# Influence of the Analytical Segment Length on the Tram Track Quality Assessment
## 2 Materials and Methods
### Selection of the Track-Quality Index  
During its 135-year history, the assessment of the tram-track geometry quality in Osijek was based on the control of individually measured values of track geometry concerning the permissible values prescribed by internal regulations of the Zagreb Municipal Transit System [23]. Recently, in parallel with the introduction of information technologies, especially regarding Big Data storage, a state-of-the-art TQI assessment was developed. For this, an overview of established TQIs was performed. As presented in [13; 14; 15], different railway infrastructure managers developed their TQI calculations, mainly for standard-gauge ballasted tracks, and established threshold values or allowable limits related to the calculation in question. Figure 6 graphically presents the distribution of TQIs for the method of calculation. Figure 4: Measured track geometry irregularities histograms. Figure 5: Tram track gauge parameter values. As can be seen from Figure 6, the TQIs can be divided primarily by the way of perceiving the track geometry, either as a single-parameter or synthetic one. They also differ according to the formulation of their indicators. Although most procedures associate TQI with standard deviation, specific methods have a different approach and use averaged square measured values per analytical segment; the length of the spatial curve of the measured value; or the ratio of geometric values that exceeded acceptable limits. In addition, there are constant proposals of new TQIs for track quality assessment, such as overall TQI [29], the adaptations of the existing TQIs to urban railway systems such as metro or subway [15], TQI based on track passenger ride comfort [30], tram-track degradation data [31], and Bayesian-based TQI [13]. This research selected the appropriate method for assessing track geometry quality for the Osijek tram network based on the following six criteria. The TQI calculation procedure had to be comprehensive (synthetic) and applicable to low-speed tram tracks. It had to allow the application of local tolerances, the weighting of parameters, and the analytical segment length changes. Most importantly, the method should not require knowledge of the track geometry quality immediately after track construction. Therefore, considering all of the mentioned criteria, it was decided to analyze the applicability of two synthesized TQIs, namely W and J, both developed for the Polish Railway [32]. The synthetic track quality index W is based on the analysis of the total effect of all five measured values of geometry parameters along each segment of the track: track  
Figure 6: Overview of existing TQIs. gauge (G); cant (C); twist (T); horizontal (H); and vertical (V) irregularities. Following the European Standard EN 13848-1 addressing characterization of track geometry [33], the geometry parameter cant refers to cross-level, horizontal irregularities refer to horizontal alignment, and vertical irregularities refer to longitudinal level. The W index is a dimensionless calculated value, characteristic for each analytical track segment, determined by the following expression:  
\[\text{W}=1-(1-\text{W}_{\text{G}})(1-\text{W}_{\text{C}})(1-\text{W}_{\text{T} })(1-\text{W}_{\text{H}})(1-\text{W}_{\text{V}}). \tag{1}\]  
The equation treats the deviations of an individual parameter as an independent event where \(\text{W}_{\text{G}}\) represents the track gauge quality indicator, \(\text{W}_{\text{C}}\) the rail height ratio quality indicator, \(\text{W}_{\text{T}}\) the track curvature quality indicator, \(\text{W}_{\text{H}}\) the horizontal irregularity quality indicator, and \(\text{W}_{\text{V}}\) the vertical irregularity quality indicator.