# A Methodology Linking Tamping Processes and Railway Track Behaviour
## 4 Proposed Methodology
### Track Geometry Data Preparation  
To analyse the track behaviour and assess the impact of a tamping operation, it is necessary to define which geometry parameter (Section 2) is analysed and which track quality index (Section 2.1) applied. Arguably the best suited and most frequently used track geometry parameter for this task is the longitudinal level D1 [22; 25]. The wavelength range 3-25 m is particularly well suited as it is most affected by tamping [2]. The most commonly applied track quality index is the standard deviation (of the longitudinal level) [1; 16; 22]. [PERSON] [9] analysed 20 years of track data of the Austrian railway network; this network represents the core of our investigations, too. In accordance with above mentioned researchers, [PERSON] stated that the (modified) standard deviation [18; 47] of the vertical track geometry, calculated with a moving window, is the best parameter to describe the track behaviour and the effect of tamping operations. Accordingly, the analyses of this study are also based on the standard deviation of the longitudinal level in the wavelength range D1 (3-25 m).  
Since we aim to analyse the effect of tamping operations on the track behaviour as precisely as possible, the influence length of the standard deviation needs to be as short as possible. A graphical approach to determine a reasonable minimum influence length is presented in Figure 8. The plot depicts the two confining wave lengths of the D1 signal: (a) lower limit 3 m and (b) upper limit 25 m. Below, standard deviations of the respective signal calculated with different window lengths--100, 25, and 10 m--are plotted. Assuming that a track geometry signal with a constant amplitude represents a homogeneous track quality, the standard deviation should represent this through a near constant value. Accordingly, the graphs in Figure 8 indicate that the window for calculating the standard deviation should at least cover one wave length, which in case of the D1 signal equals 25 m. In case the window length of the standard deviation is shorter than the signal wave length, the standard deviation takes on low values where the signal features minima or maxima and high values at its inflection points. Consequently, we used a window length of 25 m to calculate the standard deviation of the longitudinal level D1.  
Figure 7: Illustration of the outlier detection algorithm.  
Analysing time series of the standard deviation calculated with short windows requires accurately synchronised measurement signals. The signal positioning accuracy delivered by measuring vehicles, such as the EM250 used by OeBB, is generally sufficient for analyses of 200 or 100 m long track segments. In our case, however, a post processing method is necessary to improve signal synchronicity. For this purpose, a synchronisation method based on [PERSON]'s CoMPaCT algorithm [48] is applied. The algorithm selects the most recent measurement signal, which is used as reference and fixed in its position, and shifts the next oldest signal until the Euclidian distance between both signals reaches a minimum. This process is repeated for all available measurement signals. According to [PERSON] [48], the CoMPaCT algorithm delivers a synchronisation accuracy of one data break, which in case of the longitudinal level signal of the EM250 equals 0.25 m. An exemplary result of this synchronisation process is plotted in Figure 9.