# The Refined Simulation Methods of Fluctuating Wind and Aerodynamic Forces Relative to Moving Trains
## 6 Conclusions  
In the present work, the fluctuating wind spectrum for a moving train is derived, merging the inhomogeneous and non-stationary characteristics of wind environments. The time-frequency transformation method for the complex admittance function of the train is proposed. The simulation methods of the unsteady aerodynamic forces for moving trains are generated by considering the phase characteristics of the admittance function. The simulation of the refined fluctuating wind and aerodynamic forces for moving trains in different wind environments is realized. The main conclusions were obtained as follows:  
1. The comparisons validate the proposed framework for simulating fluctuating wind and aerodynamic forces relative to moving trains. Compared with the existing methods, the derived wind spectra demonstrate broader applicability, particularly in complex wind environments characterized by inhomogeneity and non-stationarity. Moreover, the time-frequency transform of the admittance function can consider the phase of the admittance function in simulating aerodynamic forces relative to a moving vehicle. However, [PERSON]'s frozen turbulence hypothesis is used in the derivation of wind spectra, which may result in errors in the case of a wind direction \(\varphi_{0}\
eq 90\) degrees.
2. The inhomogeneous characteristic of the wind environment significantly influences the moving train's fluctuating wind and aerodynamic force within a short period. This is because the actual wind environment has prominent inhomogeneous characteristics in a small distance range. Additionally, the actual wind environment only shows significant non-stationary characteristics after a few minutes. High-speed trains can travel a long distance in a short period. Meanwhile, the inhomogeneous wind environment experienced by the moving train in a short period would change considerably.
3. The admittance function filters out the high-frequency components of the aerodynamic force, resulting in a decrease in the peak value of the unsteady aerodynamic force. Moreover, the phase of the admittance function causes a 'delay' in the aerodynamic forces of the moving train.
4. The moving train's fluctuating wind and unsteady aerodynamic forces in inhomogeneous and non-stationary wind environments significantly differ from those in homogeneous and stationary wind environments. To accurately analyze train operation safety in strong wind environments, it is necessary to accurately simulate the wind field and aerodynamic forces acting on the train while considering the characteristics of wind environments.  
Conceptualization, Y.S. and Q.X.; Methodology, N.Y. and N.C.; Validation, N.C.; Formal analysis, A.T.; Investigation, N.Y.; Resources, H.G.; Writing--original draft, N.Y. and A.T.; Writing--review & editing, N.C.; Supervision, Y.S. and H.G.; Funding acquisition, N.C. and Q.X. All authors have read and agreed to the published version of the manuscript.  
This research is supported by the National Key R&D Program of China (Grant No. 2022 YFB2602900), the National Natural Science Foundation of China (Grant No. 52378509), and the Science and Technology R&D Program of China Railway (Grant No. J2022G004).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.  
**Conflicts of Interest:** The author declares no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.