基于Sobol’ 法的高速磁浮列车单点悬浮系统全局灵敏度分析

倪菲; 范琳; 徐俊起; 林国斌; 贾万涛

doi:10.3969/j.issn.0258-2724.20240545

基于Sobol’ 法的高速磁浮列车单点悬浮系统全局灵敏度分析

doi: 10.3969/j.issn.0258-2724.20240545

倪菲^{1, 2,},
范琳^{2, 3},
徐俊起^{1, 2},
林国斌^{1, 2},
贾万涛^4, ,

1.
同济大学磁浮交通工程技术研究中心，上海 201804
2.
同济大学高速磁浮运载技术全国重点实验室，上海 201804
3.
同济大学交通学院，上海 201804
4.
西北工业大学数学与统计学院，西安 710129

基金项目: 国家自然科学基金项目（52232013）；中央高校基本科研业务费专项资金（22120230311）

详细信息

作者简介:
倪菲（1985—），女，副研究员，研究方向为磁浮列车不确定性量化与鲁棒控制，E-mail：fei.ni@tongji.edu.cn

通讯作者:
贾万涛（1987—），男，副教授，研究方向为非线性随机动力学，E-mail：jiawantao@nwpu.edu.cn

中图分类号: U24；U271
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- 文章访问数: 99
- HTML全文浏览量: 56
- PDF下载量: 24
- 被引次数: 0
出版历程
- 收稿日期: 2024-10-19
- 修回日期: 2025-01-27
- 网络出版日期: 2025-04-17

Global Sensitivity Analysis of Single-Point Levitation System for High-Speed Maglev Train Based on Sobol’ Method

NI Fei^{1, 2
,},
FAN Lin^{2, 3},
XU Junqi^{1, 2},
LIN Guobin^{1, 2},
JIA Wantao^{4
, ,}

1.
National Maglev Transportation Engineering R & D Center, Tongji University, Shanghai 201804, China
2.
State Key Laboratory of High-speed Maglev Transportation Technology, Shanghai 201804, China
3.
College of Transportation, Tongji University, Shanghai 201804, China
4.
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China

摘要

摘要:
本文针对高速磁浮列车悬浮系统中不确定性参数对系统动态响应的影响展开研究，旨在为磁浮列车的优化设计提供理论依据. 首先，将高速磁浮列车悬浮系统简化为包含二系悬挂的单点悬浮系统，并构建相应的多项式混沌展开（PCE）模型；在此基础上，采用Sobol’ 法进行全局灵敏度分析，相较于在原始模型上进行蒙特卡洛仿真求解Sobol’ 灵敏度的方法，基于PCE模型的求解方法将计算效率提升了73倍，且计算误差控制在0.004以内；进一步地，深入分析车辆结构参数、轨道不平顺参数以及悬浮控制参数对悬浮系统间隙响应和车体垂向加速度的影响规律，识别了关键影响参数及其交互效应. 研究结果表明：电磁铁线圈匝数和电磁铁铁芯有效面积对车体垂向加速度及悬浮系统间隙响应影响较大，总灵敏度指数均大于0.2，而电磁铁质量和二系悬挂参数对其影响相对较小，总灵敏度指数均小于0.1；列车运行速度与轨道不平顺波长对悬浮间隙和车体垂向加速度的影响显著，总灵敏度指数均大于0.8，且二者之间存在明显的交互作用；在悬浮控制参数中，间隙响应对比例系数的变化最为敏感，总灵敏度指数接近1.
- 高速磁浮列车 /
- 电磁悬浮系统 /
- 灵敏度分析 /
- Sobol’ 法 /
- 多项式混沌展开
Abstract:
The impact of uncertain parameters on the dynamic response of the high-speed maglev train levitation system was investigated, aiming to provide a theoretical foundation for the optimal design of maglev trains. Firstly, the high-speed maglev train levitation system was simplified to a single-point levitation system incorporating secondary suspension, and a corresponding polynomial chaos expansion (PCE) model was established. On this basis, the Sobol’ method was employed for global sensitivity analysis. Compared to the method of solving Sobol’ sensitivity through Monte Carlo simulation on the original model, the PCE-based approach enhances computational efficiency by 73 times while maintaining the calculation error within 0.004. Furthermore, the influence patterns of vehicle structural parameters, track irregularity parameters, and levitation control parameters on the levitation gap response and the vertical acceleration of the train body were analyzed, identifying key influencing parameters and their interaction effects. The results indicate that the coil turns of the electromagnet and the effective area of the electromagnet core significantly affect the vertical acceleration of the train body and the levitation gap response, whereas the electromagnet mass and the secondary suspension parameters have a relatively minor impact, with total sensitivity indexes less than 0.1. The train operating speed and track irregularity wavelength significantly influence the levitation gap and the vertical acceleration of the train body, with total sensitivity indexes exceeding 0.8 and a notable interaction effect between the two. Among the levitation control parameters, the gap response is most sensitive to changes in the proportional coefficient, with the total sensitivity index approaching 1.
- high-speed maglev train /
- electromagnetic levitation system /
- sensitivity analysis /
- Sobol’ method /
- polynomial chaos expansion

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图 1 高速磁浮列车结构

Figure 1. Structure of high-speed maglev train

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图 2 单点悬浮系统结构

Figure 2. Single-point levitation system

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图 3 车辆结构参数变化下的悬浮系统动态响应

Figure 3. Dynamic responses of levitation system under variations in vehicle structural parameters

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图 4 两种灵敏度求解方法对比

Figure 4. Comparison between two sensitivity analysis methods

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图 5 车辆结构参数对车体垂向加速度响应的灵敏度

Figure 5. Sensitivity of vehicle structural parameters to vertical acceleration response of train body

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图 6 车辆结构参数对车体垂向加速度响应的二阶灵敏度

Figure 6. Second-order sensitivity of vehicle structural parameters to vertical acceleration response of train body

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图 7 车辆结构参数对悬浮间隙响应的灵敏度

Figure 7. Sensitivity of vehicle structural parameters to levitation gap response

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图 8 车辆结构参数对悬浮间隙响应的二阶灵敏度

Figure 8. Second-order sensitivity of vehicle structural parameters to levitation gap response

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图 9 轨道不平顺参数对车体垂向加速度响应的灵敏度

Figure 9. Sensitivity of track irregularity parameters to vertical acceleration response of train body

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图 10 轨道不平顺参数对车体垂向加速度响应二阶灵敏度

Figure 10. Second-order sensitivity of track irregularity parameters to vertical acceleration response of train body

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图 11 轨道不平顺参数对悬浮间隙响应的灵敏度

Figure 11. Sensitivity of track irregularity parameters to levitation gap response

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图 12 轨道不平顺参数对悬浮间隙响应的二阶灵敏度

Figure 12. Second-order sensitivity of track irregularity parameters to levitation gap response

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图 13 悬浮控制参数对车体垂向加速度、悬浮间隙响应的灵敏度

Figure 13. Sensitivity of levitation control parameters to vertical acceleration of train body and levitation gap response

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图 14 车体垂向加速度极值与单点悬浮系统负载质量关系

Figure 14. Relationship between extreme values of vertical acceleration of train body and load mass of single-point levitation system

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图 15 车体垂向加速度极值与二系悬挂阻尼关系

Figure 15. Relationship between extreme values of vertical acceleration of train body and secondary suspension damping

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表 1 单点悬浮系统模型参数

Table 1. Parameters of single-point levitation system model

参数数值

A_r/m² 0.115

m₁/kg 2000

m₂/kg 750

k_s/（N·m⁻¹） 150000

c_s/（N·s·m⁻¹） 3000

N_r/匝 270

下载: 导出CSV

表 2 轨道不平顺参数

Table 2. Parameters of track irregularities

参数数值

A_m/m 0.001

V/（km·h⁻¹） 600

L/m 25

D_m/W $ {10}^{-11} $

下载: 导出CSV

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