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Development of an online adaptive energy management strategy for the novel hierarchical coupled electric powertrain

June 2021
Energy Science and Engineering 9(9)

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CC BY 4.0

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This paper develops an online adaptive energy management strategy (EMS) for the promising hierarchical coupled electric powertrain (HCEP) to exert its energy‐saving potential while considering the adaptability to driving conditions and the suppression of mode switching frequency. First, the complex energy management issue of the HCEP is simplified by introducing a simple power allocation method. And, the simplified energy management issue is solved by the Dynamic Programming to obtain the offline optimal working mode sequences of the HCEP. Second, the online working mode decision rules of the HCEP are established according to the obtained working mode sequences. And, the auxiliary rules in the decision rules are further optimized for different types of driving conditions. Then, the principal component analysis and generalized regression neural network are used to construct the driving condition recognizer (DCR) with high prediction accuracy. And, based on the constructed DCR, working mode decision rules, and introduced power allocation method, an online adaptive EMS is developed for the HCEP. Finally, the rationality of the introduced power allocation method and the effectiveness of the developed online adaptive EMS are verified. This paper develops an online adaptive energy management strategy (EMS) for the promising hierarchical coupled electric powertrain (HCEP) applied in vehicles. This online adaptive EMS can not only ensure the energy‐saving effect of the HCEP, but also can effectively avoid frequent working mode switching, as well as has adaptive ability to different driving conditions.

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Energy Sci Eng. 2021;00:1–18.

wileyonlinelibrary.com/journal/ese3

INTRODUCTION

In our previous work, a novel distributed electric- wheel drive

configuration applied in vehicles is proposed, which is called

hierarchical coupled electric powertrain (HCEP).1 The HCEP

is composed of the upper coupling layer (the torque coupling

between the front and rear axles) and the lower coupling layer

(the dual- motor rotation speed coupling in each wheel). The

HCEP is promising because of the following two advantages:

(1) it integrates the rotation speed coupling and torque cou-

pling, which allows it to expand the efficient working range

of distributed drive electric vehicles (DDEVs) in two dimen-

sions of the vehicle speed and torque and to significantly

improve the economy of DDEVs; (2) compared with peer

powertrains proposed in2- 3 which arrange both the rotational

speed coupling and torque coupling in each wheel, the HCEP

is simpler in structure. The HCEP utilizes the independence

and controllability between the output torque of the front axle

and that of the rear axle in DDEVs and moves the torque

coupling from inside of wheels to between the front and rear

axles; thus, only the rotational speed coupling is arranged in

each wheel. According to the previous research, the HCEP

Received: 30 December 2020

Revised: 13 May 2021

Accepted: 1 June 2021

DOI: 10.1002/ese3.931

RESEARCH ARTICLE

Development of an online adaptive energy management strategy

for the novel hierarchical coupled electric powertrain

XianbaoChen

HongyuShu

YitongSong

This is an open access article under the terms of the Creat ive Commo ns Attri bution License, which permits use, distribution and reproduction in any medium, provided the original

work is properly cited.

School of Automotive Engineering,

Chongqing University, Chongqing, China

Correspondence

Hongyu Shu, School of Automotive

Engineering, Chongqing University,

Chongqing 400044, China.

Emails: cxbcqu@163.com,

shyxianbao@163.com

Funding information

Natural Science Foundation of Chongqing

(China), Grant/Award Number:

cstc2018jcyjAX0077; National Natural

Science Foundation of China, Grant/Award

Number: 51975069

Abstract

This paper develops an online adaptive energy management strategy (EMS) for the

promising hierarchical coupled electric powertrain (HCEP) to exert its energy- saving

potential while considering the adaptability to driving conditions and the suppres-

sion of mode switching frequency. First, the complex energy management issue of

the HCEP is simplified by introducing a simple power allocation method. And, the

simplified energy management issue is solved by the Dynamic Programming to ob-

tain the offline optimal working mode sequences of the HCEP. Second, the online

working mode decision rules of the HCEP are established according to the obtained

working mode sequences. And, the auxiliary rules in the decision rules are further

optimized for different types of driving conditions. Then, the principal component

analysis and generalized regression neural network are used to construct the driv-

ing condition recognizer (DCR) with high prediction accuracy. And, based on the

constructed DCR, working mode decision rules, and introduced power allocation

method, an online adaptive EMS is developed for the HCEP. Finally, the rationality

of the introduced power allocation method and the effectiveness of the developed

online adaptive EMS are verified.

KEYWORDS

energy saving, hierarchical coupled electric powertrain, online adaptive energy management

strategy, power distribution, working mode decision

CHEN Et al.

could theoretically reduce the energy consumption of DDEVs

by 5.6% to 10.6% under different driving cycles.

The HCEP is a multi- power sources drive system

(MPSDS) that cannot exert its energy- saving potential with-

out a suited energy management strategy (EMS).4 The energy

management of the HCEP is much more complicated than

that of common MPSDSs because the torque coupling and

rotation speed coupling exist together in the HCEP and the

rotation speed allocation is restricted by the torque alloca-

tion. Because of this, EMSs of common MPSDSs cannot be

directly applied to the HCEP. However, fortunately, EMSs of

common MPSDSs can provide a reference for the develop-

ment of the EMS of the HCEP.

So far, there have been many reports on EMSs of common

MPSDSs. Experience- based EMSs, for example, rules- based

EMSs and fuzzy logic- based EMSs, are widely used because

they do not require complex algorithms and are easily im-

plemented.5- 8 However, the economy and robustness of this

type of EMSs is difficult to be guaranteed. The equivalent

consumption minimum strategy is often utilized in the energy

management of hybrid electric vehicles (HEVs), but it is not

suitable for pure electric vehicles (PEVs).9

Dynamic programming (DP) is an effective method to lo-

cate the global optimal EMS, but it requires large amount

of calculation.10- 11 Compared with the DP, the computation

burden of the convex optimization is much lower.12 However,

the convex optimization of complex systems can be arduous

due to the excessive number of parameters that has to be

taken into consideration and not all systems are suitable for

linearization.13 Another usually used optimization algorithm

is the Pontryagin’s Minimum Principle (PMP) that can lo-

cate the global optimal EMS by minimizing the Hamiltonian

function. But PMP- based EMSs are difficult to be applied

directly as the costates in the Hamiltonian function need to be

determined with repeat iteration.14- 15 A predominantly limit-

ing factor for the online application of the above optimization

algorithm- based EMSs is that they need to know the precise

driving conditions in advance. Results obtained from optimi-

zation algorithm- based EMSs are usually used as the bench-

mark to improve or evaluate other EMSs.16- 18 In addition,

optimization algorithms such as the genetic algorithm and

particle swarm optimization are also often used to optimize

the parameters of EMSs to achieve better control effects.19- 20

In some researches, the model predictive control (MPC)

is applied in the EMSs of MPSDSs.21 In MPC- based EMSs,

the MPC is commonly used together with vehicle speed pre-

diction. In other words, prediction algorithms, such as the

Markov chain and neural network, are first used to predict

the near future vehicle speed, and then, the MPC is adopted

to realize the local optimal energy management of power-

trains.22- 23 Although the MPC is an instantaneous optimal

control method, the real time is the biggest obstacle to its

online application.24 When the vehicle speed prediction is

integrated in an EMS, the EMS can adapt to the change of

traffic conditions.25 However, ensuring the prediction accu-

racy of the vehicle speed is difficult.26 The near future traffic

conditions can also be obtained through the global position-

ing system, geographic information system, Internet of vehi-

cles, etc.27- 29

Another type of EMSs with adaptability to actual traffic

conditions is based on the driving condition recognition. The

idea of driving condition recognizer (DCR)- based EMSs is

that different substrategies are designed for different driving

conditions, and then, the substrategy most suitable for the cur-

rent driving condition is used.30- 32 In DCR- based EMSs, the

misrecognition of driving conditions is always unavoidable,

which decreases the performance of this type of EMSs.33

Recently, some scholars use reinforcement learning (RL)

algorithms to build EMSs.34 According to their research, it

can be concluded that RL algorithms, such as Q- learning,

deep Q- learning, double deep Q- learning, deep determinis-

tic policy gradient, and Dyna framework, can well deal with

energy management of MPSDSs.35- 39 However, RL algo-

rithms are a learning process starting from scratch because no

prior knowledge is involved, which leads to the fact that RL

algorithm- based EMSs may require a long training time.38

In MPSDSs, the improvement of energy efficiency usu-

ally leads to the increase of mode switching frequency, which

may deteriorate the ride comfort. In Ref. 40, the method of

delay mode switching is applied in the EMS of a dual- motor

drive EV to suppress the mode switching frequency. The

difficulty of this approach is how to find appropriate delay

switching rules to better balance energy efficiency and mode

switching frequency.

This paper aims to develop an online adaptive EMS for the

promising HCEP to exert its energy- saving potential as much

as possible while considering the adaptability to driving con-

ditions and the suppression of mode switching frequency.

CONFIGURATION AND

PRINCIPLE OF THE HCEP

In the novel HCEP, all four wheels are capable of power out-

put and their power output characteristics are the same. As

shown in Figure 1, each wheel is integrated with two motors

(ie, M1 and M2), two planetary gear trains (ie, PGT 1 and

PGT 2), and two brakes (ie, B1 and B2). M1 and M2 are con-

nected to the sun gear and ring gear of PGT 1, respectively.

The carrier of PGT 1 is connected to the sun gear of PGT 2,

the carrier of PGT 2 is fixed, and the ring gear of PGT 2 is

connected to the tire. B1 and B2 are responsible for braking

the sun gear and ring gear of PGT 1, respectively. In each

front axle wheel, an additional synchronizer (SY) is fitted

between PGT 1 and PGT 2 to disconnect the power trans-

mission between the tire and M1 and M2 if needed. Since

CHEN Et al.

driving conditions to be analyzed in this study are straight,

subsequent analyses are conducted from the perspective of

the front and rear axles instead of that of four wheels. The

HCEP consists of two coupling layers. One is the upper cou-

pling layer that denotes the torque coupling between the front

and rear axles; the other is the lower coupling layer that de-

notes the dual- motor rotation speed coupling in each wheel.

In the upper coupling layer, there are two working modes,

that is, single axle driving (SA) and torque coupling driving

by the front and rear axles (TC). When the vehicle demand

torque is small, the upper coupling layer adopts mode SA,

that is, the rear axle wheels output impetus while the front

axle wheels do not work. In this case, the power flow of the

vehicle is shown in Figure 2A and its dynamic model is as

follows:

where, Tv is the vehicle demand torque, Tr is the output torque

of the rear axle, and Trr and Trl are the output torque of the

right rear and left rear wheels, respectively. When the vehicle

demand torque is large, the upper coupling layer adopts mode

TC, that is, the front and rear axle wheels drive the vehicle in

the form of torque coupling. In this case, the power flow of

the vehicle is shown in Figure 2B and its dynamic model is

as follows:

where, Tf is the output torque of the front axle, and Tfr and Tfl

are the output torque of the right front and left front wheels,

respectively.

In the lower coupling layer, that is, in each wheel, there

are three working modes which are single M1 driving (SM1),

single M2 driving (SM2), and dual- motor rotation speed cou-

pling driving (SC), respectively. Mode SM1 will be selected

when the desired output torque of a wheel is not large and the

vehicle speed is low. The power flow of the wheel is shown in

Figure 3A, and its dynamic model is as follows:

where, nw and Tw are the rotation speed and output torque of the

wheel, respectively. n1 and T1 are the rotation speed and output

torque of M1, respectively. k1 and k2 are the characteristic pa-

rameters of PGT 1 and PGT 2, respectively. ηt is the total trans-

mission efficiency of PGT1 and PGT2. It should be noted that

although in theory there is a small difference between the trans-

mission efficiency when the power is input from the sun gear of

PGT1 while is output from the carrier of PGT1 and the trans-

mission efficiency when the power is input from the ring gear

of PGT1 while is output from the carrier of PGT1, this small

difference is ignored in this paper to facilitate the development

(1)

Tv=Tr=Trr +Trl

(2)

Tv=Tr+Tf=Trr +Trl +Tfr +Tﬂ

(3)

k1)k2

(4)

Tw=T1(1 +k1)k2

𝜂

FIGURE 1 Configuration of the HCEP: A) Torque coupling of

the upper layer. B) Dual- motor rotation speed coupling of the lower

layer

(A)

(B)

Tyre

PGT 1

PGT 2

FIGURE 2 Power flows (blue dashed lines with arrows) of the

vehicle: (A) The working mode of the upper coupling layer is SA. (B)

The working mode of the upper coupling layer is TC

(A)

(B)

CHEN Et al.

of the EMS. That is, we consider the transmission efficiency of

PGT1 to be the same regardless of the power is input from the

sun gear or ring gear. Thus, no matter which mode is adopted

in the wheel, ηt is the same. Mode SC will be selected when the

desired output torque of a wheel is low and the vehicle speed is

high. The power flow of the wheel is shown in Figure 3B, and

its dynamic model is as follows:

where, n2 and T2 are the rotation speed and output torque of

M2, respectively. Mode SM2 will be selected regardless of the

vehicle speed, as long as the desired output torque of a wheel is

large. The power flow of the wheel is shown in Figure 3C, and

its dynamic model is as follows:

The specifications of the vehicle are listed in Table 1. The

specifications of parts of a wheel are listed in Table 2. Figures

4 and 5 are efficiency MAPs of M1 and M2, respectively.

SIMPLIFICATION AND

SOLUTION OF THE ENERGY

MANAGEMENT ISSUE OF THE

HCEP

3.1

Energy management issue of the

HCEP

The energy management issue of the HCEP can be described

using the following discrete dynamic system:

where, ui is the action vector. ui_1 is the target torque distribu-

tion ratio between the front and rear axles at the sampling time

i, and it can be expressed as follows:

here, Tf_i_tar and Tr_i_tar are the target output torque of the front

and rear axles, respectively. ui_2 is the target rotation speed dis-

tribution ratio in front axle wheels at the sampling time i, and it

can be expressed as follows:

(5)

k1)k2

(6)

w=T1(1 +k1)k2𝜂t=

(1 +k

2𝜂t

(7)

k1)k2

(8)

(1 +k

2𝜂

(9)

i+1

=f(x

)i=0,1,2,...,N−1

ui=[ui_1,ui_2 ,ui_3]

=[x

1_1

1_2

1_3

1_4

1_5

1_6]

(10)

i_1 =

f_i_tar

r_i_tar

(11)

i_2 =

f_M1_tar

f_M2_tar

FIGURE 3 Power flows (blue dashed

lines with arrows) of a wheel: (A) The

working mode of the lower coupling layer

is SM1. (B) The working mode of the lower

coupling layer is SC. (C) The working mode

of the lower coupling layer is SM2

(A)

(B)

(C)

CHEN Et al.

here, nf_M1_tar and nf_M2_tar are the target rotation speed of M1

and M2 in the front axle wheels, respectively. ui_3 is the target

rotation speed distribution ratio in rear axle wheels at the sam-

pling time i, and it can be expressed as follows:

here, nr_M1_tar and nr_M2_tar are the target rotation speed of M1

and M2 in the rear axle wheels, respectively. xi+1 is the state

vector. xi+1_1 is the working mode of the upper coupling layer at

sampling time i+1. xi+1_2 and xi+1_3 are the working mode of the

front and rear axle wheels at sampling time i+1, respectively.

xi+1_4 is the torque distribution ratio between the front and rear

axles at sampling time i+1. xi+1_5 and xi+1_6 are rotation speed

distribution ratios in front and rear axle wheels at sampling time

i+1, respectively.

The mapping f in Equation (9) can be described as fol-

lows: (1) If ui_1 is equal to 0, xi+1_1 is SA; if ui_1 is between

0 and 1, xi+1_1 is TC. (2) If ui_2 is equal to 0, xi+1_2 is SM2;

if ui_2 is between 0 and 1, xi+1_2 is SC; if ui_2 is equal to 1,

xi+1_2 is SM1. (3) If ui_3 is equal to 0, xi+1_3 is SM2; if ui_3

is between 0 and 1, xi+1_3 is SC; if ui_3 is equal to 1, xi+1_3

is SM1. (4) xi+1_4 is equal to ui_1, xi+1_5 is equal to ui_2, and

xi+1_6 is equal to ui_3.

At any sampling time, the search range of ui_1 is [0, 1), but

the search range of ui_2 and ui_3 is not always [0, 1]. Figure6

shows the external characteristic curves (ECCs) of the rear

axle when the rear axle wheels work in modes SM1, SM2,

and SC, respectively. ECC of the vehicle is also drawn in

Figure 6. Due to the ECCs of the front axle is completely

consistent with that of the rear axle, it is not repeated to draw

in here. Assume that at the sampling time i, the target oper-

ating point of the vehicle is located at A. If ui_1 values 0, the

(12)

i_3 =

r_M1_tar

r_M2_tar

TABLE 1 Specifications of the vehicle

Item Value Item Value

Curb mass (kg) 1200 Tire rolling radius (m) 0.323

Test mass (kg) 1390 Tire rolling coefficient 0.015

Gross mass (kg) 1580 Drag coefficient 0.284

Windward area (m2) 1.97 Transmission efficiency 0.92

TABLE 2 Specifications of parts in a wheel

Item Value

M1 Rated/Peak output power

(kW)

3.74/9.5

Rated/Peak output torque

(Nm)

6.6/15

Rated/Peak rotation speed

(rpm)

5412/11000

Base speed (rpm) 6048

Peak output torque at peak

rotation speed (Nm)

4.89

M2 Rated/Peak output power

(kW)

10.71/27.2

Rated/Peak output torque

(Nm)

37.88/86.1

Rated/Peak rotation speed

(rpm)

2700/8505

Base speed (rpm) 3017

Peak output torque at peak

rotation speed (Nm)

12.44

PGT1 characteristic parameter 2.5455

Modulus 1.5

tooth number of sun gear 22

PGT2 characteristic parameter 4.6471

Modulus 2.5

tooth number of sun gear 17

FIGURE 4 Efficiency MAP of M1 in a wheel

0 3000 6000 9000 12000

Rotation speed (rpm)

-16

-12

-8

-4

Torque (Nm)

Efficiency (%)

FIGURE 5 Efficiency MAP of M2 in a wheel

0 1500 3000 4500 6000 7500 9000

Rotation speed (rpm)

-90

-60

-30

Torque (Nm)

Efficiency (%)

CHEN Et al.

upper coupling layer works in mode SA, the front axle does

not output power, the operating point of the rear axle is lo-

cated at A, the rear axle wheels can work in mode SM2 or SC,

and the rotation speed distribution range of M1 in the rear

axle wheels is [0, n1]; when the value of ui_1 is changed, such

as 0.25, then the upper coupling layer will work in mode TC,

the operating point of the front axle will locate at C, the front

axle wheels can work in modes SM1, SM2, or SC, the rota-

tion speed distribution range of M1 in the front axle wheels

is [0, n3], the operating point of the rear axle will locate at

B, the rear axle wheels can only work in mode SM2 or SC,

and the rotation speed distribution range of M1 in the rear

axle wheels is [0, n2]. It can be seen that the rotation speed

distribution range in front and rear axle wheels changes with

the torque distribution between front and rear axles, that is,

the search range of ui_2 and ui_3 varies with ui_1.

To sum up, the torque distribution exists together with the

rotation speed distribution in the HCEP, and the rotation speed

distribution is restricted by the torque distribution. The en-

ergy management of the HCEP is an optimization issue in the

three- dimensional continuous space. It is not possible to solve

the complex energy management issue online. In fact, even

if the optimization algorithm such as DP is adopted to solve

this issue offline, if the discrete lattice points are small, the

calculation amount and solution time are also not to be under-

estimated. In fact, in order to ensure the optimization effect,

the discrete lattice points of continuous variables are generally

not too large. Therefore, it is necessary to simplify the energy

management issue of the HCEP to reduce its calculation time.

3.2

Simplification of the issue

In order to decrease the complexity of the energy manage-

ment issue of the HCEP, a simple power allocation method is

introduced. The power allocation method includes two parts.

One is the rotation speed distribution submethod, and the

other is the torque distribution submethod.

1) Introduced simple rotation speed distribution sub-

method: the search of the optimal rotation speed allocation

within the wheel is simplified to look up the table. For the

working mode SM1 or SM2 of the lower coupling layer, that

is, of each wheel, only M1 or M2 works, and there is no ro-

tation speed allocation between M1 and M2. For the working

mode SC, the optimal rotation speed distribution correspond-

ing to each working point of the wheel can be obtained offline

through traversal method and stored in the controller of the

wheel in the form of a table. In the actual control, if a wheel

works in mode SC, the optimal rotation speed distribution be-

tween M1 and M2 can be obtained directly by looking up the

table. The optimal rotation speed of M1 under mode SC ob-

tained offline is shown in Figure 7. Since the rotational speeds

of the wheel, M1, and M2 satisfy the constraint of Equation

(5), no matter what the rotational speed of the wheel is, as long

as M1 works at the optimal assigned rotational speed, then

M2 will naturally work at its assigned optimal rotation speed.

Therefore, only the optimal rotation speed distribution table of

M1 needs to be stored in the memory, as well as only the op-

timal rotation speed of M1 needs to be queried in the control.

2) Introduced simple torque distribution submethod:

when the upper coupling layer works in mode TC, the re-

quired torque of the vehicle is evenly distributed to the front

and rear axles. Thus, the search range of ui_1 is changed from

[0, 1) to the two values of 0 and 0.5.

If both of the introduced rotation speed and torque distri-

bution submethods are reasonable, the energy management

issue of the HCEP can be transformed from Equation (9) to

(13)

i+1

i=0,1,2,...,N−1

Ui=[Ui_1,Ui_2 ]

=[X

1_1

1_2

]

FIGURE 6 ECCs of the rear axle and vehicle when the vehicle is

in drive

020406080 100 120140 160

Vehicle speed (km/h)

500

1000

1500

2000

Torque (Nm)

Rear axle in SM1

Rear axle in SM2

Rear axle in SC

Vehicle

(n3, T3)

(n2, T2)

(n1, T1)

FIGURE 7 Optimal rotation speed distribution of M1 under the

mode SC

CHEN Et al.

where, Xi+1 is the new state vector, Ui is the new action vec-

tor, Ui_1 and Ui_2 are the target working modes of the upper

and lower coupling layers at the sampling time i, respectively.

Xi+1_1 and Xi+1_2 are the working modes of the upper and lower

coupling layers at the sampling time i+1, respectively. It can

be seen that the front axle wheels and rear axle wheels are no

longer distinguished here, but are uniformly referred to by the

lower coupling layer. This is because when the upper coupling

layer works in mode TC, the power output of the front axle

wheels and that of rear axle wheels is the same and the front and

rear axle wheels can work in the same mode. In addition, when

the upper coupling layer works in mode SA, we can also assume

that the front axle wheels and rear axle wheels work in the same

mode, but the front axle wheels does not output power. Thus, at

any sampling time, Ui_1 has at most two values, that is, SA and

TC, while Ui_2 has at most three values, that is, SM1, SM2, and

SC. The energy management of the HCEP is transformed from

the optimization in the three- dimensional continuous space to

the optimization in the set listed in Table 3. The computational

burden is greatly reduced.

For an electric wheel, it is possible to obtain and store its

working characteristics, control parameters, and other infor-

mation before leaving the factory. Therefore, it is feasible to

simplify the search of the optimal rotation speed allocation in

the lower coupling layer to look up the table. The rationality

of the introduced torque distribution submethod can be eval-

uated by comparing the following two cases. In the first case,

the torque distribution ratio between the front and rear axles

traverses in [0, 1). In the second case, the torque distribution

ratio only traverses the two values of 0 and 0.5. As to the lower

coupling layer, regardless of the case, modes SM1, SM2, and

SC are traversed and the most efficient mode is adopted. The

difference between vehicle efficiencies obtained from the two

cases is shown in Figure 8, and the statistical analysis results

of the difference are listed in Table 4. It can be seen that there

is no significant distinction between the vehicle efficiencies

obtained from the two cases. Therefore, when the upper cou-

pling layer works in mode TC, it is reasonable to evenly assign

the required torque of the vehicle to the front and rear axles.

3.3

Solution of the simplified issue

The DP can be used to solve the simplified energy manage-

ment issue, so as to offline obtain the optimal working mode

sequences of the HCEP. The idea of the DP is to divide the

optimization issue into a series of minimization subissues

backward from the terminal sampling time. These subissues

can be expressed as follows:

At sampling time N- 1:

At sampling time i, 0≤i<N- 1:

where, J* i(Xi) is the optimal accumulated cost function which

represents the optimal cost that if at the sampling time i, the

HCEP starts at state Xi and follows the optimal control path

thereafter until the final sampling time. L(Xi, Ui) is the instan-

taneous cost function. Here, only energy consumption is con-

sidered. Thus, L(Xi, Ui) denotes the total energy consumption

(14)

J∗

N−1

(

XN−1

)

=min

N−1

[L(XN−1,UN−1

)]

(15)

J∗

(

)

=min

[L(Xi,Ui)+J

∗

i+1

(

Xi+1

)]

TABLE 3 Search domain of the simplified energy management

issue

Action vector Ui_1 Ui_2

1 SA SM1

2 SA SM2

3 SA SC

4 TC SM1

5 TC SM2

6 TC SC

FIGURE 8 Deference between vehicle efficiencies obtained from

the two cases

TABLE 4 Statistics of the difference between vehicle efficiencies

obtained from the two cases

State of vehicle Mean (%)

Standard

deviation (%)

Driving −0.01 0.40

Regenerative braking −0.03 0.96

CHEN Et al.

of all motors in the HCEP at the sampling time i, and it can be

expressed as follows:

where, Δt is the sampling interval. nr1 and Tr1 are the rotation

speed and output torque of M1 in the rear axle wheels, respec-

tively. nr2 and Tr2 are the rotation speed and output torque of

M2 in the rear axle wheels, respectively. nf1 and Tf1 are the ro-

tation speed and output torque of M1 in the front axle wheels,

respectively. nf2 and Tf2 are the rotation speed and output torque

of M2 in the front axle wheels, respectively. ηr1 and ηr2 are the

efficiencies of M1 and M2 in the rear axle wheels, respectively.

ηf1 and ηf2 are the efficiencies of M1 and M2 in the front axle

wheels, respectively. The number 2 refers to two wheels, that is,

the left and right wheels, on each axle.

In addition, the following constraints should be imposed

to ensure reasonable operation of the HCEP. For each wheel:

The last constraint is to avoid the power cycling.

To fully consider the characteristics of actual traffic situ-

ations, 12 comprehensive driving cycles listed in Table 5 are

used to solve the simplified energy management issue. These

driving cycles simultaneously include the traffic character-

istics of urban, suburban, and highway. After using the DP

to solve the simplified energy management issue, the opti-

mal working mode sequences of the HCEP are obtained, as

shown in Figures 9 and 10.

WORKING MODE DECISION

RULES OF THE HCEP

4.1

Extraction of basic working mode

decision rules

The basic working mode decision rules of the HCEP can be

extracted from the offline obtained optimal working mode

sequences. It can be seen from Figures 9 and 10 that all work-

ing modes are basically linearly separable. Thus, the extrac-

tion of basic working mode decision rules can be regarded

as a series of linear binary classification issues. The support

vector machine (SVM) is very suitable for solving these lin-

ear binary classification issues, and the separation hyperplane

in the SVM is the basic decision rule we need.

(16)

(Xi,Ui)=

2Δ

9550 (nr1Tr1𝜂

−sign(Tr1)

r1+nr2Tr2𝜂

−sign(Tr2)

nf1Tf1𝜂

−sign(Tf1)

+nf2Tf2𝜂

−sign(Tf2)

)

(17)

T1_min(n1(i))

≤

T1(n1(i))

≤

T1_max(n1(i))

(18)

n1_min

≤

n1(i)

≤

n1_max

(19)

T2_min(n2(i))

≤

T2(n2(i))

≤

T2_max(n2(i))

(20)

n2_min

≤

n2(i)

≤

n2_max

(21)

n1(i)

⋅

n2(i)

≥

TABLE 5 Driving cycles used to solve the simplified energy

management issue

No. Name No. Name

1 AQMDRTC2 7 CUEDCME

2 ARB02 8 JC08

3 INRETS 9 NEDC

4 REP05 10 NRTC

5 Viking 11 RTS95

6 WHM 12 WLTC

FIGURE 9 Offline obtained optimal working mode sequences of

the upper coupling layer

020406080 100 120 140 160

Vehicle speed (km/h)

-2700

-1800

-900

900

1800

2700

Mode SA

Mode TC

ECC of vehicle

FIGURE 10 Offline obtained optimal working mode sequences

of the lower coupling layer

CHEN Et al.

The extracted basic working mode decision rules of the

upper coupling layer are shown in Figure 11. An additional

stipulation is added in the extraction of the basic work-

ing mode decision rules of the lower coupling layer. That

is, when the vehicle speed exceeds the snapback speed of

mode SM1, that is, 45km/h, mode SM1 will be disabled.

The snapback speed of mode SM1 is corresponding to the

base rotation speed of M1. Thus, for the area in the dotted

box in Figure 10, modes SM1 and SC can be separated only

via a plumb line. The extracted basic working mode deci-

sion rules of the lower coupling layer are shown in Figure

12. The extracted basic working mode decision rules of the

upper and lower coupling layers are, respectively, formu-

lated as follows:

and

where, v is the vehicle speed and Tv is the torque.

4.2

Construction of auxiliary working

mode decision rules

If the working mode of the HCEP is determined only depends

on basic decision rules, frequent mode switching is inevitable.

Therefore, this paper draws lessons from the principle of delay

shift of automatic mechanical transmissions. Concretely, the aux-

iliary working mode decision rules are constructed by translating

the basic working mode decision rules, as shown in Figures 11 and

12. Herein, green arrows represent the translation directions. Thus,

the area between the basic and auxiliary working mode decision

rules forms the mode- hold- band that can avoid the mode switch-

ing when the working point bouncing around decision thresholds.

And, the frequency of mode switching is significantly reduced.

The auxiliary working mode decision rules of the upper and lower

coupling layers can be, respectively, expressed as follows:

and

(22)

=9.45207

⋅

v+57.2367 B_U1

v=1.39318⋅v+

289.074 B_U2

440 B_U3

v=−11.4629 ⋅v−

63.3747 B_U4

v=−0.847 ⋅v−

461.464 B_U5

=−

525 B_U6

(23)

=−0.588416

⋅

v+895 B_L1

v=8.84695⋅v+

255.877 B_L2

880 B_L3

45 B_L4

v=7.34082⋅v−

179.615 B_L5

v=−

1050 B_L6

45 B_L7

=−

8.1243

⋅v+

177.131 B_L8

(24)

=9.45207

⋅

(v−Δv)+57.2367−ΔT

D_U1

v=1.39318⋅(v−Δv)+289.074 −ΔTv

D_U2

v=440−ΔTv

D_U3

v=−11.4629 ⋅(v−Δv)−63.3747+ΔTv

D_U4

v=−0.847 ⋅(v−Δv)−461.464+ΔTv

D_U5

=−525 +ΔT

vD_U6

(25)

=−0.588416

⋅

(v+Δv)+895−ΔT

D_L1

v=8.84695⋅(v+Δv)+255.877 −ΔTv

D_L2

v=880−ΔTv

D_L3

=45−Δv

D_L4

v=7.34082⋅(v+Δv)−179.615 +ΔTv

D_L5

v=−1050 +ΔTv

D_L6

=45−Δv

D_L7

=−8.1243 ⋅(v+Δv)+177.131−ΔT

vD_L8

FIGURE 11 Online working mode decision rules of the upper

coupling layer

020406080100 120140 160

Vehicle speed (km/h)

-2700

-1800

-900

900

1800

2700

Basic decision rules

Auxiliary decision rules

ECC of vehicle

FIGURE 12 Online working mode decision rules of the lower

coupling layer

020406080100 120140 160

Vehicle speed (km/h)

-2700

-1800

-900

900

1800

2700

Basic decision rules

Auxiliary decision rules

ECC of vehicle

CHEN Et al.

where, Δv and ΔTv are the translation quantities of the vehicle

speed and torque, respectively.

4.3

Online decision logics of the working

mode of the HCEP

The working mode decision logics of the upper coupling

layer are shown in Figure 13. When the working mode of the

last sampling time is SA, B_Us 1- 6 are used as the decision

thresholds of the current working mode; otherwise, D_Us 1- 6

are used as the decision thresholds.

The working mode decision logics of the lower coupling

layer are shown in Figure 14. When the working mode of the

last sampling time is SM1, B_Ls 1- 8 is used as the decision

thresholds of the current working mode; when the working

mode of the last sampling time is SM2, D_Ls 1- 8 is used as

the decision thresholds; and when the working mode of the

last sampling time is SC, B_Ls 1- 3, 6 and D_Ls 4- 5, 7- 8 are

used as the decision thresholds.

OPTIMIZATION OF THE

AUXILIARY WORKING MODE

DECISION RULES

Although wide gaps between the basic and auxiliary working

mode decision rules, that is, large Δv and ΔTv, can greatly

reduce the mode switching frequency, the energy- saving

FIGURE 13 Working mode decision thresholds of the upper

coupling layer: (A) Previous working mode is SA. (B) Previous

working mode is TC

(A)

(B)

FIGURE 14 Working mode decision thresholds of the lower

coupling layer: (A) Previous working mode is SM1. (B) Previous

working mode is SM2. (C) Previous working mode is SC

(B)

(C)

(A)

CHEN Et al.

effect will suffer deterioration. Moreover, an EMS usually

has different optimal control parameters for different driving

conditions.31- 32 Therefore, it is necessary to optimize Δv and

ΔTv for different driving conditions.

5.1

Classification of driving conditions

Actual traffic situations can be described by the combina-

tion of the following four types of representative driving con-

ditions. The first type is the urban congestion condition, as

shown in Figure 15A, in which the vehicle speed is almost

always lower than 50km/h, while accompanied by frequent

starting and stopping. The second type is the urban unim-

peded condition, as shown in Figure 15B, in which both the

peak and average vehicle speed are improved compared with

the urban congestion condition. The third type is suburban

condition, as shown in Figure 15C, in which the average

vehicle speed is high and the peak vehicle speed is usually

close to 100km/h. The last type is the highway condition, as

shown in Figure 15D, in which the average vehicle speed is

very high and the peak vehicle speed is generally larger than

100km/h.

In this study, four groups of driving cycles listed in Table6

are selected to, respectively, express the above four types of

representative driving conditions.

5.2

Optimization of Δv AND ΔTv for

different driving conditions

The optimization of Δv and ΔTv can be regarded as a single-

objective multi- constraint issue. The objective can be written

as follows:

where, Nms denotes the mode switching times. The first con-

straint is that the increasing rate of the energy consumption can-

not exceed 0.5%. That is

where, Ewithout is the energy consumption of the HCEP when

the determination of working modes only relies on the basic

decision rules. Ewith is the energy consumption of the HCEP

when the determination of working modes relies on both the

basic and auxiliary decision rules. The second constraint is that

Δv and ΔTv obedient to

where, Tv_max and vmax are the maximum design output torque

and maximum design speed of the vehicle, respectively.

In this paper, the enumeration method is used to search

the best combinations of Δv and ΔTv for each type of repre-

sentative driving condition. The search results are listed in

Table 7.

ONLINE ADAPTIVE EMS OF

THE HCEP

6.1

Driving condition recognizer

In order to get more samples to train the driving condition

recognizer (DCR) used to identify the near future driving

condition, the driving cycles listed in Table 6 are divided

into 334 vehicle speed profile segments by the composite

equipartition method shown in Figure 16. Each segment is

a training sample. The characteristics and categories of the

334 training samples are, respectively, used as the input and

output databases to train the DCR. The categories of training

samples are known. The characteristics of training samples

can be expressed by the 25 parameters listed in Table 8. It

needs to be explained that the service coefficient of the vehi-

cle power capability is the ratio between the vehicle demand

power and the maximum design power of the vehicle.

If the 25 parameters are directly used to describe the

characteristics of training samples, the input database is

25- dimensional. Such dimension is too large for the driving

condition identification. In fact, the 25 parameters are not

independent and the principal component analysis (PCA)

can be used to treat them in dimension reduction. After PCA

treatment, the original 25 parameters become 25 principal

(26)

F=min(Nms)

(27)

with

−E

without

≤0.5

(28)

≤

ΔT

v≤

0.15T

max

≤Δ

≤

0.15vmax

FIGURE 15 Representative driving conditions: (A) Urban

congestion condition. (B) Urban unimpeded condition. (C) Suburban

condition. (D) Highway condition

(A) (B)

CHEN Et al.

components. Table 9 shows the top 10 principal components

sorted from large to small and their cumulative variance

contribution rates (CVCRs). As can be seen, the first seven

principal components contain 85.85% of the information

contained in the original 25 parameters. In other words, we

can only use the first seven principal components to describe

the characteristics of training samples. Thus, the dimension

of the input database is reduced from 25 to 7.

Due to the generalized regression neural network (GRNN)

has fast convergence speed and strong adaptability to data

with poor accuracy, it is chosen to construct the DCR to on-

line recognize the near future driving condition. The con-

structed GRNN- based DCR based on the seven principal

components can be expressed as follows:

where, X and y are the characteristic vector and predictive

category of a vehicle speed profile segment to be recognized,

respectively. Xi and yi are the characteristic vector and cate-

gory of the ith training sample, respectively. σ is the smoothing

factor.

In the GRNN- based DCR, σ is the only parameter that

can be controlled and should be controlled. As shown in

Figure 17, the prediction accuracy of the GRNN- based DCR

roughly decreases with the increase of σ, and the highest

prediction accuracy reaches 95.45%. In general, the closer σ

is to zero, the worse the generalization ability of the GRNN-

based DCR is. Therefore, the optimal value of σ is deter-

mined to be 0.16.

In addition, we also train another GRNN- based DCR

based on the original 25 parameters. For the sake of distinc-

tion, the GRNN- based DCR based on the original 25 pa-

rameters is called GRNN- based DCR1 here. The change of

the prediction accuracy of the GRNN- based DCR1 with σ is

also shown in Figure 17. It can be seen that the GRNN- based

DCR and DCR1 have similar prediction accuracy, which in-

dicates that the dimensionality reduction of the original 25

parameters is reasonable.

(29)

X=[x1,x2,...,x7]

i=[xi1,xi2,...,xi7]Ti=

1,2,...,334

y=SN

SN=

334

∑

i=1

yiexp[−(X−Xi)T(X−Xi)

2𝜎2]

SD=

334

∑

i=1

exp[ −(X−Xi)T(X−Xi)

2𝜎2]

Name Category Name Category

BUSRTE Urban congestion Artemis Rural Road Suburban

MANHATTAN Urban congestion IM240 Suburban

NYCC Urban congestion WVUINTER Suburban

New York BUS Urban congestion EUDC LOW Suburban

NurembergR36 Urban congestion CUEDC SPC240 Suburban

WVUSUB Urban unimpeded REP05 Highway

ARTERIAL Urban unimpeded HL07 Highway

EUDC_LOW Urban unimpeded HHDDT65 Highway

INDIA HWY Urban unimpeded US06 HWY Highway

WHM Urban unimpeded Artemis Motorway Highway

TABLE 6 Representative driving

condition libraries

TABLE 7 Best combinations of Δv and ΔTv

Category of

driving conditions

Upper coupling

layer

Lower coupling

layer

Δv

(km/h)

ΔTv

(Nm)

Δv

(km/h)

ΔTv

(Nm)

Urban congestion 12 90 16 190

Urban unimpeded 23 70 21 280

Suburban 24 280 24 280

Highway 24 300 15 280

FIGURE 16 Composite equipartition method used to obtain

training samples

CHEN Et al.

6.2

Online adaptive EMS of the HCEP

As shown in Figure 18, the developed online adaptive EMS

includes three parts. They are GRNN- based DCR trained in

Section 6.1, online working mode decision rules established

in Sections 4 and 5, and simple power allocation method in-

troduced in Section 3.2, respectively. In control, the devel-

oped EMS can be interpreted as the following steps. First,

a period of vehicle speed profile is recorded. Second, the

characteristics of the recorded vehicle speed profile are cal-

culated. Then, the trained GRNN- based DCR is used to rec-

ognize the category of current driving condition. And, Δv and

ΔTv are updated online according to the identified category.

Subsequently, the working mode decision logics illustrated

in Figures 13 and 14 are used to determine the target working

modes of the upper and lower coupling layers, respectively.

Finally, the introduced torque and rotation speed distribution

submethods, as stated in Section 3.2, are, respectively, used

to determine the target torque distribution of the upper cou-

pling layer and target rotation speed distribution of the lower

coupling layer.

VERIFICATION

Table 10 lists three groups of vehicle energy consumption

under the 12 comprehensive driving conditions. The first

group of energy consumption is obtained by traversing the

torque and rotation speed allocations of the HCEP (referred

to as traversal- based EMS). The second group of energy

consumption is obtained according to the following way:

First, the energy management issue of the HCEP is simpli-

fied as described in Section 3.2, and then, the simplified

issue is solved by the DP and the energy consumption is

TABLE 8 Original parameters used to express driving conditions

Parameter No.

Average vehicle speed 1

Peak vehicle speed 2

S.D. of the vehicle speed 3

Percentage of time that the vehicle speed is in 0 to 40 km/h 4

Percentage of time that the vehicle speed is in 40 to 70 km/h 5

Percentage of time that the vehicle speed is in 70 to 100

km/h

Percentage of time that the vehicle speed is above 100 km/h 7

Average acceleration 8

Peak acceleration 9

S.D. of the acceleration 10

Percentage of time that the acceleration is in 0 to 1 m/s^2 11

Percentage of time that the acceleration is in 1 to 2.5 m/s^2 12

Percentage of time that the acceleration is above 2.5 m/s^2 13

Average deceleration 14

Peak deceleration 15

S.D. of the deceleration 16

Percentage of time that the deceleration is in 0 to 1 m/s^2 17

Percentage of time that the deceleration is in 1 to 2.5 m/s^2 18

Percentage of time that the deceleration is above 2.5 m/s^2 19