# A Methodology Linking Tamping Processes and Railway Track Behaviour
## 4 Proposed Methodology
### Linking Tamping Machine Measurements to Track Geometry Data  
The tamping machine measurements are recorded at every sleeper, which are generally spaced at intervals of 0.6 m. These data points need to be allocated to the precise location  
Figure 8: (**a**) Three metre sine wave and (**b**) 25 m sine wave and respective standard deviations with influence lengths of 100, 25, and 10 m.  
Figure 9: Longitudinal level (LL) D1 signals and standard deviations (SD) calculated with a moving window over 25 m; (**a**) before, (**b**) after the synchronisation process. Each colour represents an individual measurement run. on the track, which is a precondition for reliable correlation analyses between damping data and track behaviour. This mapping is achieved in a two-stage process: (i) First, the taming data is merged with the tamping machine's internal measuring system for track geometry documentation (\"DRP\"; data recording processor). A DRP file includes the track position, the displacement of the track panel (lifting and shifting), and a control measurement of the established track geometry at a sampling rate of 0.5 m. The lift of the track panel is a parameter that is recorded by both the experimental measurement setup at the tamping unit and the DRP, hence, the lift can be used to synchronise these two data arrays. Due to the different sample rates of 0.6 m (tamping data) and 0.5 m (DRP) it is necessary to insert a common \"virtual\" sampling rate. This is achieved by adding virtual measurement points (e.g., every five centimetres) and linearly interpolating missing values between the original data points. Having established a common sampling rate, the lifting values of the tamping data file can be synchronised with the lifting values of the DRP file (Figure 10). Similar to [PERSON]'s synchronisation algorithm described above, one parameter is fixed and the other is shifting until the Euclidian distance between both curves reaches a minimum. As the DRP file includes the track position at every sampling point, the sleeper-specific tamping data are then also linked to the precise location on the track where the individual tamping processes were conducted. (ii) In a second step, the combined data set (tamping data and DRP data) needs to be linked to the track geometry measurements of the infrastructure manager. This is achieved using the longitudinal level signals. The tamping machine measures the geometry of the corrected track with a steel cord and provides values every 0.5 m. In contrast, track recording vehicles rely on an inertial measuring unit (IMU) [48] providing measurement data every 0.25 m. Although the cord measurement is not identical to the IMU measurement, the longitudinal level signal of the DRP bears a close enough resemblance with the longitudinal level of the track recording vehicle to use it as a linking element between tamping machine data and track geometry data. The issue of non-matching sampling rates is again resolved by introducing virtual data points every 0.05 m and filling the created data gaps through linear interpolation. The track geometry data set--consisting of synchronised longitudinal level D1 signals and their respective standard deviations over 25 m--is filtered for the first track recording vehicle run after the tamping operation. The longitudinal level D1 signal of this measurement run matches the longitudinal level of the DRP's control measurement best. These two signals are combined using the track position information of the track recording vehicle and the position of the tamping machine (Figure 11a). Then, the DRP signal (together with all other parameters of the DRP file) is shifted until the sum of the Euclidian distances to the longitudinal level of the track  
Figure 10: Merging process of sleeper-specific tamping data with the DRP control measurement. recording vehicle reaches a minimum (Figure 11b). Consequently, all DRP parameters recorded during damping are accurately joined with the track geometry data set.