数据驱动的磁浮列车悬浮系统长时序响应预测方法

陈张航; 徐俊起; 梁鑫; 倪菲

doi:10.19818/j.cnki.1671-1637.2026.332

数据驱动的磁浮列车悬浮系统长时序响应预测方法

doi: 10.19818/j.cnki.1671-1637.2026.332

陈张航^{1, 2,},
徐俊起^{1, 2},
梁鑫³,
倪菲^{1, 2, ,}

1.
同济大学交通学院, 上海 201804
2.
同济大学国家磁浮交通工程技术研究中心, 上海 201804
3.
高速磁浮运载技术全国重点试验室, 山东青岛 266111

基金项目:

国家自然科学基金项目 52572416

国家自然科学基金项目 52232013

国家重点研发计划 2023YFB4302500

国铁集团科技研究开发计划 K2024T005

山东省重点研发计划 2024CXPT062

详细信息

作者简介:
陈张航(2003-)，女，江苏扬州人，工学博士研究生，E-mail: 2411709@tongji.edu.cn

通讯作者:
倪菲(1985-)，女，湖北恩施人，副教授，工学博士，E-mail: fei.ni@tongji.edu.cn

中图分类号: U237
计量
- 文章访问数: 13
- HTML全文浏览量: 7
- PDF下载量: 3
- 被引次数: 0
出版历程
- 收稿日期: 2026-02-27
- 录用日期: 2026-05-27
- 修回日期: 2026-04-10
- 刊出日期: 2026-09-28

Data-driven long-term response prediction method for maglev train suspension systems

CHEN Zhang-hang^{1, 2
,},
XU Jun-qi^{1, 2},
LIANG Xin³,
NI Fei^{1, 2
, ,}

1.
College of Transportation, Tongji University, Shanghai 201804, China
2.
National Maglev Transportation Engineering R&D Center, Tongji University, Shanghai 201804, China
3.
State Key Laboratory of High-speed Maglev Transportation Technology, Qingdao 266111, Shandong, China

Funds:

National Natural Science Foundation of China 52572416

National Natural Science Foundation of China 52232013

National Key R&D Program of China 2023YFB4302500

Science and Technology R&D Program of China State Railway Group Co., Ltd. K2024T005

Key R&D Program of Shandong Province 2024CXPT062

More Information

Corresponding author: NI Fei, associate professor, PhD, E-mail: fei.ni@tongji.edu.cn

Article Text (Baidu Translation)

摘要

摘要:
为克服高速磁浮列车悬浮系统动态响应长时域预测中的误差累积问题，提出了一种无需显式动力学微分方程的数据驱动响应预测方法。在深度未知方程(DUE)流映射学习框架基础上提出了2项改进，其一采用状态-干扰解耦策略，将轨道不平顺作为已知外部输入在网络输入端与状态变量拼接、在输出端仅预测状态变量，从根本上消除干扰通道的误差传播，其二引入初始状态锚定机制，将轨迹起始段的真实观测作为固定锚点持续注入网络输入，为递推链提供不受预测误差污染的全局参考基准；以电磁悬浮型高速磁浮列车单点悬浮系统为对象，分别在理想轨道不平顺与实测轨道不平顺2种干扰场景下进行验证。研究结果表明：DUE基线模型的预测曲线随递推步数增加出现明显漂移与发散；引入状态-干扰解耦与初始状态锚定后，在理想轨道不平顺场景下，改进方案相较于基线在各项误差指标上均实现了80%以上的降幅；消融试验表明，状态-干扰解耦是保障递推不发散的基础，初始状态锚定则有效抑制初始信息消退引起的累积偏差，二者具有明确的功能互补性；在实测轨道不平顺场景下，预测平均相对误差仍控制在4%以内，且在不同初始条件与干扰序列下表现出良好的统计一致性。所提方法可为高速磁浮悬浮系统的快速动态响应预测提供一种不依赖显式动力学方程的新途径。
- 磁浮列车 /
- 悬浮系统动态响应 /
- 流映射学习 /
- 数据驱动智能预测 /
- 误差累积抑制 /
- 轨道不平顺
Abstract:
To overcome the error accumulation problem in long-term prediction of dynamic responses of high-speed maglev train suspension systems, a data-driven response prediction method was proposed without requiring explicit dynamic differential equations. Two improvements are proposed on the basis of the deep unknown equations (DUE) flow map learning framework. First, a state-disturbance decoupling strategy was adopted. Track irregularity was treated as a known external input and concatenated with state variables at the network input, while state variables were predicted alone at the network output. Error propagation through the disturbance channel was thus fundamentally eliminated. Second, an initial-state anchoring mechanism was introduced. Real observations from the initial segment of the trajectory were used as fixed anchor points and continuously injected into the network input. A global reference baseline free from prediction error contamination was thereby provided for the recursive chain. The single-point suspension system of an electromagnetic suspension type high-speed maglev train was taken as the study object. Validation was conducted under two excitation scenarios, namely, ideal track irregularity and measured track irregularity. The results show that the prediction curves of the DUE baseline model exhibit obvious drift and divergence as the number of recursive steps increases. After the introduction of state-disturbance decoupling and initial-state anchoring, the improved scheme achieves a reduction of over 80% in all error metrics compared with the baseline under the ideal track irregularity scenario. Ablation experiments demonstrate that state-disturbance decoupling serves as the fundamental safeguard against recursive divergence, while initial-state anchoring effectively suppresses the cumulative error caused by the decay of initial information. The two strategies exhibit clear functional complementarity. Under the measured track irregularity scenario, the mean relative error of prediction is still kept within 4%. Good statistical consistency is also demonstrated under different initial conditions and disturbance sequences. The proposed method can provide a new approach for rapid dynamic response prediction of high-speed maglev suspension systems without relying on explicit dynamic equations.
- maglev train /
- suspension system dynamic response /
- flow map learning /
- data-driven intelligent prediction /
- error accumulation suppression /
- track irregularity

HTML全文

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 suspension system

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图 3 改进残差网络单步前向计算架构

Figure 3. Improved residual network single step forward computation architecture

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图 4 理想轨道不平顺干扰下DUE基线方法对车体垂向位移的预测结果

Figure 4. Prediction results of the DUE baseline method for vehicle body vertical displacement under ideal track irregularity disturbances

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图 5 理想轨道不平顺干扰下DUE基线方法对电磁铁垂向位移的预测结果

Figure 5. Prediction results of the DUE baseline method for electromagnet vertical displacement under ideal track irregularity disturbances

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图 6 理想轨道不平顺干扰下DUE+干扰自回归方法对车体垂向位移的预测结果

Figure 6. Prediction results of the DUE with disturbance autoregression method for vehicle body vertical displacement under ideal track irregularity disturbances

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图 7 理想轨道不平顺干扰下DUE+干扰自回归方法对电磁铁垂向位移的预测结果

Figure 7. Prediction results of the DUE with disturbance autoregression method for electromagnet vertical displacement under ideal track irregularity disturbances

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图 8 理想轨道不平顺干扰下GRU基线方法对车体垂向位移的预测结果

Figure 8. Prediction results of GRU baseline method for vehicle body vertical displacement under ideal track irregularity disturbances

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图 9 理想轨道不平顺干扰下GRU基线方法对电磁铁垂向位移的预测结果

Figure 9. Prediction results of GRU baseline method for electromagnet vertical displacement under ideal track irregularity disturbances

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图 10 理想轨道不平顺干扰下改进方案对车体垂向位移的预测结果

Figure 10. Prediction results of improved method for vehicle body vertical displacement under ideal track irregularity disturbances

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图 11 理想轨道不平顺干扰下改进方案对电磁铁垂向位移的预测结果

Figure 11. Prediction results of improved method for electromagnet vertical displacement under ideal track irregularity disturbances

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图 12 理想轨道不平顺干扰下仅解耦方案对车体垂向位移的预测结果

Figure 12. Prediction results of decoupling-only scheme for vehicle body vertical displacement under ideal track irregularity disturbances

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图 13 理想轨道不平顺干扰下仅解耦方案对电磁铁垂向位移的预测结果

Figure 13. Prediction results of decoupling-only scheme for electromagnet vertical displacement under ideal track irregularity disturbances

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图 14 理想轨道不平顺干扰下仅锚定方案对车体垂向位移的预测结果

Figure 14. Prediction results of anchoring-only scheme for vehicle body vertical displacement under ideal track irregularity disturbances

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图 15 理想轨道不平顺干扰下仅锚定方案对电磁铁垂向位移的预测结果

Figure 15. Prediction results of anchoring-only scheme for electromagnet vertical displacement under ideal track irregularity disturbances

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图 16 实测轨道不平顺干扰下改进方案对车体垂向位移的预测结果

Figure 16. Prediction results of improved method for vehicle body vertical displacement under measured track irregularity disturbances

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图 17 实测轨道不平顺干扰下改进方案对电磁铁垂向位移的预测结果

Figure 17. Prediction results of improved method for electromagnet vertical displacement under measured track irregularity disturbances

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表 1 理想轨道不平顺干扰下DUE基线、GRU基线与改进方案的预测误差对比

Table 1. Prediction error comparison between DUE baseline, GRU baseline and improved method under ideal track irregularity disturbances

方法	状态变量	MRE/%	RRMSE/%	Max RE/%
DUE基线	z₁	4.430 8	7.814 5	21.789 7
DUE基线	z₂	8.310 6	19.773 0	48.655 3
GRU基线	z₁	5.866 7	7.439 5	14.407 5
GRU基线	z₂	32.863 4	54.552 6	71.228 0
改进方案	z₁	0.754 0	1.067 4	2.512 7
改进方案	z₂	1.226 8	2.592 5	5.975 9

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表 2 实测轨道不平顺干扰下改进方案的预测误差

Table 2. Prediction errors of improved method under measured track irregularity disturbances

评估范围	典型轨迹		100条统计
状态变量	z₁	z₂	z₁	z₂
MRE/%	1.880 1	3.912 1	2.342 6±0.636 3	3.515 2±0.730 2
RRMSE/%	2.304 2	4.841 9	2.883 3±0.739 4	4.445 9±0.957 5
Max RE/%	6.410 3	13.992 4

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