## 3 Methodology  
In this paper, vertical axle box accelerations, acquired on in-service high-speed vehicles, are analysed in the wavelength range of rail corrugation. The observed excitations are investigated, and the root causes are identified. The acceleration content that cannot be otherwise explained is considered as potential rail corrugation. The final step is to verify these track sections through visual inspections or laser optical measurements of the rail surface. The effects that have a significant impact on the vehicle response in the vertical direction at high frequency are several: vehicle and track modes of vibration, wheel defects, rail defects, construction singularities, (bridges, tunnels, viaducts, etc. ), switches, welds, changes in track stiffness, etc. [23]. These can be divided into three categories according to the vibrations caused: frequency-constant (vibration mode), wavelength-constant (wheel and rail defects) and impulse excitations (stiffness changes, switches, welds, etc.) which excite a very wide range of frequencies/wavelengths. The proposed methodology can be summarised in four steps, as shown in Figure 1:  
1. Data pre-processing: the vehicle measurements are transformed into distance domain;
2. Fast Fourier transform (FFT) analysis within track sections;
3. Spectrogram analysis to exclude excitations not caused by rail corrugation;
4. Hypothesis of rail corrugation for excitations not attributed to other sources. In the data pre-processing phase, the vertical axle box accelerations are transformed into distance domain by integrating the vehicle speed and synchronised with the track data based on the curvature. The time and distance domain signals are used respectively to investigate the frequency/wavelength content observed in the accelerations. Since there is no available information about where to search for rail corrugation, the section to be analysed is selected based on the noise level. The microphone measurements are A-weighted to filter the signal in the audible range of frequencies [24], and then a high equivalent pressure level (\(Leq\)) is searched in the wavelength range of interest (ripple: 10-100 mm; slip waves: 30-300 mm). The (\(Leq\)) is evaluated as [25]:  
\[Leq=10\text{log}_{10}\left(\frac{\frac{1}{\tau}\int\limits_{t1}^{t2}p^{2}(t)dt}{ {p_{0}}^{2}}\right) \tag{1}\]  
where \(p\) is the instantaneous sound pressure and \(p_{0}\) is the reference pressure which is equal to \(2\times 10^{-5}\) Pa.  
Once the section is selected, the FFT analysis is performed to evaluate whether the excitations found in the microphones are also observed in the accelerations. Then, some FFT comparisons are made to further understand the excitations: axle box accelerations acquired on the same side of the vehicle should have the same peaks if caused by rail corrugation. Comparing the left and right axle box accelerations, the effect of corrugation is expected to be different, especially in curves where slip waves are expected to be on the inner (low) rail. On the contrary, wheel and rail modes of vibration are expected to be the same on both sides. Furthermore, if there are runs at different vehicle speeds over the same section, an FFT comparison can be made to assess whether the observed excitations are constant in the frequency or wavelength domain. This comparison makes it possible to clearly distinguish modes of vibration from rail or wheel defects. From the FFT analysis, a preliminary hypothesis can be formulated about the excitations found in the wavelength range of interest. To finalise the hypothesis, a spectrogram analysis is carried out. This analysis consists in excluding all known excitations, so that the remaining effect is considered as potential rail corrugation. By evaluating the spectrogram in the frequency domain over a longer section (a few kilometres), known excitations can be identified: the  
Figure 1: Overview of the proposed methodology.