## 5 Prediction of Dynamic Ride Comfort of High-Speed Train  
### Train Seat-Human Body Coupled Dynamics Model  
The train seat-human body coupled dynamics model was established to predict the ride comfort of high-speed trains based on the train-track rigid-flex coupled dynamics model and seat-human body coupled dynamics model. In the model, the structure of the track, wheelset, and bogie were established as a multibody dynamics model. The carriage was established as an elastomer model, and the seat and human body were established as a multibody dynamics model. The seat-human body coupled model was installed in the middle of the carriage, as shown in Figure 9.  
A comparison between the predicted and measured acceleration of the seat was carried out to verify the accuracy of the train seat-human body coupled dynamics model of high-speed trains. The power spectral density (PSD) of track irregularity of Chinese high-speed railway was applied to the model at the speeds of 250 and 350 km/h. The detailed calculation method, fitting function, and fitting spectrum of PSD of track irregularity can be found in [21], which has also become the main part of the national railway standard of China as TB\(\backslash\)T3352: 2014. The simulated seat vibration accelerations were collected at the interface between the human body and the seat cushion. Simulation lasted for 5 s with a sampling frequency of 512 Hz. The comparisons of seat vibration spectrums in the X-, Y-, and Z-directions were shown in Figures 10-12. The results showed that the vibration peaks (e.g., 15, 20, and 50 Hz) in different directions of the seat could be accurately captured by the proposed coupled dynamics model. As the vibration peaks represented the vibration response of the interface between human body and seat cushion, it could be inferred that the proposed model represented the dynamic characteristics of the coupled system. Although the errors of the simulation model might have caused fluctuations in the frequency domain, the overall trends were basically consistent with the experimental results in the analysis frequency band. In addition, the r.m.s. value of the error in different directions were all less than 10%, which indicated the accuracy of the train seat-human body coupled dynamics model. In conclusion, the proposed model can be used for the prediction of dynamic ride comfort of high-speed trains. Figure 9: Train seat–human body coupled dynamics model. the floor vibration. Detailed information about the four frequency-weighted functions are presented clearly in Annex C of the standard BS EN 12299:2009 [15]. After calculating the r.m.s. weighted acceleration values for different directions at each position, the vibration comfort of the carriage floor (\(N_{MV}\)) and the ride comfort of the seated passenger (\(N_{VA}\)) were evaluated separately. The comfort evaluation and grading of the vibration comfort indicators of the carriage in different ranges are shown in Table 3. As ride comfort is greatly affected by individual subjectivity and there is no specific evaluation standard, it was also evaluated in the same evaluation scale as the vibration comfort of the carriage floor. The experimental results obtained in Section 2 and the predicted results by the proposed train seat-human body coupled dynamics model were used to calculate the weighted r.m.s. accelerations and ride comfort indicators \(N_{VA}\) for 350 km/h based on BS EN 12299:2009, as shown in Table 4. The predicted \(N_{VA}\) was 1.28 m/s\({}^{2}\) and the measured value was 1.29 m/s\({}^{2}\), with a prediction error of 2.3%, which further verified the accuracy of the proposed train seat-human body coupled dynamics model. In order to study the distribution of ride comfort, the position of seat-human body coupled dynamics model was changed, and the response of each seat was obtained for 350 km/h. There were 17 rows of seats in the carriage of the high-speed train.