## 5 Conclusions  
In this study, large eddy simulation and Ffowcs Williams-Hawkings analogy are used to study the aerodynamic drag and noise characteristics of the pantograph area of a train  
Figure 16: Aerodynamic noise directivity caused by pantograph in different planes. (**a**) X-Y plane; (**b**) X-Z plane; (**c**) Y-Z plane. roof model with three cars at a speed of 400 km/h with different diversion strategies. Specifically, the flow field characteristics and pressure fluctuation, noise spectrum characteristics, and noise directivity of the computational models are analyzed. The main conclusions are as follows:  
1. The utilization of pantograph fairing on the train roof can ameliorate the aerodynamic drag of HSTs effectively, with a drag reduction rate up to 5.42%. The pantograph noise sources are mainly at the panhead, lower arm rod, and base frame. In addition, the installation of the fairing changes the position of pressure fluctuation when the airflow hits the pantograph. 2. The performance of aerodynamic noise reduction by the sinking platform and the pantograph fairing are different. The configuration of the pantographs installed on the sinking platform brings about 2 dBA reduction in SPL at 20 sound monitoring points along the train's running direction. In addition, the fairing mainly decreases the noise near the pantograph, and the largest SPL reduction is up to 3 dBA among the monitoring points. 3. Analysis of 1/3 octave band frequency spectra shows that the noise reduction effect of the sinking platform on the pantograph in the frequency band of 200-1000 Hz is not clear. The installation of the fairing prominently decreases the noise in the frequency band above 1000 Hz. Further analysis of spectral characteristics also shows that the influence of different diversion strategies on the spectral characteristics actually changes the noise spectral characteristics of the panhead. 4. The installation of the fairing weakens the OASPL of the pantograph effectively. In the X-Y plane, the noise directivity of the pantograph installed alone on the train roof is similar to the fairing installed, while both the noise directivity and OASPL changes when the pantograph is installed on the sinking platform, especially within \(50^{\circ}\leq\theta\leq 90^{\circ}\); in the X-Z plane, the OASPL for the fairing and sinking platform cases is significantly smaller within \(40^{\circ}\leq\theta\leq 180^{\circ}\). A similar distribution can be observed in the Y-Z plane. Overall, the prominent aerodynamic drag reduction effect of the pantograph fairing makes it a competitive solution for HSTs engineering. For the installation of the fairing, it is important to reduce the aerodynamic drag and noise of the faring itself. Furthermore, the combination type of the fairing and pantograph rod deserves further investigation. Conceptualization, Y.Z. and S.Z. ([PERSON]); methodology, H.L., S.Z. ([PERSON]), and Z.L. ; software, S.Z. ([PERSON]) and R.C. ; validation, H.L., S.Z. ([PERSON]), and R.C. ; formal analysis, H.L. and S.Z. ([PERSON]); investigation, R.C. and Z.L. ; resources, H.L. and S.Z. ([PERSON]); data curation, R.C. and Z.L. ; writing--original draft preparation, S.Z. ([PERSON]); writing--review and editing, H.L., Y.Z., S.Z. ([PERSON]), and R.C. ; visualization, S.Z. ([PERSON]); supervision, R.C. and Z.L. ; project administration, H.L. and Z.L. ; funding acquisition, H.L. and Y.Z. All authors have read and agreed to the published version of the manuscript. This research received external funding by the Science and Technology Research and Development Plan of China National Railway Group Co., Ltd. [grant numbers P2020J025, P2021J003, and P2021J036]. Not applicable. The authors acknowledge the computing resources provided by the High Performance Computing Public Platform of Central South University, China.