2022年亚太地区数学建模大赛问题B高速列车的优化设计
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2022年亚太地区数学建模大赛
问题B
高速列车的优化设计
2022年4月12日，中国高铁复兴CR450多机组成功实现单列列车速度435 km/h，相
对速度870 km/h，创造了高铁多机组列车穿越明线和隧道速度的世界纪录。新一代标
准动车组“复兴”是中国自主研发的具有全知识产权的新一代高速列车。它集成了国
内大量的现代高科技产品，在牵引、制动、网络、转向架、车轴等关键技术上取得了
重大突破。这是中国科技创新的另一项重大成就。图1是一个简化的模型
是高铁的几何结构。
图1。高速轨道几何形状的简化模型。[1]
中国高铁头部结构为弹头结构，鸭嘴兽结构采用日本高铁结构。图2为TP1、TP2、
TP3、TP4等4种典型高速铁路线头结构的简化模型。其中，高铁车头结构的设计主要考
虑了抗风性和噪声水平。
图2。四种典型的高铁轨头结构的简化模型。[2]
高速铁路弹头的设计过程不仅要以空气动力学为基本原理，还要反复进行仿真和
试验。经过数千次计算和实验，可以实现车头与车身周围的气流、气动力等相关参数
之间的优化方案。
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图3显示了流线型高速钢轨机头结构的不同区域。
图3。不同区域的流线型高铁火车头结构。[3]
请收集相关数据，建立多个数学模型，并回答以下问题：
问题1：请建立高速铁路空气阻力数学模型，考虑高速铁路几何形状与一般情况和
极端天气（如雨、雪、风）力的关系，模拟锥形和四条典型高速铁路的风阻力分布，
如图2所示，选择空气阻力最小的最佳高速铁路形状。
问题2：请分析高铁轨头曲线弧度对空气阻力的影响，建立高铁形状优化模型，设
计最佳的高铁形状，使高铁受空气阻力最小，并绘制优化后的高铁形状草图。
问题3：请建立高铁噪声的数学模型，分析锥形类型产生的噪声的强度和四个典型
的高铁如图2所示，模拟各自的噪声的分布，并选择最佳产生最小的高铁形状。
问题4：请结合前三个问题的结果，建立高速列车形状的综合优化模型，设计出最
佳的高铁形状，同时提高高速列车的速度，降低噪声。绘制高速轨道的形状草图，并
给出相应的结构参数。
23
您的PDF解决方案总共不超过25页，应该包括：
l一页汇总表。
l目录。
l你的完整解决方案。
注：APMCM竞赛的页面限制版数为25页。您提交的所有方面都达到了25页的限制（摘要
表，目录，您的完整解决方案）。但是，参考文献列表和附录的页面并不受限制。
附件：
图4。一般高速铁路的不同区域结构示意图。
参考文献
孙[1]振旭，姚山包和杨国伟（
2020）高速列车滑流的空气动力学优化研究，计算流体
力学的工程应用，14：1,11061127，DOI： 10。1080/19942060.2020.1810128.
孙[2]、振旭、姚书包、同学魏、姚永芳、杨国伟。2021.高速列车鼻子流线结构对气
动力学性能影响的数值研究”应用科学11，no。2:
784.
2022亚太建模思路免费获取:2973101684
https://doi.org/10.3390/app11020784
[3]孙振旭、姚永芳、郭地龙、杨国维、姚山包、张叶、陈大为、李贵博、尚克明、贾
玲。高速列车气动优化的研究进展1)。中国理论与应用力学杂志[J]，2021年，531：
51-74 DOI：10.6052/04591879-20-205。
[4]王，M。Y.，哈什米，S。A., 太阳，Z.X。以及其他人表面粗糙度对横风作用下高
速列车空气动力学的影响。Mech报。罪。37,
1090– 1103
(2021).
https://doi.org/10.1007/s10409-021-01099-7
[5]太阳，Z。X.，王，先生，魏，林立。以及其他人一种城市磁悬浮列车的空气动力
学形状优化。Mech报。罪。37, 954–969 (2021).https://doi.org/10. 1007/s10409-
021-01094-y
[6] Yao，Y.，孙，Z.，李，G。以及其他人在高速列车转向架舱附近采用被动控制装
置的气动力学优化。Mech报。罪。38,
321363
(2022).
https://doi.org/10.1007/s10409-022-21363-x
[7] Wang，M，孙，Z，朱，S，&杨，G。矩形条带尺寸对横风高速列车气动力学性能的
影响。ASME 2021流体工程部门夏季会议的会议记录。第2卷：流体应用和系统；流体
测量和仪器仪表。虚拟、在线。2021年8月10日至12日。V002T03A003.美国机械工程师
协会https://doi.org/10. 1115/FEDSM2021-65692
[8] Wang，Y，& Sun，Z。高速磁悬浮列车鼻部拓扑结构对气动性能的影响。ASME
2021流体工程部门夏季会议的会议记录。第2卷：流体应用和系统；流体测量和仪器仪
表。虚拟、在线。2021年8月10日至12日。V002T03A004.美国机械工程师协会
https://doi.org/10. 1115/FEDSM2021-65711
[9]孙，Z，姚，Y，孔，F，和杨，G。“城市磁悬浮列车非定常尾流特性的数值研究。
ASME-JSME-KSME 2019年第8届联合流体工程会议论文集。第3A卷：流体应用和系统。
圣弗朗西斯科
美国加利福尼亚州。2019年7月28日-8月1日。v03在03a003。美国机械工程师协会
https://doi.org/10.1115/AJKFluids2019-5041
2022亚太建模思路免费获取:297310168
1
Problem B
Optimal Design of High-speed Train
On April 12, 2022, China High Speed Railway Fuxing CR450 multiple units successfully
achieved a single train speed of 435 km/h and a relative speed of 870 km/h on the open line,
creating a world record for the speed of high-speed rail multiple units trains crossing open lines
and tunnels. The new generation standard EMU "Fuxing" is a new generation of high-speed
train independently researched and developed by China with full intellectual property rights. It
integrates a large number of modern domestic high-tech, and achieves important breakthroughs
in key technologies such as traction, braking, network, bogie, and axle. It is another major
achievement of China's scientific and technological innovation. Figure 1 is a simplified model
of the high-speed rail geometric structure.
Figure 1. Simplified model of high-speed rail geometry.[1]
The head structure of China's high-speed railway is bullet head, and the duckbill structure
is adopted by Japan's high-speed railway. Figure 2 shows the simplified models of four typical
high-speed railway head structures including the types of TP1, TP2, TP3 and TP4. Among
them, the design of high-speed rail head structure mainly considers air resistance and noise
level.
Figure 2. Simplified models of four typical high-speed rail head structures.[2]
The design process of bullet head of high-speed railway should not only take aerodynamics
as the basic principle, but also conduct simulation and experiment repeatedly. To achieve the
optimal scheme between the air flow, aerodynamic force, other relevant parameters around the
car head and the car body can be optimized after thousands of calculations and experiments.
2022 Asia and Pacific Mathematical Contest in Modeling2
Figure 3 shows the different areas of the streamlined high-speed rail head structure.
Figure 3. Different areas of streamlined high-speed rail head structure.[3]
Please collect relevant data, establish several mathematical models, and answer the
following questions:
Question 1: Please establish a mathematical model for the air resistance of the high-speed
railway, consider the relationship between the high-speed railway geometry and the force under
the general condition and extreme weather (such as rain, snow and wind), simulate the
distribution of air resistance for the conical type and the four typical high-speed railways as
shown in Figure 2, and select the best high-speed railway shape with the smallest air
resistance.
Question 2: Please analyze the influence of the radian of the high-speed rail head’s curve
on the air resistance, establish an optimization model of the high-speed rail’s shape, design the
best high-speed rail’s shape, making the high-speed rail suffer the least air resistance, and draw
a sketch of the optimized high-speed rail’s shape.
Question 3: Please establish a mathematical model for the noise generated by high-speed
rail, analyze the intensity of the noise generated by the conical type and the four typical high
speed rail as shown in Figure 2, simulate the distribution of their respective noise, and select
the best high-speed rail shape which generates the least noise.
Question 4: Please combine the results of the previous three questions to establish a
comprehensive optimization model of the high-speed rail shape and design the best high-speed
rail shape, while improving the speed of high-speed trains and reducing noise. Draw a sketch
of the high-speed rail’s shape and give the corresponding structural parameters.3
Your PDF solution of no more than 25 total pages should include:
l One-page Summary Sheet.
l Table of Contents.
l Your complete solution.
Note: The APMCM Contest has a 25-page limit. All aspects of your submission count toward
the 25-page limit (Summary Sheet, Table of Contents, your complete solution). However, the
pages of Reference List and Appendices are not limited.
Attachment:
Figure 4. Schematic diagram of different regional structures of general high-speed railway.
References:
[1] Zhenxu Sun, Shuanbao Yao & Guowei Yang (2020) Research on aerodynamic optimization
of high-speed train’s slipstream, Engineering Applications of Computational Fluid Mechanics,
14:1, 1106-1127, DOI: 10.1080/19942060.2020.1810128.
[2] Sun, Zhenxu, Shuanbao Yao, Lianyi Wei, Yongfang Yao, and Guowei Yang. 2021.
"Numerical Investigation on the Influence of the Streamlined Structures of the High-Speed
Train’s Nose on Aerodynamic Performances" Applied Sciences 11, no. 2: 784. 4
https://doi.org/10.3390/app11020784
[3] Sun Zhenxu, Yao Yongfang, Guo Dilong, Yang Guowei, Yao Shuanbao, Zhang Ye, Chen
Dawei, Li Guibo, Shang Keming, Jia Ling. RESEARCH PROGRESS IN AERODYNAMIC
OPTIMIZATION OF HIGH-SPEED TRAINS 1). Chinese Journal of Theoretical and Applied
Mechanics[J], 2021, 531: 51-74 DOI:10.6052/0459-1879-20-205.
[4] Wang, M.Y., Hashmi, S.A., Sun, Z.X. et al. Effect of surface roughness on the aerodynamics
of a high-speed train subjected to crosswinds. Acta Mech. Sin. 37, 1090–1103 (2021).
https://doi.org/10.1007/s10409-021-01099-7
[5] Sun, Z.X., Wang, M.Y., Wei, L.Y. et al. Aerodynamic shape optimization of an urban maglev
train. Acta Mech. Sin. 37, 954–969 (2021). https://doi.org/10.1007/s10409-021-01094-y
[6] Yao, Y., Sun, Z., Li, G. et al. Aerodynamic optimization using passive control devices near
the bogie cabin of high-speed trains. Acta Mech. Sin. 38, 321363 (2022).
https://doi.org/10.1007/s10409-022-21363-x
[7] Wang, M, Sun, Z, Ju, S, & Yang, G. "Influence of Rectangular Strips’ Size on Aerodynamic
Performance of a High-Speed Train Subjected to Crosswind." Proceedings of the ASME 2021
Fluids Engineering Division Summer Meeting. Volume 2: Fluid Applications and Systems;
Fluid Measurement and Instrumentation. Virtual, Online. August 10–12, 2021. V002T03A003.
ASME. https://doi.org/10.1115/FEDSM2021-65692
[8] Wang, Y, & Sun, Z. "Influence of the Topological Structures of the Nose of High-Speed
Maglev Train on Aerodynamic Performances." Proceedings of the ASME 2021 Fluids
Engineering Division Summer Meeting. Volume 2: Fluid Applications and Systems; Fluid
Measurement and Instrumentation. Virtual, Online. August 10–12, 2021. V002T03A004.
ASME. https://doi.org/10.1115/FEDSM2021-65711
[9] Sun, Z, Yao, Y, Kong, F, & Yang, G. "Numerical Study on Unsteady Wake Characteristics
of an Urban Maglev Train." Proceedings of the ASME-JSME-KSME 2019 8th Joint Fluids
Engineering Conference. Volume 3A: Fluid Applications and Systems. San Francisco,
California, USA. July 28–August 1, 2019. V03AT03A003. ASME.
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