## 3 Methodology  
The analysis of relevant track quality indices and their application on a test section (Section 2.3) demonstrates that existing indices exhibit disadvantages to varying degrees. Consequently, a new TQI is proposed, aiming to improve this situation. Thus, the following criteria are defined with which the new TQI must comply:  
* The index must describe the overall geometrical quality of the track, which includes both peak values and scattering of the individual signals. * The index must rely on physical and objective principles while avoiding subjective weighting factors. * The index must enable the combination of all main track geometry parameters (Table 1). Figure 3: Measurement data and normalized track quality indices of the 5-km test section. * The index must be universally applicable for different types of track, varying line speeds, and different nominal track gauges. * The index must not be negatively affected by gauge widening in curves and intended twist in transition elements. * The index must be easy to understand and should be simple to implement. Among the analyzed track quality indices, the index of Federal Railroad Administration (FRA TQI) already fulfils the above criteria to a substantial extent. This index thus forms the basis of the track quality index of Graz University of Technology (TUG_TQI; TUG = Technische Universitat Graz). The principle of the FRA TQI, and therefore of the TUG_TQI, is calculating the space curve length L\({}_{i}\) of a measurement signal. This length is put in relation to the base length L\({}_{0}\), which represents the theoretical situation of a perfect track without any irregularities. The more irregularities occur on a segment and the higher their amplitudes are, the longer the space curve length L\({}_{i}\) is. Consequently, the resulting index will also be higher (Figure 4). [33; 35]  
The TUG_TQI is calculated in seven subsequent steps, which are depicted in Figure 5. Measurement signals of all main track geometry parameters are used as input data. In a first step, the gauge signal is dissected into a positive and a negative part along the zero line. This is a necessary preparatory work for the subsequent normalization process, because of the different threshold levels for positive and negative measurements (gauge narrowing and gauge widening). Next, all measurement signals are normalized with respect to a predefined threshold level, e.g., the intervention limits of EN 13848-5 [26] as in this paper. Only then can signals featuring different  
Figure 4: Principle of the TUG_TQI (adapted from [33]). Figure 5: Workflow depicting the compilation of the TUG_TQI. units and value ranges be combined to a holistic index without weighting factors. For example, the longitudinal level [mm] has less strict tolerances in absolute terms than the twist [mm/m] and therefore typically exhibits higher amplitudes. The affect a longitudinal level signal has on a combined index would thus be stronger, while a certain twist value, even if lower in its absolute value, might be significantly more critical for the overall track quality. In order to normalize the signals, the measurement values are divided by their absolute threshold values. Different threshold levels (e.g., alert level versus intermediate action level [26]) increase or decrease the TQI while its characteristics remain largely constant. Because of the normalization process, the TUG_TQI is calculated with utilization levels rather than signal amplitudes, and it implicitly considers the maximum line speed, which (co-) defines the threshold values. Figure 6 illustrates the normalization process by means of the split gauge signal. After combining the positive and negative normalized gauge signals, fictive space curve lengths \(\text{L}_{i}\) for all the geometry parameters are calculated, using the normalized measurement values (24). Subsequently, the individual TQIs for all signals are calculated according to (25).