A Grey Relation Projection-Random Forest Prediction Model of Energy Consumption for Electric Buses Considering Driving Style
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摘要: 为探索驾驶员驾驶行为与电动公交车能耗之间的关系，采用随机森林算法建立电动公交车能耗预测模型。为克服驾驶行为特征参数和样本数据的随机性对电动公交车能耗预测模型的负面影响，运用灰色关联投影法计算各驾驶行为特征参数的灰色关联度以及各样本数据的投影值，筛选出与能耗具有高关联性的驾驶行为特征参数作为模型的输入变量，以及相似度较高的样本数据作为训练集和测试集。同时，引入了与能耗具有显著相关性的驾驶风格变量以进一步提升模型的预测能力，运用K-means聚类方法将驾驶风格分类并得到驾驶风格标签。将驾驶风格标签和筛选后驾驶行为特征参数作为输入变量，单位里程能耗作为输出变量，基于筛选后的数据集建立了考虑驾驶风格的电动公交车能耗灰色关联投影-随机森林（GRP-RF）预测模型。基于广州市某线路电动公交车运营数据对模型进行检验，并运用该模型分析加速、制动和运行3种典型场景下相应驾驶行为特征参数对电动公交车能耗的影响。结果表明：该模型预测能耗的均方根误差（RMSE）和平均绝对百分比误差（MAPE）分别为0.001 8 kW·h/km和3.42%。相比于不考虑驾驶风格的GRP-RF模型和随机森林模型，该模型的RMSE分别降低了35.71%和48.57%，MAPE分别降低了38.82%和46.81%。研究结果表明：加速、制动和运行阶段的平均能耗分别为1.066，0.903 7，0.955 2 kW·h/km；为使各阶段能耗在相应均值以下，加速阶段应控制加速踏板开度在55%以内；制动阶段应控制制动踏板开度在25%以内；运行阶段应控制车速在40 km/h以内。Abstract: In order to study the relationship between driving behaviors and energy consumption of electric buses, a prediction model of energy consumption based on the random forest algorithm is developed for electric buses. In order to address the negative impacts from the randomness of the sample data and the parameters characterizing driving behaviors, the grey relational grades of the parameters for representing driving behaviors and the projection values of the sample data are calculated by a grey relational projection method. The parameters representing driving behaviors that have a high correlation with energy consumption are selected as the input variables, and the sample data with a high similarity are used as the training and testing dataset. The variables representing driving styles, which are significantly correlated with energy consumption, are introduced into the model to further improve the accuracy. Driving styles are classified and labelled by a K-means clustering method. In addition, a grey relation projection-random forest(GRP-RF)model for predicting energy consumption of electric buses is developed by taking the driving styles and the selected parameters for representing driving behavior as input variables, and the energy consumption per kilometer as the output variable. The model is tested based on the operation data of electric buses from a bus line in the City of Guangzhou, and the impacts of the parameters representing driving behaviors on the energy consumption is analyzed under the following three typical scenarios: acceleration, braking, and operation stage. The results show that the root mean square error(RMSE)and mean absolute percentage error(MAPE)of the prediction model are 0.001 8 kW·h/km and 3.42%, respectively. Compared with the GRP-RF model and the random forest model without considering the driving styles, the RMSE is decreased by 35.71% and 48.57% and the MAPE is decreased by 38.82% and 46.81%, respectively. Moreover, study results show that the average energy consumption at the acceleration, braking, and operation stage is 1.066, 0.903 7, 0.955 2 kW·h/km, respectively. To keep the energy consumption lower than the average value at each stage, the accelerator pedal opening should be within 55% of its full capacity at the acceleration stage; the brake pedal opening should be controlled within 25%of its full capacity at the braking stage, and the speed should be limited within 40 km/h at the operation stage.
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图 1 不同驾驶风格各行为特征参数
Figure 1. The characteristic parameters of each behavior of different driving styles
图 3 各特征参数与能耗的灰色关联度
Figure 3. The grey relation degree of each characteristic parameter and energy consumption
图 6 随机森林中决策树棵数对性能的影响
Figure 6. The influence of the number of decision trees on the performance in RF
图 9 加速踏板开度与能耗关系
Figure 9. Relationship between accelerator pedal opening and energy consumption
图 10 制动踏板开度与能耗关系
Figure 10. Relationship between brake pedal opening and energy consumptions
表 1 驾驶员驾驶行为特征和能耗统计描述
Table 1. Statistical description of driver driving behavior characteristics and energy consumption
特征参数 最小值 最大值 平均值 标准差 离散系数 加速踏板平均开度/% 7.185 25.76 17.03 2.780 0.163 182 加速踏板开度标准差/% 19.20 40.49 28.54 3.562 0.124 813 制动踏板平均开度/% 1.046 7.600 3.440 1.354 0.393 651 制动踏板开度标准差/% 4.950 11.06 7.519 1.357 0.180 453 平均车速/（km/h） 1.115 13.66 11.27 1.310 0.116 266 车速标准差/（km/h） 2.422 13.37 11.97 0.909 4 0.075 992 加速踏板比例/% 0.153 8 0.463 7 0.336 1 0.041 77 0.124 295 制动踏板比例/% 0.049 77 0.416 0 0.233 2 0.077 57 0.332 617 制动踏板开度＞30%比例/% 0 0.040 62 0.011 79 0.007 332 0.622 107 车速＞40 km/h比例/% 0 0.022 31 0.004 857 0.004 593 0.945 595 单位里程能耗/（kW∙h/km） 0.686 7 1.123 0.831 3 0.076 00 0.091 426 
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表 2 部分驾驶员各评测指标
Table 2. The evaluation indicators of some driver
驾驶员编号 车速平均值/（km/h） 车速标准差/（km/h） 车速最大值/（km/h） 加速度平均值/（m/s2） 加速度标准差/（m/s2） 1 13 12.6 45 0.767 2 0.992 0 2 10.8 11.15 40 0.750 6 0.933 0 3 10.77 10.86 40 0.841 4 1.103 4 12.27 12.52 44 0.653 5 0.839 7 5 8.05 11.1 43 0.618 6 0.766 8
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表 3 不同K值下的平均轮廓系数
Table 3. The value of S under different values of K
参数 平均轮廓系数S K = 3 0.696 7 K = 4 0.743 2 K = 5 0.704 9
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表 4 各模型预测误差
Table 4. Prediction error of each model
误差指标 RMSE/ (kW∙h/km) MAPE/% 运算时间/s 本模型 0.001 8 3.42 1.756 3 GRP-RF 0.002 8 5.59 1.738 0 RF 0.003 5 6.43 1.731 4
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