Energy Consumption Estimation Method of Battery Electric Buses Based on Real-World Driving Data

Abstract

The estimation of energy consumption under real-world driving conditions is a prerequisite for optimizing bus scheduling and meeting the requirements of route operation, thereby promoting the large-scale application of battery electric buses. However, the limitation of data accuracy and the uncertainty of many factors, such as weather conditions, traffic conditions, and driving styles, etc. make accurate energy consumption estimation complicated. In response to these challenges, a new method for estimating the energy consumption of battery electric buses (BEBs) is proposed in this research. This method estimates the speed profiles of different driving styles and the energy consumption extremes using real-world driving data. First, this research provides the constraints on speed formed by environmental factors including weather conditions, route characteristics, and traffic characteristics. On this basis, there are two levels of estimation for energy consumption. The first level classifies different driving styles and constructs the corresponding speed profiles with the time interval (10 s), the same as real-world driving data. The second level further constructs the speed profiles with the time interval of 1 s by filling in the first-level speed profiles and estimating the energy consumption extremes. Finally, the estimated maximum and minimum value of energy consumption were compared with the true value and the results showed that the real energy consumption did not exceed the extremes we estimated, which proves the method we proposed is reasonable and useful. Therefore, this research can provide a theoretical foundation for the deployment of battery electric buses.

1. Introduction

In recent years, energy conservation, emission reduction, and ecological protection are getting more and more attention. Due to the continuous development of urbanization, the contradiction between transportation and the environment has become more and more significant. In this case, the application of battery electric buses (BEBs) has become one of the breakthrough points to solve this contradiction. Compared with traditional diesel buses, BEBs have the advantages of zero emission, low noise, and higher energy efficiency [1,2], which make them favored by society to become the first choice for urban buses. However, due to the limitations of their short driving range and long charging time, the promotion and use of BEBs has been restricted to a certain extent [3,4,5]. Therefore, before the further development of battery technology, accurately predicting the energy consumption of BEBs is a prerequisite for optimizing vehicle scheduling and meeting the requirements of route operation, thereby laying the foundation for the continuous expansion of the deployment scope of BEBs. The operation of BEBs is characterized by fixed routes, which means that the speed profile of the buses will follow a certain pattern, so the energy consumption of BEBs can be predicted by reasonably predicting their speed profile.

In reality, the speed profile will depend on factors such as road characteristics, traffic conditions, driver style, and weather conditions. Qi et al. believed that traffic congestion can affect average vehicle speed, which in turn can affect vehicle energy consumption [6]. Gupta et al. developed a virtual driver model for simulation research so that people can understand the impact of specific driver behavior on the vehicle speed profile [7]. Li et al. pointed out that road characteristics, including traffic light density, road grade, etc., can affect speed [8]. Ellison et al. indicated that when the weather conditions are bad, such as snow, fog, or other conditions, driving behavior can be more cautious, which can affect the change of the speed profile [9]. Therefore, when predicting the speed profile, the influence of environmental factors and the driving style of the drivers should be considered.

Reasonable prediction of the speed profile is the basic premise for accurately predicting the required energy consumption. The current research mainly focuses on energy consumption, and the prediction of the speed profile is relatively simple and rough. Gallet et al. roughly estimated the speed profile on a bus route by dividing the speed into three parts: uniform acceleration, uniform speed, and uniform deceleration [10]. El-Taweel et al. divided the generation of the speed profile on a bus route into two stages. The first stage estimated the bus stop probability, average speed, and stay time, and the second stage generated the speed profile under the constraints of the first stage [11]. Some documents calculate energy consumption but ignore the prediction of the speed profile [12,13]. Some documents use actual data or Markov chains obtained from standard operating conditions to predict the speed profile. A Markov chain is a promising and important method utilized in modeling and predicting velocity [14]. Shin et al. proposed a speed prediction method using a Markov chain with speed constraints. Under the geometric constraints of the road, the Markov chain is used to randomly generate the speed profile [15]. Zhang et al. used the Markov Monte Carlo algorithm to predict the future speed profile based on the transition probability matrix and the current state and speed of the vehicle [16]. Most Markov methods require large amounts of actual driving data at high frequencies.

In addition to Markov chains, deep learning is also an important method for predicting speed. Sun et al. applied a speed prediction method based on an artificial neural network to the energy management problem of hybrid electric vehicles and compared this speed prediction method with the generalized exponentially varying predictor and the Markov-chain-based predictor [17]. Wang et al. proposed a path-based deep learning framework that can predict the speed of various road segments within a city [18]. Gu et al. combined long and short-term memory neural networks and gated recurrent unit neural networks to establish a two-layer deep learning framework to predict road speed [19].

Some documents take driving style into consideration when making speed predictions. Lin et al. proposed a vehicle speed prediction model based on driving pattern recognition and Markov chains and obtained a Markov state transition matrix corresponding to three clustered driving modes [20]. Morlock et al. derived a speed curve from real-time traffic data obtained by HERE Technologies, considering personal driving style and random parking at traffic lights and intersections [21]. There is a lack of a speed profile prediction method of buses that takes both environmental factors, including weather conditions, route characteristics and traffic characteristics, and driver style of drivers into account.

In order to accurately estimate energy consumption, it is necessary to establish a quantitative relationship between the energy consumption of electric vehicles and various factors. At present, there are two major types of methods used to capture this relationship. The first type is theoretical modeling based on the vehicle’s physical model, which fully considers the energy required by various power systems in operating modes and studies the correlation between the parameters of the mechanical and electrical components and the vehicle energy consumption [22,23]. Wu et al. analyzed the relationship between electric vehicle power, vehicle speed, acceleration and road gradient, and further proposed an analytical electric vehicle power estimation model [24]. Miri et al. modeled the energy consumption of electric vehicles based on the BMW i3 and developed a regenerative braking strategy based on the series braking system [25]. The second approach is to use data-driven processes to establish energy consumption models. Some literature uses data from standard driving cycles based on traffic measurements in different cities to derive their data [26], but the standard operating conditions and the real situation are inaccurate and therefore their results are inaccurate. More and more research has focused on using real-world driving data for analysis and modeling.

Data-driven methods can be roughly divided into two types, statistical analysis methods and machine learning algorithms. Based on the GPS observation data of 68 EVs, Liu et al. established a vehicle energy consumption model using ordinary least squares regression and multi-level mixed-effects linear regression [27]. Cedric et al. used multiple linear regression to establish three models, each of which uses different levels of parameters as input to predict energy consumption [28]. In recent years, the rapid development of artificial intelligence technology has provided new methods for energy consumption modeling. Irfan et al. used an ensemble stacked generalization method to combine three independent basic models of decision trees, random forests and k nearest neighbors to predict the energy consumption of EVs [29]. Yao et al. used machine learning algorithms to develop large-scale learning predictions for different models [30]. Although data-driven methods can be combined with actual driving data to mine more energy consumption factors, they only rely on data-driven methods and are usually not closely related to the underlying physical principles, and an accurate energy consumption model cannot be established.

In summary, accurate energy consumption estimation needs a reasonable estimation of speed profiles, which requires a large amount of accurate driving data. Some research uses standard driving cycles or simulation experiments to obtain driving data with the frequency of 1 Hz, but these driving data are far from real-world driving conditions. Some research directly simplifies the formation of the speed profile for convenience. As mentioned above, it is not easy to obtain a practical and accurate speed profile to estimate energy consumption. In addition, although some research does use real-world driving data with a sampling frequency of 1 Hz, it is very difficult and inconvenient to obtain a large number of them as far as current technology is concerned. Therefore, in this research, we propose a method to reasonably estimate speed profiles with the time interval of 1 s using real-world driving data with a sampling frequency of 0.1 Hz, and accurate energy consumption can be predicted.

Based on the method proposed in this paper, the energy consumption of BEBs for any trip can be estimated by constructing the two levels of speed profiles. Firstly, the first-level speed profiles with a time interval of 10 s are constructed, which fully consider the impacts of environmental factors and different driving style on the speed. They reflect the driving characteristics of real-world driving data. Next, combined with the energy consumption model, the second-level speed profiles are obtained by filling the first-level speed profiles with the highest and lowest energy consumption goals. Further, they are optimized to be more practical and then used to obtain the more reasonable energy consumption extremes. Finally, the estimated energy consumption values are compared with the true values to verify the validity of our estimates. The overall framework of this paper is shown in Figure 1.

The contributions of this research mainly include three aspects: First the effects of environmental factors and different driving styles were taken into consideration when predicting the first level speed (with time interval of 10 s) profile using real-world driving data. Then, the constraints of environmental factors on velocity and acceleration limits were considered, and the first level speed profile was rationally populated into a second speed profile (with time interval of 1 s) based on energy consumption. Finally, the possible maximum and minimum values of the energy consumption of a bus on a particular route were estimated. This means that any driver on duty driving a bus on that route will always have the actual energy consumption values within the estimated interval.

The remainder of this paper is organized as follows: Section 2 describes the collection and pre-processing of real-world driving data. Section 3 presents the influencing factors of speed and the construction method of speed profiles in the first level. Section 4 introduces the speed profile filling method in the second level and the estimation of energy consumption extremes, which are compared with the true values, followed by the conclusions summarized in Section 5.

2. Data Collection and Pre-Processing

The data used in this study came from the National Monitoring and Management Platform for New Energy Vehicles (NEVs). The data format collected by this platform is consistent with the Technical specifications of remote service and management systems for electric vehicles-Part 3: Communication protocol and data format (GB/T 32960.3-2016 [31]), covering 73 data items such as the vehicle, vehicle location, etc. This study obtained the real-world driving data of all BEBs on the No. 4 bus route in Changchun City from 1 January to 11 October 2020. The total length of this bus route is 11.6 km. Each data field records the bus VIN, current time, vehicle speed, accumulated mileage, vehicle location, battery voltage, battery current and other data, and the sampling frequency is 0.1 Hz.

Table 1. Part of driving data samples of BEBs.

VIN	Time	Accumulated Range (0.1 km)	Velocity (0.1 km/h)	Longitude (0.0000001°)	Latitude (0.0000001°)	…
a28d15…	20200309085620	389274	340	125364133	43848481	…
ee7f6c…	20200309085622	395804	21	125369614	43879980	…
73ac7b…	20200309085622	371595	252	125370243	43878843	…
2d48de…	20200309085622	377382	17	125346695	43894232	…
a28d15…	20200309085622	388709	53	125346810	43894345	…
ee7f6c…	20200309085623	360104	567	125321736	43890836	…

summarizes the detailed specifications of part of the driving data samples from this platform. In addition to the data obtained from the platform, the given route was divided into road sections with every two bus stops as the boundary, and the information of each section of the bus route, including the length of the road section, the number of lanes in the road section, the number of traffic lights, the number of intersections, etc. were collected through AMAP (www.amap.com (accessed on 10 September 2022)) and actual surveys for this study.

Table 2. Road section information of Changchun No. 4 bus line.

Index	Bus Station	Length (m)	Number of Lanes	Number of Intersections	Number of Lights
1	The Children’s Hospital→Cultural Street	650	1	3	1
2	Cultural Street→City Hospital	390	1	2	2
3	City Hospital→Dajing Road	450	2	3	1
…	…	…	…	…	…
24	The Fourth Zone→Technical Secondary School	250	2	2	1

summarizes the detailed data of each section of the No. 4 bus route in Changchun City. In addition, hourly or every three hours weather data were collected from Houzhi Weather (https://airwise.hjhj-e.com/ (accessed on 5 October 2023)), including sunny, rain, snow, fog, etc.

The operation of buses has the following features: travel along a fixed route and stop at each station. Accordingly, the bus route is divided into road sections between the stations. The routes between every two stations are a road section, which is a unit of the speed profiles and predicted energy consumption. The processing of raw data was as follows:

• The driving data for each complete route of each BEB are divided according to the vehicle identification number (VIN) of the BEBs and the latitude and longitude data of the starting point and the ending point.
• Then, the driving data for each complete route of each BEB are divided into road sections according to the latitude and longitude data of each station.
• The driving data of all BEBs on the same road section in chronological order are integrated, and then we obtain the driving data of all BEBs on the same road section in each time period.
• Match the driving data of each road section with the fixed attributes (length, number of lanes, number of intersections, etc.) and the weather data for one hour or three hours. Finally, the driving data, fixed attributes, and weather data of each road section are obtained.

In addition, as shown in Figure 2, there are some missing data points and exceptional data points that deviate from the actual route. For missing data in which the time interval between adjacent data points is greater than 10 s, if the number of missing data points is small, linear interpolation is used to fill the missing part. If large, the related sample is deleted directly because the size of the total sample is big. For the exceptional data points that deviate from the actual route, if the distance between the data point and the previous data point and the next data point exceeds a certain value, it is judged as an abnormal point and deleted.

The ArcGIS software 10.2 and the open-source map OpenStreetMap (www.openstreetmap.org (accessed on 10 October 2023)) are used to check whether the processed data is correct. First, the area containing the route is imported into ArcGIS from OpenStreetMap, and then we randomly extract the latitude and longitude data of a certain complete route from all of the divided data for matching. As shown in Figure 3, the red trajectory, which is the bus route, and the blue points, which are the processed data points, are almost overlapping, which proves the processed data is correct.

3. The First-Level Speed Profile Construction

3.1. The Influence of Environmental Factors on Speed

The environmental factors considered in this study include weather conditions, route characteristics and traffic characteristics. When analyzing the impact of a certain type of environmental factor it is necessary to set the other types to be consistent. For example, when considering the impact of weather on vehicle speed, only the driving data corresponding to the same route and traffic characteristics, but different weather conditions, are used for analysis.

The weather conditions were divided into four categories in this study: sunny, rainy, snowy, and foggy. The average and maximum speeds during different weather were calculated. As can be seen from the box diagram in Figure 4, the average and maximum speeds under different weather conditions are quite different. They are both highest on sunny days, followed by rainy days, and they are lower on snowy and foggy days, that is, snowy and foggy days have a greater impact on reducing speed.

Generally, the buses travel along a fixed route. The route characteristics, which include length, number of lanes, number of intersections and number of traffic lights will affect the driving state of the vehicle. According to Section 2, the above fixed attribute of each road section is obtained. Figure 5 shows the distance $l_{ij}$ and the number of lanes $c_{width\_ij}$ of different road sections, and Figure 6 shows the intersection density ${\rho }_{in\_ij}$ and traffic light density ${\rho }_{light\_ij}$ of the corresponding road sections, which are calculated through Equations (1) and (2):

$${\rho }_{in\_ij}={\displaystyle \frac{c_{in\_ij}}{l_{ij}}}$$

(1)

$${\rho }_{light\_ij}={\displaystyle \frac{c_{light\_ij}}{l_{ij}}}$$

(2)

where $c_{in\_ij}$ is the number of intersections in road section $ij$ and $c_{light\_ij}$ is the number of traffic lights in road section $ij$.

Figure 7 shows the average and maximum speeds of each road section. It can be seen that the average and maximum speeds of different road sections are quite different. It should be noted that this statistical result shows the effect of the combined effect of different route characteristics on the speed. Therefore, the road sections were divided into three levels according to their average speed. The higher the level, the higher the average speed of the road section.

Table 3. Classification levels corresponding to different road sections.

Level	No.
1	2, 4, 5, 6
2	3, 11, 14, 15, 17, 18, 20, 22, 24
3	1, 7, 8, 9, 10, 12, 13, 16, 19, 21, 23

shows the classification level corresponding to each section of the bus route.

Traffic characteristics are another important environmental factor that needs to be considered. In urban travel, the morning and evening peaks of working days and holidays present different traffic characteristics, which have a great impact on the speed profile. Figure 8a,b shows the average speed and maximum speed during different periods of workdays and holidays, respectively. It can be seen from the shaded part that on working days, the average and maximum speeds corresponding to the morning and evening peak are lower than those on holidays, and the morning and evening peak hours are earlier.

According to the above, environmental factors have a greater impact on the speed profile. So, when estimating the speed profile, we must take the environmental factors into account to make the prediction more accurate. In the following text, we regard the maximum velocity under different road sections, workdays and holidays, different weather conditions, and different time periods as constraints of environmental factors. For example, the maximum velocity of the No. 1 road section under sun weather on workdays is shown in

Table 4. Maximum velocity of the No. 1 road section under sun weather on workdays.

No.	Workdays (or Holidays)	Weather	Time Period	Maximum Velocity (km/h)
1	workdays	sunny	5:50–8:00	48
1	workdays	sunny	8:00–9:00	42
			9:00–10:00	52
			10:00–11:00	55
			11:00–12:00	50
			12:00–13:00	45
			13:00–14:00	47
			14:00–15:00	41
			15:00–16:00	53
			16:00–17:00	46
			17:00–18:00	40
			18:00–19:00	42
			19:00–20:30	56

.

3.2. Driving Style Classification

Driving style refers to the way the driver chooses to drive, which is an instant preference behavior or driving habit [32], especially how the driver puts pressure on the acceleration and brake pedals, which have a significant impact on the vehicle’s speed. Under the same environmental factors and route, different driving styles will produce completely different speed profiles. Driver styles are generally divided into two, three, or more categories [33]. For example, aggressive driving styles have higher speeds and more sudden accelerations and decelerations, while normal or conservative driving styles are accompanied by smoother and slower speeds. Generally, there are two ways to classify driving styles. One is through questionnaire surveys [34,35], and the other is by analyzing the driving data of the vehicle [36,37]. This research used the second method.

It is worth noting that different weather, traffic conditions, and route characteristics will affect the driving style. For example, an aggressive driver will drive the vehicle at smooth and slower speeds like a normal-style driver under bad weather, such as heavy rain. Therefore, the data with the sunny weather conditions, non-traffic congestion, and highest level of the road section were used for classifying the driving styles. In this research, 23 types of driver style indicators were selected: average speed, the standard deviation of speed, maximum speed, average acceleration, acceleration standard deviation, maximum acceleration, average deceleration, the standard deviation of deceleration, maximum deceleration, maximum stroke value of the accelerator pedal, average accelerator pedal stroke value, average rate of change of the accelerator pedal stroke value, maximum change rate of the accelerator pedal stroke value when pressing, maximum change rate of the accelerator pedal stroke value when loosening, standard deviation of the rate of change of the accelerator pedal stroke value when pressing, standard deviation of the rate of change of the accelerator pedal stroke value when loosening, maximum stroke value of the brake pedal, average brake pedal stroke value, average rate of change of the brake pedal stroke value, maximum rate of change of the brake pedal stroke value when pressing, maximum rate of change of the brake pedal stroke value when loosening, standard deviation of the rate of change of the stroke value of the brake pedal when pressing, and standard deviation of rate of change of the brake pedal stroke value when loosening. The specific indicators are shown in

Table 5. Driving style indicators.

Drivers’ Number	Average Velocity (km/h)	Velocity Standard Deviation	Maximum Velocity (km/h)	Average Accelerator Pedal Stroke Value (%)	Average Decelerator Pedal Stroke Value (%)	⋯
0506_22487a_4	18.15	18.56	56.6	49.00	34.44	…
0506_2c62b9_4	21.05	18.39	60.2	48.48	32.95	…
0506_7a0784_4	15.72	16.79	55.7	33.85	30.79	…
0506_c032c0_4	19.97	15.81	46	40.47	31.25	…
0507_22487a_4	17.39	17.43	53.8	48.91	27.96	…
0508_22487a_3	16.58	15.92	49.1	35.78	31.00	…
…	…	…	…	…	…	…

.

Firstly, the above 23 indicators are standardized by Equation (3):

$$y_i={\displaystyle \frac{x_i-\frac{1}{n}{\sum }_{i=1}^n{x}_i}{\sqrt{\frac{1}{n-1}{\sum }_{i=1}^n(x_i-\overline{x}{)}^2}}}$$

(3)

where $x_i$ is the value before processing, $y_i$ is the processed value, and the standardized data $y_1,y_2,\dots ,y_n$ have a mean value of 0, a variance of 1, and are dimensionless.

Secondly, perform principal component analysis (PCA) on the standardized indicators. The PCA is used to convert the original correlated variables into new linearly independent variables by calculating the eigenvalues and eigenvectors through the covariance matrix. The new variable is a linear combination of the original variable and is arranged in descending order of the covariance with the original variable. The larger the covariance, the greater the amount of information contained in the original data. The new variables in the first k dimensions that contain more than a certain proportion of the original information are chosen to replace the original variables so as to reduce the dimensionality of the original data. The specific calculation uses Equations (4)–(6):

$$F_k=e_{k1}{Y}_1+e_{k2}{Y}_2+\dots +e_{k23}{Y}_{23}$$

(4)

$$C_k={\displaystyle \frac{{\lambda }_k}{{\sum }_{i=1}^{23}{\lambda }_i}}$$

(5)

$$Z={\displaystyle \frac{{\sum }_{i=1}^n{\lambda }_i}{{\sum }_{i=1}^{23}{\lambda }_i}}$$

(6)

Equation (4) is used to calculate the principal component (PC), where $Y_k$ is the kth PC and $e_{ki}$ is the eigenvector of the covariance matrix $Cov(Y,Y)$. Equation (5) is used to calculate the contribution rate of PCs, where $C_k$ is the contribution rate of the kth PC and $\lambda$ is the eigenvalues of the covariance matrix $Cov(Y,Y)$. Equation (6) is used to calculate the cumulative contribution rate, where $Z$ is the cumulative contribution rate of the first $n$ PCs.

After standardization and PCA of 23 indicators, the contribution rate of each PC and the cumulative contribution rate of the first n PCs are shown in Figure 8a,b. As shown in Figure 8, the cumulative contribution rate of the first six PCs exceeds 0.95, which means the first 6 PCs contain most of the original information. Therefore, the first 6 PCs were selected to replace the original variables, and the dimensionality of the original data is reduced from 23 to 6.

Based on that, the K-means clustering algorithm is used to classify the driver styles. The clustering algorithm is a type of unsupervised learning algorithm that is different from the classification algorithm. It judges the category of a data point by calculating the distance between it and the cluster center. And it does not need to define the classification criteria of each category in advance. The K-means algorithm is a typical partition-based clustering algorithm, which has fast calculation speed and high calculation accuracy and is widely used.

The principle of the K-means algorithm is to divide the data into $M$ clusters so that the distance between each data point inside each cluster is as close as possible while the distance between cluster centers is as large as possible. Euclidean distance is selected to measure the distances in this research. The Euclidean distance between any two points $X=\left(x_1,x_2,\dots ,x_n\right)$ and $Y=(y_1,y_2,\dots ,y_n)$ in n-dimensional space is calculated as Equation (7):

$$D(X,Y)=\sqrt{\sum _{i=1}^n(x_i-y_i{)}^2}$$

(7)

The specific calculation steps of the K-means algorithm are described as follows:

• Randomly determine $M$ cluster center points.
• Calculate the Euclidean distance between the data point and the cluster center.
• Assign each data point to the category of the cluster center with the smallest distance, then calculate the average of all data points in the category as the new cluster center.
• Iterative until the cluster center of each category no longer changes and the data will not be redistributed.

The clustering effect is evaluated by the Silhouette coefficient and Calinski–Harabaz (CH) index. The range of the Silhouette coefficient is [−1, 1]. The closer the distance between samples of the same cluster while the farther the distance between samples of different clusters, the higher the value of the Silhouette coefficient. The CH index has similar changing regularity as the Silhouette coefficient. In general, the higher the value of the Silhouette coefficient and the CH index, the better the clustering effect. The Silhouette coefficient and CH index are calculated as Equations (8) and (9), respectively:

$$S={\displaystyle \frac{b-a}{\mathit{max}(a,b)}}$$

(8)

$$CH(M)={\displaystyle \frac{T_r\left(B_M\right)}{T_r\left(W_M\right)}}\times {\displaystyle \frac{N-M}{M-1}}$$

(9)

where $a$ is the average distance of other samples in the same category, $b$ is the average distance of samples in different categories that are closest to it, $B_M$ is the covariance matrix between categories, $W_M$ is the covariance matrix within the category, $T_r$ is the trace of the matrix, $N$ is the number of samples, and $M$ is the number of categories.

We set $M=2$, $M=3$, and $M=4$, and the corresponding Silhouette coefficient and CH index are shown in Figure 9. It can be seen that when the number of cluster centers is 2, both the Silhouette coefficient and the CH index are the largest, respectively 0.57 and 536, which means the clustering effect is the best. And when the number of cluster centers is four, the clustering effect is the worst. According to that, the driving styles were divided into two categories.

In the above, we used PCA to reduce the dimensionality of the original data from 23 to 6. However, 6-dimensional data cannot be visualized. To better display the clustering results, the t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm was used to reduce the 6-dimensional data to two dimensions to realizes the visual display of high-dimensional data. The t-SNE algorithm is a deep learning algorithm for nonlinear dimensionality reduction. The clustering results of driving styles after dimensionality reduction using the t-SNE algorithm are shown in Figure 10.

As shown in Figure 10, the driving styles are classified into two categories, aggressive and calm. To facilitate further analysis, we attached labels to the different driving styles and obtained the corresponding driving data.

Table 6. Statistical values of driving style indicators with different labels.

Label	Average Velocity (km/h)	Velocity Standard Deviation	Maximum Velocity (km/h)	Average Accelerator Pedal Stroke Value (%)	Average Decelerator Pedal Stroke Value (%)	⋯
0	18.04	17.54	57.67	50.37	31.88	⋯
1	16.52	15.55	51.86	33.19	27.88	⋯

shows the statistical values of the 23 driving style indicators under the different labels. It can be seen that the driver with the label 0 has a larger average velocity, velocity standard deviation, etc. than the driver with the label 1, that is, the driver corresponding to the label 0 has an aggressive driving style, and the driver corresponding to the label of 1 has a calm driving style.

Table 7. Driving style labels corresponding to different drivers.

Driver	Label
0506_22487a_4	0
0506_2c62b9_4	0
0506_7a0784_4	1
0506_c032c0_4	0
0507_22487a_4	0
0508_22487a_3	0
…	…

shows the classification labels corresponding to the different drivers.

3.3. The First-Level Speed Profile Prediction

In this section, the first-level speed profiles are synthesized based on real-world driving data, which considers the effect of different environmental factors and driving styles. Since the change of the vehicle speed is a random process with Markov properties, the speed profile can be modeled as a Markov chain [38]. According to Section 3.1 and Section 3.2, the real-world driving data can be divided into six types based on different road section levels and different driving styles:

• Road section level is 1, aggressive driving style
• Road section level is 2, aggressive driving style
• Road section level is 3, aggressive driving style
• Road section level is 1, calm driving style
• Road section level is 2, calm driving style
• Road section level is 3, calm driving style

To model the above six types of real-world driving data as Markov chains, first, the kinematic fragments need to be divided. The definition of kinematic fragments in this research is the driving process with constant velocity or a certain range of acceleration or deceleration. According to that, the complete speed profile can be divided into four types of kinematic fragments: accelerating, decelerating, cruising, and idling. As shown in Figure 11, a complete speed profile can be divided according to different road section levels or kinematic fragments. Then, the transition probability matrix (TPM) can be calculated, and the steps are briefly described as follows:

• Classify the kinematic fragments to different speed states according to the average speed. Here, we divide the speed states into six in intervals of $10 \mathrm{k}\mathrm{m}/\mathrm{h}$, and label them with $k=\left\{\mathrm{1,2},\mathrm{3,4},\mathrm{5,6}\right\}\left(\left\{0-10 \mathrm{k}\mathrm{m}/\mathrm{h}:1,20-30 \mathrm{k}\mathrm{m}/\mathrm{h}:2,\cdots ,50-60 \mathrm{k}\mathrm{m}/\mathrm{h}:6\right\}\right)$.
• The transfer probability between speed states is calculated based on their time sequence. Considering the large number of samples of historical data, the maximum likelihood estimation is used to calculate the transfer probability between speed states, as shown in Equation (10).

$$P_{ij}={\displaystyle \frac{N_{ij}}{{\sum }_j{N}_{ij}}}$$

(10)

where $P_{ij}$ is the probability of transitioning to the state j in the next phase when the system is in the state $i$ in the current phase. $N_{ij}$ is the number of kinematic fragments that transfer from the state $i$ to the state $j$.

Figure 11. Examples of dividing the speed profile according to the road section level and kinematic fragments.

Figure 11. Examples of dividing the speed profile according to the road section level and kinematic fragments.

In addition, $P_{ij}$ also needs to satisfy Equation (11):

$$\left\{\begin{array}{c}0\le P_{ij}\le 1, i,j=\mathrm{1,2},\dots ,6\\ {\displaystyle \sum _{j=1}^6}{P}_{ij}=1, i=\mathrm{1,2},\dots ,6\end{array}\right.$$

(11)

3.

Then, the TPM of the six types of historical data is obtained as shown in Equation (12):

$$P=\left[\begin{array}{cccc}{P}_{11}& P_{12}& \cdots & P_{16}\\ P_{21}& P_{22}& \cdots & P_{26}\\ ⋮& ⋮& \ddots & ⋮\\ P_{61}& P_{62}& \cdots & P_{66}\end{array}\right]$$

(12)

4.

According to the TPM, the matrix $\pi$ that denotes the steady state distribution of the Markov chain is obtained as shown in Equation (13):

$$\pi =\underset{n\to \infty }{\lim }{P}^n=\left[\begin{array}{cccc}\mathsf{\pi }\left(1\right)& \mathsf{\pi }\left(2\right)& \cdots & \mathsf{\pi }\left(6\right)\\ \mathsf{\pi }\left(1\right)& \mathsf{\pi }\left(2\right)& \cdots & \mathsf{\pi }\left(6\right)\\ ⋮& ⋮& \ddots & ⋮\\ \mathsf{\pi }\left(1\right)& \mathsf{\pi }\left(2\right)& \cdots & \mathsf{\pi }\left(6\right)\end{array}\right]$$

(13)

After the TPM and the steady state matrix $\pi$ are obtained, the first-level speed profile can be predicted by utilizing the Metropolis–Hastings (MH) algorithm. For a certain road section $R_i$ and a certain driving style, the steps of synthesizing the first-level speed profile using the MH algorithm are described as follows:

• A certain acceleration fragment is randomly selected from the set of kinematic fragments of the road section $R_i$ and the corresponding driving style as the starting fragment of the speed profile. This acceleration fragment needs to meet: the initial speed of 0 and the maximum speed cannot exceed the constraints formed by the environmental factors in Table 4. According to the average speed of the kinematic fragment, the corresponding state label is determined as $k\left(i\right)$.
• According to the current state labels $k\left(i\right)$ and $P$, the next moment state label $k\left(j\right)$ is obtained by sampling from the uniform distribution $u~uniform\left[\mathrm{0,1}\right]$.
• Calculate acceptance rate $\alpha (k(i),k(j))=\mathit{min}\left\{{\displaystyle \frac{\pi \left(j\right)P(j,i)}{\pi \left(i\right)P(i,j)}},1\right\}$, if $u<\alpha \left(k\right(i),k\left(j\right))$, then accept the transfer at the next moment, that is, $k(i)\stackrel{\hspace{1em}t+1\hspace{1em}}{\to }k(j)$. Otherwise, the transfer is not accepted, and re-sampling proceeds according to the state labels $k_i$ and $P$ until $u>=\alpha$.
• After determining the state label $k\left(j\right)$ at the next moment, select a kinematic fragment marked with the state label $k\left(j\right)$ that meets two conditions: the difference between the initial speed of it and the final speed of the previous kinematic fragment is less than 1 km/h, and its maximum speed cannot exceed the constraints formed by the environmental factors in Table 4.
• The obtained kinematic fragment is added to the end of the speed profile, and the state label $k\left(j\right)$ of the kinematic fragment is taken as the current state and the kinematic fragment at the next moment continues to be predicted according to the above method. Until the travel distance corresponding to the speed profile reaches the actual distance of $R_i$, the predicting ends.

According to the process described above, the speed profiles of different driving styles on all road sections are obtained. After splicing the speed profiles of the road sections from the starting point to the ending point of a complete route, the first-level speed profiles are obtained.

4. The Second-Level Speed Profile and Energy Consumption Prediction

4.1. Establishment of the Energy Consumption Model

The energy demand model proposed in this research is based on the longitudinal dynamics model of electric vehicles, which consists of aerodynamic drag, rolling resistance, uphill driving force, and inertial force. The four parts are combined to form the traction force, which is then transmitted to the wheels to push the vehicle forward. The specific calculation is shown in Equations (14)–(18):

$$F_t=F_{drag}+F_{roll}+F_{uphill}+F_{inertial}$$

(14)

$$F_{drag}=0.5\rho C_{d}A{v}^2$$

(15)

$$F_{roll}=Mgf\mathit{cos}\alpha$$

(16)

$$F_{uphill}=Mg\mathit{sin}\alpha$$

(17)

$$F_{inertial}=\delta Ma$$

(18)

where $\rho$ is the air density in kg/m³, $C_d$ is the drag coefficient, $A$ is the reference frontal area of the BEB in ${\mathrm{m}}^2$, $v$ is the speed of the vehicle in m/s (it is assumed that the flow velocity of the air around the vehicle is equal to the vehicle speed, i.e., wind speed is neglected),$f$ is the rolling resistance coefficient, $M$ is the total mass of the BEB in kg, $g$ is the gravitational acceleration in m/s², $\alpha$ is the gradient of the road, and $\delta$ is the coefficient that is related to the BEB’s mass.

The BEBs as the data collection objects in this research have a regenerative braking system. When the vehicle brakes or drives on a steep enough downhill, that is, when the traction force is negative, the system converts part of the kinetic energy into electrical energy and stores it in the battery. Therefore, the energy consumption per unit time of the vehicle is as in Equations (19) and (20):

$$E_t=\eta (0.5\rho C_{d}A{v}^2+Mgf+\delta Ma(t\left)\right)v\left(t\right)$$

(19)

$$\eta =\left\{\begin{array}{l}{\displaystyle \frac{1}{{\eta }_t{\eta }_{in}{\eta }_m{\eta }_b}}, F_t(t)\ge 0\\ r_{reg}{\eta }_t{\eta }_{in}{\eta }_m{\eta }_b, F_t\left(t\right)<0\end{array}\right.$$

(20)

where ${\eta }_t$ is the drivetrain and gearbox efficiency, ${\eta }_{in}$ is the efficiency of the inverter, ${\eta }_m$ is the efficiency of the motor, ${\eta }_b$ is the efficiency of the battery, and $r_{reg}$ is the regeneration factor, which determines how much of the kinetic energy can be regenerated. The above energy consumption model ignores the influence of slope.

4.2. The Second-Level Speed Profile Prediction

In Section 3.3, the first-level speed profiles with a time interval of 10 s are obtained, which do not meet the requirements for an accurate estimation of energy consumption. Therefore, in this section, the first-level speed profiles were filled in to obtain the second-level speed profiles with a time interval of 1 s. For the first-level speed profiles, every 10 s is regarded as a part, the final speed point of the previous part is the initial speed point of the next part, and each part is discretized into nine segments, which need to be filled with nine speed points. As shown in Figure 12, except for the initial speed point and the final speed point in each part, nine segments in the middle need to be filled with new speed points. For different driving styles, the speed profiles of the aggressive style are filled with the maximum energy consumption goal, and the speed profiles of the calm style are filled with the minimum energy consumption goal. The following is the specific process:

• Limit the speed points filled in each part

Some related factors need to be considered that limit the speed range. On the one hand, acceleration affects the subjective comfort of the passengers. According to the “Test Method for Vehicle Ride Comfort (National Standard of the People’s Republic of China, GB/T 4970-2009 [39])“, when the acceleration is greater than $2 \mathrm{m}/{\mathrm{s}}^2$, the human feels extremely uncomfortable. Therefore, in this research, the acceleration of the vehicle is limited to $-2 \mathrm{m}/{\mathrm{s}}^2\le a\le 2 \mathrm{m}/{\mathrm{s}}^2$. On the other hand, the speed is also constrained by environmental factors as analyzed in Section 3.1. Table 4 gives the maximum speed limit $v_{\mathit{lim}it}$ under different road sections, workdays and holidays, weather conditions and time periods, i.e., $v\le v_{\mathit{lim}it}$. Taking these two aspects together, the limitation of the speed points filled in each part can be obtained by the following steps:

• From the starting speed point, according to the acceleration and the maximum speed limit, the speed range of the next segment is obtained based on the previous segment and so on, until it stops at the last segment of the final speed point. The speed range of each segment is $\left\{[v_{start1\_min},v_{start1\_max}], \cdots ,[v_{start9\_min},v_{start9\_max}]\right\}$.
• Starting from the last speed point, according to the acceleration and the maximum speed limit, the speed range of the previous segment is obtained by backward deduction, and so on, until it stops at the next segment of the starting speed point. The speed range of each segment is $\left\{\left[v_{end1\_min},v_{end1\_max}\right],\cdots ,\left[v_{end9\_min},v_{end9\_max}\right]\right\}$.
• In the above two steps, the two speed ranges from the forward and reverse directions of each segment are obtained. We take the intersection of the two speed ranges: the maximum speed of the segment can be obtained by $\mathit{min}\{v_{\mathit{starti}\_\mathit{max}},v_{\mathit{endi}\_\mathit{max}}\}$ and the minimum speed of the segment can be obtained by $\mathit{max}\{v_{\mathit{starti}\_\mathit{min}},v_{\mathit{endi}\_\mathit{min}}\}$. Finally, the speed limit range that meets the constraint conditions at each segment is obtained, that is, $\left\{\left[v_{1\_min},v_{1\_max}\right],\cdots ,\left[v_{9\_min},v_{9\_max}\right]\right\}$.

Figure 12. Fill each part with speed points.

Figure 12. Fill each part with speed points.

2.

Convert each segment into a weighted directed graph and store the adjacency relationship and weight information of the speed points

Through step 1, for a segment $i$ of any part, the maximum velocity $v_{i\_max}$ and minimum velocity $v_{i\_min}$ are obtained. Within the speed range, the discrete velocity at 0.5 m/s occurs in intervals of each segment. The arbitrary velocity point after dispersion is noted as $v_{ij}$, where $i$ is the label of segment, $i=\mathrm{1,2},\cdots ,9$; and $j$ is the number of the velocity point after dispersion. According to $-2 \mathrm{m}/{\mathrm{s}}^2\le a\le 2 \mathrm{m}/{\mathrm{s}}^2$, the theoretically reachable speed range of the $v_{ij}$ in the next segment $i+1$ is $\left[v_{ij}-2,v_{ij}+2\right]$. Then, take the intersection of $\left[v_{ij}-2,v_{ij}+2\right]$ and $\left[v_{i+1\_min},v_{i+1\_max}\right]$, i.e., $\left[\mathit{max}\{v_{ij}-2,v_{i\_min}\},\mathit{min}\{v_{ij}+2,v_{i\_+1max}\}\right]$ to get the speed range of the next segment $i+1$, which the $v_{ij}$ can really reach. The energy consumption as a weight for each speed point can be obtained by the energy consumption model in Section 4.1. Finally, each part can be converted into a weighted directed graph as shown in Figure 13. The weighted directed graph stores the adjacency relationship of each speed point and the weight information between every two speed points.

3.

Use the Depth-First-Search (DFS) algorithm to determine the speed points filled in each part corresponding to the maximum and minimum energy consumption

The DFS algorithm is used for searching the weighted directed graph to find the speed points filled in each part with the maximum and minimum energy consumption. The basic idea of the DFS algorithm is to expand from the initial point, with the sequence of expanding the newly generated node first. This feature makes the DFS algorithm continue along a single path in the state space until the last node cannot generate a new node or find the target node location. When the end point is found, look for nodes that can produce new nodes in the opposite direction of the node generation sequence and expand it to form another search path until all possible paths from the start point to the end point are obtained. The specific steps are as follows:

• Set the distance constraints: When looking for the speed points, one should not only consider energy consumption but also the travel distance corresponding to the speed profile. The travel distance under each segment of each part is different because the segments are discretized by the same time interval. As a result, under the same segment, different speed profiles will lead to different travel distances. However, the travel distance of each road section is fixed. Therefore, it is necessary to set the travel distance as a constraint condition. The speed profiles selected from the second-level speed profiles formed by the speed points after they are discretized should satisfy the distance constraint. Denote the length of a road section as s and the first-level speed profile obtained from Section 3 as $V=\{v_0,v_1,v_2,\dots ,v_n\}$, then this speed profile is divided into n parts in which the new speed points will be filled with a time interval of 1 s. The corresponding distance constraint of each part is shown in Equations (21) and (22):

$$0.95s_{o\_ij}\le s_{ij}\le 1.05s_{o\_ij}$$

(21)

$$s_{o\_ij}={\displaystyle \frac{v_i+v_j}{(v_0+v_1)+(v_1+v_2)+\cdots +(v_{n-1}+v_n)}}\times s$$

(22)

where $s_{ij}$ is the actual travel distance corresponding to a certain part after filling in.

• Obtain the candidate second-level speed profiles: Suppose the starting speed point $v_{start}$ is the source point. At this time, the set of speed points is $R=\left\{v_{start}\right\}$. Add an adjacent point $v_{1j}$ in the next segment of the $v_{start}$, $R=\{v_{start},v_{1j}\}$. Then add an adjacent point $v_{2j}$ in the next segment of the $v_{1j}$, $R=\{{v_{start},v}_{1j},v_{2j}\}$, and repeat this until the added speed point is the final speed $v_{end}$, and finally $R=\{v_{start},v_{1j},v_{2j},\cdots ,v_{9j},v_{end}\}$.
• Store the speed profile that meets the conditions and the corresponding energy consumption: For a certain speed profile, $R=\{v_{start},v_{1j},v_{2j},\cdots ,v_{9j},v_{end}\}$ and the corresponding travel distance is $s_{ij}={\displaystyle \frac{1}{2}}\left[(v_{start}+v_{1j})+(v_{1j}+v_{2j})+\cdots +(v_{9j}+v_{end})\right]$. If $s_{ij}$ satisfies the distance constraint condition of step 1, then this speed profile and the corresponding energy consumption are recorded.
• Traverse all possible speed profiles: If a certain speed profile $R=\{v_{start},v_{1j},v_{2j},\cdots ,v_{9j},v_{end}\}$ is obtained, look for a speed point that can generate a new adjacent point along the opposite direction of its speed point generation sequence, and expand it to form a new speed profile, then go to step 3. Repeat this process until all possible speed profiles in the weighted directed graph have been traversed.
• Obtain the second-level speed profiles we want: sort the energy consumption and select the speed profile corresponding to the highest or lowest energy consumption according to different driving styles.

4.

Re-select the speed profiles corresponding to the minimum energy consumption.

Figure 14 shows the estimated speed profile corresponding to the minimum energy consumption of a certain road section. It can be seen that when the speed is low, frequent start–stops occur. However, the driver will not frequently start and stop during driving under actual driving conditions. In order to be more practical, we should not only take the lowest energy consumption as the criterion, but also add the constraints of the frequency of starts and stops. Therefore, within a certain range of lower energy consumption, the speed profile with the least number of starts and stops is selected as the speed profile corresponding to the minimum energy consumption, and the corresponding energy consumption is the actual minimum energy consumption. As shown in Figure 15, the number of starts and stops of the re-selected speed profile is significantly reduced compared with the speed profiles before. Figure 16 shows an example of the speed profiles corresponding to the estimated lowest and highest energy consumption.

4.3. Estimation Results and Validation

The estimated energy consumption results are compared with the true energy consumption results to verify the accuracy and reasonableness of the estimation methods.

Based on the real-world driving data, the true energy consumption of the BEBs from the start point to the end point for any trip is calculated as Equation (23):

$$E_a={\displaystyle \frac{C_b\times U_b}{1000}}\times \Delta SOC$$

(23)

where $C_b$ is the battery capacity in $A\cdot h$, $U_b$ is the battery voltage in $V$, and $\Delta SOC$ is the percentage of electricity that has been consumed.

Table 8. Constant parameters used in the case study.

Parameter	Value	Unit
$\rho$	1.18	kg/m3
$C_d$	0.7	-
$A$	8.3	m2
$M_k$	10,700	kg
$f$	0.008	-
$\delta$	1.1	-
${\eta }_t$	0.96	-
${\eta }_{in}$	0.95	-
${\eta }_b$	0.99	-
$r_{reg}$	0.5	-
$C_b$	400	AH
$U_b$	6180	V

lists the values of the constant parameters in this research. Among them, the calculation of the vehicle mass is as in Eq. (24):

$$M_z=M_k+M_p$$

(24)

where $M_k$ is the curb weight of the vehicle and $M_p$ is the passenger mass. According to actual observations, the average number of passengers on the No. 4 bus in Changchun City is about 30 people. Assuming that the mass of each person is 70 kg, the passenger mass $M_p=2100 \mathrm{kg}$. The values of the other parameters are the data corresponding to the actual vehicle or the typical parameter values in the literature. In addition, the efficiency of the motor is different under different speeds and torque. This paper determined the motor efficiency ${\eta }_m$ at different speeds and torques according to the motor map corresponding to the BEB. The motor map is shown in Figure 17.

Five samples were arbitrarily selected and their true energy consumption was compared with the estimated values. As shown in Figure 18, the true values for all five samples are between the maximum and minimum energy consumption we estimated. And the true values are much closer to the estimated minimum values. This is because the minimum energy consumption represents the ideal value for energy consumption under real-world constraints, but in real-world driving conditions, energy consumption is affected by the different ways in which the driver operates. For example, for Samples 1 and 5, although the real energy consumption of Sample 5 is greater than that of Sample 1, its estimated energy consumption minimum is greater than that of Sample 1, i.e., its ideal energy consumption is greater than that of Sample 1 under real-world constraints, which reflects the better economic driving ability of the driver of Sample 5. Therefore, the estimation results are also able to contribute to the assessment of drivers’ economic driving ability.

5. Discussion and Conclusions

Given the regularity of bus operation, vehicle energy consumption can be predicted by predicting the speed profile. Based on the real-world driving data of BEBs on the No. 4 bus in Changchun City from January to October 2020, the method proposed in this paper takes the environmental factors, including weather conditions, route characteristics and traffic characteristics, as well as the different driving styles of drivers, into account when predicting the speed profile.

In addition, reasonable prediction of speed profiles usually requires a large amount of accurate driving data. Existing speed profile prediction methods use standardized driving cycles or simulation experiments to obtain driving data at a frequency of 1 Hz, but these driving data are far from the actual driving conditions, and it is difficult to obtain large amounts of high-frequency actual driving data. The method proposed in this paper provides ideas for the effective use of low-frequency real driving data. The first level speed profile predicted by the Markov method is based on the actual driving cycles with a time interval of 10 s, but it is filled reasonably to obtain a second speed profile with a time interval of 1 s.

Typically, buses travelling on the same bus route do not always have the same driver, which is attributed to the shift change system of buses. We are not predicting energy consumption for a single run, but for a certain route, and therefore we have to take the disparity in energy consumption due to different driver styles into account, which results in a predicted energy consumption that is a range rather than a specific value. For the buses, the estimation of energy consumption for a single run may have biases due to the driver’s style and make the prediction not generalizable. Therefore, unlike existing methods for predicting bus energy consumption, we estimated the maximum and minimum values of energy consumption on a particular route, rather than simply estimating a specific value for a particular run. The method proposed in this paper contributes to optimizing vehicle scheduling and meeting the operational requirements of a route and lay a foundation for the continuous expansion of BEBs deployment.

In the future, this energy consumption model will consider changes in temperature and dynamic load to make the results more accurate. Furthermore, with the improvement of the automobile big data platform and the rapid development of the Internet of Vehicles, the forecasting framework will not just be limited to a single fixed route, but can also be used to estimate the energy consumption of BEBs in the area, optimize urban traffic, and be used for intelligent navigation, etc.