# Dynamic Load Test and Contact Force Analysis of the AERORail Structure
## 3 AERORail Dynamic Load Test and Analysis
### Dynamic Load Identification  
#### 3.2.1 5 m Span Dynamic Load Identification  
For the acceleration and displacement data measured in the 5 m span under the working condition, we use an improved time domain method (ITDM) based on moments to be processed. Taking the speed of 20 km/h as an example, the measured mid-span acceleration signal is shown in Figure 9. As shown in Figure 9, the original signal sampling time is much longer than the actual loading time, and there is a long static time; the displacement signal has relatively strong noise, and it is necessary to use a certain filtering method to process the signal before subsequent analysis. The signal trough position is close to the acceleration signal peak position, which is the approximate time when the vehicle travels to the mid-span. In this paper, when processing the original signal, the dmev wavelet is used as the base wavelet to decompose and retain the real signal frequency band and remove the noise component to achieve filtering and noise reduction [24; 25]. The wavelet decomposition level is set to 12, and the approximate components are retained, that is, the filtered displacement-time curve is obtained as shown in Figure 10.  
Figure 8: Finite element model of three spans. (**a**) 5 m span finite element model, (**b**) 10 m span finite element model, (**c**) 15 m span finite element model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Vertical Vibration Frequency (Hz)**} & \multicolumn{2}{c}{**Transverse Vibration Frequency (Hz)**} \\ \cline{2-7}
**Span (m)** & **First** & **Second** & **Third** & **First** & **Second** & **Third** \\  & **Order** & **Order** & **Order** & **Order** & **Order** & **Order** \\  & \(f_{1}\) & \(f_{2}\) & \(f_{3}\) & \(f_{1}\) & \(f_{2}\) & \(f_{3}\) \\ \hline
5 & 16.40 & 65.57 & 117.80 & 13.95 & 28.64 & 69.57 \\
10 & 4.18 & 15.90 & 30.40 & 3.77 & 10.68 & 17.81 \\
15 & 2.1 & 8.18 & 12.57 & 1.70 & 27.62 & 48.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of fundamental frequency calculation results. Utilizing the time domain identification method [26] and the filtered displacement signal in Figure 10, the actual moving speed and the loading start time and end time in the test can be identified; the acceleration signal actually used for calculation is intercepted at the two time points and is filtered as shown in Figure 11. Similarly, by using the time domain identification method and substituting parameters such as fundamental frequency and speed, the time-history curve of the vehicle-rail contact force can be identified (see Figure 12). Figure 11: Filtered signal of mid-span acceleration at a speed of 20 km/h. Figure 12: Identifying contact force at a speed of 20 km/h. Note: positive is pull and negative is press, the same as below. Figure 10: Mid-span displacement signal after filtering at a speed of 20 km/h. Figure 9: Mid-span acceleration at 20 km/h. The contact force-time curve after identification contains certain unreal data points, including the sudden change of the value at the start and end times or the crossing of the zero point. A contact force time-history curve that can be used for analysis can be obtained by removing the unreal data numerically. Using the same method to process the data of the 5 m span under other speed conditions, the data curve is shown in Figure 13.  
The results of the 5 m span generally show the following rules: (1) There are two absolute peak values of the contact force at the front and the back of the curve; (2) the contact force has a certain volatility; (3) there are data at the head and tail of the curve \"Jitter\"; (4) the recognition effect at low speed is not ideal, and there may be large errors.