Subway passenger flow prediction based on optimized PSO-BP algorithm with coupled spatial-temporal characteristics
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摘要: 为提高地铁客流预测的准确性，以西安地铁1号线为例，分析了地铁客流的耦合时空特征，提取了影响地铁客流变化的5个主要因素，包括节日、非节日、时间段、站点和天气，构建了反向传播(BP)神经网络，预测了地铁客流；利用引入自适应变异与均衡惯性权重的粒子群优化(PSO)算法，优化了BP神经网络，形成了考虑复杂因素影响的地铁客流预测系统；选取了换乘站、非换乘站的首站与中间站，引入天气、节日、非节日因素，对比了不同时间段下的BP神经网络模型，优化了PSO-BP神经网络模型的预测误差。研究结果表明：考虑天气、节日、非节日因素，换乘站点分时段优化PSO-BP神经网络模型预测的平均绝对误差、均方根误差和平均绝对百分比误差，较不分时段的优化PSO-BP神经网络模型分别平均下降了40.13%、31.46%和23.89%，较分时段的BP神经网络模型分别平均下降了17.50%、17.86%和17.32%；非换乘站点分时段优化PSO-BP神经网络模型预测的平均绝对误差、均方根误差和平均绝对百分比误差，较不分时段的优化PSO-BP神经网络模型分别平均下降了16.50%、20.99%和32.59%，较分时段的BP神经网络模型分别平均下降了11.48%、12.10%和17.73%；各站点分时段优化PSO-BP神经网络模型预测的平均绝对误差、均方根误差、平均绝对百分比误差，较不分时段的优化PSO-BP神经网络模型分别平均下降了24.37%、24.48%和29.69%，较分时段的BP神经网络模型分别平均下降了13.49%、14.02%和17.59%，因此，利用考虑多影响因素的优化PSO-BP神经网络模型能提高地铁客流预测的准确性。Abstract: To improve the accuracy of subway passenger flow prediction, by considering the Xi'an Metro Line 1 as an example, five main factors affecting subway passenger flow variations, such as festival, non-festival, time period, station, and weather, were extracted to analyze the coupled spatial-temporal characteristics of subway passenger flow. A back propagation (BP) neural network was constructed to predict the subway passenger flow. The proposed BP neural network was further optimized by using a particle swarm optimization (PSO) algorithm that introduced adaptive mutation and balanced inertia weights to form a subway passenger flow prediction system that could consider complex influence factors. Transfer stations and non-transfer stations including a first and an intermediate station were selected, the weather, festival, and non-festival factors were considered, and the BP neural network models for different time periods were compared. Then, the prediction errors of the PSO-BP neural network model were optimized. Research results show that by considering the weather, festival and non-festival factors, the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) of the optimized PSO-BP neural network model predictions at transfer stations within the optimized time periods decrease by 40.13%, 31.46% and 23.89%, respectively, compared with the optimized PSO-BP neural network models prediction errors without the time periods, decrease by 17.50%, 17.86% and 17.32% compared with the BP neural network models prediction errors within the optimized time periods. The MAE, RMSE, and MAPE of the optimized PSO-BP neural network model predictions in the non-transfer stations within the optimized time periods decrease by 16.50%, 20.99% and 32.59%, respectively, compared with the optimized PSO-BP neural network model prediction errors without time periods, and decrease by 11.48%, 12.10% and 17.73%, respectively, compared with the BP neural network model prediction errors within the optimized time periods. The MAE, RMSE, and MAPE of the optimized PSO-BP neural network model predictions at each station within the optimized time periods decrease by 24.37%, 24.48% and 29.69%, respectively, compared with the optimized PSO-BP neural network model prediction errors without time periods, and decrease by 13.49%, 14.02% and 17.59%, respectively, compared with the BP neural network model prediction errors within the given time periods. Therefore, using the optimized PSO-BP neural network model and considering the influencing factors can improve the accuracy of subway passenger flow prediction. 8 tabs, 12 figs, 30 refs.
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图 2 北大街、通化门、五路口换乘站客流量变化
Figure 2. Passenger flow variations at transfer stations of Beidajie, Tonghuamen and Wulukou
图 3 北大街站各时间段客流量变化
Figure 3. Passenger flow variations in time periods at Beidajie Station
图 4 纺织城站各时间段客流量变化
Figure 4. Passenger flow variations in time periods at Fangzhicheng Station
图 5 康复路站各时间段客流量变化
Figure 5. Passenger flow variations in time periods at Kangfulu Station
图 10 劳动路站客流真实值与预测值
Figure 10. Actual and predictive passenger flows at Laodonglu Station
图 11 后卫寨站客流真实值与预测值
Figure 11. Actual and predictive passenger flows at Houweizhai Station
图 12 五路口站客流真实值与预测值
Figure 12. Actual and predictive passenger flows at Wulukou Station
表 1 站点早晚高峰类型划分
Table 1. Classification of morning and evening peak types at stations
工作日早晚高峰类型 站点 双峰早高峰客流较多 后卫寨、纺织城、三桥、皂河、枣园、汉城路、开远门、劳动路、半坡、北大街、五路口 双峰晚高峰客流较多 朝阳门 双峰早晚高峰客流一致 通化门 单峰为早高峰 长乐坡、浐河 单峰为晚高峰 康复路 早晚高峰客流基本一致 玉祥门、洒金桥、万寿路 
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表 2 雨雪天气与客流之间量的Spearman相关系数
Table 2. Spearman correlation coefficients between rainy/snowy day and passenger flow
天气类型 相关系数 显著性(双侧) 雨天 -0.813 0 雪天 -0.913 0
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表 3 通化门站周内欧氏距离
Table 3. Euclidean distances in a week at Tonghuamen Station
星期 一 二 三 四 五 六 日 一 0.000 0 0.999 0 1.235 9 1.504 2 7.233 6 7.709 5 7.361 4 二 0.999 0 0.000 0 0.714 7 1.468 2 6.887 1 7.336 9 6.901 5 三 1.235 9 0.714 7 0.000 0 1.835 4 7.154 4 7.597 4 6.958 5 四 1.504 2 1.468 2 1.835 4 0.000 0 7.175 1 7.554 2 7.344 3 五 7.233 6 6.887 1 7.154 4 7.175 1 0.000 0 4.846 8 8.070 4 六 7.709 5 7.336 9 7.597 4 7.554 2 4.846 8 0.000 0 4.679 1 日 7.361 4 6.901 5 6.958 5 7.344 3 8.070 4 4.679 1 0.000 0
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表 4 站点不同日期聚类结果
Table 4. Clustering results on different dates at each station
站点 周一 周二 周三 周四 周五 周六 周日 五路口 L1 L1 L1 L1 L2 L3 L4 通化门 L1 L1 L1 L2 L3 L4 L5 北大街 L1 L2 L2 L2 L3 L4 L5 后卫寨 L1 L2 L2 L2 L3 L4 L5 三桥 L1 L1 L2 L2 L3 L4 L5 皂河 L1 L2 L2 L2 L3 L4 L5 枣园 L1 L2 L1 L2 L3 L4 L5 汉城路 L1 L2 L2 L2 L3 L4 L5 开远门 L1 L2 L2 L2 L3 L4 L5 劳动路 L1 L1 L2 L2 L3 L4 L5 玉祥门 L1 L2 L1 L1 L3 L4 L5 洒金桥 L1 L1 L1 L2 L3 L4 L5 朝阳门 L1 L2 L2 L2 L3 L4 L5 康复路 L1 L1 L1 L2 L3 L4 L5 万寿路 L1 L2 L2 L2 L3 L4 L5 长乐坡 L1 L2 L2 L1 L3 L4 L5 浐河 L1 L2 L1 L1 L3 L4 L5 半坡 L1 L2 L2 L2 L3 L4 L5 纺织城 L1 L1 L2 L2 L3 L4 L5
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表 5 换乘站不同时间段聚类结果
Table 5. Clustering results in different time periods at transfer station
时间段 周一至周三 周四 周五 周六 周日 06:00~07:00 M1 M1 M1 M1 M1 07:00~08:00 M2 M2 M2 M2 M2 08:00~ 09:00 M2 M2 M3 M3 M2 09:00~10:00 M3 M3 M1 M2 M2 10:00~11:00 M3 M3 M1 M2 M2 11:00~12:00 M3 M3 M1 M2 M2 12:00~13:00 M3 M3 M1 M3 M3 13:00~14:00 M3 M3 M2 M3 M3 14:00~15:00 M3 M3 M2 M3 M3 15:00~16:00 M3 M3 M2 M3 M3 16:00~17:00 M3 M3 M2 M3 M3 17:00~18:00 M2 M2 M3 M3 M3 18:00~19:00 M2 M2 M3 M3 M3 19:00~20:00 M3 M3 M2 M3 M3 20:00~21:00 M3 M3 M1 M2 M2 21:00~22:00 M3 M3 M1 M2 M2 22:00~23:00 M1 M1 M1 M2 M2 23:00~24:00 M1 M1 M1 M1 M1
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表 6 劳动路站客流预测误差
Table 6. Passenger flow prediction errors at Laodonglu Station
客流预测 不分时段 分时段 BP神经网络模型 优化PSO-BP神经网络模型 BP神经网络模型 优化PSO-BP神经网络模型 误差评价指标 E1/[人次·(30 min)-1] 28.98 27.40 26.48 24.52 22.24 23.42 19.61 20.68 29.95 23.81 22.86 22.20 23.26 23.27 25.16 20.24 E2/[人次·(30 min)-1] 39.70 37.33 34.49 32.72 29.71 32.27 27.82 28.60 40.50 32.59 31.34 29.81 31.78 31.08 35.76 28.18 E3/% 8.69 8.81 8.78 8.13 6.78 6.96 6.86 6.62 8.73 8.42 6.75 7.10 9.00 7.20 7.36 5.91
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表 7 后卫寨站客流预测误差
Table 7. Passenger flow prediction errors at Houweizhai station
客流预测 不分时段 分时段 BP神经网络模型 优化PSO-BP神经网络模型 BP神经网络模型 优化PSO-BP神经网络模型 误差评价指标 E1/[人次·(30 min)-1] 35.57 36.01 29.01 25.16 23.52 23.44 21.05 20.80 36.55 29.27 25.61 20.53 35.91 26.19 21.20 20.82 E2/[人次·(30 min)-1] 40.26 40.20 35.04 34.38 27.82 27.85 25.21 24.28 41.98 32.56 26.53 23.06 38.35 35.54 29.19 24.57 E3/% 8.03 8.07 7.11 7.23 5.94 5.56 3.58 3.86 7.61 7.58 5.38 3.93 8.56 7.00 5.35 4.06
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表 8 五路口站客流预测误差
Table 8. Passenger flow prediction errors at Wulukou Station
客流预测 不分时段 分时段 BP神经网络模型 优化PSO-BP神经网络模型 BP神经网络模型 优化PSO-BP神经网络模型 误差评价指标 E1/(人次·h-1) 47.80 47.98 40.51 41.17 30.28 29.88 24.37 24.65 47.26 42.49 29.54 25.06 48.89 40.52 29.81 24.52 E2/(人次·h-1) 56.64 56.04 49.84 47.99 41.02 40.04 32.79 32.89 54.84 48.88 39.58 33.24 56.65 45.26 39.52 32.65 E3/% 4.75 4.79 3.35 3.39 3.02 3.06 2.81 2.53 4.82 3.38 3.19 2.74 4.79 3.45 2.98 2.05
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