Global Sensitivity Analysis of Single-Point Levitation System for High-Speed Maglev Train Based on Sobol’ Method
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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0.20,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0.10;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0.80,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1.00.
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, with total sensitivity indexes exceeding 0.20, whereas the electromagnet mass and the secondary suspension parameters have a relatively minor impact, with total sensitivity indexes less than 0.10. 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 0.80 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 1.00.
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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 Ar/m2 0.115 m1/kg 2000 m2/kg 750 ks/(N·m−1) 150000 cs/(N·s·m−1) 3000 Nr/匝 270 表 2 轨道不平顺参数
Table 2. Parameters of track irregularities
参数 数值 Am/m 0.001 v/(km·h−1) 600 L/m 25 Dm/W 10−11 -
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