This paper proposes a scientific and systematic methodology for the development of a representative electric vehicle (EV) urban driving cycle. The methodology mainly includes three tasks: test route selection and data collection, data processing, and driving cycle construction. A test route is designed according to the overall topological structure of the urban roads and traffic flow survey results. The driving pattern data are collected using a hybrid method of on-board measurement method and chase car method. Principal component analysis (PCA) is used to reduce the dimensionality of the characteristic parameters. The driving segments are classified using a hybrid k-means and support vector machine (SVM) clustering algorithm. Scientific assessment criteria are studied to select the most representative driving cycle from multiple candidate driving cycles. Finally, the characteristic parameters of the Xi’an EV urban driving cycle, international standard driving cycles, and other city driving cycles are compared and analyzed. The results indicate that the Xi’an EV urban driving cycle reflects more aggressive driving characteristics than the other cycles.
Fuel depletion, environmental disruption, and air pollution have contributed to the development of electric vehicles (EVs) [
The driving cycle is a speed-time profile that represents a typical real-world driving pattern in a certain city or region [
Many researchers have also successfully developed real-world driving cycles, such as the Dublin driving cycle [
This paper is organized as follows. The test route selection and data collection method are presented in Section
The test routes must cover various urban road types, business and nonbusiness districts, densely populated areas and nonpopulated areas and consider the urban topological structure, driving speed, traffic flow, travel time, and origin-destination (O-D) pattern [
Details of the test route.
Number | Road name | Road type | Road length (km) | Number of traffic lights |
---|---|---|---|---|
1 | Wenyi south road | Secondary road | 1.2 | 3 |
2 | Mingsheng road | Branch road | 0.6 | 0 |
3 | Jiandong road | Branch road | 1.7 | 5 |
4 | Leju road | Branch road | 0.6 | 1 |
5 | East Gate south road | Main road | 1.1 | 1 |
6 | East Gate road | Main road | 0.4 | 1 |
7 | Changle road | Branch road | 1.5 | 0 |
8 | Xingqing road | Main road | 0.6 | 3 |
9 | Changle west road | Main road | 1.6 | 2 |
10 | North section of the east first ring road | Express way | 1.0 | 0 |
11 | Taihua south road | Main road | 0.8 | 2 |
12 | Hanyuan road | Secondary road | 2.0 | 0 |
13 | East second ring road | Express way | 2.0 | 0 |
14 | North second ring road | Express way | 1.8 | 0 |
15 | Taihua south road | Main road | 0.7 | 1 |
16 | Xuanwu road | Secondary road | 1.6 | 3 |
17 | Weiyang road | Main road | 0.7 | 0 |
18 | Fangxin road | Branch road | 1.6 | 2 |
19 | Mingguang road | Secondary road | 1.0 | 3 |
20 | Gongnong road | Secondary road | 0.5 | 3 |
21 | Ziqiang west road | Secondary road | 0.8 | 0 |
22 | Xinghuo road | Main road | 1.3 | 1 |
23 | Daqing road | Main road | 2.1 | 1 |
24 | Taoyuan road | Secondary road | 1.5 | 4 |
25 | Fengqing road | Main road | 1.4 | 2 |
26 | West section of south second ring road | Express way | 5.0 | 0 |
27 | Chang’an road | Secondary road | 0.5 | 0 |
28 | Xingshan temple east road | Branch road | 1.0 | 1 |
29 | Cuihua road | Secondary road | 0.3 | 1 |
30 | South second ring road | Express way | 1.5 | 0 |
Lengths and proportions of urban road types.
Traffic flow survey results.
Test route. Note: the red data in the A-B-C format represents road information, where A represents the serial number of the roads, B represents the length of the roads, and C represents the number of traffic lights.
In driving cycle construction, the common data acquisition methods include the on-board measurement method and chase car method. On-board measurement method uses on-board diagnostics (OBD) installed in a test vehicle to collect trip activity information. The advantage of this approach is that the collected data can accurately represent the actual driving cycle based on large-scale studies. However, the test costs to obtain a reasonable sample size can be extremely high, and the data processing workload is large [
Considering on-board measurement method and chase car method has distinct merits and demerits, and this paper used a hybrid method of on-board measurement method and chase car method to collect test data. When an available EV was driving on the preset test route, the test vehicle chased it and imitated its driving pattern; when no target EV was available, the driving patterns of the test vehicle were collected. The GPS signal is easily influenced by the urban buildings, which can cause signal loss and data spikes; therefore, both GPS and OBD were used to collect driving pattern data. Speed-time data obtained by OBD were mainly used to supplement and improve abnormal GPS data. Moreover, 14 trained professional drivers were selected to minimize the influence of the driver on the collected data. In addition, a BYD E6 pure EV, which is the most commonly owned EV in the market, was selected as the test vehicle. The technical characteristics of the test EV are shown in Table
Technical characteristics of the test EV.
Characteristic parameter | Value |
---|---|
Curb weight (kg) | 2380 |
Mass (kg) | 2755 |
Length (mm) | 4560 |
Width (mm) | 1822 |
Height (mm) | 1630 |
Wheel based (mm) | 2830 |
Front/rear track width (mm) | 1585/1560 |
Centroid height (mm) | 640 |
Maximum speed (km/h) | 140 |
Maximum endurance mileage (km) | 400 |
Rated voltage (V) | 600 |
Maximum torque (Nm) | 450 |
Maximum power (kW) | 120 |
Test equipment.
In the data processing procedure, the raw data were first denoised and smoothed by using a wavelet decomposition and reconstruction method. Then, the preprocessed data were partitioned into 36388 kinematic segments according to (
PCA was proposed and applied by statisticians K. Pearson and H. Hotelling in 1901 [
According to the existing literature, eight characteristic parameters are selected: the maximum speed, minimum speed, average speed, standard deviation of speed, maximum acceleration, maximum deceleration, average acceleration, and standard deviation of acceleration [
We assume that the sample size is
The principal component expressions obtained after orthogonal transformation using the PCA are as follows:
The principal component variance contribution ratio
The principal components corresponding to the eigenvalues whose cumulative variance contributions ratio are greater than 90% are selected to form the comprehensive evaluation index that encompasses 90% of the entire data information.
The number of principal components with cumulative variance contribution ratio exceeding 90% is obtained, where
The calculated principal component expression is shown in (
The PCA algorithm is used to reduce the dimensionality of the characteristic parameters. The principal component variance, variance contribution ratio, and the cumulative variance contribution ratio are shown in Table
PCA results.
Number of principal component | Principal component variance | Variance contribution rate /% | Cumulative variance contribution rate /% |
---|---|---|---|
1 | 2.892 | 36.15 | 36.15 |
2 | 2.635 | 32.94 | 69.09 |
3 | 2.280 | 28.50 | 97.59 |
4 | 0.182 | 2.27 | 99.86 |
5 | 0.005 | 0.06 | 99.92 |
6 | 0.004 | 0.05 | 99.97 |
7 | 9.9e-4 | 0.02 | 99.99 |
8 | 5.9e-4 | 0.01 | 100.00 |
Principal component score matrix.
Segment | Principal | Principal | Principal |
---|---|---|---|
1 | 2.569 | 0.748 | 0.271 |
2 | 1.909 | 1.510 | -0.645 |
3 | 1.998 | 0.898 | -0.158 |
4 | 1.853 | 1.552 | 0.188 |
5 | 1.829 | 0.467 | -0.316 |
| | | |
10000 | -0.459 | 1.424 | -0.054 |
10001 | 0.026 | 0.102 | 1.151 |
10002 | 0.306 | -1.141 | 0.380 |
10003 | 0.217 | 0.946 | 0.817 |
10004 | -0.644 | 1.510 | -0.258 |
| | | |
36384 | 1.972 | 0.619 | 0.470 |
36385 | 0.865 | 1.777 | -1.059 |
36386 | 1.472 | 0.200 | 0.742 |
36387 | 2.110 | -1.821 | -0.838 |
36388 | 2.670 | 0.368 | 0.373 |
Component matrix.
Characteristic parameters | Principal | Principal | Principal |
---|---|---|---|
maximum speed | 0.965 | -0.245 | -0.010 |
minimum speed | 0.848 | -0.074 | -0.514 |
average speed | 0.955 | -0.155 | -0.252 |
standard deviation of speed | 0.268 | -0.317 | 0.866 |
maximum acceleration | 0.346 | 0.720 | 0.597 |
maximum deceleration | 0.125 | 0.973 | -0.177 |
average acceleration | 0.254 | 0.939 | 0.225 |
standard deviation of acceleration | 0.243 | -0.313 | 0.874 |
The k-means algorithm has been widely used in cluster computing in the existing literature [
The number
k-means clustering result.
The analysis of the k-means clustering effect shows that when the distances between the segment and other cluster centers are large enough, and the characteristic parameters of the segment are close to those of a certain class, the clustering effect is good. In contrast, when the distance between the segment and all cluster centers is similar and the characteristic parameters of the segment are significantly different from those of most of the segments in the class, the clustering effect is poor. There are two main reasons for these results. First, k-means is a hard clustering algorithm. When clustering involves multiple classes or the distance between cluster centers is small, the clustering effect is poor, and it is easy to reach local optima that cannot be incrementally clustered. Second, the convergence condition of the k-means clustering algorithm is iterated until the cluster center no longer changes. This approach may cause the data within the class to be very similar but does not fully consider the distance between classes; therefore, only local optima are guaranteed, and the global optimization is not achieved.
The SVM method was first proposed by Cortes and Vapnik in 1995 and has significant advantages in solving nonlinear and high-dimensional pattern recognition problems [
Schematic diagram of the optimal hyperplane.
We assume that the size of the sample set is
If the interval from the sample point to the classification hyperplane is
The above problem can be transformed into a dual problem according to the Lagrange theory and then solved with a quadratic programming method. In the linear inseparability problem, the nonlinear mapping of
Assuming that
This paper builds a multiclassification model based on SVM to classify the driving segments. The specific classification processes include training set screening, kernel function parameter optimization, classification prediction, and clustering result evaluation.
The first step is training set screening. Because a SVM is a supervised learning algorithm, selecting an appropriate training set before classification is extremely important. To improve the classification accuracy and efficiency, the optimal segments were selected from the k-means clustering results as the SVM training set, and the remaining segments were used as the testing set. The selection principles of the optimal segments are as follows. We selected an appropriate number of training sets to avoid under-learning and over-learning issues. Moreover, we selected representative segments from the k-means clustering results, and these segments were as close to a cluster center as possible and as far from the other cluster centers as possible. According to the above principles, 2353 representative segments were selected as the training set of the SVM, and the remaining segments were used as the testing set. Additionally, all segments were normalized to eliminate the influence of the dimensions on the classification results.
The second step is kernel function parameter optimization. Kernel functions can map the sample data in the original low-dimensional space to a high-dimensional feature space and transform them into linearly separable data. Meanwhile, the optimal classification hyperplane in the high-dimensional space can be obtained. Because the radial basis kernel function (RBF) can precisely express the features of the training set, accurately reflect the structure feature of the high-dimensional space, effectively control the dimension of the model solution set, and obtain the global optimal solution, this paper uses a RBF as the basic kernel function of the SVM.
Based on
Optimization results.
The third step in the proposed method involves classification prediction and clustering result evaluation. The SVM model was trained using the optimal parameters. The clustering results of driving segments using the k-means and SVM hybrid model are shown in Figure
k-means and SVM hybrid model clustering results.
To evaluate the clustering results, this paper introduces two indicators: compactness and separation [
Compactness (CP) is an internal cluster evaluation criterion that uses the norm distance between all data sets in each cluster and the cluster center to evaluate the compactness of the cluster. A small
Separation (SP) is an external evaluation criterion between clusters that uses the average Euclidean distance between each two cluster centers to evaluate the degree of separation of the clusters. A high
Table
The calculation results of
Calculation results | k-means | k-means and SVM |
---|---|---|
| 1.393 | 1.317 |
| 4.954 | 5.242 |
The categorized driving segment characteristics are shown in Table
Driving segment characteristics.
Category number | The number of segments | Average speed | Average acceleration | Definition |
---|---|---|---|---|
1 | 10914 | 5.47 | -0.008 | low constant speed driving segments |
2 | 9238 | 22.62 | -0.006 | medium constant speed driving segments |
3 | 6503 | 40.54 | 0.007 | high constant speed driving segments |
4 | 3729 | 18.75 | 0.463 | weak acceleration driving segments |
5 | 1341 | 24.41 | 0.840 | strong acceleration driving segments |
6 | 3573 | 18.00 | -0.489 | weak deceleration driving segments |
7 | 1090 | 21.38 | -0.946 | strong deceleration driving segments |
The driving cycle is constructed by connecting the most representative driving segments according to predetermined rules until the driving cycle duration is reached. Generally, the duration of the general international standard driving cycles and real-world representative driving cycles is between 600 s and 1800 s. Therefore, according to the Hong Kong, Colombo, and Sydney driving cycles, the duration of the Xi’an EV urban driving cycle in this paper is set to 1200 s [
Time proportion and length of seven driving segments.
Driving segments | Time proportion (%) | Time length (s) |
---|---|---|
1 | 30.53 | 366 |
2 | 13.98 | 168 |
3 | 12.51 | 150 |
4 | 14.28 | 171 |
5 | 7.84 | 94 |
6 | 14.72 | 177 |
7 | 6.14 | 74 |
According to the test data and classification results, the time proportion and length of the seven driving segments are shown in Table
Considering the randomness in the construction process of the driving cycle, one construction result is difficult to fully represent the Xi’an EV urban driving cycle. Therefore, the construction process is repeated to generate a large number of candidate driving cycles. Moreover, the scientific assessment criteria are set, and the most representative driving cycle is selected from candidate driving cycles to form the Xi’an EV urban driving cycle.
The assessment criteria flow diagram is shown in Figure
Assessment criteria flow diagram.
The construction of Xi’an EV urban driving cycle is shown in Figure
Comparison of the Xi’an EV urban driving cycle and test data.
Characteristic parameters | Test data | Driving cycle | RE | MRE | RMSE |
---|---|---|---|---|---|
Average speed (km/h) | 20.01 | 20.74 | 3.65% | 4.03% | 1.32% |
Maximum speed (km/h) | 68.22 | 63.86 | 6.39% | ||
Average acceleration (m/s2) | 0.76 | 0.78 | 2.63% | ||
Average deceleration (m/s2) | 0.78 | 0.77 | 1.28% | ||
Standard deviation of acceleration (m/s2) | 0.84 | 0.79 | 5.95% | ||
Proportion of acceleration(%) | 34.5 | 32.9 | 4.64% | ||
Proportion of deceleration(%) | 32.1 | 31.9 | 0.62% | ||
Proportion of uniform speed(%) | 15.9 | 17.3 | 8.81% | ||
Proportion of idling(%) | 17.5 | 17.9 | 2.29% |
Note: RE is the relative error of the assessment parameters of the candidate driving cycles and the overall test data; MRE is the mean relative error of all assessment parameters; and RMSE is the root mean square error of the SAPD.
Xi’an EV urban driving cycle.
SAPD of the Xi’an EV urban driving cycle.
SAPD of the test data.
To study the differences between the Xi’an EV urban driving cycle constructed in this paper and the international standard driving cycles, eight characteristic parameters of seven general international standard driving cycles are compared as shown in Figure
Comparison of results for the Xi’an and international standard driving cycles.
Driving cycle | Xi’an | ECE15 | NEDC | JC08 | J10/15 | FTP-72 | FTP-75 | WLTC |
Vehicle type | EV | ICEV | ICEV | ICEV | ICEV | ICEV | ICEV | ICEV |
Road type | Urban | Urban | Composite | Composite | Urban | Urban | Urban | Composite |
Average speed(km/h) | 20.74 | 18.4 | 33.6 | 24.4 | 17.7 | 31.5 | 34.1 | 46.5 |
Maximum speed(km/h) | 63.86 | 50.0 | 120 | 82.0 | 70.0 | 91.3 | 91.3 | 131.3 |
Average acceleration(m/s2) | 0.78 | 0.64 | 0.51 | 0.42 | 0.63 | 0.59 | 0.60 | 0.42 |
Average deceleration(m/s2) | 0.77 | 0.75 | 0.71 | 0.44 | 0.62 | 0.69 | 0.70 | 0.44 |
Proportion of acceleration(%) | 32.9 | 21.5 | 23.8 | 27.8 | 25.9 | 32.8 | 32.4 | 29.4 |
Proportion of deceleration(%) | 31.9 | 18.5 | 17.6 | 25.9 | 26.4 | 28.3 | 28.2 | 27.8 |
Proportion of uniform speed(%) | 17.3 | 29.2 | 34.8 | 17.4 | 22.2 | 20.9 | 21.2 | 30.3 |
Proportion of idle(%) | 17.9 | 30.8 | 23.8 | 28.9 | 25.4 | 18.0 | 18.2 | 12.5 |
Driving cycles.
To verify the advanced and scientific nature of the construction method of the driving cycle proposed in the paper, the driving cycles constructed by the k-means and SVM hybrid clustering algorithm, k-means clustering algorithm, and fuzzy c-means (FCM) clustering algorithm were compared. The driving cycles constructed by the k-means clustering algorithm and FCM clustering algorithm are shown in Figures
Comparison of the characteristic parameter results.
Characteristic parameters | Test data | k-means and SVM | k-means | FCM |
---|---|---|---|---|
Average speed (km/h) | 20.01 | 20.74 | 21.59 | 22.47 |
Maximum speed (km/h) | 68.22 | 63.86 | 63.07 | 61.42 |
Average acceleration (m/s2) | 0.76 | 0.78 | 0.69 | 0.74 |
Average deceleration (m/s2) | 0.78 | 0.77 | 0.76 | 0.79 |
Standard deviation of acceleration (m/s2) | 0.84 | 0.79 | 0.76 | 0.8 |
Proportion of acceleration(%) | 34.5 | 32.9 | 36.0 | 38.33 |
Proportion of deceleration(%) | 32.1 | 31.9 | 32.6 | 30.92 |
Proportion of uniform speed(%) | 15.9 | 17.3 | 14.3 | 14.01 |
Proportion of idling(%) | 17.5 | 17.9 | 17.1 | 16.74 |
MRE (%) | - | 4.03 | 6.11 | 6.88 |
RMSE (%) | - | 1.32 | 1.89 | 2.04 |
Driving cycle based on k-means clustering algorithm.
Driving cycle based on FCM clustering algorithm.
To study the differences between the Xi’an EV urban driving cycle and other typical city driving cycles, this paper introduces the Winnipeg, Dublin, Mashhad, Hongkong, Ningbo, and Tianjin driving cycles and studies the difference and similarity among driving cycles through comparing the characteristic parameters. A comparison of the results is shown in Table
Comparison of the results for typical city driving cycles.
Driving cycle | Xi’an | Winnipeg | Dublin | Mashhad | Hongkong | Ningbo | Tianjin |
Vehicle type | EV | PHEV | EV | ICEV | ICEV | ICEV | ICEV |
Road type | Urban | Composite | Urban | Urban | Urban | Urban | Urban |
Size of experiment | 56 trips, 428 hours, 2158 km | 76 volunteers, one year | 1485 journals | 450 km | 29 hours | 24 hours | 25 hours |
Average speed(km/h) | 20.74 | 31.4 | 30.87 | 20.27 | 25.0 | 23.7 | 22.5 |
Maximum speed(km/h) | 63.86 | 100 | 84.5 | 60.90 | 77.7 | 60.2 | 70.2 |
Average acceleration(m/s2) | 0.78 | 0.60 | 0.62 | 0.53 | 0.60 | 0.51 | 0.36 |
Average deceleration(m/s2) | 0.77 | 0.60 | 0.64 | 0.54 | 0.60 | 0.58 | 0.43 |
Proportion of acceleration(%) | 32.9 | 31.4 | 26.7 | 37.67 | 34.5 | 37.0 | 36.0 |
Proportion of deceleration(%) | 31.9 | 31.2 | 25.0 | 37.48 | 34.2 | 33.0 | 30.0 |
Proportion of uniform speed(%) | 17.3 | 14.9 | 27.6 | 3.16 | 12.0 | 11.0 | 21.0 |
Proportion of idle(%) | 17.9 | 21.8 | 20.7 | 21.70 | 17.8 | 20.0 | 12.0 |
Reference | - | [ | [ | [ | [ | [ | [ |
According to an analysis of the results, the Xi’an EV urban driving cycle reflects a more aggressive driving pattern than other driving cycles. The reasons for this finding are threefold. First, car ownership and the urban population have increased rapidly in Xi’an. The city size and transportation infrastructure construction cannot keep up with the increase in car ownership, and urban traffic congestion is serious. Second, the urban driving cycle in this paper is based on EVs, but general international standard driving cycles are based on traditional ICEVs. The start-up acceleration of EVs is obviously higher than that of ICEVs due to the low-speed constant torque characteristics of the motor [
This paper proposes a scientific and systematic methodology for the development of a representative EV urban driving cycle. The methodology mainly includes three tasks: test route selection and data collection, data processing, and driving cycle construction. For test route selection and data collection, the overall topological structure of urban roads and traffic flow monitoring results are used as the main factors for the selection of test routes. We combine the advantages of the on-board measurement and chase car methods to collect driving pattern data. In the data processing stage, the PCA algorithm is used to reduce the dimensionality of the characteristic parameters. The driving segments are classified using a k-means and SVM hybrid clustering algorithm, and the classification results of the hybrid method are obviously superior to those of the k-means method. In the driving cycle construction stage, scientific assessment criteria are studied to select the most representative driving cycle from multiple candidate driving cycles. In addition, the SAPDs of the representative Xi’an EV urban driving cycle and real-world test data are compared, and the results show that the Xi’an EV urban driving cycle constructed in this paper effectively represents the speed-time driving pattern of the real-world cycle. Finally, the characteristic parameters of the Xi’an EV urban driving cycle, international standard driving cycles, and other typical city driving cycles are compared and analyzed. The results indicate that the Xi’an EV urban driving cycle reflects a more aggressive driving characteristic than other driving cycles, mainly due to the difference in the start-up acceleration and regenerative braking characteristics of EVs and ICEVs. Therefore, a representative EV driving cycle should be used for energy optimization, state of charge estimation, and driving mileage prediction for EVs, as well as the evaluation and certification of new EV models.
The
The authors declare that they have no conflicts of interest.
This research is funded by the National Key R&D Program of China (2017YFC0803904), National Natural Science Foundation of China (51507013), China Postdoctoral Science Foundation (2018T111006, 2017M613034), Postdoctoral Science Foundation of Shaanxi Province (2017BSHEDZZ36), Shaanxi Province Industrial Innovation Chain Project (2018ZDCXL-GY-05-03-01), Shaanxi Provincial Key Research and Development Plan Project (2018ZDXM-GY-082), and Shaanxi Innovative Talents Promotion Plan Project (2018KJXX-005).
The “Test Data” file records some of the speed-time data collection during the test. The “Driving Cycle” file records the speed-time data of driving cycle based on k-means and SVM proposed in this paper.