# Evaluating Short-Wave Effects in Railway Track Using the Rail Surface Signal
## 2 Positioning Method  
For the detection and evaluation of short-wave effects, we use the original output of an available measurement system. This data is obtained from the rail surface measurement system, a chord-based system in which three optical distance sensors are mounted in a row. Figure 1 illustrates the basic setup of the laser sensors. The first and the last laser build a virtual chord. The actual measurement value describes the distance between the rail surface of the middle laser and the chord surface at the same position. The measurement system can be mounted onto vehicles with speeds up to 250 km/h and still returns a data point every 5 mm. The recorded wavelength range is between 0.01 and 1 m. The combination of a sampling rate of 5 mm and the high frequency spectrum of the system makes us confident for possible use cases, as other measurement systems (in Austria) cannot provide this. The asymmetrical chord principle with three measuring points leads to very stable measuring results. Whereas a direct measuring method would lead to a lack of accuracy if vehicle movements occur, the chord principle can handle these very well. Linear correlated shifts influence all three outputs in the same way and are thus automatically compensated. Small pitch motions lead to linear correlated but opposite shifts of the first and last laser and therefore do not influence the output of the chord value. The chord measurement system's output-signal reflects the corrugation of the railroad with distorted amplitudes. The amount of distortion depends on the wavelengths of the output signal characteristics and can be extracted from the transfer function of the measuring system. If the actual space curve of the rail corrugation is needed, relatively complicated algorithms have to be used for the recalculation of the space curve. These algorithms can only deliver an approximated space curve and thus a lower data quality. As for many evaluations, it is sufficient to work with chord-values and signal characteristics of chord values; pros and cons of a recalculation of the space curve must be weighed against each other. Although, the measurement system has been mounted onto the EM250 since 2005 and some modified parameters have been partly in use since then, the original output signal was not investigated up to now. The main reason might be the already mentioned precondition of an exact positioning process. Without re-positioning, the potential of the small sampling rate cannot be exploited. For re-positioning we use an algorithm shifting signals of different measurement runs synchronously to each other. For this purpose, signal characteristics are used and a synchronicity criterion is defined. We chose the sum of the Euclidean distance as it delivers the most reliable results. To determine the best possible relative position of two measurement runs, the signal of one measurement run is shifted sequentially by a certain distance and the similarity measure to the second run is calculated anew each time. In contrast to Fellinger, the signal is shifted by only 25 mm per iteration. The relative displacement with the smallest summed Euclidean distance is therefore carried out for all measurement runs with synchronous measurements as result. To demonstrate synchronicity, Figure 2 shows input and output of the computing process. Figure 1: Measurement principle of the rail surface signal [21]. The different colors of the signals in Figure 2 reflect different runs of the measuring car. In this case five measurement runs are processed corresponding to about 1.5 years. The lines in the upper half of the figure represent the filtered signal without exact positioning. While the signal characteristics appear to match each other, the different runs are displaced to each other. The lower half of the figure shows the same signals after precise positioning. Here, all signal characteristics match each other.