HIGH-SPEED TRAIN TREAD WEAR PREDICTION MODEL BASED ON I-ML-ELM
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摘要: 针对高速列车车轮踏面磨耗单一模型无法对各种复杂工况下列车车轮踏面磨耗进行定量计算的问题, 提出一种基于恒等映射多层极限学习机的高速列车车轮踏面磨耗测量方法. 首先将恒等映射引入到多层极限学习机中, 提出一种基于恒等映射的多层极限学习机模型(identity multilayer extreme learning machine, I-ML-ELM), 采用机器学习公共数据集对该模型进行性能验证, 数值结果表明I-ML-ELM模型具有较好的准确性与泛化性; 然后基于车辆-轨道耦合动力学理论建立高速列车的车辆-轨道耦合动力学模型, 模拟列车运行的不同工况, 观测和分析高速列车的车轮踏面磨耗情况, 并通过I-ML-ELM预测模型对高速列车车轮踏面磨耗量进行学习及预测; 最后应用高速列车车轮踏面磨耗的实际测量值对I-ML-ELM预测模型进行进一步的验证, 结果表明: I-ML-ELM预测模型的各项性能参数指标在整体上优于以下五种网络: ELM, FLN, ML-ELM, ML-KELM和DLSFLN, 通过高速列车线路实测数据的进一步验证表明, 本文提出的基于I-ML-ELM的高速列车车轮踏面磨耗预测模型能较好地反映不同参数对高速列车车轮踏面磨耗值的影响规律.Abstract: For purpose of solving the problem that a single model of high-speed train wheel tread wear cannot be used for quantitative calculation of train wheel tread wear under various complicated working conditions, we propose a feasible measurement method of wheel tread wear of high-speed trains based on the multilayer extreme learning machine with identity mapping. Firstly, we introduce the identity mapping into the multilayer extreme learning machine, then we propose an identity multilayer extreme learning machine (I-ML-ELM) model. In order to test the I-ML-ELM validity, it is applied to four multivariate regression data sets which are from machine learning public data sets. And experimental results show that the I-ML-ELM can achieve a perfect generalization performance and stability at a fast training speed and a quick reaction of the trained network to new observations. Secondly, based on the vehicle-track coupled dynamics theory, we establish the vehicle-track coupling dynamics model of high-speed trains. By simulating different working conditions, we observe the wheel tread wear of high-speed trains, and the I-ML-ELM prediction model is used to learn and predict the wheel tread wear of high-speed trains. Finally, in order to further test the effectiveness of I-ML-ELM prediction model, it is applied to the actual measurement value of wheel tread wear of high-speed train. The results show that compared with those five learning machines (extreme learning machine, fast learning machine, multilayer extreme learning machine, multilayer kernel extreme learning machine and derived least square fast learning network), the performance parameters of I-ML-ELM prediction model are the best as a whole and the model achieves a very good prediction precision and generalization ability. The further verification of the measured data of high-speed train lines show that the prediction model based on I-ML-ELM can not only reflect the influence of different operating parameters on the wheel tread wear value of high-speed trains better, but also realize the prediction of wheel tread wear.
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Key words:
- wheel tread wear /
- extreme learning machine /
- wear prediction /
- model identification /
- high-speed train
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图 3 不同隐层神经元条件下的网络回归精度变化趋势
Figure 3. Variation trend of network regression accuracy under different hidden layer neurons
图 5 列车运行不同里程时踏面廓形及磨耗深度
Figure 5. The tread profile and wear depth under different mileage of train operation
图 6 不同车速下列车运行100000 km 磨耗深度
Figure 6. 100000 km wear depth of train running at different speeds
图 8 实测列车运行不同里程下车轮踏面廓形图
Figure 8. Measured wheel tread profile under different mileage of train operation
图 9 测试样本的踏面磨耗预测值和实际测量值对比图
Figure 9. Comparison between predicted value and sample value of testing sample of wheel tread wear value
表 1 数据集的基本数据信息
Table 1. Basic data information of data set
Data set Attributes Training samples Testing samples machine CPU 6 150 59 wine quality 11 3429 1469 California housing 8 14448 6192 estate valuation 6 290 124 
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表 2 算法在不同网络下数据集RMSE值比较
Table 2. Obtained RMSE by different networks of the algorithm
Algorithms Machine CPU Wine quality California housing Estate valuetion ELM 0.1616 0.0019 0.1791 0.0011 FLN 0.4185 0.0019 0.2308 0.0011 DLSFLN 127.87 0.0016 195.63 0.0012 ML-ELM 0.0652 0.0019 0.2269 0.0017 ML-KELM 0.0568 0.0018 0.2468 0.0018 I-ML-ELM 0.0322 0.0015 0.1399 0.0012
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表 3 算法在不同网络下数据集MAXE值比较
Table 3. Obtained MAXE by different networks of the algorithm
Algorithms Machine CPU Wine quality California housing Estate valuation ELM 0.9052 0.0387 7.9992 0.0049 FLN 2.4028 0.0340 14.1135 0.0052 DLSFLN 982.19 0.0094 1.53 × 104 0.0052 ML-ELM 0.2665 0.0077 0.7508 0.0058 ML-KELM 0.2515 0.0065 0.6028 0.0060 I-ML-ELM 0.1284 0.0072 1.2638 0.0048
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表 4 算法在不同网络下数据集MAPE值比较
Table 4. Obtained MAPE by different networks of the algorithm
Algorithms Machine CPU Wine quality California housing Estate valuation ELM 0.6851 0.1029 0.2837 0.1502 FLN 0.8469 0.1036 0.2921 0.0011 DLSFLN 17.2561 0.0994 9.5098 0.1649 ML-ELM 1.2494 0.1082 0.5394 0.2583 ML-KELM 1.0452 0.1055 0.5580 0.2946 I-ML-ELM 0.5684 0.0900 0.2831 0.1764
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表 5 算法在不同网络下数据集MAE值比较
Table 5. Obtained MAE by different networks of the algorithm
Algorithms Machine CPU Wine quality California housing Estate valuation ELM 0.0586 0.0013 0.1090 8.13 × 10−4 FLN 0.1159 0.0013 0.1094 8.08 × 10−4 DLSFLN 16.7033 0.0013 2.5887 9.13 × 10−4 ML-ELM 0.0450 0.0014 0.1813 1.30 × 10−3 ML-KELM 0.0379 0.0014 0.1923 1.40 × 10−3 I-ML-ELM 0.0234 0.0011 0.1023 9.36 × 10−4
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表 6 算法在不同网络下数据集的测试时间(s)比较
Table 6. Data test time (s) comparison of the algorithm under different networks
Algorithms Machine CPU Wine quality California housing Estate valuation ML-ELM 0.6360 0.8133 1.2236 0.7140 ML-KELM 0.0029 0.5296 0.2468 0.0025 I-ML-ELM 0.0028 0.0034 0.0043 0.0029
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表 7 高速列车主要参数
Table 7. Basic parameters of high-speed vehicle
Name Specification car body mass/kg 33766 length between bogie centers/m 17.5 frame mass/kg 2280 wheelset mass/kg 1901.8 running circle diameter/m 0.86 wheelset semibase/m 1.493
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表 8 不同网络模型在仿真数据下的性能参数
Table 8. Performance parameters of different network models under simulation data
Algorithms RMSE MAXE MAPE MAE ELM 0.0950 0.2000 165.0150 0.0702 FLN 0.1108 0.2529 279.5350 0.0826 DLSFLN 0.0355 0.1850 20.3785 0.0158 ML-ELM 0.0021 0.0034 12.2321 0.0019 ML-KELM 0.0018 0.0060 0.2946 0.0014 I-ML-ELM 2.111 × 10−4 5.5786 × 10−4 0.4781 1.6527 × 10−4
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表 9 不同模型在现场数据下的性能参数
Table 9. Performance parameters of different algorithms under field data
Algorithms RMSE MAXE MAPE MAE ELM 0.0055 0.0102 0.2343 0.0046 FLN 0.0055 0.0102 0.2343 0.0046 DLSFLN 0.0055 0.0102 0.2343 0.0046 ML-ELM 0.0101 0.0171 0.3456 0.0081 ML-KELM 0.0106 0.0178 0.3614 0.0087 I-ML-ELM 0.0032 0.0047 0.1539 0.0029
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