Study of the Drive-By Method for Damage Detection in Railway Bridges
## 3 Plan of the Simulations
### Effects of Track Irregularities  
In real operating conditions, the track profile is affected by deviations from its nominal geometry, which are described as the vertical and lateral alignments of each rail. The vertical track irregularity, also named the \"longitudinal level\" in current terminology, is the one that is relevant for the present work. It is simulated to include wavelengths from 100 m down to 1 m, corresponding to time frequencies from 0.39 Hz to 39 Hz at a maximum speed of 140 km/h. The irregularity profile is characterized by an RMS level that is equal to 2.1 mm in the wavelength range from 1 to 100 m, and an RMS that is equal to 0.8 mm in the wavelength range from 3 to 25 m. (The latter is the wavelength range that is adopted by the Italian infrastructure manager to qualify longitudinal irregularity). The peak-to-peak amplitude of the profile is equal to 8.2 mm. A first consequence due to vertical track irregularity is the excitation of the modes of vibration of the vehicles in the above-mentioned frequency range, namely the carbody bounce and pitch (usually below 2 Hz), and the bogie bounce and pitch (usually between 4 and 11 Hz). These frequencies fall within the ranges of analysis of the two methods that are described in Sections 3.3 and 3.4. In particular, the low-pass filter of the quasi-static method removes from the analysis only the natural frequencies related to the bogie, whereas both the carbody and bogie natural frequencies are included in the range that is related to RMS analysis. The background acceleration level is increased, hardening the comparison of the signals generated on the train crossing a healthy bridge and a defective bridge. The damage detection algorithms rely on the comparison of the acquired signal against a reference condition, so that the evolution of the track irregularity between subsequent data acquisitions is another effect that could affect the feasibility of the method. Track geometry degradation in railway lines can generate long wavelengths, usually due to ground settling, and shorter wavelengths, due to ballast settling. The former is a slow process, which is more likely to happen in the track sections on ground before and after the bridge, and not on the bridge structure. It can be monitored by performing a trend analysis of the acquired data, and updating the reference signal constantly. Short wavelength irregularities can evolve more quickly, and they may occur also on a bridge track section, even if in a mitigated way, due to the fact that the ballast is contained within the deck side walls, and its settling is partially prevented. To evaluate the effect of an evolution of track irregularity on the bridge in the wavelengths related to ballast degradation, the algorithms for damage detection were run on accelerations obtained with different irregularity profiles for the healthy bridge and for the damaged bridge. The reference irregularity already mentioned (RMS 2.1 mm, 1-100 m range) was adopted for the healthy bridge simulation. This profile was then modified in the wavelength range from 1 to 6 m, by doubling the spectral amplitudes and randomly shifting their phases, and adopting for the  
Figure 15: Damage signal obtained through the algorithm calculating RMS on the moving window. simulation of the damaged bridge. The modified wavelengths, corresponding to time frequencies ranging from 3.7 to 39 Hz in the 80 to 140 km/h speed range considered in this work, influence the level of excitation of the bogie natural frequencies. The consequences of this process on the results of the damage detection algorithms are described in the next section. A last effect that is investigated is related to the possible variation of the track vertical stiffness encountered by the train when entering the bridge. Since the ballast on the bridge is directly placed on the deck instead than on the soil subgrade, and the ballast layer normally has a lower depth on the bridge, the train may be subjected to an increase of vertical track stiffness.