Signal Processing and Control Techniques for Intelligent Vehicles – Research Article
Support vector machine–based driving cycle recognition for dynamic equivalent fuel consumption minimization strategy with hybrid electric vehicle
Advances in Mechanical Engineering 2018, Vol. 10(11) 1–17 Ó The Author(s) 2018 DOI: 10.1177/1687814018811020 journals.sagepub.com/home/ade
QIN Shi, Duoyang Qiu , Lin He, Bing Wu and Yiming Li
Abstract For a great influence on the fuel economy and exhaust, driving cycle recognition is becoming more and more widely used in hybrid electric vehicles. The purpose of this study is to develop a method to identify the type of driving cycle in real time with better accuracy and apply the driving cycle recognition to minimize the fuel consumption with dynamic equivalent fuel consumption minimization strategy. The support vector machine optimized by the particle swarm algorithm is created for building driving cycle recognition model. Furthermore,the influence of the two parameters of window width and window moving velocity on the accuracy is also analyzed in online application. A case study of driving cycle in a medium-sized city is introduced based on collecting four typical driving cycle data in real vehicle test. A series of characteristic parameters are defined and principal component analysis is used for data processing. Finally, the driving cycle recognition model is used for equivalent fuel consumption minimization strategy with a parallel hybrid electric vehicle. Simulation results show that the fuel economy can improve by 9.914% based on optimized support vector machine, and the fluctuations of battery state of charge are more stable so that system efficiency and batter life are substantially improved. Keywords Driving cycle recognition, particle swarm optimization, support vector machine, equivalent fuel consumption minimization strategy, parallel hybrid electric vehicle
Date received: 4 June 2018; accepted: 11 October 2018 Handling Editor: Zhixiong Li
Introduction Hybrid electric vehicles (HEVs) are considered very effective vehicles in terms of fuel economy and exhaust emission. Many previous studies have been conducted on logic threshold control, fuzzy control, dynamic programming, and model predictive control, which have been developed and used in HEVs.1–5 These methods have higher control precision and make a positive contribution to fuel economy. Driving cycles, also known as driving conditions, refers to a velocity sequence on the course of time of a
certain type of vehicles (such as passenger cars, buses, commercial vehicles) in the specific conditions which are representative6 (such as urban roads, suburban roads, freeways). Driving cycles in typical cities is the
School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei, China Corresponding author: Duoyang Qiu, School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei 230009, China. Email:
[email protected]
Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/ open-access-at-sage).
2 velocity and time curves reflecting the running state of vehicles, which are based on the investigation of the actual traffic flow and the data processing of a real car experimental test. It is well known that the effectiveness of energy management strategy (EMS) for HEVs is greatly influenced by the driving cycles.7 So in the process of research and development of electric vehicles, driving cycle recognition (DCR) is becoming more and more widely used. For HEVs, the EMS should keep accordance with the features of current driving cycle and adjust control parameter values in real time. So different power sources can achieve optimal power distribution and further improve the vehicle fuel economy.8–16 DCR mainly collects and analyzes driving cycles information the by global positioning system(GPS) or the on-board sensors in predicting future driving cycles. However, no matter which method, a high-precision recognition algorithm is the key. The current recognition methods of driving cycle can be roughly divided into three categories: first, using DCR based on the neural network algorithms: J Wang et al.17 applied a mathematical statistic’s method to select recognition parameters and proposed learning vector quantization (LVQ) neural network for DCR; SI Jeon et al.18 described driving cycle by defining a series of characteristic parameters and adopted DCR with Hamming neural network; Y Ren et al.19 applied extreme learning machine (ELM) to train and recognize driving cycles and extract control parameters from a database to distribute the torque engine and motor sensible; Q Zhu et al.20 used artificial neural network (ANN) in the driving cycle model predictive control. The prediction accuracy is better than using the previous active set directly; second, adopting fuzzy controller as a DCR tool: S Zhang and R Xiong developed a driving pattern recognition method with the fuzzy logic controller and proposed an adaptive energy management method for a plug-in HEV. Simulation results indicate that DCR with fuzzy logic controller can make better fuel efficiency than the original and conventional dynamic programming–based control strategies21; L Niu et al. presented an adaptive power matching controlling strategy of driving cycle fuzzy recognition. The simulation based on ADVISOR software shows that the newly designed controlling strategy with DCR could adapt driving cycles and enhance intellectualization of full vehicle22; Y Tian et al.23 recognize the arterial road and secondary main road of Guangzhou and Shanghai in China by optimized fuzzy controller; third, applying clustering theory in DCR: Z Lei et al. confirmed current driving cycle type by computing the Euclid distance of the characteristic parameters between standard driving cycle and current driving cycle. The simulation results show that compared with the original rule-based EMS, DCR can reduce the fuel consumption by
Advances in Mechanical Engineering 11.68%24; J Wang et al.25 also adopted DCR by computing the Euclid distance and used in equivalent consumption minimization strategy (ECMS) so as to realize an optimization of fuel economy; S Zhan et al.10 applied K-means clustering method, which is optimized by genetic algorithm to conduct DCR in order to adjust the equivalent fuel consumption factor in realtime control. These studies provide an important basis for the study of DCR. However, there is still room for further improvement in recognition accuracy. Uncertainty of the neuron number exists in hidden layer while applying a neural network algorithm, so it is difficult to obtain an optimal DCR model; for fuzzy recognition controller, membership functions are usually chosen according to experience, so the recognition accuracy can be improved only after many times debugging, which adds the developing workload and extends the period of vehicle development; for various clustering theories, the initial value of the clustering center has great effect on recognition results, which may lead to fall into local optimum, such as Euclid’s algorithm. Furthermore, clustering algorithms also are very sensitive to the number of input parameters. Support vector machine (SVM) is a kind of machine learning theory aiming at limited samples, which is put forward based on Vapnik–Chervonenkis (VC) dimension theory and structural risk minimization principle from statistics learning theory. The algorithm does not involve probability measure and law of large numbers and avoids the traditional process from induction to deduction, so it effectively implements the transductive reasoning from training samples to texting samples and greatly simplifies the classification and regression problems. As a supervised learning theory, there is no problem of setting the initial clustering center of the clustering theory. Meanwhile, it avoids the problems of network structure selection, over learning and insufficient learning of ANN. However, SVM has not been applied to the study of DCR. The current paper presents a DCR method with SVM algorithm using the time window. In order to further improve the recognition accuracy, particle swarm optimization (PSO) algorithm and SVM algorithm are combined for building optimal off-line DCR model. Furthermore, the influence on the online recognition accuracy of window width and window moving velocity is also analyzed. Finally, the DCR model is applied in ECMS for a parallel HEV with P2 configuration. Simulation is carried on MATLAB/Simulink platform, and the results show that the fuel economy can improve by 9.914% with DCR based on optimized SVM algorithm and improve by 5.231% with DCR based on SVM without optimization, and the fluctuations of battery state of charge (SOC) are more stable in two cases so that system efficiency and batter life are substantially improved.
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Control flow of dynamic ECMS based on the DCR The driving cycle has a great influence on the fuel economy of HEVs.6 Therefore, in order to further improve the fuel economy, the EMS should adjust the value of the control parameters in real time according to the characteristics of the current driving cycle, so as to realize the optimal power distribution to different power sources. ECMS has the advantages of simple structure, the small amount of calculation, and no need of prior knowledge. By introducing a penalty function, the strategy makes a good charging sustaining characteristic and is better suitable for charging sustaining period of the plug-in HEV, so it is widely studied.26–28 As shown in figure 1, the values of charging and discharging equivalent factor must be set well before calculating ECMS. At the same time, the values are related to the driving cycle type. That is, there is a couple of optimal charging and discharging equivalent factors under different driving cycles. Therefore, the control parameters whose values are adjusted according to driving cycle type are lchg and ldis . The main
Figure 1. Calculation flow chart of ECMS.
3 control idea of ECMS is as follows: according to the driver request power, the actual output power of the engine and motor is allocated reasonably in the range of power, which minimizes the total instantaneous equivalent fuel consumption. The total instantaneous equivalent fuel consumption rate is equal to the sum of engine instantaneous fuel consumption rate m_ e (t) and motor instantaneous equivalent fuel consumption m_ m (t). That is m_ equ (t) = min (m_ e (t) + m_ m (t))
ð1Þ
where m_ equ (t) denotes the total fuel consumption rate; m_ e (t) denotes the instantaneous fuel consumption of the engine, which can be obtained by the engine fuel model; m_ m (t) denotes the motor instantaneous equivalent fuel consumption; the calculation equation is as follows Pm (t) hdis (t) HL Pm (t) hchg (t) + (1 k) lchg HL
m_ m (t) = k ldis
ð2Þ
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Figure 2. Control block diagram of dynamic ECMS based on the DCR.
k = 0:5 f1 + sgn½Pm (t)g
ð3Þ
where Pm (t) denotes the power of the motor; HL is the heat value of the gasoline; hdis (t), hchg (t) denotes the efficiency of the discharging and charging of battery, respectively; ldis (t), lchg (t) denotes the discharging and the charging equivalent factors during driving mode and power generation mode, respectively, which are related to the driving cycle type. Since the original ECMS could not maintain the SOC balance of the battery well, the penalty function is introduced to modify the equivalent fuel consumption to keep it near the target SOC. The penalty principle is that when the SOC of the battery is higher than the target SOC, the penalty coefficient is less than 1, so the equivalent fuel consumption of the motor is reduced by the penalty coefficient, which makes the control strategy more inclined to use electricity. The SOC of the battery is less than the target SOC and the penalty coefficient is greater than 1. By increasing the equivalent fuel consumption of the motor, the control strategy is more inclined to use fuel. The penalty function is as follows u(SOC) = 1
!b SOC(t) SOCtar SOChigh SOClow =2
ð4Þ
SOCtar = 0:5 SOChigh + SOClow
ð5Þ
b = 2 n + 1, n 2 N
ð6Þ
where u denotes the penalty coefficient; SOCtar denotes the target value of SOC; SOChigh and SOClow respectively denote the upper and lower limit maintenance range, respectively. The corrected charging and discharging equivalent factors can be expressed as follows
ldis = u ldis lchg = u lchg
ð7Þ
Replacing the equivalent factors and considering the recovery power of braking, the modified equivalent fuel consumption equation of the motor is as follows Pm (t) + Preg (t) hdis (t) HL Pm (t) hchg (t) + (1 k) lchg HL
m_ 0m (t) = k ldis
ð8Þ
The calculation flow chart of ECMS is shown in Figure 1. As described above, ECMS should be well combined with DCR and dynamically regulates charging and discharging equivalent factors. Figure 2 shows the control block diagram of the dynamic ECMS based on the DCR. A library of optimal charging and
Shi et al. discharging equivalent factor was built by the offline global optimization on different standard driving cycles. Once a certain type of driving cycle is identified, a pair of optimized charging and discharging equivalent factor will be selected.
The PSO-SVM recognition algorithm Through the study of given sets of training samples to build the DCR model, SVM algorithm has been widely used in the control field of prediction and identification because of its simplicity and high accuracy. The basic idea of SVM algorithm is to map the input data of low dimensional space to high dimensional feature space through nonlinear mapping, making it linear separable and getting the optimal discrimination function in high dimensional space. Finally, the classification boundary can be gotten. The value of the penalty coefficient C and the width parameter g of the kernel function in the SVM algorithm are the main factors that affect the recognition performance. Therefore, the best C and g should be determined in order to guarantee the recognition accuracy. PSO algorithm is inspired from the behavior characteristics Dt of Dv the biological population and is used to solve the optimization problem. The PSO algorithm has the advantages of simple search mechanism, fast convergence speed, small computation, and so on and can avoid falling into the local optimal solution. Considering recognition accuracy as the fitness function, the parameters C and g as the optimization objects, PSO algorithm is used to optimize the
Figure 3. PSO-SVM algorithm flow.
5 SVM algorithm. The combination algorithm is defined as PSO-SVM and the optimal DCR model is established further. The PSO-SVM algorithm flow is shown in Figure 3. The steps of the PSO-SVM algorithm are described as follows: Step 1: Set the particle number of swarm to be m, the maximum number of iteration to be M; set the range of particle position and particle velocity; Step 2: The tth particle position is ut , ut = ½ut1 , ut2 , . . . , uti , . . . , utm ; the tth particle velocity is vt , vt = ½vt1 , vt2 , . . . , vti , . . . , vtm (t denotes the number of current iterations; the initial value is 1). The search space includes C and g, so each particle position is two dimensional; Step 3: i is initialized to 1; Step 4: Particle position uti is subjected to the SVM algorithm for training model with a large number of training samples; Step 5: Obtain the driving cycle type for each test sample using the trained model, the results stored in Zrec (k), (k = 1, . . . , n); Step 6: Calculation the result of the fitness function. The fitness function of PSO algorithm is defined as follows n P
Z=
(Zrec (k) = Zact (k))
k=1
n
3 100%
ð9Þ
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Table 1. Typical driving cycle. Drive cycle type code
Drive cycle name
Characteristics of drive cycle
Maximum velocity
1
Urban
60
2
Suburban
3
Viaduct
4
Freeway
Mainly concentrated in the central area of a city with many crossroads, traffic lights, heavy traffic flow and frequent road congestion and start-stop, low velocity and long idle time Moderate velocity, the idle time decreases compared with the urban driving cycle, velocity fluctuation is still large Vehicles usually drive with relatively high-velocity, bidirectional segmentation, no pedestrian or non-motorized vehicles, no traffic lights, a chance of congestion at peak hours Similar to the driving cycle of the viaduct, the difference is that the maximum velocity and the complete control at entrance and exit for charge, almost no congestion
60 80
120
denote the learning factors. The population of the next generation ut + 1 is as follows ut + 1 = ½ut1+ 1 , ut2+ 1 , . . . , uti + 1 , . . . , utm+ 1 Step 12: t = t + 1, jump back to step 2; Step 13: Output individual optimal position pbest and global optimal position gbest ; Step 14: Output best C and g corresponding to the gbest .
A case study for building and application DCR model Database and processing for DCR
Figure 4. Road route of real vehicle experiment.
where Zrec is the type of recognition drive cycle; Zact is the type of target drive cycle; n is the number of test samples. Step 7: Update the individual optimal position pbest ; Step 8: If i ø m, jump to step 9; otherwise, i = i + 1, jump back to step 4; Step 9: Update the global optimal position gbest ; Step 10: If t ø M, jump to step 13; otherwise, jump to step 11; Step 11: Update the velocity and position of the each particle as follows vt + 1 = v vt + c1 r1 (ptbest ut ) t ut ) + c2 r2 (gbest
u t + 1 = u t + vt + 1
ð10Þ ð11Þ
where v denotes the inertia weight; r1 and r2 are the random numbers in the [0, 1] interval; c1 and c2
Data acquisition in real vehicle experiment. The first thing is to define the typical driving cycle and collect enough data for driving cycle database. Three typical driving cycles are classified in the previous studies on DCR, namely urban driving cycle, suburban driving cycle, and freeway driving cycle.29 However, as the gradual formation of urban three-dimensional transportation network, the number of viaducts has gradually increased and the driving cycles of the viaduct road are different from the above three types of driving cycles. Therefore, four types of driving cycles are defined in this article and the characteristics of each driving cycle are shown in Table 1. Taking the typical medium-sized city of Hefei as an example, representative urban roads, suburban roads, viaduct and freeway were selected to carry out real vehicle experiment. Part of the experimental route is shown in Figure 4 in red line. The data-acquisition system was developed to store the real-time data of the experimental vehicle. The composition of the data-acquisition system is shown in Figure 5. In total, 6000 sets of data were collected for each type of driving cycle and further were preprocessed using the interpolation method to complete individual missing
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Figure 5. Data acquisition system.
data and removing the singular values generated. The total driving cycle data processed is shown in Figure 6. Extraction of driving cycle samples. For guaranteeing the model recognition accuracy, a randomly generated driving cycle sample method was proposed to obtain enough parameter samples from the four standard driving cycles. Figure 7 shows the randomly generated sample method. In Figure 7, Dt is the window width, the vehicle drive cycle information extracted time window; Dv is the window moving velocity, which is based on the current conditions to predict future conditions after the Dv seconds; T is the maximum time length for the specific drive cycle; a is the random parameter, where a 2 (0, 1); t0 is the current time, so the equation for extraction can be expressed as t0 = a (T Dt)
ð12Þ
The proposed method randomly extracted 400 samples for each type of driving cycle. Window width is set to 80 as an example, that is, the recognition period is 80 s. The best value of the window width will be discussed later. Processing of driving cycle samples. Sufficient and effective input parameters must be determined to ensure the accuracy of online DCR. Especially in the urban area,
the velocity fluctuates greatly, start and stop situation frequently happens. Therefore, the selected characteristic parameters should reflect not only the velocity characteristics, but also the fluctuation characteristics. According to the literature,7,30,31 14 characteristic parameters are defined to describe each DCR sample, such as Table 2. The characteristic parameters’ values of each sample are calculated by programming. Furthermore, the matrix with the number of samples (row) and characteristic parameters (column) is obtained based on a normalization process, which is expressed as Y=
X Xmin Xmax Xmin
ð13Þ
where Xmax and Xmin are the maximum and minimum value of the sample data X, respectively. The correlation between the 14 characteristic parameters will cause negative interference to the recognition model and reduce the recognition accuracy. Principal component analysis (PCA) algorithm can effectively overcome the correlation among parameters and convert a number of indexes into several comprehensive indexes. Based on this, PCA is applied to the characteristic parameters, and 14 principal components are finally obtained, which are expressed as Mn , n = 1, 2, . . . , 14. The contribution rate of each principal component and cumulative contribution rate are
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Figure 6. Experimental data of the typical driving cycle.
Table 2. Characteristic parameters.
Figure 7. Random samples extraction.
shown in Table 3. When the cumulative contribution rate is above 80%, the corresponding principal components are usually selected to represent all the original variables for analysis. Meanwhile, if the characteristic value of the principal component is less than or equal to one, so the information contained in the principal component is less than or equal to that of the original variable which was previously defined. Therefore, when choosing the principal component, the characteristic value should be greater than one. Table 3 shows that the characteristic values of the first three principal
Number
Characteristic parameters
Significance
Unit
1 2 3 4 5 6 7 8 9 10
Pa Pd Pc Pi Vm Vmr Vmax +amax –amax vsd
% % % % km/h km/h km/h m/s2 m/s2 km/h
11
asd
12
S
13 14
+a_average –a_average
Acceleration ratio Deceleration ratio Uniform ratio Idle speed ratio Average velocity Average running velocity Maximum velocity Maximum acceleration Maximum deceleration Velocity standard deviation Acceleration standard deviation Cumulative driving distance Average acceleration Average deceleration
m/s2 m m/s2 m/s2
components are greater than one and their cumulative contribution rate reaches 84.772%, so the first three
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Table 3. The contribution rate and cumulative contribution rate. Principal component
Characteristic value
Contribution rate (%)
Cumulative contribution rate (%)
M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14
8.956 1.707 1.198 0.783 0.632 0.475 0.156 0.063 0.019 0.010 0.001 2.944 3 1024 1.403 3 1026 8.145 3 10216
63.974 12.192 8.557 5.590 4.512 3.392 1.117 0.449 0.136 0.072 0.007 0.002 1.002 3 1025 5.818 3 10215
63.974 76.165 84.772 90.312 94.824 98.216 99.333 99.782 99.918 99.991 99.998 100.00 100.00 100.00
Figure 8. The scores of the first three principal components.
principal components are selected as the input parameters for DCR model in place of the 14 original characteristic parameters. The scores of the first three principal components of each sample are shown in Figure 8.
Build of optimal off-line DCR model The DCR model based on PSO-SVM algorithm is shown in Figure 9. The extracted velocity sample data are first used to calculate 14 characteristic parameter values. Then, the score values of these 14 characteristic parameters on the first three principal components were calculated. The scores of the above three principal components are used as the input feature parameter vectors of the PSO-SVM recognition model. Furthermore,
80% samples were randomly chosen from the 1600 samples as training samples to train the DCR model. The remaining 20% is used as test samples to verify the accuracy of the DCR model. The population size of PSO is set to 100, and the maximum iteration number is 100. pbest and gbest in the iterative process of PSOSVM algorithm is shown in Figure 10. Figure 10 shows pbest and gbest in the iterative process of PSO-SVM algorithm. The pbest and gbest are stable after 100 iterations, and the recognition accuracy of the PSO-SVM algorithm reaches 90.313%, while the corresponding optimal particles are C = 89:152, g = 0:489. In order to verify the superiority of the PSO-SVM algorithm proposed in this article on the application of DCR, PSO-SVM algorithm is compared with the classical back propagation (BP) neural network recognition algorithm. Figure 11 shows the mean squared error of output result of test samples in the BP network training process. The network is relatively stable from the 35th iteration. Figure 12 shows the recognition results of 320 test samples when selecting the optimal particle. It can be seen that the identification error rate of the freeway driving cycle sample is the lowest, primarily due to the high-velocity level and the better stability. In contrast, the error rate of suburban samples is the highest, mainly because of the wide range of velocity fluctuation. However, the overall recognition precision is high, which meets the demand of online recognition. Figure 13 shows the test samples’ confusion matrix for the recognition results of BP neural network. In the confusion matrix, the diagonal data in the green grid are the correct number and percentage of test samples under four typical driving cycles. Same as PSO-SVM algorithm, the error rates of suburban and viaduct samples are higher. In contrast, the recognition accuracy of BP neural network is 82.5%, which is lower than that of the PSO-SVM algorithm.
Analysis of the influence of Dt and Dv on the accuracy of online recognition In the process of building offline DCR model and online application, there is uncertainty in the value of window width Dt and window moving velocity Dv. The window width Dt determines the length of the sample and further determines the amount of information contained in the sample. If the Dt is too small, the amount of information contained is less and the credibility is reduced. On the contrary, the increase of useless information is also not conducive to the reflection of the cycle characteristics. The value of window moving velocity Dv determines the updating speed of the sample information. If the Dv is too small, increase in computational complexity will increase the load of the
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Figure 9. DCR model.
Figure 10. The iteration process of PSO-SVM algorithm.
processor and may lead to a high switching frequency of the control system. On the other hand, large value of Dv will reduce the sensitivity of DCR. As a result, the selection of appropriate window width and window moving velocity is the guarantee of the accurate
Figure 11. The mean squared of error of the BP neural network training process.
identification of DCR. A cross validation method is used to determine the best window width and window moving velocity in this article. Window width is set to 30, 80, 130, and 180 s, respectively, for building offline
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11 It can be seen that when Dt increases from smaller value, online recognition accuracy is improved. However, when Dt increases further, there is a downward trend in recognition accuracy. This is also consistent with the analysis that the identification period too small or too large is not conducive to real-time online identification. When Dt is set to 30 and 180 s, the accuracy of online recognition decreases with the increase of Dv. When Dt takes 80 or 130 s, and Dv takes the intermediate value 10 , the recognition accuracy is the highest. To summarize, when Dt = 80 s, Dv = 10 s is used, the PSO-SVM recognition algorithm has the highest accuracy and meets the accuracy requirement.
Optimal charging and discharging equivalent factors for dynamic ECMS Figure 12. Training results of PSO-SVM algorithm.
Figure 13. Test samples’ confusion matrix of BP neural network.
DCR models. Then taking a random driving cycle as an example, optimal offline DCR models are used for online recognition by setting the window moving velocity with 5, 10, and 20 s. Random driving cycle and online recognition result with different Dt and Dv, as shown in Figures 14 and 15. According to equation (9), the results of online recognition are counted. The accuracy of the algorithm at Dt = 80 s, Dv = 10 s is 90.313%, while the precision of the algorithm at Dt = 180 s, Dv = 5 s is 83.168%. As mentioned above, the best Dt and Dv can be gotten through a series of repeated crossover tests. The recognition results in all combinations are shown in Figure 16.
In order to find the optimal charging and discharging equivalent factors under different driving cycles, a parallel HEV with P2 configuration is taken as the research object, as shown in Figure 17. The physical models of vehicle and dynamic ECMS based on MATLAB/ Simulink platform were built for finding the optimal charging and discharging equivalent factors, which corresponding to the best fuel economy. The main parameters of the vehicle and powertrain parameters are shown in Table 4. By setting lchg = ½0:015 and ldis = ½0:015, the relationship between the equivalent factors and the fuel consumption, also and the DSOC can be obtained with repeated calculation of ECMS. Figure 18 shows the relation between the equivalent factors and fuel consumption of four different typical driving cycles. It can be seen that not only the fuel consumption levels of different typical driving cycles under the same equivalent factors are different, but also the fuel consumption levels of different equivalent factors under the same driving cycle are very different. Figure 19 shows the relation between equivalent factors and DSOC. DSOC denote the difference between the final SOC value and the SOCtar, the smaller the difference means the better the performance of charging sustaining. Because the step size of the lchg and the ldis is small, some areas in Figures 18 and 19 look like the same. However, there are tiny differences in values in areas of similar color. Based on the range of difference in 1% of DSOC, there is a pair of optimal equivalent factors corresponding to the lowest fuel consumption under four typical driving cycles, as shown in Table 5. The data in Table 5 constitute the optimal charging and discharging coefficients library in Figure 2.
Simulation and validation Simulation experiment of ECMS was carried out under three cases for comparison analysis. Three cases are,
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Figure 14. Random driving cycle.
Figure 15. Online recognition results.
Figure 16. Cross-validation results.
the ECMS without DCR, the ECMS with DCR based on traditional SVM algorithm and the ECMS with DCR based on PSO-SVM algorithm, which are called mode 1, mode 2, and mode 3, respectively. The initial SOC is set to 0.24, and the upper and lower limits of the battery SOC are 0.3 and 0.2, respectively. In order to get good charge sustaining performance, the value of parameter b is set to 7. Figure 20 shows the velocity contrast curves under the test random driving cycle. The actual velocity follows the test cycle well under three cases and is basically consistent with the target speed, proving that the vehicle has enough power for driving in this cycle. Figure 21 shows charging and discharging equivalent factors changing with results of the DCR under mode 2 and mode 3. ECMS algorithm can update equivalent
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Figure 17. A parallel hybrid electric vehicle with P2 configuration.
Table 4. Vehicle and powertrain parameters. Project
Parameters
Value
Vehicle parameters
Curb weight (kg) Frontal area (m2) Drag coefficient Rolling radius (m) Rolling resistance coefficient Maximum torque (N m) Peak power (kW) Transmission ratio
1590 2.030 0.290 0.287 0.013 160 93 0.440–2.390
Final ratio Peak power (kW)
5.141 55
Maximum torque (N m) Battery capacity (A h) Nominal voltage (V)
160 25 346
Engine Continuously variable transmission Final drive Integrated starter generator motor Battery
factors in real-time relative to DCR results to achieve better vehicle fuel economy. Figures 22 and 23 show the comparison curves of fuel consumption and the battery SOC, respectively. The cumulative fuel consumption of mode 1 is 727.218 g, and the fuel consumption of 100 km is 5.322 L. The corresponding fuel consumption under model 2 is 685.230 g, the fuel consumption of 100 km is 5.015 L, and the fuel economy is increased by 5.774%. The cumulative fuel consumption is 647.772 g and 4.733 L at mode 3, which is raised by 10.925% compared with model 1 and 5.466% compared with model 2. Table 6 shows the target SOC, final value of batter SOC, and the errors under three cases. It can be seen that the errors are all within 5% under three cases. So
Figure 18. Relation between equivalent factors and fuel consumption.
Table 5. The optimal equivalent factors under the typical driving cycles. Driving cycle type
Discharge equivalent factor (ldis )
Charge equivalent factor (lchg )
Urban Suburban Viaduct Freeway
1.66 3.22 2.93 2.34
1.92 2.71 2.95 3.61
the strategy has good charge sustaining performance. However, as shown in Figure 23, the SOC of mode 1
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Figure 19. Relation between equivalent factors and DSOC.
Figure 20. Velocity following condition.
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Figure 21. Charging and discharging equivalent factors charging curve.
Figure 22. Cumulative fuel consumption. Figure 23. The curves of SOC.
has a large fluctuation, and the charging and discharging times are more. The fluctuation of mode 2 decreases, but it is still larger than that of mode 3. The SOC is the most stable under mode 3, and the charging and discharging times further reduced compared with mode 2, which is conducive to improving the system efficiency and battery life. 2.
Conclusion 1.
In this article, the traffic characteristics of a medium-sized city (Hefei) are analyzed, and the actual vehicle experiments are carried out on typical roads, which representing four standard
driving cycles for collecting enough driving cycle data. Fourteen parameters describing the characteristics of driving cycle are defined, and the data are processed by multivariate statistical theory for extracting the final parameters which were used as the input of DCR model. The proposed PSO-SVM algorithm was used for building DCR model. The calculation results show that the recognition accuracy of PSO-SVM is high enough for online DCR. The effect of window width and window moving velocity on recognition accuracy is further discussed. The results show that when
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Table 6. Final SOC under three conditions. Case
Target SOC
Final SOC
Error
Traditional ECMS ECMS with DCR based on SVM ECMS with DCR based on PSO-SVM
0.250 0.250 0.250
0.260 0.259 0.261
4.000% 3.600% 4.400%
SOC: state of charge; ECMS: equivalent fuel consumption minimization strategy; DCR: driving cycle recognition; PSO: particle swarm optimization; SVM: support vector machine.
3.
Dt = 80 s, Dv = 10 s, the recognition accuracy is the highest, but there is still space for further promotion. The DCR technology is applied to the ECMS of a parallel HEV with P2 configuration. The simulation results show that the fuel economy with PSO-SVM algorithm is further improved compared to the strategy without DCR and the strategy with traditional SVM algorithm, and the fluctuations of battery SOC are more stable in two cases so that system efficiency and batter life are substantially improved.
In future research work, real vehicle experiments can be carried out to verify the effect of the DCR method. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to thank the School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei, Anhui, P.R. China as well as the National Natural Science Foundation of China (grant no. 71431003) and the Research Project of University Natural Science of Anhui province (grant no. KJ2018A0782).
ORCID iDs Duoyang Qiu https://orcid.org/0000-0001-6284-0441 https://orcid.org/0000-0002-9705-1503 Yiming Li
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