Construction of Typical Driving Cycle for Tram
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摘要: 为合理评估有轨电车在轨道交通中的行驶特征及运行指标，为有轨电车设计与控制提供依据，对有轨电车典型行驶工况进行构建. 首先，以巴黎、布达佩斯、墨尔本城市的有轨电车线路及行驶数据为基础，采用聚类方法获取降维行驶特征；然后，基于马尔可夫链理论，构建有轨电车典型行驶工况；最后，将构建工况与实际工况进行特征值对比分析，并基于所构建的典型工况进行仿真验证. 结果表明：构建的典型行驶工况与实际工况样本数据库总体特征的平均偏差仅为2.63%，满足偏差低于5%的开发精度要求；此外，典型行驶工况与实际行驶工况下的需求功率误差也仅为1.78%，验证了典型工况模型的准确性和有效性.Abstract: In order to reflect the real driving characteristics and operating parameters of new-energy trams in rail transit, and provide a basis for the design and control of trams, a typical driving cycle was constructed. Firstly, according to the tram operation data and tram lines in the cities of Paris, Budapest and Melbourne, the clustering analysis was used to obtain the driving features with dimensional reduction; and then the typical driving cycle based on Markov chain principle was built. Finally, a comparative analysis was made between the constructed typical tram driving cycle and the existing driving conditions, and the constructed typical driving cycle was validated by simulation. The results show that the average deviation of driving characteristic parameters between the constructed driving cycle and driving database population is 2.63%, which meets the development accuracy requirement, i.e., the deviation should be less than 5%. In addition, the demand power error under the typical driving cycle and actual driving cycle was only 1.78%, which verifies the accuracy of typical driving cycle.
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Key words:
- driving cycle /
- tram /
- cluster analysis /
- Markov chain
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图 6 不同工况下能耗对比
Figure 6. Comparison of energy consumption with different driving cycles
表 1 短行程特征参数
Table 1. Characteristic parameters of short stroke
符号 含义 符号 含义 Vavg/（km•h−1） 平均速度 V0-30 低速因子 Vstd/（km•h−1） 速度标准差 V30-70 中速因子 Vmax/（km•h−1） 最大速度 a0-0.5 低加速因子 aavg/（m•s−2） 平均加速度 a0.5-1 中加速因子 astd/（m•s−2） 加速度标准差 r0-0.5 低减速因子 amax/（m•s−2） 最大加速度 r0.5-1 中减速因子 rstd/（m•s−2） 减速度标准差 a= 0 匀速因子 ravg/（m•s−2） 平均减速度 tD/s 怠速时间 
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表 2 短行程样本数据库
Table 2. Database of short stroke samples
序号 Vavg/（km•h−1） Vstd/（km•h−1） ··· tD/s a= 0 1 34.98 22.40 ··· 29 20.30 2 28.81 20.89 ··· 31 3.84 $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ 400 48.81 25.96 ··· 30 44.77
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表 3 主成分特征值和贡献率
Table 3. Eigen values and contribution rates of principal components
主成分序号 主成分特征值 主成分贡献率/% 主成分序号 主成分特征值 主成分贡献率/% 1 7.355 4 45.97 9 0.105 9 0.67 2 3.890 3 24.31 10 0.061 8 0.39 3 2.190 2 13.69 11 0.052 5 0.33 4 0.759 7 4.75 12 0.037 8 0.24 5 0.481 3 3.01 13 0.030 0 0.19 6 0.390 5 2.44 14 0.026 8 0.17 7 0.322 4 2.02 15 0.015 5 0.10 8 0.274 4 1.72 16 0.005 5 0.03
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表 4 短行程主成分得分矩阵
Table 4. Score matrix of short-stroke principal components
样本序号 T1 T2 T3 1 3.836 1.990 −0.206 2 4.467 2.133 −0.912 $ \vdots $ $\vdots$ $ \vdots $ $ \vdots $ 400 −1.853 1.410 2.026
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表 5 聚类结果特征值对比
Table 5. Characteristic value comparison of clustering results
工况 样本占
比/%tD/s Vavg/
（km•h−1）Vmax/
（km•h−1）aavg/
（m•s−2）V0-30 a=0 类1 10.3 23 51.9 70 0.91 16.1 47.1 类2 17.3 27 38.3 60 0.94 27.6 43.5 类3 27.6 30 23.4 38 0.91 64.0 53.2 类4 44.8 30 32.5 50 0.70 32.0 24.1
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表 6 构建工况与数据库样本特征参数对比
Table 6. Comparison of characteristic parameters between constructed cycle and sample population
特征参数 样本总体 构建工况 绝对偏差/% Vavg/（km•h−1） 32.99 31.65 4.06 Vstd/（km•h−1） 18.52 18.81 1.56 Vmax/（km•h−1） 70 70 0 aavg/（m•s−2） 0.82 0.80 2.44 astd/（m•s−2） 0.19 0.18 4.58 amax/（m•s−2） 1.30 1.25 3.85 rstd/（m•s−2） 1.26 1.31 3.78 ravg/（m•s−2） −1.34 −1.40 4.24 V0-30 0.38 0.37 3.04 V30-70 0.62 0.63 1.90 a0-0.5 0.08 0.08 2.33 a0.5-1 0.15 0.16 1.93 r0-0.5 0.02 0.02 2.03 r0.5-1 0.01 0.01 1.78 a= 0 37.86 36.82 2.75 tD/s 28.76 29.29 1.84
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