Study on Multi-objective Optimization Method of Dynamic Performance Parameters of High-speed Maglev Train
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摘要: 为提升高速磁浮列车动力学性能，提出一套高效的多目标优化设计方法，对磁浮列车悬挂参数、系统控制参数和轨道梁参数进行多目标优化设计。为保证仿真模型有效逼近高速磁浮列车实际运行状况以获得准确的输出响应，构建出磁浮系统分布式协同仿真模型，实现磁浮列车动力学模型、轨道梁有限元模型及控制系统的实时耦合，并选取5个关键设计参数作为优化设计变量；采用最优拉丁超立方试验设计方法均匀抽取20组样本，基于分布式协同仿真模型获得各样本点对应的7项动力学性能值；针对20组小样本、5输入7输出的高非线性问题，分析不同代理模型预测精度，建立优化设计变量和性能指标之间的代理模型；采用NSGA-Ⅱ（非支配排序遗传算法-Ⅱ）优化算法对设计变量进行多目标优化。计算表明7项性能指标经优化后均得到显著提升。Abstract: In order to improve the dynamic performance of the high-speed maglev train, an efficient multi-objective optimization design method is proposed to optimize the suspension parameters, system control parameters and track beam parameters of the maglev train.A distributed cooperative simulation model for the maglev system including the dynamic model, the finite element model is constructed to obtain the output response that approximates the actual operating conditions of the high-speed maglev train, and five key design parameters are selected as optimization design variables; 20 sets of samples are uniformly drawn by using the optimal Latin hypercube experimental design method, and 7 dynamic performance values corresponding to each sample point are obtained based on the distributed collaborative simulation model. For 20 sets of small samples, 5 input and 7 output high nonlinear problems, the prediction accuracy of different surrogate modelsis analyzed, and a surrogate model between optimizedis established
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Key words:
- maglev train /
- surrogate model /
- multi-objective optimization /
- NSGA-Ⅱ
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表 1 高速磁浮系统基本参数
参数名称 数值及单位 车体质量Mc 39000 kg 悬浮电磁铁质量Msm 603 kg 导向电磁铁质量Mgm 387 kg 电磁铁安装点刚度Km 1 × 108 N/m 电磁铁安装点阻尼Cm 1 × 105 N·s/m 空簧垂向刚度Ks 1.5 × 105 N/m 空簧垂向阻尼Cs 3000 N·s/m 
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表 2 磁浮列车系统性能评价指标
悬浮间隙
波动量Y1线圈
电流Y2车体垂向
振动加速度Y3车辆Sperling
平稳性指标Y4悬浮架振动
加速度Y5轨道梁振动
位移幅值Y6轨道梁振动
加速度Y7± 4 mm ≤ 50 A ≤ 0.125 g ≤ 2.5(V≤500 km/h)
≤ 2.75 (V > 500 km/h)– – ≤ 0.5 g
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表 3 磁浮列车系统关键设计变量
车辆二系悬挂参数 电磁铁悬浮控制参数 磁浮轨道梁 空簧垂向
刚度（单个）X1空簧垂向
阻尼（单个）X2间隙反馈
系数X3间隙速度
反馈系数X4轨道梁刚度
（25/31 m梁挠跨比）X5120 ~ 200 kN/m 2000 ~ 4000 N/(m/s) 5000 ~ 10000 A/m 5 ~ 50 A/(m/s) 1/15000 ~ 1/8000
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表 4 BP神经网络训练参数设置
参数名称 训练函数 传递函数 误差函数 迭代次数 学习率 隐层节点数 隐含层数 程序指令 ‘trainlm’ ‘logsig’ 、‘purelin’ ‘mse’ 100 0.02 13 1
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表 5 LSSVM训练参数设置
参数名称 核函数类型 优化算法 误差函数 交叉验证方式 程序指令 ‘RBF_kernel’ ‘simplex’ ‘mse’ ‘crossvalidatelssvm’
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表 6 LSSVM惩罚参数与核参数值
LSSVM 惩罚参数 核参数 Model_Y1 547401.1 12.4613 Model_Y2 58381.1 5.1644 Model_Y3 785154.3 16.2154 Model_Y4 2.84 × 1020 2.62 × 107 Model_Y5 276.6 22.0308 Model_Y6 6490883.9 307.7520 Model_Y7 410605.5 18.4973
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表 7 设计变量优化结果
优化解 空簧垂向刚度 空簧垂向阻尼 间隙反馈系数 间隙速度反馈系数 轨道梁刚度(25/31 m梁挠跨比) 1 132.42 kN/m 3736.59 N/(m/s) 5446.64 A/m 46.35 A/(m/s) 10/147027 2 132.84 kN/m 2890.5 N/(m/s) 7944.92 A/m 46.375 A/(m/s) 7/100099
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表 8 磁浮列车系统优化前后动力学性能对比
评价指标 初始性能 优化解1 性能指标改善百分比/% 优化解2 性能指标改善百分比/% 悬浮间隙波动量Y1 1.47 0.865 41.16 0.729 50.41 线圈电流Y2 30 28.630 4.57 28.920 3.60 车体垂向加速度Y3 0.049 0.037 24.49 0.039 20.41 车辆Sperling平稳性指标Y4 2.51 2.339 6.81 2.414 3.82 悬浮架振动加速度Y5 2.59 1.867 27.92 2.123 18.03 轨道梁振动位移幅值Y6 4.76 2.247 52.79 2.315 51.37 轨道梁振动加速度Y7 0.411 0.121 70.56 0.125 69.59 平均性能指标改善百分比 32.61 31.03
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