# The Influence of Track Irregularity in Front of the Turnout on the Dynamic Performance of Vehicles
## 3 The irregularity of cross level
### Comprehensive Assessment of Different Irregularities on Vehicle Dynamics  
According to the study of the dynamic responses of different irregularities in the previous section, it can be seen that different types of irregularities in front of the turnout have different effects on different dynamic indicators. To further quantify the influence of different irregularities on different dynamic indicators, this paper adopts normalized Power Spectral Density (PSD) for a comprehensive evaluation by referring to Reference [37]. Firstly, derailment coefficient (\(Y\)/\(Q\)), wheel unloading rate (\(\Delta Q\)/\(Q\)), lateral and vertical acceleration of the vehicle body (\(\dot{y}\) and \(\ddot{z}\)), and wheelset lateral force (\(\sum\)\(Y\)) are selected as evaluation indicators.  
The results of the PSD are closely related to the selection of the calculation length and frequency range. Therefore, according to the time-frequency analysis results in Section 4.2.2, the calculated length and frequency of the PSD are determined, as shown in Table 2.  
The PSD is calculated by performing a Hamming window. The PSDs for different irregularities at different wavelengths are obtained. Then, the Influence Factor (\(IF\)) is defined according to Equation (6):  
\[IF_{ij}=\frac{P_{ij}}{P_{0}} \tag{6}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**The Calculation** & \(Y\)/\(Q\) & \(\Delta Q\)/\(Q\) & \(\dot{y}\) & \(\ddot{z}\) & \(\Sigma\)Y \\ \hline Calculated length range & 0–30 m & 0–70 m & 0–30 m \\ Calculated frequency range & 0–50 Hz & 0–20 Hz & 0–200 Hz \\ \hline \hline \end{tabular}
\end{table}
Table 2: The calculation parameters for the PSD.  
Figure 17: Time-frequency graphs of dynamic indicators at the CL in front of the turnout: (**a**) Wheel-rail vertical force; (**b**) wheel unloading rate; (**c**) Lateral acceleration of the vehicle body.  
where \(P_{0}\) is the PSD without irregularities in front of the turnout; \(P_{ij}\) represents the PSD under an irregularity at a certain wavelength; \(i\) and \(j\) represent different wavelengths and different irregularities, respectively.  
Since the study is to compare the effect of different types of irregularities, the maximum PSD in all cases is selected for normalization. The \(IF\) is shown in Equation (7) after normalization by the maximum:  
\[IF_{ij,norm}=\frac{IF_{ij}}{\left(IF_{ij}\right)_{max}} \tag{7}\]  
The comprehensive evaluation of the effect of the irregularities in front of the turnout is shown in Figure 18. The values in the figures represent the IFs, ranging from 0 to 1. The closer the value is to 1, the greater the influence of the irregularity on the indicator. As can be seen from the figures, for the safety indicators: the greatest influence on the derailment coefficient is the AL at the wavelength of 40 m. The AL, LL, and CL at the wavelength of 3 m all have a great influence on the wheel unloading rate, among which the LL has the greatest effect. As for the acceleration indicators, the AL at wavelengths of 3 m, 5 m, 10 m, and 40 m, and the CL at wavelengths of 3 m and 5 m have a significant influence on the lateral acceleration of the vehicle body, and the greatest effect is the CL at the wavelength of 3 m; while the greatest influence on the vertical acceleration of the vehicle body is the LL at the wavelength from 3 m to 10 m. The CL at the wavelength of 3 m has the greatest influence on the wheelset lateral force, and the AL at the wavelength of 40 m also has a significant influence, with an IF of 0.852.  
Figure 18: Comprehensive influence factors for the dynamic indicators of the irregularities in front of the turnout: (**a**) Derailment coefficient; (**b**) Wheel unloading rate; (**c**) The lateral acceleration of the vehicle body; (**d**) The vertical acceleration of the vehicle body; (**e**) Wheelset lateral force.