Forecast and Early Warning of Regional Bus Passenger Flow Based on Machine Learning

Liu, Wusheng; Tan, Qian; Wu, Wei

doi:https://doi.org/10.1155/2020/6625435

Mathematical Problems in Engineering

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Recent Advances in Industrial Mathematics and Applications

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Research Article | Open Access

Volume 2020 | Article ID 6625435 | https://doi.org/10.1155/2020/6625435

Forecast and Early Warning of Regional Bus Passenger Flow Based on Machine Learning

Wusheng Liu,¹Qian Tan,²and Wei Wu³

Academic Editor: Hussein Abulkasim

Received03 Nov 2020

Revised25 Nov 2020

Accepted04 Dec 2020

Published15 Dec 2020

Abstract

This paper mainly forecasts the short-term passenger flow of regional bus stations based on the integrated circuit (IC) card data of bus stations and puts forward an early warning model for regional bus passenger flow. Firstly, the bus stations were aggregated into virtual regional bus stations. Then, the short-term passenger flow of regional bus stations was predicted by the machine learning (ML) method of support vector machine (SVM). On this basis, the early warning model for regional bus passenger flow was developed through the capacity analysis of regional bus stations. The results show that the prediction accuracy of short-term passenger flow could be improved by replacing actual bus stations with virtual regional bus stations because the passenger flow of regional bus stations is more stable than that of a single bus station. The accurate prediction and early warning of regional bus passenger flow enable urban bus dispatchers to maintain effective control of urban public transport, especially during special and large-scale activities.

1. Introduction

Urban public transport is a traffic mode to alleviate traffic congestion and make efficient use of road resources. To realize intelligent dispatching of buses, it is important for decision makers to know well the change law of bus passenger flow and accurately predict the passenger flow in the short term. Burst passenger flows cause a huge amount of traffic demand in a short time, which may bring great pressure to public security. Early warning of passenger flow is required to have some preparation by the administration. However, the urban bus stops lack real-time early warning tools with good accuracy nowadays.

The short-term bus passenger flow is affected by various random, complex, and space-varying factors. In areas with large passenger flow, it is difficult to forecast the short-term change of bus passenger flow. Currently, short-term traffic is generally predicted by traditional statistical methods, novel intelligent methods, and hybrid methods.

Originating from time series analysis in the 1980s, the traditional statistical methods are built on the data collected by manual surveys. Over the years, these methods have been evolving and intellectualized in the context of traffic flow prediction. In the forecast of short-term passenger flow at a bus station, the entry and exit volumes mainly come from the card swiping records of the automatic fare collection (AFC) system. Taking such continuous data as a time series, many models have been designed for traffic flow prediction based on statistical principles, including autoregressive (AR) model, moving average (MA) model, autoregressive integrated moving average (ARIMA) model, and seasonal ARIMA (SARIMA) model [1–4]. In addition, many have introduced k-nearest neighbors (k-NN) [5], nonparametric regression [6, 7], and Kalman filter [8] to predict short-term traffic flow.

Since the dawn of the big data era, the amount of public transport data has exploded with the application of novel techniques such as the integrated circuit (IC) card. The traditional statistical methods could no longer adapt to the complex environment and changing passenger flow at bus stations. With the rapid development of computational intelligence (AI) and data mining, data-driven intelligent methods have become popular in the prediction of short-term passenger flow [9]. The novel intelligent methods include long short-term memory (LSTM) [10–12], neural network (NN) [13–20], random forest (RF) [21, 22], support vector machine (SVM) [23, 24], fusion convolutional LSTM (FCL Net) [25], agent-based model (ABM) [26], and Bayesian network [27].

Recent years have witnessed the emergence of many hybrid forecast methods, most of which are combinations of novel intelligent methods such as NN and ML. For instance, Ke et al. [25] fused the FCL Net into a new deep learning (DL) method for the projection of short-term passenger demand. Xiao et al. [28] developed a new hybrid forecast strategy for air transport demand, which couples singular spectrum analysis (SSA), adaptive network fuzzy inference system (ANFIS), and optimized particle swarm optimization (OPSO). Sun et al. [29] combined wavelet transform (WT) with SVM into a hybrid prediction model for passenger flow; the model decomposes, predicts, and reconstructs the data on passenger flow in three stages and inherits the merits of both WT and SVM. Tan et al. [30] put forward a total traffic flow prediction method based on NN, MA, exponential smoothing (ES), and autoregressive MA (ARIMA).

In addition, Hinton and Salakhutdinov [31] applied DL to solve short-term prediction. Hu et al. [32] optimized the parameters of support vector regression (SVR) through particle swarm optimization (PSO), introduced historical momentum to reduce the impact of noise in traffic flow data, and then established a PSO-SVR model for the forecast of short-term traffic flow. Doğan [33] designed the periodic outstaring and prediction (PCP) algorithm, adopted the algorithm to improve the training set of artificial neural network (ANN), and proved that the improved ANN could predict short-term traffic flow based on selected clusters. Bagloee et al. [34] proposed a hybrid ML-based method to solve the bilevel optimization problem. Han et al. [35] derived a hybrid, optimized LSTM from Nesterov accelerated adaptive moment estimation (Nadam) and stochastic gradient descent (SGD).

To sum up, the traditional statistical methods mostly treat the current traffic state as a linear combination of the previous states and errors. On the upside, the traffic flow can be predicted simply by mathematical statistics, with relaxed data requirements. On the downside, the traditional methods fail to reflect the randomness and nonlinearity of traffic flow, consume too much manpower and financial resources in data acquisition, and have a low accuracy in the prediction of traffic flows, especially that with sudden changes. The novel intelligent methods are better than the traditional methods in data fitting and prediction accuracy, but the computing process is much more complex. The hybrid methods generally consider the features of actual traffic flow. The prediction accuracy of these methods varies with the coupled algorithms. Compared with the intelligent methods, the hybrid methods are highly complicated. The advantages, disadvantages, and applicability of common short-term prediction methods are shown in Table 1.

Despite the abundant results on short-term forecast, only a few scholars have explored the prediction or early warning of the passenger flow at urban bus stations. Gong et al. [36] proposed an ARIMA model and a Kalman filter to predict the number of passengers waiting at a bus station. Han et al. [35] created a hybrid and optimized LSTM to project the bus passenger flow. Van Oort et al. [37] converted the IC card data to the number of passengers per line, constructed an origin-destination (OD) matrix between stations, and assigned the matrix to the network to reproduce the measured passenger flow. Kumar et al. [38] developed a bus travel-time prediction method that considers both spatial and temporal variations in travel time. Wu et al. [39] built a convolutional LSTM (ConvLSTM) model with a self-attention mechanism, which accurately predicts the travel time on each segment of a trip and the waiting time at each station. Considering the small size, strong time-variation, and extraction difficulty of short-term passenger flow at bus stations, some scholars have taken account of connected and autonomous vehicles to alleviate the variability of travel time [40, 41]. Albeit these efforts, it is still difficult to make realistic forecast of the short-term passenger flow at bus stations. Wang et al. [42] designed a new framework to solve the problem of sudden passenger flow early warning. Pereira et al. [43] detected overcrowding with a threshold-based method and defined the point whose arrivals exceed the 90% percentile as overcrowding point. Bai et al. [44] monitor passenger flow to display the distribution trend of real-time passenger flow with GIS technology. To sum up, the current research mainly focuses on the early warning of traffic flow, and there is little research on the monitoring and early warning methods of passenger flow at bus stops.

We firstly analyze the features of passenger flow at bus stations and propose a novel concept called regional bus station, which is aggregated from actual bus stations in this paper. Then, the SVM was introduced to predict the short-term passenger flow at regional bus stations. The results show that the prediction accuracy of short-term passenger flow could be improved by replacing actual bus stations with virtual regional bus stations. On this basis, we designed an early warning model for regional bus passenger flow, which monitors the passenger flow in important areas during the period of special activities (e.g., large events) and takes control measures in advance to ensure the smooth progress of these activities.

The remainder of this paper is organized as follows: Section 2 puts forward the concept of regional bus stations by analyzing the IC card data of Shenzhen from November 7 to December 4, 2016, and summarizes the features of regional bus passenger flow; Section 3 selects and trains the prediction variables and employs the SVM to make short-term prediction of the passenger flow at regional bus stations; Section 4 analyzes the accuracy of prediction results; Section 5 carries out the capacity analysis and derives the early warning model for regional bus passenger flow; Section 6 puts forward the conclusions.

2. Bus Station Distribution and IC Card Data Processing

2.1. Bus Station Data and IC Card Data

The IC card used in this paper is Shenzhen Tong. It is a kind of stored value card for consumption by Shenzhen bus and Shenzhen Metro, which is manufactured under the supervision of Shenzhen Transport Bureau and issued by Shenzhen public transport settlement management center. The bus data only displays the valid information such as the user card number, card swiping time, and bus license plate number. It is shown in Table 2.

We extracted the GPS data and the card data of passengers and mapped the bus stops according to the time-space relationship.(1)The GPS records of each line for 20 days are selected, and the GPS records are sorted according to the license plate number and the return time of GPS to get the track of the bus.(2)Select the track point closest to the card swiping time as the boarding point, calculate the distance between the boarding point and each bus stop on the bus operation line, and select the nearest bus stop with the actual distance less than 100 as the actual bus stop, as shown in Figure 1.

The GPS data of 28 days from November 7 to December 4, 2016, are used in this paper, which contain about 541,115,294 pieces of time and location information of 10,314 vehicles. Therefore, we can study the characteristics of working day and non working bus passenger flow.

The passenger flows of bus stations in Shenzhen were acquired from the IC card data during the bus operation time (6:00–22:00) from November 7 to December 4, 2016. Figure 2 shows the distribution of the number of card swipes on buses in Shenzhen on a typical day.

To pinpoint the bus line number of each card swipe, the geographical positioning system (GPS) data were matched with the location data of bus stations, as shown in Figure 3. Through the matching, the bus arrival time was obtained for each bus station. Then, the boarding station of each card user was identified by acquiring the boarding time and bus line number from his/her IC card and matching the bus line number with the arrival time obtained in the previous step.

According to the time-varying distribution of bus trips in many days, it is found that the bus trips have obvious peak characteristics, and the peak hours are concentrated at 7:00 a.m. and 18:00 p.m. 7:00–9:00 and 17:00–19:00 are selected as the morning and evening peak hours of bus travel, as shown in Figure 4.

2.2. Regional Bus Station

To facilitate the passenger flow prediction of all bus stations in a region of Shenzhen (E: 113.76°–114.62°; N: 22.45°–22.87°), the road network in the region was meshed into 3,612 1 km × 1 km grids. 933 grids were found to have bus stations. In this way, the 53,914 bus stations in the region were aggregated into 993 regional bus stations (the black spots in the lower part of Figure 5).

3. Short-Term Passenger Flow Prediction at Regional Bus Stations

3.1. Principles

The short-term regional passenger flow was predicted in the following steps: Step 1. Encode all the grids, and count the number of stations in each grid. Step 2. Taking 1 h as the time window, count the number of passengers boarding buses at each station from 6:00 to 23:00 in the four days from December 1 to December 4, 2016. Step 3. Allocate the data in four time windows (19:00-20:00, 18:00-19:00, 17:00-18:00, and 16:00-17:00) of the first 3 days (December 1–3, 2016) to the training set and the data in the same time windows of the last day (December 4, 2016) as the test set. Train the data by the ML-based forecast procedure. Step 4. Select the features of short-term regional bus passenger flow through ML, producing a set of valid features R. Step 5. Select the top N features that influence the target period the most from the feature set R, and take them as the input of the regression model for SVM-based prediction.

3.2. Feature Training

Let be the collected data, where is the training data of the lst day, d is feature dimension, is the set of passengers boarding on the lst day under feature d, and is the test data of the lst day.

Details of alternative features are shown in Table 3. The alternative feature for a target grid is the 1 km × 1 km grids around that grid, and the alternative feature set for the 993 grids in the region is whether the target grids are surrounded by 1 km × 1 km grids. If there are i grids in the set, then the number of boarding passengers should be counted in the previous j time windows of each grid in the set. Therefore, the feature dimension can be expressed as .

The number of alternative features varies from grid to grid, that is, the d value is a variable in . Here, the value of j is set to 3. The details of alternative features are presented in Table 3.

Let T be the target time window. Then, the N = 3 most important features were selected through recursive feature elimination (Algorithm 1).

	Input: training set and linear regression model
(1)	Initialization: original feature set , and feature sort set
(2)	While do
(3)	Obtain the training samples of candidate feature set
(4)	Obtain the weight of each feature by linear regression model, i.e., the coefficient of linear regression model
(5)	Find out the features of the minimum score of sorting criteria:
(6)	Update feature set
(7)	Exclude feature in S
(8)	End while
	Output: feature sort set R

3.3. SVM-Based Regression Prediction

The regression prediction takes the N features that influence the target period the most as the inputs. Thus, the dimension of sample is equal to N.

Let be the training set. Then, the training samples were mapped into a higher dimension by function , turning nonlinear regression inputs into high-dimensional inputs for linear regression.

The nonlinear mapping function can be expressed as . Then, the SVM-based nonlinear regression can be defined aswhere is the penalty parameter and is the error term.

The optimum solution can be calculated as . The positive subsector of or of was chosen. Then, the can be calculated by

Then, the decision function can be described as

For target grids, the number of passengers boarding in time window t can be forecasted based on the same N most important features on the given day. The radial basis function (RBF) was chosen as the kernel function: .

4. Prediction Results and Model Test

4.1. Prediction Results

Two time windows were randomly selected, namely, 11:00-12:00 and 19:00-20:00 on December 4, 2016, and the number of boarding passengers in the 993 grids was counted. The results predicted by our method are compared with the actual data in Figures 6 and 7.

4.2. Verification of Time Window

The target time window for prediction was set as 1 h. To verify the correctness of the time window, the real number of passengers boarding in 19:00-20:00 on December 4, 2016, was selected as the current period and compared with the real number of the previous period (18:00-19:00), the real number of the subsequent period (20:00-21:00), and the predicted value of the current period (19:00-20:00) (Figure 7).

As shown in Figures 8 and 9, the points were scattered, and the degree of linear fitting was poor, indicating that the number of passengers at each station in the grid fluctuates significantly within the time window of 1 h. Hence, it is necessary to set 1 h as the time window.

Moreover, the regression result of Figure 8 was (is the slope of the linear fitting line), that is, the result is greater than the actual boarding number in 19:00–20:00 of all grids. The regression result of Figure 9 is < 1, indicating that the actual boarding number in 19:00–20:00 of all grids is more than that in the following hour. Therefore, the data in the current time window cannot be replaced by the data of the previous or subsequent time window. In addition, in Figures 6 and 7, the slope β of linear fitting approaches to 1, indicating that it is better to use 1 hour as the time window. This further confirms the rationality of the 1 h time window.

4.3. Verification of Grid Size

We cross-grained the road network into 3,612 square grids with an area of 1 × 1 sq. km. Within the partitioned 3,612 square grids, 993 had at least one bus station inside. We cross-grained the road network with an area of 0.5 × 0.5 sq, and we found that 10% of the area had no bus stops. Moreover, the division of regional bus stations should be combined with the average length of urban road sections, and the area enclosed by each road section should be taken as the regional bus station as far as possible, and the average length of the road section in this paper is 0.78 km. In addition, we forecast the passenger flow of regional bus stations with different flows in different regions. We find that, with the increase of passenger flow of regional bus stations, the prediction accuracy increases, as shown in Figure 10. Therefore, it is appropriate to select 1 × 1 sq as the size of regional bus stations.

4.4. Model Test

It can be directly inferred from Figure 6 that the actual value and the predicted value follow a linear relationship. Thus, unary linear regression was adopted for data fitting:where and both obey the normal distribution. If approaches to 0 and approaches to 1, then the model has a high degree of regression. The dataset to be regressed was defined as (i = 1, 2, …, n, n = 993).

Next, the linear regression problem was solved by the least squares (LS) method. The results of time window 11:00-12:00 were with its confidence being (2.42, 5.94) on the level of 95%, with its confidence being (0.885, 0.907) on the level of 95%, and coefficient of correlation R² = 0.96.

The predicted results were measured by three metrics: the mean absolute percentage error (MAPE), mean absolute error (MAE), variance of absolute percentage error (VAPE), and root mean square error (RMSE):

For the predicted results on the time window 11:00-12:00, the MAPE, MAE, VAPE, and RMSE were 0.18, 35.16, 0.12, and 65.42, respectively.

The results of time window 19:00-20:00 is that with its confidence being (−0.08, 4.55) on the level of 95%, 0.96 with its confidence being (0.95, 0.97) on the level of 95%, and coefficient of correlation R² = 0.98. The MAPE, MAE, and RMSE of these results were 0.16, 26.29, and 54.29, respectively.

The R² values of the two time windows demonstrate the significant correlation between variables X and Y. In both time windows, the value approached to 0, and the values approached 1. The error metrics of the results on the two time windows were both satisfactory. Therefore, the proposed ML method is favorable for predicting bus passenger flow in the short term.

4.5. Comparative Analysis of Prediction Accuracy between Single Bus Stop and Regional Bus Stop

In order to analyze the prediction accuracy of single bus stop and regional bus stop, we select the window of the world regional station, in which there are three bus stops: world window stop, Baishizhou stop, and Meilu Jinyuan stop. Bus passenger flow of November 28 is predicted, and the prediction results are shown in Figures 11 and 12.

(a)

(b)

(c)

(d)

The accuracy of regional bus station prediction results is significantly higher than that of single stops, especially for stops with relatively little passenger flow, the prediction accuracy is obviously low, and the prediction results have no practical application value.

5. Early Warning Model for Regional Bus Passenger Flow

5.1. Model Construction

The passenger capacity of a regional bus station can be calculated bywhere is the capacity of the regional bus station and is the residual capacity of the regional bus line.

According to the Traffic Engineering Manual, the capacity of station i can be computed bywhere is the green light ratio of the intersection in front of station i; R is the adjustment coefficient reflecting the degree of impact from bus arrival time and boarding time on station capacity (the empirical value is 0.833); D is the average boarding/alighting time (the value is generally 20–50 s); is the average clearance time of bus station, i.e., the time required for the former bus to depart from and the current bus to arrive at the same position at the station (the value is generally 9–20 s); m is the total number of regional bus stations; is the effective berth on the ith station.

The residual capacity of regional bus line j can be calculated bywhere is the load factor of line at acceptable service level (%), i.e., 80% of the rated passenger capacity; is the departure interval of line j (min); is the capacity of single bus online j (person) (the value is generally 60 persons); is the actual capacity of line j (%).

The early warning coefficient K can be calculated bywhere is the predicted short-term passenger flow of a regional bus stop and is the proportion of IC card swiping passengers in the total number of bus passengers in the region.

5.2. Value of Early Warning Coefficient

Early warning generally refers to the prewarning of potential dangerous situation information. The early warning coefficient is used to judge what kind of situation needs to be issued and what degree of alarm is issued. In this paper, the early warning method adopts the method of combining the early warning index and the warning limit interval. If the value of the early warning index is in the corresponding warning limit interval, it corresponds to the alarm of this degree. Combined with the setting method of traffic flow warning interval [45], considering the level of public transport service, that is, considering the passenger comfort, reliability, and safety of operation service [46], the early warning interval of regional bus stops is divided into four levels. The first-level warning interval corresponds to the first level of service. The overall full-load rate of regional public transport vehicles is extremely low, and the passengers’ comfort is very high, and the safety factor is very high. The second-level warning interval corresponds to the second-level service level. The overall full-load rate of regional public transport vehicles is not high, the waiting time of passengers is small, the congestion is low, and the safety factor is relatively high. The third level of warning interval corresponds to the third level of service, and the public transport vehicles are at the edge of full load. At this time, the safety factor is low, and the bus is crowded, which represents the general safety level; the fourth-level of warning interval corresponds to the fourth level of service, the safety factor is very low, the departure frequency cannot meet the needs of passengers, and the bus congestion is high, which represents the danger. The warning coefficients of the four levels are shown in Table 4.

If K falls in (0, 0.75), the region is safe; if K falls in (0.75, 0.9), the region needs to be monitored; if K surpasses 0.9, the region must be alarmed.

5.3. Case Analysis

The case analysis targets the grid at the junction of Shennan Avenue and Qiaocheng Road (Figure 13). Shennan Avenue is one of the busiest roads in Shenzhen. Involving 16 bus stations and many bus lines, the target grid is highly representative of the public transport in Shenzhen. As shown in Figure 13, there are 35 bus lines at Kongjia Group Station on Shennan Avenue alone.

The proposed SVM-based algorithm was adopted to train and learn the historical boarding number of stations in the target grid and predict the daily number of boarding passengers of 20 days (6:00–23:00). Then, the predicted results were compared with the real values in the grid (Figure 14).

It can be seen from Figure 15 that our algorithm achieved a good prediction effect, as the predicted results followed the same trend as the real values. The MAE and MAPE were small, and the RMSE was smaller than 10%.

Through capacity analysis, the capacity of regional bus stations in 6:00–24:00 was 4,113 person times/h, while the residual capacity of bus lines was 3,840 in 6:00-7:00, 5,760 in 7:00–9:00, 4,032 in 9:00–17:00, 5,760 in 17:00–19:00, and 4,860 in 19:00–24:00. The regional bus capacity and K value in each period are presented in Figure 15.

According to the K values in Figure 15, the early warning coefficient in the target grid was 0.9 in 18:00-19:00. Hence, in this period, the bus capacity in the region is saturated and needs to be monitored. To reduce the K value, it is necessary to increase the regional bus capacity by stepping up departure frequency, improving the capacity of some stations, and expanding the effective parking spaces at stations.

6. Conclusions

This paper analyzes the IC card swiping data of all buses in Shenzhen during November 7–4, 2016 (6:00–22:00), and introduces the ML method of SVM to predict the short-term passenger flow of urban bus stations. The main conclusions are as follows:(1)The training samples of candidate feature sets and the weight of each feature were through linear regression. The N features with the greatest impact on the target period were selected as the input of the regression model. The SVM-based regression prediction was adopted to predict the bus passenger flow in the target time window. The model achieved high prediction accuracy when the time window is 1 h. The MAPE, MAE, and RMSE of these results were 0.16, 26.29, and 54.29, respectively.(2)The capacity and early warning coefficient K of regional bus passenger was analyzed in detail. According to the K values, the capacity of some bus stations and bus lines in the target region should be improved to further optimize the service of public transport.(3)The concept of regional bus stop is put forward in this paper; a suitable short-term prediction method for the passenger flow of regional bus stops is constructed, and the classification method and early warning coefficient of regional bus stop service level are developed.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The project was supported by Open Fund of Engineering Research Center of Catastrophic Prophylaxis and Treatment of Road & Traffic Safety of Ministry of Education (Grant no. kfj180401, Changsha University of Science and Technology); Natural Science Foundation of Hunan Province, China (Grant no. 2019JJ40306); and National Natural Science Foundation of China (Grant no. 61773077).

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Copyright © 2020 Wusheng Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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