## 4 Methodology for the Modernization of ATLAS-LG System Software Operational Algorithms  
### Criteria for Evaluation of ATLAS-LG System Operation Results  
The performed investigation [38] showed that, using the ATLAS-LG system, according to the modernized criteria of dynamic factor, the detection of wheels with rolling surface defects is not sufficiently reliable. This effect is most evident when checking freight wagons on which wheel defects occur more often than other types of carriages. This is due to the fact that the operation of the system is influenced by the speed of the freight wagons and the axle load. For creating a mathematical model for the analysis, we used methodology to apply inverse Laplace transformation, as used in [32; 33; 34; 35; 36; 37]. This methodology was selected considering that the infrastructure and the rolling stock of Lithuanian railways is 1520 mm gauge, where the agreed technical parameters and methodologies of the railway infrastructure operators of the Organization for Cooperation between Railways (OSJD) prevail. A mathematical model of wheel damage was derived from the frequency characteristics. Frequency characteristics that describe the dynamic system, using the input as the uneven location (which occurs as the mass of the wheel center moves) and the output as the dynamic force at the wheel and rail contact location, can be expressed using Equation (1) [38]. \[W_{p}=\frac{1}{1/c_{\text{i}}+W_{y}(0,iw)-W^{0}(iw)}, \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Country and** & **Driving** & **Acceleration in Journal Box \(g\)** & **Maximum Vertical Force, kN** & **The Ratio of the** \\
**Additional Information** & **Speed,** & **(Multiply by \(g=9.81\) m/s\({}^{2}\))** & **For Repairs** & **Uncouple** & **Maximum Force to the** & **Background** \\ \hline In Russia, for wagons & 60 & 25-30 & 370 & 450 & - \\ \hline \multirow{2}{*}{
\begin{tabular}{c} In Russia, for \\ passenger wagons \\ \end{tabular} } & 20 km & Winter: 45 & \multirow{2}{*}{-} & \multirow{2}{*}{-} & \multirow{2}{*}{3} \\  & length on & & Summer: 30 & & \\ \hline In Russia (letter of V.A. & & & & \\ Gapanovich & - & - & 370 & 450 & - \\
13 May 2013) & & & & & \\ \hline USA & & & & & \\ (WM-WIM) & 45 & - & 270 & 450 & - \\ \hline USA (TTCI, & & & & \\ Transportation & 72 & - & 273 & 350 & - \\ Technology Center Inc.) & & & & & \\ \hline India & 55-65 & - & 200 & 350 & 2.0–4.5 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Lithuania, \\ ATLAS-LG system \\ \end{tabular} } & \multirow{2}{*}{-} & \multirow{2}{*}{-} & \multirow{2}{*}{-} & \multirow{2}{*}{-} & \multirow{2}{*}{-} & 3-5 locomotives and \\  & & & & & electrical trains \\ \multicolumn{2}{c}{} & & & & 6.5–11 wagons \\ \hline Poland, & - & - & 300 & 350 & 4.5–5.0 \\ System ATLAS & & & & & \\ \hline Sweden, & & & 300 locomotive & 425 locomotive & 4.7 locomotive \\ System ATLAS & - & - & 190 wagon & 320 wagon & 5.2 wagon \\ \hline UK, system ATLAS & - & - & 350 & 400 & - \\ \hline Germany, system ATLAS & - & - & - & 0 & 1.7 (three times) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Defective wheel definition normative according to two factors of strength group parameters (factor). The table was constructed on the basis of the literature presented in Sections 3.1–3.5. where \(W_{p}\) represents the frequency characteristics (N/m), \(C_{k}\) is the elasticity at the wheel and rail contact location (N/m), \(W_{y}(0,iw)\) represents the frequency characteristics of the dynamic force transformations into the rail indentation, while the first argument indicates the distance where the value is determined (m/N), and \(W^{0}(iw)\) represents the frequency characteristics, which relate the wheel displacement (under weight located above the spring) to the dynamic force at the point of contact (m/N).