# A Methodology Linking Tamping Processes and Railway Track Behaviour
## 4 Proposed Methodology
### Tamping Data Preparation  
The tamping machine measurements used in this study were recorded by the universal single-sleeper tamping machine Unimat 09-4x4/45 E3 by Plasser & Theurer (Vienna, Austria), which mainly operates in the networks of the Austrian Federal Railways (CeBB) and Swiss Federal Railways (SBB). The machines' tamping unit comprises four tamping unit segments, two of which are located at each side of the track. One tamping unit segment sits at the outer side of the rail (towards the ballast shoulder) and one at the inner side (towards the track centre), respectively. Every tamping unit segment consists of two tamping arms--one before the sleeper and one behind--with two tamping times each. The tamping machine has been equipped with an experimental measurement setup: strain gauges are fitted into the tamping times, angle encoders and accelerometers are attached to the frames of the tamping unit segments, and pressure sensors are incorporated in the hydraulic system of the tamping unit segments (Figure 5). This sensor system continuously records a large quantity of parameters during every working shift of the tamping machine. Of particular relevance for the present study are the moving distance of the tamping arms and the normal forces in the tamping times during the squeezing movement. The movements of the tamping arms are traced by the angle encoders; the forces are recorded by the strain gauges and additionally calculated from pressure measurements. The sample rate of said measurement data is 1000 Hz. In addition to the sensor measurements, all relevant tamping parameters (Section 3.1) are also recorded at every tamping process. This allows a correct interpretation of the measurement data, which to a certain extent correlate with the applied machine settings (e.g., the applied squeezing pressure affects the measured squeezing force in the tamping times). The high quantity of measured parameters combined with the sample rate of 1000 Hz yields a large amount of raw data at every tamping process. Therefore, we calculated meaningful parameters from the raw measurements of each sensor for each relevant phase of the squeezing process (Section 3), i.e., ballast penetration and squeezing movement. These calculated parameters are a compressed expression of the raw measurements and reduce the data volume drastically, while significantly fostering statistical analyses. Figure 6 displays examples of the tamping machine measurements. Plot (a) depicts the squeezing distance of one tamping arm during one squeezing movement. The plot includes raw measurements, low-pass filtered data, and the calculated parameters: the maximum squeezing distance and the x-coordinate of the centre of gravity of the area beneath the curve up to the tamping arms point of return. This parameter indicates the deceleration of the tamping arm during the squeezing movement. Plot (b) of Figure 6 depicts the squeezing force (normal force in one tamping time) during a squeezing movement. Once again, the plot includes raw measurements, low-pass filtered data, and the derived parameters, which in this case are the average low-pass filtered squeezing force during the squeezing movement and the highest dynamic squeezing force. As all tamping unit segments, tamping arms, and tamping lines of the Unimat 09-4x4/45 E\({}^{3}\) are equipped with sensors, every measurement parameter is recorded at multiple positions per sleeper. Consequently, all parameters calculated from the raw data (squeezing distance, centre of gravity of the squeezing distance, average low-pass filtered squeezing force, maximum dynamic squeezing force) are also available severalfold. These calculated values are averaged to one per tamping unit segment (left outside, left inside, right inside, right outside), yielding four values per measurement parameter, sleeper, and squeezing process phase.