# Analysis of Train Car-Body Comfort Zonal Distribution by Random Vibration Method
## 5 Conclusions  
This study established a spatial train model that adopted the random vibration method to study the zonal distribution of train comfort; the model could overcome the uncertainty caused by the randomness of track irregularities and the zonal difference in the vibratory acceleration in a car body. Our relevant conclusions are as follows:  
1. Compared with the Monte Carlo method and depending on a large amount of samples, the pseudo-excitation Method, based on the linearity of the power spectrum density of the car-body vibratory acceleration, was more efficient to derive the accurate zonal distribution of the Sperling index.
2. The realistic evaluation of train comfort can be roughly characterized by the average value of the Sperling index during train operation, while the theoretical design of train comfort can be accurately determined using the pseudo-excitation method.
3. The vibration acceleration of the train during track irregularities is a stationary Gaussian random process with a zero mean value, the statistical properties of which can be described by the 3\(\sigma\)-principle.
4. The Sperling index is a stationary indicator of comfort that is independent of the order of the vehicle elements when the train is subjected to a track irregularity. In this way, train comfort can be characterized by simply selecting a vehicle element to analyze.
5. The zonal distribution of train comfort is not strictly symmetrical with respect to the center of the car body. The most comfortable area for the vertical component was located near the front of the center of the car body, while the most comfortable area for the horizontal component was located on the axis of the tilt axis of the center of the car-body center.
6. The comfort of the train deteriorated with a loss in mass of the Car-Body and with irregularities in the tracks, while reasonable control of the train speed, regular maintenance of the tracks, and reasonable distribution of the number of passengers when changing trains improved the comfort of the train.
7. The overall comfort of the train deteriorated even if only one local vertical spring damper in the secondary suspension system was damaged. It suffered more on the side where the damage was present. The comfort of the train was not independent of the horizontal and vertical components. To optimize the comfort of the train, it is therefore important to consider both components comprehensively.  
[PERSON] came up with the concept, realized the simulation, analyzed the data, and edited the draft of manuscript. [PERSON] conducted the literature review, checked the computations, wrote the draft of the manuscript, replied to reviewers' comments, and revised the final version. [PERSON] verified the simulated data and polished the article. [PERSON] corrected the model of simulation and debugged the programming. All authors have read and agreed to the published version of the manuscript.  
This project received funding from the National Natural Science Foundation of China (Grant No. 52178101).  
Not applicable.  
The data presented in this study are available upon request from the corresponding author.  
We thank the National Natural Science Foundation of China for the support of this work.  
The authors declare no conflict of interest.