An intelligent braking system composed single-pedal and multi-objective optimization neural network braking control strategies for electric vehicle

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An intelligent braking system composed single-pedal and multi-objective optimization neural network braking control strategies for electric vehicle ⁎

Hongwen Hea, , Chen Wanga,b, Hui Jiaa, Xing Cuic a

National Engineering Laboratory for Electric Vehicles, School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China Shanghai E-propulsion Auto Technology Co., Ltd (SEAT), Shanghai 201804, China c China North Vehicle Research Institute, Beijing 100072, China b

H I GH L IG H T S

intelligent braking is proposed to improve energy economy and braking stability. • An adaptive fuzzy controller is developed for single-pedal regenerative braking. • An multi-objective optimization neural network is used to step on the brake pedal. • AControl effect of the proposed intelligent braking is verified via HIL experiment. •

A R T I C LE I N FO

A B S T R A C T

Keywords: Electric vehicle Single-pedal braking Multi-objective optimization Neural network model Energy economy Braking stability Driving intelligence

The braking system is significant to improve the total energy efficiency and ensure driving security of electric vehicles. An intelligent braking system (IBS) composed single-pedal and multi-objective optimization neural network braking control strategies is proposed in this paper to improve the energy economy, braking stability and driving intelligence for electric vehicles. The braking operations of drivers are divided into two parts: (1) releasing the accelerator pedal and (2) stepping on brake pedal. In the first braking operation, a single-pedal regenerative braking control strategy (RBCS) of accelerator pedal based on adaptive fuzzy control algorithm is proposed to improve energy recovery and driving intelligence. Simulation results illustrate that the simulation velocities under the control of adaptive single-pedal RBCS can follow several standard test cycles (including US06, UDDS, LA92 and ECE) very well. The braking energy can be recovered effectively with a less usage of brake pedal. In the second braking operation, a neural network (NN) controller for the composite braking system (CBS) is proposed to optimize the energy economy and braking stability at the same time. The control effect is verified by simulation results under NEDC cycles. The hardware-in-loop (HIL) experiments of the IBS are also conducted in this paper. Compared with a parallel braking strategy used in EU260 electric vehicles, the energy economy of IBS is improved by 3.67% than EU260 in 3 NEDC cycles. IBS performs more closely to the I curve in a specific braking condition with a decreasing braking severity. The time ratio of hydraulic braking in IBS is 2.27% less than EU260 with an increasing driving intelligence.

1. Introduction Pure electric vehicle possesses the regenerative braking system (RBS), which provides electric vehicles with the capability to recapture kinetic energy during braking processes, reduce the energy consumption and prolong the endurance mileage. Research indicates that 50% energy of pure electric vehicle driving system is discarded to the atmosphere in the form of heat by a conventional braking system during deceleration in urban conditions. Even in suburban conditions, the

⁎

proportion of discarded energy is as high as 24% [1]. Therefore, in order to solve the deficiency of the endurance mileage, it is crucial to investigate methods for enhancing the regenerative braking technology of pure electric vehicle. In the literature, there are two important topics to improve the regenerative braking technology, namely the system design and regenerative braking control strategy. Kalinin et al. [2] designed a kinetic energy recovery system (KERS), which is in the form of a rotating flywheel. Metz [3] examined the potential energy savings benefits

Corresponding author. E-mail address: [email protected] (H. He).

https://doi.org/10.1016/j.apenergy.2019.114172 Received 1 December 2018; Received in revised form 30 October 2019; Accepted 13 November 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Hongwen He, et al., Applied Energy, https://doi.org/10.1016/j.apenergy.2019.114172

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In order to give a systemic solution to these problems, an intelligent braking system (IBS) is proposed in this paper. IBS considers two kinds of braking operations, including (1) drivers only release the accelerator pedal and (2) drivers step on brake pedal. In both two braking operations, intelligent braking control strategies are applied. The main contributions made in this paper include:

available with a KERS and analyzed the effect of the parameters of flywheel on the potential of energy saving. The deficiency of KERS is the complex structure, which might be a massive change for vehicles. Midgley et al. [4] proposed hydraulic regenerative braking, which has been almost applied in heavy vehicles. The control strategy of hydraulic regenerative braking was studied by Hui et al. [5]. However, the low energy density of the hydraulic accumulator makes it difficult to fully utilize the regeneration potential. Making a trade-off between performance and cost, the electro-mechanical RBS becomes the most popular choice in all kinds of vehicles [6]. In this system, the electric motor will be controlled to operate as a generator converting the vehicle’s kinetic energy into electricity and improving vehicle’s energy efficiency significantly [7]. More and more studies are gradually focusing on the better regenerative braking control strategy of electro-mechanical RBS. The existing regenerative braking control strategies (RBCS) mainly start with distributing the braking force of the front and rear axles. Geng et al. [8] studied the effect of the optimal braking force distribution curve I on regenerative braking, which achieves the best braking effect during deceleration. Zhang et al. [9] proposed an energyefficient torque allocation scheme for distributed drive electric vehicles. The results demonstrate that this scheme considerably improves the vehicle efficiency compared with the conventional approach. Guo et al. [10] defined series and parallel regenerative braking control strategy. They found the parallel regenerative braking control strategy is stable and simple. While the series regenerative braking control strategy can achieve the best effect of energy recovery. On the above basis, Xu et al. [11] developed a fuzzy-logic-based regenerative braking strategy integrated with series regenerative braking. The result shows that the strategy can ensure braking safety and stability and improve the maximum driving range by 25.7%. Zhang et al. [12] designed a cooperative regenerative braking control (CRBC) strategy. Results show the improvement of the fuel economy enhanced by this strategy reaches 16% and 9% respectively, compared to bus without regenerative brake and with the parallel regenerative braking control strategy. Lv et al. [13] also proposed a novel pressure-difference-limiting control method to optimize the performance of hydraulic brake, which improves the validity and feasibility of CRBC. Kumar and Subramanian [14] proposed a new cooperative control strategy called ‘combined braking’ to adjust the proportions of regenerative braking and friction braking. Combined braking ensures that the driver’s feel remains the same as before and can regenerate more than twice the braking energy of conventional parallel braking. Akhegaonkar et al. [15] investigated a longitudinal controller for a smart and green autonomous vehicle (SAGA) which aims at minimizing energy expenditure and maximizing energy regeneration. This strategy is confirmed to control the longitudinal motion while actively balancing efficiency and safety. Kangkang et al. [16] researched the hardware requirements of different regenerative braking control strategies. The results indicated that the electric vehicle could only adopt the greatest regenerative braking control strategy with ABS and an adjustable pedal. Xiaokun [17] and Xu et al. [18] studied the limiting factors of the maximum regenerative braking force. However, existing regenerative braking control strategies all concentrate on the process that drivers have already stepped on brake pedal. In this process, no matter how to optimize the proportions of regenerative and hydraulic braking force, regenerative braking force only accounts for a fraction of the total braking force. It is a waste of motor-braking characteristics to some extent because most braking requirements of drivers can be satisfied by the motor alone. Moreover, existing braking control strategies always have a fixed distribution proportion front axle and rear axle hydraulic braking force and lack coordination between regenerative and hydraulic braking, which will cause either braking security operations or poor braking economic. Both regenerative braking system (RBS) and hydraulic braking system (HBS) together make up the composite braking system (CBS) in electric vehicles. Therefore, highlighting composite braking strategy is a meaningful but challenging problem.

• A single-pedal regenerative braking control strategy (RBCS) of ac-

•

celerator pedal for electric vehicles based on adaptive fuzzy control algorithm is proposed in the first braking operation. In most braking conditions, drivers can realize the vehicle braking simply via releasing accelerator pedal, which makes driving more intelligent and increase the energy recovery rate. A neural network (NN) model of CBS is established in the second braking operation, which considering the multi-objective optimization of energy recovery and braking stability. The NN control strategy of CBS changes the regenerative braking force, hydraulic braking force of front and rear axle into optimal range to regenerate more braking energy with a higher braking stability.

The remainder of the paper is organized as follows: The content and principle of adaptive single-pedal RBCS is proposed in Section 2; Section 3 establishes the multi-objective neutral network control model; Simulation results of these two intelligent braking control strategies are presented in Section 4; Section 5 describes the hardware-in-loop (HIL) experiences of the completed IBS with conclusions given in Section 6. 2. Adaptive single-pedal regenerative braking control strategy The framework of single-pedal regenerative braking control strategy (RBCS) of accelerator pedal based on adaptive fuzzy control algorithm is shown in Fig. 1. It can be seen that the strategy consists of four parts. The first part is to recognize the intent of drivers. The second part is to confirm the ability of regenerative braking torque. The third part is to calculate regenerative braking torque, and the final part is to update the ability of regenerative braking torque adaptively 2.1. Recognizing the intent of drivers Time set is set at 1 s. The expressions of the stroke of accelerator and brake pedal are pedalacc and pedalbra , respectively. The balance point of accelerator pedal is introduced in this section, which is expressed in terms of pedalbal . Comparing the stroke of accelerator pedal at any moment t and the last moment t-1, namely, pedalacc (t ) and pedalacc (t − 1) . The Schematic diagram of recognizing driving intent is shown in Fig. 2.

Fig. 1. The framework of adaptive single-pedal RBCS. 2

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Fig. 2. Schematic diagram of recognizing driving intent.

same time, according to the driving behaviors and driving conditions, the value of T0 is always changing so that the regenerative braking torque generated finally can better meet drivers’ braking intents. The specific changing by driving behavior is discussed later while the prechanging process via driving conditions is finished in this part as follow: When a strong braking intent is recognized, comparing the velocity now and the average velocity in the past 40 s, namely V (t ) and Vaverage . The expression of the pre-changed ability T0' is shown in Eq. (3):

(1) If the stroke of accelerator now is not less than the last moment, as shown in Eq. (1):

pedalacc (t ) ≥ pedalacc (t − 1)

(1)

The driver press down the accelerator pedal with driving intents. According to the MAP of driving torque and accelerator pedal stroke, the driving torque generated by motor can be calculated. (2) If the stroke of accelerator now is shallower than the last moment, as shown in Eq. (2):

T0' = T0 − k1 (V (t ) − Vaverage )

pedalacc (t ) < pedalacc (t − 1)

where k1 is a correction factor and the value is 1.1, preferably.

(2)

• If the velocity now is higher than the average velocity in past 40 s,

Then to compare the stroke of pedalacc (t ) with pedalbal and make detailed judgements, as follows:

• If the stroke of pedal •

(3)

•

acc (t ) is not less than pedalbal . It means even though drivers release the pedal, the brake intent is not aggressive. The motor still works as an electric motor and outputs driving torque. If the stroke of pedalacc (t ) is less than pedalbal . It means that drivers have an intense intention of braking. Then the single-pedal RBCS comes into effect.

•

the braking intent of drivers could be strong. Then the ability of regenerative braking torque should be improved. If the velocity now is slower than the average velocity in past 40 s, the requirement of braking may be small. Then the ability of regenerative braking torque should be reduced. If the velocity now is equal to the average velocity in past 40 s, the ability should remain unchanged.

Meanwhile, in order to reflect the actual characteristics of braking conditions, the values of Eq. (3) are negative and meet the restrictions of motor’s torque-speed characteristic. In addition, when the velocity is slower than 8 km/h, the ability T0 and T0' decrease to zero and the motor does not generate regenerative braking torque.

2.2. Confirming the ability of regenerative braking torque In order to calculate the regenerative braking torque that drivers expect, the ability of regenerative braking torque is defined as the limit of the motor, which is expressed in terms of T0 and set as a constant negative value first. Based on the torque-speed characteristic of the motor, the ability T0 further tightens the maximum regenerative braking torque that motor can generated. Then the ability T0 and pedal-control operations codetermine the regenerative braking torque now. At the

2.3. Calculating regenerative braking torque In order to calculate the regenerative braking torque, a one output and two-dimensional fuzzy controller is established, in which a specific fuzzy control logic is designed to recognize the intensity of braking

Fig. 3. Schematic diagram of fuzzy controller. 3

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Degreem of Membership

1

Z

VS

S

MS

MB

B

VB

the results of fuzzy inference into a correct output value, which is the output signal K g . According to the fuzzy rules, the grades of regenerative braking torque K g is increasing with the releasing of accelerator pedal. Therefore, in order to guarantee the stable driving experience, the final torque Tmotor produced by motor contains the driving torque Tdri and the regenerative braking torque Treg all the time. The expression of Tmotor is shown in Eq. (4).

0.8 0.6 0.4 0.2

Tmotor = Tdri + Treg = Mappedal (pedalacc , v ) + T0'·K g

0 0

0.167

0.333 0.5 0.667 Input and Output Signals

0.833

1

where Tdri is a positive value calculated by interpolation method according to the Torque-Pedal Map and comes into effect all the time. While Treg only comes into effect when the single-pedal RBCS works. According to the Eq. (4), Tdri is decreasing with the releasing of accelerator pedal and the Treg is increasing at the same time. When the final torque Tmotor is negative, then the motor will be translated into a dynamo and recovery braking energy. The vehicle is decelerating.

Fig. 4. The simulation results of membership functions.

Grades of Regenerative Braking Torque

intent. Fig. 3 illustrates the schematic diagram of fuzzy controller. The change of stroke (COS) is defined as the difference of pedal stroke between now and the last moment and the gradient of stroke (GOS) is defined as the COS in unit time. Obviously, the COS and GOS of accelerator pedal can reflect drivers’ braking intent. Therefore, both COS and GOS are chosen as the inputs of fuzzy controller. Meanwhile, the grades of regenerative braking torque K g (value between 0 and 1) is chosen as the output of the fuzzy controller. The actual regenerative braking torque can reach the optimum to meet the braking requirements of drivers by real-time controlling K g . In this paper, each of COS, GOS and K g contains seven fuzzy subsets {Z,VS,S,MS,MB,B,VB}, which denotes zero, very small, small, less than medium, more than medium, big and very big, and the continuity domain is [0, 1]. In the process of fuzzification and defuzzification, type Z and type S membership functions are used respectively on each side of domains. The triangular membership functions are used in the midst of domains. Then the MATLAB simulations are adopted and the membership diagram of all the input and output signals are the same, as shown in Fig. 4. Fuzzy rule is the core of fuzzy controller. The fuzzy control rules are established according to driving experiences of drivers. Given that the stroke of accelerator pedal is always in the middle for most conditions. It is rare to see the stroke of accelerator pedal change from maximum to zero. In order to improve the regenerative braking strength, the fuzzy control rules are established as shown in Fig. 5. According to the membership functions and fuzzy control rules, each group of the input signals will match several possible output signals. The subset of all these possibilities is regarded as the results of fuzzy inference. Finally, the barycenter method [19] is used to translate

2.4. Updating the ability of regenerative braking torque adaptively Finally, the ability of regenerative braking torque is updated adaptively in accordance with drivers’ pedal operation in the next moment. (1) If the driver only stomps the accelerator pedal in the next moment, as shown in Eq. (5):

pedalacc (t + 1) > pedalacc (t )

(5)

It means the regenerative braking torque applied now is too large and the driver has the intention of accelerating. The absolute value of T0 should be decreased with the stroke increasing of acceleration pedal. The change of acceleration pedal stroke in the next moment is expressed as Δpedalacc . Then the ability of regenerative braking torque T0 after updating is shown in Eq. (6):

T0 = (T0' + k2 Δpedalacc )

(6)

where k2 is a correction factor and the value is 10.5 preferably to maintain a consistent order of magnitude. (2) If the driver releases the accelerator pedal or stomps the brake pedal in the next moment, as shown in Eq. (7):

pedalacc (t + 1) < pedalacc (t ) or pedalbra (t + 1) > 0

VB B MB MS S VS Z VB

B

MB

MS

S VS

GOS

Z

(4)

VS

Z

MS

S

COS

Fig. 5. Spatial distribution of the input and output for fuzzy rules. 4

MB

B

VB

(7)

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It means the regenerative braking torque applied now is too small and the driver has the intention of braking. The absolute value of T0 should be increased with the stroke decreasing of acceleration pedal or stroke increasing of brake pedal. Δpedalacc is negative now and the change of brake pedal stroke in the next moment is defined as Δpedalbra . Then the ability of regenerative braking torque T0 after updating is shown in Eq. (8):

T0 = (T0' − k2 Δpedalacc ) or T0 = (T0' + k3 Δpedalbra )

(8)

where k2 and k3 are also correction factors and the value are both 10.7 preferably. (3) If neither the stroke of accelerator pedal nor brake pedal is changed in the next moment, which means the regenerative braking torque applied now exactly satisfies the braking requirements of drivers. Keep the value of T0 unchanged.

Fig. 6. The re-calibrated Torque-Pedal Map of motor.

braking system (CBS), which includes regenerative braking system (RBS) and hydraulic braking system (HBS), must be adopted to respond the driver’s braking intentions quickly. Specially, the HBS controlled by drive-by-wire technology will produce a variable hydraulic braking force distribution ratio between the front and rear shaft. Under this condition, a smart braking control strategy is required to satisfy the energy recovery and braking stability at the same time. Therefore, a multi-objective optimal neural network control strategy for CBS is proposed in this section. EU260 electric vehicle produced by BAIC is selected as the test vehicle in this paper. EU260 is a front-wheel drive (FWD) electric vehicle with the braking force distribution sketch shown in Fig. 7. In the second braking process, the total braking torque on wheels TB and the braking strength z are expressed as follow:

2.5. Parameter calibration of single-pedal RBCS Recently, single-pedal regenerative braking control strategy receives the attention of every automobile manufacturers and has already been applied in some mass production vehicles such as BMW i3 and Nissan Leaf. However, the feedbacks of driving experience are not satisfactory. The reason is that there are two other common driving conditions beside accelerating and braking conditions under traditional braking control strategy: creep and coast conditions. However, the existing single-pedal condition is hard to achieve these two conditions. (1) Creep Condition: When the velocity is slow and the accelerator and braking pedal are released entirely, the vehicle will move at a very slow speed. (2) Coast Condition: When the velocity is high and the accelerator and braking pedal are released entirely, the vehicle will move depend on oneself of inertial.

TB = Tm·i 0 + Thf + Thr = δmzgr − Fa r

z=

dv /g dt

(9)

(10)

where Tm is the regenerative braking torque generated by motor. i 0 is main reduction ratio. Thf and Thr are the hydraulic braking torque on front and rear axle, respectively. δ is the rotating mass conversion coefficient. m is the full mass of vehicle. g is the gravitational acceleration. r is the radius of wheels. Fa is the driving resistance. v is the velocity and t is time. Normally, the driving resistance covers rolling, air, acceleration and slope resistance. In this paper, Fa is obtained by fitting revolving drum test data of EU260 and shown in Eq. (11)

Using BMW i3 as an example, when the accelerator and braking pedal are both released entirely, the deceleration produced by singlepedal RBCS is 0.2 g, which is three times larger than traditional strategy. Therefore the creep condition is very hard to achieve and the gliding distance is reduced drastically. In order to solve these problems, a conception called balance point of accelerator pedal is proposed in our single-pedal RBCS, firstly. The value of this balance point is calibrated at 10%. Only if the driver release accelerator pedal over this balance point, the single-pedal RBCS will come into effect. According to the Eq. (4), If the driver release accelerator pedal slightly over the balance point, the positive Tdri will offset the negative Treg and the final torque Tmotor is equal to zero. Then the vehicle can move into coast condition. Secondly, our single-pedal RBCS limits Treg to zero when the velocity is less than 8 km/h. Meanwhile, the Torque-Pedal Map of motor is recalibrated, which is shown in Fig. 6. When the velocity is less than 8 km/h and the accelerator and brake pedal are both released entirely, the driving torque Tdri is equal to 8 N.m. Then the creep condition can also be guaranteed to achieve successfully. Moreover, the growth of torque is slow when the stroke of pedalacc is increasing from 0% to 10%. But then, the growth of torque is high. The purpose is to concentrate more pedal operation on the region of 10%-100%, which reserves space for single-pedal operation. As a result, the driving experience of our single-pedal RBCS is pretty better than the control strategy in BWM i3 and Nissan Leaf.

Fa = 0.0367v 2 + 0.3667v + 204.4134

(11)

According to the definition of braking force distribution coefficient β , the expression of β is shown in Eq. (12)

β=

Tm·i 0 + Thf (12)

Thr

3. A neural network control strategy for composite braking system In the second braking operation, drivers step on brake pedal and show aggressive braking intentions. For security reasons, the composite

Fig.7. Braking force distribution sketch for EU260. 5

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3.1. Multi-objective optimization model of CBS based on energy economy and braking stability An optimal CBS can enhance the energy regeneration rate and braking stability of electric vehicles. As for energy regeneration rate, the larger the regenerative braking torque produced, the better. However, as for braking stability, braking force distribution coefficient β should be adjusted as close to I curve as possible. Therefore, there is a relationship of restriction between these two optimization objectives. Then the optimization of CBS control strategy can be transferred into a multi-objective optimization problem. When solving multi-objective optimization problems, as the global optimal solution is usually hard to find out, only a set of compromises can be obtained to make more and more objectives optimized or comparatively ideal. The set of compromises is called Pareto set in multi-objective optimum. In this paper, a weight coefficient method is used to solve Pareto set [20]. Denoting Tm and Thr as the design variables. Denoting the deviations between braking force distribution coefficient β and regenerative braking force to their respective optimization as the objective function, the optimization model of CBS can be formulated as: β − βI 2 ) βI

+ ω2 (

Fig. 9. The braking stability zone.

. . .

w1=0.99, w2=0.01

300

Tm − Tmax 2 ) Tmax

200

s. t . 0 ≤ Tm ≤ Tm _max 0 ≤ Thr ≤ Th _max 0 ≤ Thf ≤ Th _max

w1=0.5, w2=0.5

100 w1=0, w2=1

0

β ∊ Zstable

(13)

where J1 and J2 are objective functions of braking stability and energy economy, respectively. ω1 and ω2 are weight coefficient of these two objectives. βI is the ideal braking force distribution ratio calculated by I curve. Tmax is the maximum regenerative braking torque of the CBS. Tm _max is the maximum torque of the motor. Th _max is the maximum hydraulic braking torque that the HBS can provide. Zstable is the stable region of braking according to national standards ZBT24007-1989. Tmax is constrained by the charging ability of the battery and the torque characteristics of the motor.

Tmax = min (Tm _max , Tbat )

Pbat =

1000

2000

3000

4000 5000 6000 Speed of motor (r/min)

βI =

where Pbat is the maximum charging power of the EU260 battery which is associated with SOC, see Eq. (16); n is the rotary speed of the motor; η is the regeneration efficiency of the motor related to n and Pbat , as shown in Fig. 8.

0% ≤ SOC ≤ 90% ⎧ 69.3 1 − SOC ≤ SOC ≤ 100% 69.3 90% ⎨ 0.1 ⎩

regenerative braking torque(N.m)

9000

(16)

lr + z · h L

(17)

250

0.9 0.85

200

0.8 0.75

150

0.7 0.65

100

0.6 0.55

50

0.5 2000

8000

where lr is the length between the vehicle centroid and rear axle; h is the height of the centroid; L is the wheelbase. Although the closer β to βI the better, it is really hard and meaningless to achieve. Therefore, the constraint condition of β should be considered. A conception called stable braking zone Bstable is presented. If the value of β is in the stable braking zone, the braking condition is deemed safe. According to the braking regulation ZBT24007-1898 [21],

(15)

1000

7000

βI is the ideal braking force distribution coefficient in accordance with the I curve, which represents high braking stability. It can be calculated as follows:

(14)

9550Pbat η·n

0

Fig.10. The distribution of weight coefficient ω1 and ω2

where Tbat is the maximum charging torque and can be calculated by:

Tbat =

The maximum torque of motor The rated torque of motor The maximum braking torque by road

4000

Torque (N.m)

minJ (Tm, Thr ) = ω1 J1 + ω2 J2 = ω1 (

The Braking Stable Zone

3000 4000 5000 6000 rotary speed of the motor (r/min)

7000

8000

Fig.8. The efficiency MAP and torque-speed characteristic of motor. 6

9000

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Fig.11. SMSA algorithm based on DOE.

the constraint formulas of β is shown as follow andBstable is pictured in Fig. 9.

SOC

100

⎧ β ≥ βI ⎪ (z − 0.08)(lr + zh) (z + 0.08)(lr + zh) ≤β≤ ⎪ zL zL ⎪ (z + 0.25) L ≥ − β 1 ⎨ 7.4(l f − zh) z ⎪ z − 0.1 z − 0.1 + 0.2) (l f − zh) ( + 0.2) (lr + zh)( ⎪ 0.85 0.85 ≤ ≤ β ⎪1 − Lz Lz ⎩

50

0 135 90 45 Velocity (km/h)

0

0

0.1

0.3

0.2

0.4

0 ≤ z ≤ 0.8 0.15 ≤ z ≤ 0.3 0.3 ≤ z ≤ 0.8 0.2 ≤ z ≤ 0.8

(18)

0.5

3.2. Solution of multi-objective optimization based on energy economy and braking stability

Braking strength z

In order to weight the importance of these two objectives in different braking conditions reasonably. Considering the motor rated torque Tm _rated and the maximum braking torque that can be provided by road TB _max , three different combinations of the weight coefficient ω1 and ω2 are chosen in this paper.

Fig.12. 500 samples chosen by OLHD. Table 1 The optimal results calculated by SMSA algorithm. Sequence numbers

SOC

v

z

Tm

Thr

1 2 3 4 5 6 7 8 ⋮ 497 498 499 500

86.77 6.41 48.1 31.06 13.43 10.82 51.5 92.38 ⋮ 70.34 20.24 89.18 28.86

70.38 54.6 56.1 78.65 86.41 70.88 43.58 75.14 ⋮ 8.01 78.4 7.76 95.68

0.3066 0.3677 0.2104 0.1553 0.4038 0.3798 0.1142 0.478 ⋮ 0.4459 0.3287 0.4519 0.498

117.28 146.45 82.41 55.57 117.38 143 39.48 102.05 ⋮ 184.57 120.68 187.46 106.04

509.62 609.90 318.15 218.28 724.15 675.69 183.36 844.82 ⋮ 733.71 581.00 741.22 859.39

(1) when TB < Tm _rated , as shown in green region of Fig. 10. The objective of braking stability is ignored and only the objective of energy economy is considered, that is ω1 = 0 , ω2 = 1; (2) when Tm _rated ≤TB < Tm _max , as shown in blue region of Fig. 10. Optimization is more focused on the objective of energy economy, that is ω1 < ω2 . The exact values of ω1 and ω2 are calculated via the corresponding location of TB in Fig. 7. The marginal values are ω1 = 0.5, ω2 = 0.5; (3) when Tm _max ≤TB < TB _max , as shown in red region of Fig. 10. Optimization is more focused on the objective of braking stability, that is ω1 > ω2 . The exact values of ω1 and ω2 are also calculated via the corresponding location of TB in Fig. 10. The marginal values are 7

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Fig.13. Topology of RBF-NN model.

Table 2 Basic characteristic parameters of standard test cycles. characteristic parameters

US06

UDDS

LA92

ECE

Average Velocity (km/h) Maximum Velocity (km/h) Average Braking Intensity Braking to Driving energy ratio ηe

77.2 129 0.07 20%

31.5 91.2 0.06 42%

39.6 108 0.07 40%

18.3 50.0 0.07 51%

ω1 = 0.99, ω2 = 0.01. In this section, in order to obtain the multi-objective optimal results, design of experiments (DOE) method is applied to draw samples from all kinds of braking conditions. Simplex method simulated annealing (SMSA) algorithm is used at each sample point to find the optimal results of Tm , Thr and Thf , which lays the foundation for establishing the neural network control model as well as improving the energy economy and braking stability. The technology roadmap is shown in Fig. 11. In the process of DOE, optimal Latin hypercube design (OLHD) is used to draw 500 samples from the three-dimensional space of SOC, v and z. The sampling procedure has three parts [22,23]: Fig.14. The principle of RBF-NN control strategy.

(1) Dividing each dimension of the 3-D space into 500 regions without overlap evenly. (2) Draw a sample point from each region in each dimension, totally 1500 points. (3) Selecting a sample from each dimension of the whole 1500 points to 250 200

200

Thr (Nm)

Tm (Nm)

300

150

100 0 135 110

100 85

60

v (km/h)

(a)

35

10

0

0.2

0,1

0.3

50

1000 750 500 250 0 135 110 85

800 600 400 200

60 35 10 0 v (km/h)

z

(SOC=65%)

(b)

0.1 z

0.2 0.3

(SOC=65%)

250 200

150

100

100

0 135 110

60 35 10 0 v (km/h)

(c)

0.1

0.2

800

1000

600

500

400

0 135 110

50 85

1000

1500

200

Thr (Nm)

Tm (Nm)

300

0.3

200 85

60

v (km/h)

z

(SOC=95%)

(d) Fig.15. Training result of RBF-NN model. 8

35

10 0

0.1

0.2 0.3

z

(SOC=95%)

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30

40

target udds velocity 20

Velocity(m/s)

Velocity(m/s)

30 20 10 0

real velocity

10

real velocity target us06 velocity 0

100

200

300 T ime(s)

400

500

0

600

0

200

400

(a) US06 Cycle 40

target ECE velocity

10

0

200

400

1200

real velocity

target LA92 velocity

Velocity(m/s)

Velocity(m/s)

15

20

0

1000

(b) UDDS Cycle

real velocity

30

600 800 T ime(s)

600 800 T ime(s)

1000

1200

1400

10

5

0

0

50

(c) LA92 Cycle

100 T ime(s)

150

(d) ECE Cycle

Fig.16. The relationship between simulation velocities and target velocities.

Simulation results

US06

LA92

UDDS

ECE

The maximum deviation (m/s) Standard deviation (m/s) Time of mechanical braking (s) Time of deceleration conditions (s) Time ratio of mechanical braking ηm

2.5012 0.3222 32 206 15.53%

1.3096 0.1446 135 487 27.72%

1.1677 0.1082 166 452 36.73%

0.5418 0.0854 15 37 40.54%

distribution proportion (%)

Table 3 Characteristics of simulation conditions.

make up a vector, totally 500 vector samples. All the 500 samples are drew in 3-D space as shown in Fig. 12. For each sample, SMSA algorithm figures out a pre-result to minimum the objective function by simplex method. Then the simulated annealing algorithm is used to try to search a better result on a global scale. If the better result is found, simplex method is applied again to search a new better result in adjacent area until the precision of the last result is satisfied. The final result is regard as global optimum [24]. The optimal Tm and Thr of these 500 samples are calculated by SMSA algorithm and the results are shown in Table 1.

40

US06 UDDS LA92 ECE

30 20 10

0 -0.1 -0.3 -0.5 -0.7 -0.9 -1.1 -1.3 -1.5 -1.7 -1.9 -2.1 -2.3 -2.5 -2.7 distribution of deceleration (m/s2) Fig.17. The deceleration distribution of all test cycles.

recognition, state estimation, condition prediction and other field [25]. The radial basis function adopts Gaussian function in this paper and the topology of RBF-NN model is shown in Fig. 13. The principle of RBF-NN control strategy is shown in Fig. 14. All the 500 braking condition samples are divided into two parts, training sample database (350 samples) and testing sample database (150 samples). The RBF-NN model takes corresponding SOC, v and z of training sample database as input, and optimal result of Tm and Thr as output. Then the relationship between input layer and output layer is fitted by model training. Multiple correlation coefficient method is applied to analyze the model error through testing sample database. The expression of multiple correlation coefficient is shown in Eq. (19).

3.3. A neural network control strategy model for CBS of electric vehicles In order to summarize the control strategy of CBS, a radial basis function neural network (RBF-NN) model is trained through the optimal braking force in section B. Due to the faster training speed and the higher fitting accuracy, RBF-NN method is widely applied in pattern Table 4 Energy recovery simulation results of these test cycles.

Recovered Energy (J) Expended Energy (J) RERR ηe

US06

LA92

UDDS

ECE

1.3117 × 106 1.1829 × 107 55.40%

2.4578 × 106 9.3237 × 106 65.90%

1.4908 × 106 4.6121 × 106 76.93%

1.1232 × 105 2.6278 × 105 83.71%

9

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0.88

60

Motor Torque (N.m)

0.90

SOC

0.86 0.84 0.82 0.8 0.78

RBF-NN Control Strategy Paralel Control Strategy in EU260 500 1000 1500 2000

0

40 20 0 -20 -40 -60

2500

3000

Driving Torque 0

3500

500

1000

Regenerative Braking Torque

1500

2000

2500

3000

3500

Time (s)

Time (s)

(a) SOC

(b) Motor Torque Fig.18. The simulation result of energy economy.

Energy consumption (kWh)

Final SOC

Average regenerative braking torque (N.m)

the trained RBF-NN model in this paper is 0.991, which is larger than 0.95 and satisfy precision requirement. The training results of RBF-NN model when the SOC are 65% and 95% respectively are shown in Fig. 15.

4.58 4.73

0.819 0.788

23.65 17.63

4. Simulation results

Table 5 Simulation results comparative between NN and parallel strategy.

120

0.4

80

0.3

40

0.2

0 0

Braking Strength Velocity 2 4

6 Time (s)

8

10

In order to verify the accuracy of single-pedal RBCS based on adaptive fuzzy control algorithm mentioned above as well as the energy economy and braking stability of RBF-NN control strategy for CBS, simulations of these two strategies based on Matlab\Simulink are finished, respectively.

Braking Strength

velocity ( km/h )

RBF-NN Parallel control strategy

4.1. Simulation results of adaptive single-pedal RBCS The single-pedal RBCS is simulated under several standard test cycles, including US06, UDDS, LA92 and ECE. Table 2 shows the characteristic parameters of these test cycles [16]. Specifically, US06 is a high-speed cycle while others are all urban diving cycles. The purpose of this simulation is to find an appropriate stroke sequence of accelerator pedal to satisfy the intentions of drivers, realize the following of all those standard test cycles under the control of single-pedal RBCS and determine whether the energy recovery is great. In the process of simulation, these standard test cycles are regard as target conditions. The stroke of accelerator and brake pedal are regard as simulation results instead of priori conditions. Therefore, unlike the logic of adaptive single-pedal RBCS, the difference between target velocity Vtar and simulated velocity Vsim is used to reflect the driving intention of drivers:

0.1

Fig.19. The specific braking condition. n

R2 = 1 −

∑ (yi − yi∗ )2 RMSE = 1 − in= 1 Variance ∑i = 1 (yi − y¯i )2

(19)

where RMSE is root-mean-square error and yi is the optimal result. yi∗ is corresponding observed value output by RBF-NN model. y¯i is the average observed value. Obviously, the data range of R2 is from 0 to 1, and the closer the R2 is to 1, the more accurate the model is. The R2 of

Braking force distribution coefficient ȕ

0.7 0.68

I Curve RBF-NN Control Strategy Parallel control Strategy in EU260

0.66

Part A

Split point P

0.64

Part B

0.62 0.6 0.58

0

10

20

30

40

50

60

70

80

Time (s) Fig.20. The trajectory of β for NN and parallel control strategy. 10

90

100

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Tm (Nm)

140 110 80 50

Thf (Nm)

Thr (Nm)

750

Split point P 0

1

2

3

0

1

2

3

4

5

6

7

8

9

10

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6

7

8

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7

80

9

10

600 450 300

Split point P

400

4

Split point P

200 0 0

1

2

3

4

Tm

Thr Time (s)

Thf

Fig.21. Simulation result of Tm , Thf and Thr for NN model.

Fig.22. The topology of IBS HIL experimental platform.

target velocities are shown in Fig. 16. It can be seen that the simulation velocities can follow all the target test cycles very well, which indicates that this strategy can meet the driving demand completely. Table 3 indicates the characteristics of simulation conditions. It can be seen that the value of the maximum deviations and standard deviations between these test cycles and simulation velocities are really small. Table 3 also indicates the time ratio of mechanical braking. Obviously, under the control of single-pedal RBCS, drivers rarely need to stomp brake pedal to realize deceleration. The single-pedal RBCS makes driving behavior more simple and intelligent. In order to verify whether the adaptive single-pedal RBCS benefits the energy recovery and compare the energy efficiency performance among these test cycles. A proper evaluation method called relative energy recovery rate (RERR) is proposed in this paper. RERR represent that how much energy is recovered from braking energy. The expression of RERR is shown in Eq. (21)

(1) If Vtar ≥ Vsim , which means drivers have intentions of accelerating or keeping the velocity. (2) If Vtar < Vsim , which means drivers have intentions of braking. The value of required braking force can be calculated based on the target deceleration. If the ultimate regenerative braking force that the motor can generate is far from enough to satisfy braking demand. Then the mechanical braking force is required, which means drivers stomp the brake pedal. Meanwhile, in the calculation of ability of regenerative braking torque, the velocity differences are used instead of COS. the expressions of updating the ability of regenerative braking torque adaptively is showed in Eq. (20):

T0 − k 4 (Vsim (t + 1) − Vtar (t + 1))

(20)

where k 4 is a correction factor with the value is 1.1. In the simulation, the initial value of the ability of regenerative braking torque T0 is set to − 180 N ·m . The simulation curves of all the four simulation velocities and their

ηr = 11

Wreg / Wdrive η = ηe ηe

(21)

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energy. This is the reason why RERR of US06 is the least. The decelerations of other three test cycles all focus on −0.1 ~ −0.2 m/s2 and −0.7 m/s2. While the average velocity of ECE is the smallest, which causes the air resistance is also low and regenerated braking force will be generated more. The average velocity of UDDS is slightly smaller than LA92 and distribution proportion at low decelerations of UDDS is higher than LA92. Therefore, the RERR of UDDS cycle is less than ECE cycle and larger than LA92 cycle. 4.2. Simulation results of neural network model for CBS The neural network control strategy model for CBS has two optimization objectives: energy economy and braking stability. Therefore, the simulation of NN model is also aimed at these two respects. 4.2.1. Simulation of energy economy In order to fully reflect the performance without too much time, the NN model is simulated under 3 continuous NEDC driving cycles. A comprehensive comparison of the proposed NN controller and the common parallel braking strategy used by the test vehicle EU260 is provided in this paper. Fig. 18(a) shows SOC trajectories controlled by the two controllers. The blue line is fitted directly from the revolving drum test data. The both initial SOC is set as 90%. The final SOC of NN controller is 81.86%, which is 3.04% higher than parallel braking strategy. Therefore, the proposed NN control strategy is more energy-efficient. The simulation data of these two control strategies is listed in Table 5. The energy economy of the proposed NN control strategy is increased by 3.4% than the parallel braking strategy. Meanwhile, the average regenerative braking torque of proposed NN control strategy is also increased by 34.1%. That means RBF-NN control strategy can improve the energy economy effectively.

Fig.23. The physical diagram of HIL experiment platform.

Velocity (km/h)

150 100 50 0

Velocity Error (km/h)

10 5 0 -5 -10

Velocity (km/h)

150 100 50 0

Velocity Error (km/h)

where η is energy recovery rate [26] and ηe is proportion of braking energy to driving energy, which is listed in Table 2. Wreg and Wdrive represent energy recovered in regenerative braking conditions and energy consumed in driving conditions, respectively. Table 4 shows the RERR simulation results of these test cycles. These data indicates that braking energy can be recovered effectively under the control of adaptive single-pedal RBCS. Considered the differences of RERR for all test cycles, deceleration becomes the overriding factor. Then the distributions of deceleration are recorded in Fig. 17. In this figure, the decelerations of US06 focus on −0.7 m/s2 and −1.4 m/s2. On the one hand, the average velocity of US06 is so large that the air resistance is high enough to keep the deceleration in most braking conditions and then regenerative braking force is no need to produce. On the other hand, in order to achieve the larger deceleration, the mechanical braking torque is required for more braking conditions, which also cause the consumption of braking

20 10 0 -10

NEDC Cycle

4.2.2. Simulation of braking stability Aiming at the performance of braking stability, the proposed NN model is simulated under a certain braking condition. The initial vehicle velocity of this braking condition is 120 km/h. The initial braking strength of this braking condition is 0.4 and the braking strength decreases 0.02 per second. This braking condition will be finished till the velocity is decrease to 10 km/h, as shown in Fig. 19. Taking the SOC at 60% as an example, the braking force distribution

HIL Experimental Velocity

0

200

400

600 (a)

800

1000

1200

0

200

400

600 (b)

800

1000

1200

NEDC Cycle

Bench-testing Velocity

0

200

400

600 (c)

800

1000

1200

0

200

400

600 (d) Time (s)

800

1000

1200

Fig.24. The simulated velocity of IBS and the bench-testing vehicle of EU260 under NEDC cycle. 12

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150

IBS control srategy Parallel control strategy in EU260

Motoe Torque (N.m)

100

50

0

-50

-100

0

200

400

600

800

1000

Time (s) Fig.25. The motor torque comparative between IBS and EU260.

Table 6 Energy economy comparative between IBS and EU260. Control strategy

Average Braking Torque (Nm)

Energy Consumption for 100 km (kWh)

Energy Recovery Rate (%)

Final SOC (From 90% start)

Time ratio of hydraulic braking (%)

IBS EU260

38.2344 30.3867

13.92 14.45

26.15 18.84

87.42% 86.77%

9.09% 11.36%

braking torque in front axle consists Tm and Thf . Before the split point P, Tm increases while Thf decreases with the braking strength. After the split point P, the braking torque in front axle is only provided by RBS. The position of point P is related to SOC and v.

Table 7 Braking stability comparative between IBS and EU260. Control strategy

maximum

IBS EU260

β − βI βI

β − βI

0.1126 0.1538

average

0.0612 0.0937

(%)

mean square error

maximum

0.0271 0.0384

17.24 22.75

average

11.56 15.30

mean square error

5. Hardware-in-loop experiment of the intelligent braking system Simulation environment is highly fault-tolerant and too ideal for control strategies. However, in the real environment, Controllers is limited by self-hardware capabilities and usually cannot perform as well as simulation. Hardware-in-loop (HIL) experiment is a good method to verify the effect of control strategies in hardware environments. As the single-pedal RBCS and RBF-NN model are proposed above, an intelligent braking system (IBS) control strategy is established by integrating these two braking control strategies. Then the HIL experiment of IBS is applied in this section. The code of IBS control strategy is regarded as the real-time control kernel and generated by Simulink\MotoHawk. Then the control kernel is wrote in real-time emulation (VT system) through MotoTune software. Correspondence between VT system and controller is established via controller area network (CAN) bus. The model of IBS is built in Simulink environment, including motor model, HBS model, dynamic model and power battery model. The topology of IBS HIL experimental platform is shown in Fig. 22. There are two CAN channels in this topology: (1) CAN I realize the communication between IBS controller and upper computer software MotoTune. The interrelated control parameters are monitored via this channel. (2) CAN II realize the communication between IBS controller and VT system. Therefore, the software CANoe connected with VT system can monitor the messages, including SOC, v, z, Tm and Thf . In order to simulate the driving situations more real, the experimenter controls the vehicle model to follow the target condition via electronic accelerator pedal and brake pedal. The physical diagram is shown in Fig. 23. NEDC driving cycle is chosen to be the target cycle in HIL

3.95 4.31

coefficients of RBF-NN and EU260 under this specific braking condition are shown in Fig. 20. In the whole braking process, the distribution coefficient of RBF-NN control strategy is much closer to I curve. That means the RBF-NN model makes the most of adhesion situations on road and improves the braking stability greatly. The braking process of RBF-NN model can be divided in two parts. In the part A of the Fig. 20, NN can maintain the braking severity along the I curve. While in the part B of the Fig. 20, the distribution coefficient β controlled by NN is a little higher than the I curve with the largest deviation is 0.0336. The reasons are: (1) In the braking process of part A, there is no incompatibility between these two objectives. Therefore, NN model can control Tm , Thf and Thr to distribute braking force as I curve as well as maximize the regenerative braking force at the same time. (2) In the braking process of part B, There is incompatibility between energy economy and braking stability. NN model will harmonize these two objectives by ω1 and ω2 to realize the global optimum. The result is that NN model guarantees braking stability first and recovers energy as more as possible. Under this specific braking condition, Tm , Thf and Thr generated by NN model are shown in Fig. 21. Because the braking torque in rear axle is only provided by HBS, Thr decreases with braking strength. The 13

Applied Energy xxx (xxxx) xxxx

H. He, et al.

Acknowledgements

experiment again. Under the control of IBS control strategy, the equipment of accelerator pedal and brake pedal is operated by the experimenter to make simulation velocity follow the target velocity in real time as far as possible. The velocity and error in HIL experiment are shown in Fig. 24(a) and (b). It can be seen clearly that although there are only slight differences between the two lines, the simulation velocity of HIL experiment is roughly consistent with the target NEDC velocity. In order to verify the control effect of IBS, a comparative analysis between simulated velocity and bench-testing velocity of EU260 electric vehicle is proposed in this paper. The bench-testing results of EU260 are shown in Fig. 24(c) and (d). The simulated motor torque in HIL experiment and bench-testing torque of EU260 are shown in Fig. 25. It can be seen that regenerative braking torque of IBS starts earlier than parallel braking control strategy in some braking conditions because of the single-pedal RBCS. Obviously, regenerative braking torque value of IBS is larger than parallel control strategy for most braking conditions because of the RBF-NN control strategy. The specific results of HIL and bench experiment are listed in Table 6. In a NEDC driving cycle, IBS save 3.67% energy more than EU260. The final SOC of IBS is 0.65% higher than EU260. The time ratio of hydraulic braking for IBS is 2.27% less than EU260. The results indicate that IBS will improve the energy economy of electric vehicle effectively. The performance of braking in advance and braking torque increasing makes driving more intelligent and effectively. In order to evaluate the braking stability performance of IBS in HIL experiment, the absolute and relative deviation between β and βI of IBS and EU260 are calculated in Table 7. It is observed that the braking stability of IBS is much closer than optimum. The braking stability of IBS improved a lot compared with that in EU260 testing vehicle.

This project is supported by National Key R&D Program of China (Grand No. 2017YFB0103701) in part, and supported by the National Natural Science Foundation of China (grant number 51675042). References [1] Zhang J, Lv C, Gou J, et al. Cooperative control of regenerative braking and hydraulic braking of an electrified passenger car. Proc Inst Mech Eng, Part D: J Automob Eng 2012;226(10):1289–302. [2] Kalinin V, Lohr R, Leigh A, et al. High-speed high dynamic range resonant SAW torque sensor for kinetic energy recovery system. In: EFTF-2010 24th European frequency and time forum. IEEE; 2010. p. 1–8. [3] Metz LD. Potential for passenger car energy recovery through the use of kinetic energy recovery systems (KERS). In: SAE 2013 World Congress & Exhibition; 2013. [4] Midgley WJB, Cathcart H, Cebon D. Modelling of hydraulic regenerative braking systems for heavy vehicles. Proc Inst Mech Eng, Part D: J Automob Eng 2013;227(7):1072–84. [5] Sun H, Yang L, Jing J, et al. Control strategy of hydraulic/electric synergy system in heavy hybrid vehicles. Energy Convers Manage 2011;52(1):668–74. [6] González-Gil A, Palacin R, Batty P. Sustainable urban rail systems: strategies and technologies for optimal management of regenerative braking energy. Energy Convers Manage 2013;75:374–88. [7] Zhang J, Li Y, Lv C, et al. New regenerative braking control strategy for rear-driven electrified minivans. Energy Convers Manage 2014;82:135–45. [8] Geng C, Liu L, Zhang K, et al. A study on control strategy for regenerative braking in EQ6110 hybrid electric vehicle. Automotive Eng 2004;3:253–6. [9] Zhang X, Göhlich D, Li J. Energy-efficient toque allocation design of traction and regenerative braking for distributed drive electric vehicles. IEEE Trans Veh Technol 2018;67(1):285–95. [10] Guo J, Wang J, Cao B. Regenerative braking strategy for electric vehicles. In: Intelligent Vehicles Symposium. IEEE; 2009. p. 864–68. [11] Xu Guoqing, Li Weimin, Xu Kun, et al. An intelligent regenerative braking strategy for electric vehicles. Energies 2011;4(9):1461–77. [12] Zhang J, Lv C, Qiu M, et al. Braking energy regeneration control of a fuel cell hybrid electric bus. Energy Convers Manage 2013;76(76):1117–24. [13] Lv C, Zhang J, Li Y, et al. Hardware-in-the-loop simulation of pressure-differencelimiting modulation of the hydraulic brake for regenerative braking control of electric vehicles. Proc Instit Mech Eng Part D J Automobile Eng 2014;228(6):649–62. [14] Kumar CN, Subramanian SC. Cooperative control of regenerative braking and friction braking for a hybrid electric vehicle. Proc Instit Mech Eng Part D J Automobile Eng 2016;230(1). [15] Akhegaonkar S, Nouvelière L, Glaser S, et al. Smart and green ACC: energy and safety optimization strategies for EVs. IEEE Trans Syst Man Cybernet Syst 2017;PP (99):1–12. [16] Zhang Kangkang, Xu Liangfei, et al. A comparative study on regenerative braking system and its strategies for rear-wheel drive battery electric vehicles. Automotive Eng 2015(02). 125-131+138. [17] Sun X. Study on electro-mechanical braking control strategy for a distributed driving electric vehicle. Beijing: Beijing Institute of Technology; 2015. [18] Xu G, Li W, Xu K, et al. An intelligent regenerative braking strategy for electric vehicles. Energies 2011;4(9):1461–77. [19] Wang JW, Tsai SH, Li HX, et al. Spatially piecewise fuzzy control design for sampled-data exponential stabilization of semi-linear parabolic PDE systems. IEEE Trans Fuzzy Syst 2018. [20] Zhang L, Hu X, Wang Z, et al. Multi-objective optimal sizing of hybrid energy storage system for electric vehicles. IEEE Trans Veh Technol 2017;1(99). 1-1. [21] Guo HQ, He HW, Sun FC. A combined cooperative braking model with a predictive control strategy in an electric vehicle. Energies 2013;6(12):6455–75. [22] Brooks KP, Sprik SJ, Tamburello DA, et al. Design tool for estimating chemical hydrogen storage system characteristics for light-duty fuel cell vehicles. Int J Hydrogen Energy 2018. [23] Roshani A, Giglio D. Simulated annealing algorithms for the multi-manned assembly line balancing problem: minimising cycle time. Int J Prod Res 2017;55(10):2731–51. [24] Omran MG, Clerc M. APS 9: an improved adaptive population-based simplex method for real-world engineering optimization problems. Appl Intell 2018;48:1–13. [25] Barati-Harooni A, Najafi-Marghmaleki A, Mohammadi AH. A Reliable Radial Basis Function Neural Network Model (RBF-NN) for the prediction of density of ionic liquids. J Mol Liq 2017;231:462–73. [26] Lv C, Zhang J, Li Y, et al. Mechanism analysis and evaluation methodology of regenerative braking contribution to energy efficiency improvement of electrified vehicles. Energy Convers Manage 2015;92:469–82.

6. Conclusion This article proposed an intelligent braking system (IBS) composed adaptive single-pedal regenerative braking control strategy (RBCS) and a multi-objective optimization neural network (NN) control model. When drivers release the accelerator pedal, the adaptive single-pedal RBCS is adopted to produce proper regenerative braking force in advance, which leads to the improvement of energy recovery and driving intelligence. When drivers stomp brake pedal, the NN control model is adopted to optimize the regenerative and hydraulic braking force in both axles, which leads to the improvement of energy economy and braking stability. A simulation analysis of adaptive single-pedal RBCS is attained based on US06, UDDS, LA92 and ECE. All the simulation velocities can follow these target velocities very well with a low utilization rate of brake pedal. The results indicate that the braking energy can be recovered effectively under the control of adaptive single-pedal RBCS. Another simulation analysis of multi-objective NN model is attained based on 3 continuous NEDC cycles. Simulation results indicate that the NN model recover 3.4% energy more than traditional parallel control strategy with the better braking stability. A comparative analysis between HIL experiment results of IBS and bench-testing data of EU260 is also conducted in this paper. The results demonstrate that drivers can realize the following of NEDC cycle basically with under the control of IBS. The braking energy recovered by IBS is 3.67% more than EU260 as well as the hydraulic braking usage of IBS is 2.27% less than EU260. Moreover, the braking stability of IBS is always better than EU260. IBS is more energy-efficient, intelligent and secure than the braking control strategy in EU260.

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