Driver-Oriented Adaptive Equivalent Consumption Minimization Strategy for Plug-in Hybrid Electric Buses

Abstract

The adaptability of the supervisory control strategy of plug-in hybrid electric buses (PHEBs) to different driving styles determines the energy-saving performance. This paper proposes a driver-oriented adaptive equivalent consumption minimization strategy (ECMS) for PHEBs. The strategy aims to improve the fuel economy of PHEBs as much as possible by adapting to different driving styles while satisfying the physical constraints of the hybrid power system. Firstly, an online driving style recognition algorithm based on the Fuzzy K-means (FKM) algorithm and the random forest (RF) method is devised, in which the FKM algorithm is used to preprocess the feature parameters related to driving styles and the RF method is utilized to identify the driver’s driving style. Secondly, the driving style recognition results are introduced into the ECMS framework to form a driver-oriented energy management strategy. Finally, the proposed control strategy is verified using both Matlab/Simulink and Hardware-in-the-Loop. The verification results demonstrate that the proposed control strategy improves the fuel economy of PHEBs.

1. Introduction

With the increasingly serious problems of oil resource shortages and global warming, the development of new energy vehicles has received widespread attention [1,2,3]. Compared with gas-powered vehicles, plug-in hybrid electric vehicles (PHEVs) offer lower emissions and improved energy efficiency, thus attracting much attention from the market [4]. However, the energy-saving performance of PHEVs is influenced by factors such as supervisory control strategy, driver style, and traffic conditions. Research from Oak Ridge National Lab indicates that incorporating driver style into the supervisory control strategy for PHEVs can reduce fuel consumption by 25% to 68%, or even up to 100%. Clearly, tailoring the supervisory control strategy to individual drivers is essential for improving the fuel economy of vehicles [5,6].

Many studies have been executed to investigate the relationship between driving behavior and vehicle fuel consumption. It is well known that frequent sharp acceleration and deceleration by drivers will lead to an increase in fuel consumption [7,8,9]. When the driver gently uses the accelerator and brake pedals, it is beneficial for improving the vehicle fuel economy. The influence of driving behavior should be considered when devising a supervisory control strategy. According to existing studies, several representative features, such as signals from the accelerator and brake pedals, vehicle velocity, jerk, and acceleration and deceleration, can be selected for driving style recognition. Based on these features, drivers are generally divided into aggressive, normal, and conservative drivers by using categorization algorithms. In [10], a two-step algorithm was proposed for the segmentation and clustering of driver’s driving behaviors based on eight state–action variables. The results demonstrate that this algorithm exhibits a better classification effect. However, the selection of segment duration has a remarkable impact on the performance of the algorithm. Additionally, an artificial neural network (ANN) was used to classify a person’s driving style, and its normalized average mean squared error was less than 11% [11]. The probabilistic Auto Regressive with eXogenous input (ARX) model was developed to recognize the style of individual drivers based on the labeled driving data collected from different drivers [12]. Both ANNs and the ARX model require extensive high-quality feature vector datasets for offline training. In [13], a statistical pattern recognition framework is introduced that employs kernel density estimation and entropy theory to categorize drivers into six distinct classes ranging from moderate to aggressive. Determining the entropy weight coefficients for aggressive and moderate styles is a challenging task. In [14], a hybrid algorithm composed of the K nearest neighbor (KNN) and the expectation maximization method was applied to identify driving styles. However, the complexity of the algorithm affects the real-time performance of its online applications. Hence, developing an efficient and accurate driving style recognition algorithm is particularly crucial for improving the fuel economy of vehicles.

The fuel economy of PHEVs is influenced by the relevant supervisory control strategies. Existing supervisory control strategies fall into categories such as rule-based, learning-based, and optimization-based strategies [15,16,17]. The charge-depleting and charge-sustaining (CDCS) strategy is a representative rule-based strategy for PHEVs noted for its robust reliability. However, its control performance depends on the engineer’s experience and calibration. With the development of artificial intelligence technology, many learning-based strategies have received widespread attention. Xu et al. proposed a reinforcement learning strategy to improve the fuel economy of hybrid electric vehicles, wherein parametric studies were conducted on four key factors [18]. In [19], deep reinforcement learning (DRL) is developed to improve the fuel economy for HEVs under different driving conditions. Learning-based strategies deliver near-optimal control and are readily deployable, yet their computational load remains a bottleneck. To overcome the limitations, optimization-based strategies have been explored in depth. The equivalent consumption minimization strategy (ECMS), as one representative of optimization-based strategies, has been widely used to optimize energy management for PHEVs. The core idea of ECMS is to improve fuel efficiency by translating battery energy consumption into the equivalent fuel consumption and then minimizing total fuel consumption. The determination of an equivalent factor is a key step during ECMS design. Musardo et al. proposed an adaptive ECMS for HEVs, and the equivalent factor was modified by using an on-the-fly algorithm [20]. Shi et al. proposed an adaptive energy management strategy for PHEVs considering traffic information, in which the equivalent factor was adjusted using a fuzzy controller [21]. In [22], an online adaptive optimization framework is devised to coordinate the optimization of battery aging and energy management for plug-in hybrid electric buses (PHEBs), in which a proportion–integral controller was employed to update the equivalent factor in real time. Many other methods, such as the adaptive neuro-fuzzy inference system [23] and DRL method [24,25] were also employed to update the equivalent factor. In addition, updating the equivalent factors based on the driver’s style to generate a modified version of the ECMS has become an important research hotspot in this field.

Motivated by existing studies, a driver-oriented adaptive ECMS for PHEBs is proposed in this paper. To accurately identify the driver’s driving style, an online driving style recognition algorithm based on the Fuzzy K-means (FKM) algorithm and random forest (RF) method is developed. The feature parameters related to the driving styles are processed to generate the labeled data by using the FKM algorithm. According to the labeled data, RF is constructed to recognize the driving styles. To adapt to individual drivers, an adaptive ECMS is designed to improve the vehicle fuel economy. Finally, the proposed control strategy is verified and verification results are systematically compared. The main contributions of this study are summarized as follows:

(1)

An online driving style recognition algorithm based on the FKM algorithm and RF method is devised.

(2)

According to the recognition results, a driver-oriented energy management strategy is formulated to determine the power distribution for PHEBs.

(3)

The Hardware-in-the-Loop (HiL) technique is used to verify the effectiveness and realizability of the proposed control strategy.

The rest of this paper is organized as follows. Section 2 describes the modeling of studied PHEB system. Section 3 presents the driver-oriented adaptive ECMS for PHEBs. Section 4 demonstrates the verification results of the proposed control strategy. Finally, Section 5 concludes the paper.

2. PHEB System Modeling

The PHEB contains two propulsion sources, an electric motor, and a diesel engine, which are assembled on the same axis, as depicted in Figure 1. An electrically controlled clutch is installed between the two propulsion sources to enable switching between different modes. The output electric motor is connected to the final drive via automated manual transmission. The technical parameters of the PHEB are listed in

Table 1. Technical parameters of PHEB.

Parameter	Symbol	Value
Gross mass	m	15,000 kg
Aerodynamic drag coefficient	CD	0.6
Rolling resistance coefficient	fr	0.019
Air density	ρ	1.293 kg/m3
Windward area	A	6.05 m2
Acceleration of gravity	g	9.8 m/s2
Tire rolling radius	rw	0.512 m
Rotating mass correction coefficient	δ	1.02

.

2.1. Vehicle Longitudinal Dynamic Model

To reduce the complexity of the vehicle model, a steady-state vehicle model that only considers longitudinal motion is described as follows [26,27]:

$$T_{drive}=r_w\left(mg{f}_r\cos \theta +mg\sin \theta +{\displaystyle \frac{C_{D}A{v}^2}{21.15}}+\delta m\dot{v}\right)$$

(1)

where T_drive is the driving torque, θ is the road slope, and v is the vehicle velocity.

2.2. Engine Model

Due to the nonlinear dynamics of the engine, it is difficult to design a high-fidelity engine model [28]. Based on the data provided by the original manufacturer, a data-driven model is built in this paper. Considering that the engine is a machine that operates using fuel, the engine fueling rate is expressed by

$${\dot{m}}_{\mathrm{f}}=f_{\mathrm{fuel}}\left(T_{\mathrm{e}},{\mathsf{\omega }}_{\mathrm{e}}\right)$$

(2)

where ${\dot{m}}_{\mathrm{f}}$ denotes the engine fueling rate. T_e and ω_e denote the torque and speed of engine, respectively. Figure 2 shows the data of brake-specific fuel consumption (BSFC).

2.3. Motor Model

The motor has two operating modes: one is the motor mode and the other is the generator mode [29]. During the brake action, the motor can generate the power to charge the battery [30,31]. Neglecting the electromagnetic dynamic features, the motor power P_m can be calculated by

$$P_{\mathrm{m}}=\left\{\begin{array}{c}{\displaystyle \frac{T_{\mathrm{m}}{\mathsf{\omega }}_{\mathrm{m}}}{{\mathsf{\eta }}_{\mathrm{m}}}},\mathrm{Motor}\\ T_{\mathrm{m}}{\mathsf{\omega }}_{\mathrm{m}}{\mathsf{\eta }}_{\mathrm{m}},\mathrm{Generator}\end{array}\right.$$

(3)

where T_m, ω_m, and η_m are the torque, speed, and efficiency of the motor, respectively. The motor efficiency is determined using an interpolation method, which can be represented as follows:

η_m = f_mot(T_m, ω_m)

(4)

where f_mot(.) represents the efficiency map of the motor.

2.4. Battery Model

In this paper, an equivalent circuit model is selected to simulate the electrical performance of the battery [32,33]. This circuit model includes internal resistance R_B and open circuit voltage V_OC, as shown in Figure 3. The state of charge (SOC) can be calculated as follows [34,35]:

$$\left\{\begin{array}{c}{I}_{\mathrm{B}}={\displaystyle \frac{1}{2R_{\mathrm{B}}}}\left(V_{\mathrm{OC}}-\sqrt{V_{\mathrm{OC}}^2-4R_{\mathrm{B}}{P}_{\mathrm{B}}}\right)\\ soc=so{c}_0-{\displaystyle {\int }_0^t{I}_{\mathrm{B}}dt}/Q_{\mathrm{I}}\end{array}\right.$$

(5)

where I_B and P_B denote the current and power of the battery, respectively. Q_I denotes the nominal battery capacity, and soc₀ denotes the initial SOC.

3. Vehicle Control Problem Formulation

The supervisory control strategy of PHEBs is to coordinate the control of the engine and electric motor to achieve the lowest fuel consumption while keeping the battery SOC at an appropriate low level over a driving cycle [36,37,38,39]. However, different drivers show different driving behaviors [40,41]. For example, an aggressive driver may manipulate the accelerator and brake pedals frequently even in congested traffic conditions. Conservative drivers attach more importance to ride comfort and fuel consumption, so the frequency and amplitude of the acceleration and brake pedal operations are low [42,43,44]. To improve the adaptability, the supervisory control strategy can be designed with driving styles. Figure 4 illustrates the framework of the proposed control strategy. The FKM algorithm is applied to preprocess the collected data, then the labeled data is used to generate the RF model for identifying the driving style. According to the recognition results, the equivalent factor can be updated online. Finally, the adaptive ECMS framework is formulated to determine the power distribution for PEHBs.

3.1. Driver’s Driving Type Recognition

The driving style plays a crucial role in the details of vehicle velocity changes and has a non-negligible impact on vehicle energy consumption. If the driver’s driving style can be identified from historical data, the power distribution function becomes more accurate, which is further conducive to improving the fuel economy. To better recognize the driver’s driving style, feature parameters related to driving style need to be extracted from historical velocity segments and the instant opening information of the pedal. Inspired by previous research works [45], the maximum velocity, average velocity, maximum acceleration, and average acceleration are chosen as the feature parameters. These parameters can be obtained from the velocity segment of m seconds by using the sliding time window. The instant opening information of the pedal includes the accelerator pedal and brake pedal. Hence, the vector of feature parameters can be expressed by

D = [v_max, v_avg, a_max, a_avg, pd_a, pd_b]

(6)

where v_max denotes maximum velocity, v_avg denotes average velocity, a_max denotes maximum acceleration, a_avg denotes average acceleration, and pd_a and pd_b denote the instant opening of the accelerator and brake pedals, respectively.

3.1.1. FKM Algorithm

In this study, the FKM algorithm is utilized to preprocess the feature parameters related to the driving styles. The FKM algorithm is an unsupervised classification approach, which aims to identify each sample to a certain cluster based on a membership degree [46,47,48]. Its implementation of the classification process is to minimize the fuzzy objective function [49]. Given a dataset X = [x₁, x₂, …, x_i, …, x_N] ∈ R^D×N, where N and D denote the number of samples and features, respectively, the fuzzy objective function is formulated by

$$\begin{array}{l}J(U,F)={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{j=1}^K{u}_{ij}^m{‖x_i-f_j‖}_2^2}}\\ U={\left[u_{ij}\right]}_{N\times K},F=[f_1,f_2,\dots ,f_i,\dots ,f_K]\\ s.t.{\displaystyle \sum _{j=1}^K{u}_{ij}=1,}0\le u_{ij}\le 1,i=1,\dots ,N\end{array}$$

(7)

where J denotes the fuzzy objective function, K denotes the number of clusters, u_ij denotes the membership degree of the i-th sample belonging to the j-th cluster, m denotes the fuzziness index, and f_j denotes the centroid of the j-th cluster, which can be calculated as follows:

$$f_j={\displaystyle \frac{{\displaystyle \sum _{i=1}^N{u}_{ij}^m{x}_i}}{{\displaystyle \sum _{i=1}^N{u}_{ij}^m}}}$$

(8)

The membership degree u_ij can be expressed by

$$u_{ij}={\left[{\displaystyle \sum _{n=1}^K{\left(\frac{{‖x_i-f_j‖}_2^2}{{‖x_n-f_j‖}_2^2}\right)}^{\frac{1}{m-1}}}\right]}^{-1}$$

(9)

The membership degree can be regarded as the probability that a sample belongs to a category. If a sample shows a high degree in a cluster, it can be assigned to that cluster. In this study, driver’s driving styles are divided into aggressive, normal, and conservative types. The flow chart of the FKM algorithm is presented in Figure 5.

3.1.2. RF Method

RF is a powerful ensemble learning algorithm including a set of decision trees [50,51]. It is widely applied to solve regression and classification problems. The key idea of the RF method is ensemble learning, which improves model robustness and accuracy by combining the predictions of several decision trees [52]. For the RF method, each decision tree is independently constructed and randomness is integrated into the construction process. The training data for each tree are generated by using the bagging or boosting method. Furthermore, at each decision node, feature selection is conducted using a random subset of features, not all available features. This manner is conducive to a reduction in the risk of overfitting and an improvement in the resilience of the model toward noise in the data. In the prediction stage, the final prediction result of the RF method is available by averaging or majority voting across all trees. This is also beneficial for balancing the prediction error of a single tree and improving the generalization ability. Here, the driving style recognition function is realized using the RF method, and the implementation process contains the following steps:

Step 1 (sampling): random subsample for constructing the decision tree is available by randomly selecting a portion of samples from the original dataset;

Step 2 (feature selection): subset of features is obtained by randomly selecting from all available features;

Step 3 (individual decision tree generation): generate a decision tree by using selected feature subsets and subsamples;

Step 4 (multiple decision trees construction): repeat steps 1 to 3 when the termination conditions are not satisfied, otherwise go to step 5;

Step 5 (voting processing): for classification problems, votes are cast on the recognition results of each decision tree, and the category with the most votes is chosen as the final output result. The whole voting process can be summarized as

$$h=\mathrm{mod}e\left\{h_1\left(z\right),h_2\left(z\right),\dots h_K\left(z\right)\right\}$$

(10)

where h is the voting result from the RF method, h_k(z) is the prediction result of k-th tree, and K is the number of the decision trees. The RF structure is shown in Figure 6.

3.2. Energy Management Problem Formulation

The energy flow of PHEBs can be optimized through supervisory control strategies, thereby minimizing energy consumption. In this study, the control variable u and state variable x are expressed as

$$\left\{\begin{array}{c}x\left(t\right)=soc\left(t\right)\\ u\left(t\right)=T_m\left(t\right)\end{array}\right.$$

(11)

Due to the physical limitations of some power components, the following constraints should be satisfied by

$$\left\{\begin{array}{c}{T}_{\mathrm{e}}^{\min }\le T_{\mathrm{e}}\left(t\right)\le T_{\mathrm{e}}^{\max },{\omega }_{\mathrm{e}}^{\min }\le {\omega }_{\mathrm{e}}\left(t\right)\le {\omega }_{\mathrm{e}}^{\max }\\ T_{\mathrm{m}}^{\min }\le T_{\mathrm{m}}\left(t\right)\le T_{\mathrm{m}}^{\max },{\omega }_{\mathrm{m}}^{\min }\le {\omega }_{\mathrm{m}}\left(t\right)\le {\omega }_{\mathrm{m}}^{\max }\\ so{c}_{\mathrm{in}}\le soc\left(t\right)\le so{c}_{\mathrm{end}}\end{array}\right.$$

(12)

where superscript max represents the maximum value and min represents the minimum value. soc_in is the initial battery SOC and soc_end is the expected final battery SOC. Here, the ECMS algorithm is applied to obtain the optimal control variables. The crucial principle of ECMS is to equate electrical energy into virtual fuel consumption based on a specific equivalent conception. The whole optimal control problem can be formulated by

$$\left\{\begin{array}{c}{\dot{m}}_{eqv}\left(u\left(t\right),t\right)={\dot{m}}_f\left(T_{\mathrm{e}}\left(t\right),t\right)+{\dot{m}}_{ele}\left(u\left(t\right),t\right)\\ \left[T_{\mathrm{e}\_\mathrm{best}},T_{\mathrm{m}\_\mathrm{best}}\right]=\arg \underset{[T_e,T_m]}{\min }\left\{{\dot{m}}_{eqv}\left(u\left(t\right),t\right)\right\}\end{array}\right.$$

(13)

where ${\dot{m}}_{eqv}$ is instantaneous equivalent fuel consumption. T_{e_best} and T_{m_best} are the optimal engine and motor torque derived from the above control problem, respectively. ${\dot{m}}_{ele}$ is the virtual fuel consumption converting from the motor power, which can be expressed by

$${\dot{m}}_{ele}\left(u\left(t\right),t\right)=s\left(t\right){\displaystyle \frac{P_m(u\left(t\right),t)}{H_l}}$$

(14)

where H_l is the fuel lower heating value and s(t) is the equivalent factor. The equivalent factor s(t) is inextricably linked to the fuel consumption of vehicles. If the equivalent factor is small, it means that more electrical energy is consumed to drive the vehicle, while conversely, more fuel is consumed.

Unlike the charge-sustaining HEV, PHEBs equipped with a large-capacity battery can provide more electrical energy to generate the kinetic power for vehicle moving and reduce the fuel consumption. Considering the operation characteristic of PHEBs, the battery SOC should follow the targeted value to achieve a sound fuel economy. Hence, s(t) can be defined by

$$s\left(t\right)=s_0\left(t\right)+k_{\mathrm{p}}\left(soc\left(t\right)-so{c}_{\mathrm{f}}\left(t\right)\right)+k_{\mathrm{i}}{\displaystyle {\int }_0^t\left(soc\left(t\right)-so{c}_{\mathrm{f}}\left(t\right)\right)}dt$$

(15)

where k_p denotes the proportional coefficient and k_i denotes the integral coefficient. s₀(t) denotes the initial equivalent factor and soc_f(t) denotes the reference SOC. Here, a reference SOC trajectory can be planned as [53,54]

$$so{c}_{\mathrm{f}}\left(t\right)=so{c}_{\mathrm{in}}-\left({\displaystyle \frac{L_n\left(t\right)}{L_N}}-R_{\mathrm{d}}\left({\displaystyle \frac{L_n\left(t\right)}{L_N}}\right)\right)\left(so{c}_{\mathrm{in}}-so{c}_{\mathrm{end}}\right)$$

(16)

where L_n(t) is the current travel distance and L_N is the total mileage of one driving mission. R_d(·) is the round-down function. To adapt to individual drivers, the equivalent factor is adjusted through the following equation based on the recognition results of the driver’s driving type:

$$s^{\prime }\left(t+T\right)=s\left(t\right)+\phi \cdot L\left(t+T\right)$$

(17)

where φ denotes the constant coefficient, s’ denotes the adjusted equivalent factor, and L(·) denotes the updating function regarding the driver’s driving type.

$$L\left(t+T\right)={\displaystyle \frac{1}{N}}\left({\displaystyle \sum _{n=1}^{N}h\left(t+n{T}_0\right)}\right)$$

(18)

where T₀ and T denote the sampling and update periods, respectively. N denotes the sampling number within one update cycle. h(t + nT₀) denotes the voting result from the RF method in the last update period.

4. Discussion

In this section, the vehicle model, the recognition method of the driver’s driving style, and the proposed control strategy are constructed in Matlab/Simulink R2023a.

4.1. Vehicle Model Verification

According to the modeling equations, the component modules that make up the vehicle transmission system are constructed in the Simulink platform. To verify the validity of the constructed modules, the China typical city bus driving cycle (CCBC) is chosen as the test cycle. The verification results regarding the vehicle model, including the vehicle velocity and the signal of the acceleration and brake pedals, are shown in Figure 7.

The signal of the accelerator and brake pedals displayed in Figure 7a shows that these constructed models operate normally. Under these control signals, the output of the vehicle transmission system can satisfy the power demand for vehicle operation. According to Figure 7b, it can be discerned that the velocity in the simulation follows the reference profiles well. Hence, the constructed model can meet the requirements of subsequent verification.

4.2. Driving Style Recognition Assessment

All feature parameters related to driving style are gathered using a driving simulator, and its schematic diagram is shown in Figure 8. The driving simulator contains a virtual environment, a vehicle model, and the driver’s operation input equipment. The driver’s operation equipment consists of the brake/accelerator pedal, steering wheel, and gear shift. The virtual environment is implemented using PreScan software 8.5. In addition, the feature parameters are collected using a data acquisition model. In this study, five human drivers with different driving styles are invited to participate. Before testing, all participants need to label their own driving style using a questionnaire.

The RF method is compared with widely used classification models, including decision tree (DT), KNN, and support vector machine (SVM). The original datasets are divided into two subsets: training and testing. The training dataset is applied to determine the parameters of the classification model, while the testing dataset is dedicated to assessing the performance of the model. The comparison of the confusion matrix of different models is demonstrated in Figure 9. In Figure 9a, the RF method exhibits the preferable recognition performance, and the average accuracy rate is at about 85.07%. In the specific driving style identification, the normal styles are often wrongly classified as aggressive styles or conservative styles, and the accuracy rate for the normal driving style is only 80.66%. This is because the boundary between the normal driving style and the other two styles is not very clear. In Figure 9b, the accuracy rates of the DT method for aggressive, normal, and conservative styles are 82.07%, 78.29%, and 81.66%, respectively. These results fully demonstrate that the identification performance of a single tree is inferior to that of the RF composed of multiple trees. In Figure 9c, the accuracy rates of the KNN method for aggressive, normal, and conservative styles are 80.15%, 75.45%, and 76.99%, respectively. The choice of the k value has a remarkable impact on the algorithm’s performance, and currently there is no adequate theory to guide its selection. In Figure 9d, the identification performance of the SVM algorithm is unsatisfactory, and the accuracy rates for the three styles are almost all below 75%. The above results demonstrate the superiority of the proposed driving style identification model.

4.3. Optimization Performance Analysis

To verify the performance of the proposed control strategy, the CCBC was repeated seven times in this test. The aggressive driver’s operations are simulated in the test. In addition, the initial battery SOC was set as 90%.

The simulated velocity and battery SOC trajectory are shown in Figure 10. It can be observed from the figure that the simulated velocity accurately follows the reference value, and the maximum error of the velocity is less than 3 km/h. The battery SOC curve illustrated in Figure 10b shows a downward trend along with the mileage increase, and this phenomenon also conforms to the pre-set requirements. The engine torque and motor torque during the whole testing cycle are demonstrated in Figure 11. It can be discerned that the coupling of engine torque and motor torque can satisfy the demand torque for PHEB operation. In particular, the engine can operate as much as possible in the high-efficiency area due to the regulating effect of the motor. In regenerative braking mode, the motor operates in generator mode to convert the vehicle’s kinetic energy into electrical energy and store it in the battery.

To show the advantage of the proposed control strategy, CDCS, ECMS, and model predictive control (MPC) were chosen as references for the comparison of fuel-saving performance. The detailed comparison results between the proposed control strategy and other strategies, including final SOC, computing time, 100 km fuel consumption, and reduction, are shown in

Table 2. Control performance of different control methods.

Method	Final SOC	Computing Time (s)	100 km Fuel Consumption (L)	Reduction
CDCS	0.7015	96.3	23.69	14.4%
ECMS	0.7194	400.5	21.62	6.2%
MPC	0.7119	447.2	21.81	7.3%
Proposed control strategy	0.7213	482.7	20.27	---

. It can be discerned that the final SOC of these strategies is basically the same after the test: all around 0.71. The fuel consumptions of CDCS, ECMS, MPC, and the proposed control strategy are 23.69 L/100 km, 21.62 L/100 km, 21.81 L/100 km, and 20.27 L/100 km, respectively. Compared with that of CDCS, ECMS, and MPC, the 100 km fuel consumption of the proposed control strategy can be reduced by 14.4%, 6.2%, and 7.3%, respectively. The awareness of driver’s driving style noticeably increases the adaptiveness of the proposed control strategy. Compared with CDCS, ECMS, and MPC methods, the proposed control strategy exhibits an outstanding fuel economy performance. Because the control rules of the CDCS method are simple, its computing time only requires 96.3 s. The computing time of the ECMS and MPC methods are 400.5 s and 447.2 s, respectively. In addition, the computing time of the proposed control strategy is 482.7 s, which is longer than that of the other methods. It can be inferred that the proposed control strategy with driving style recognition and equivalent factor adjustment functions needs more time to handle these processes. Nevertheless, this will not affect the practical application of the proposed control strategy.

The distribution of engine operating points is an important indicator for evaluating the performance of the control strategy. Figure 12 illustrates the distribution of engine operating points of different control strategies. Constrained by the fixed rules, the CDCS method loses optimality, resulting in a markedly dispersed distribution of engine operating points. The fixed equivalent factor can also cause the same problem for the ECMS method. In addition, it can be discerned that the distribution of engine operating points in high-efficiency regions under the proposed control strategy rises from 35% to 37% compared with the MPC method, while their presence in low-efficiency regions falls sharply from 14% to 9%. This also explains the reason why the proposed control strategy exhibits a better performance for the fuel economy.

4.4. HiL Verification

In this section, the HiL manner is selected to validate the performance of the proposed control strategy in real time. The hardware units include the processor card (PXI-8108 RT), CAN interface module (PXI-8512/2), multifunctional RIO board (PXI-7831 R), programmable power supply (HS052/2U), and product-level vehicle control unit. The HiL testing equipment is shown in Figure 13. To make a fair comparison, the aggressive driver’s operations are also modeled using HiL testing.

The HiL testing results are demonstrated in Figure 14. According to Figure 14, the velocity generated from the HiL testing also follows the reference value well. There are slight differences between the testing and simulation results in terms of engine torque and motor torque. That is because of the difference in signal transmission and processing between HiL testing and simulations. Nevertheless, the testing results still indicate that the proposed control strategy is feasible in practical applications.

5. Conclusions

In this paper, a driver-oriented adaptive ECMS for PHEBs is proposed to determine the energy allocation. To adapt to individual drivers, an online driving style recognition algorithm is devised using the FKM algorithm and RF method. According to the recognition results, an adaptive supervisory control strategy based on the ECMS method is formulated. Finally, numerous verifications are executed. The results demonstrate the desirable performance of the proposed control strategy. The major conclusions are summarized as follows:

(1)

To handle the mass of data collected from a driving simulator, the FKM algorithm is applied to label feature parameters related to driver’s driving styles. Then, the driving style recognition model is developed based on the RF method.

(2)

According to the recognition results, the equivalent factor can be updated online and the energy allocation framework is constructed. Compared with the ECMS method, the 100 km fuel consumption of the proposed control strategy can be reduced by 6.2% over the testing cycle.

(3)

Our future work will focus on real vehicle experiment validation to further verify the realizability of the proposed control strategy. With the development of intelligent traffic systems, traffic information will be incorporated into the vehicle control framework, thereby further improving the fuel economy of vehicles.