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Energy Sci Eng. 2021;00:1–18.

1
wileyonlinelibrary.com/journal/ese3
1

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
XianbaoChen

HongyuShu

YitongSong
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.
© 2021 The Authors. Energy Science & Engineering published by the Society of Chemical Industry and John Wiley & Sons Ltd.
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
2

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.
2

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

3
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)
n
w=
n
1
(1
+
k1)k2
(4)
Tw=T1(1 +k1)k2
𝜂
t
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)
M1
B1
B2
B2
M2
Tyre
Tyre
PGT 1
PGT 2
SY
M2
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)
4

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.
3

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)
n
w=
n
1
+k
1
n
2
(1
+
k1)k2
(6)
T
w=T1(1 +k1)k2𝜂t=
T
2
(1 +k
1
)k
2𝜂t
k1
(7)
n
w=
k
1
n
2
(1
+
k1)k2
(8)
T
w=
T
2
(1 +k
1
)k
2𝜂
t
k1
(9)
x
i+1
=f(x
i
,u
i
)i=0,1,2,...,N−1
ui=[ui_1,ui_2 ,ui_3]
xi
+
1
=[x
i
+
1_1
,x
i
+
1_2
,x
i
+
1_3
,x
i
+
1_4
,x
i
+
1_5
,x
i
+
1_6]
(10)
u
i_1 =
T
f_i_tar
T
f_i_tar
+T
r_i_tar
(11)
u
i_2 =
n
f_M1_tar
n
f_M1_tar
+k
1
n
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)

5
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]. Figure6
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)
u
i_3 =
n
r_M1_tar
n
r_M1_tar
+k
1
n
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
60
60
85
85
92
92
60
60
85
85
92
92
0 3000 6000 9000 12000
Rotation speed (rpm)
16
12
8
4
0
4
8
12
1
6
Torque (Nm)
Efficiency (%)
FIGURE 5 Efficiency MAP of M2 in a wheel
60
60
85
85
92
92
60
60
85
85
92
92
0 1500 3000 4500 6000 7500 9000
Rotation speed (rpm)
90
60
30
0
30
60
90
Torque (Nm)
Efficiency (%)
6

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)
X
i+1
=U
i
i=0,1,2,...,N−1
Ui=[Ui_1,Ui_2 ]
X
i
+
1
=[X
i
+
1_1
,X
i
+
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)
0
500
1000
1500
2000
Torque (Nm)
Rear axle in SM1
Rear axle in SM2
Rear axle in SC
Vehicle
(n3, T3)
A
B
C
(n2, T2)
(n1, T1)
FIGURE 7 Optimal rotation speed distribution of M1 under the
mode SC

7
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
U
N−1
[L(XN−1,UN−1
)]
(15)
J∗
i
(
Xi
)
=min
U
i
[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
8

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.
4

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)
L
(Xi,Ui)=
2Δ
t
9550 (nr1Tr1𝜂
−sign(Tr1)
r1+nr2Tr2𝜂
−sign(Tr2)
r2
+
nf1Tf1𝜂
−sign(Tf1)
f1
+nf2Tf2𝜂
−sign(Tf2)
f2
)
(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)
≥
0
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
0
900
1800
2700
Mode SA
Mode TC
ECC of vehicle
FIGURE 10 Offline obtained optimal working mode sequences
of the lower coupling layer

9
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)
T
v
=9.45207
⋅
v+57.2367 B_U1
T
v=1.39318⋅v+
289.074 B_U2
T
v=
440 B_U3
T
v=−11.4629 ⋅v−
63.3747 B_U4
T
v=−0.847 ⋅v−
461.464 B_U5
Tv
=−
525 B_U6
(23)
T
v
=−0.588416
⋅
v+895 B_L1
T
v=8.84695⋅v+
255.877 B_L2
T
v=
880 B_L3
v
=
45 B_L4
T
v=7.34082⋅v−
179.615 B_L5
T
v=−
1050 B_L6
v
=
45 B_L7
Tv
=−
8.1243
⋅v+
177.131 B_L8
(24)
T
v
=9.45207
⋅
(v−Δv)+57.2367−ΔT
v
D_U1
T
v=1.39318⋅(v−Δv)+289.074 −ΔTv
D_U2
T
v=440−ΔTv
D_U3
T
v=−11.4629 ⋅(v−Δv)−63.3747+ΔTv
D_U4
T
v=−0.847 ⋅(v−Δv)−461.464+ΔTv
D_U5
Tv
=−525 +ΔT
vD_U6
(25)
T
v
=−0.588416
⋅
(v+Δv)+895−ΔT
v
D_L1
T
v=8.84695⋅(v+Δv)+255.877 −ΔTv
D_L2
T
v=880−ΔTv
D_L3
v
=45−Δv
D_L4
T
v=7.34082⋅(v+Δv)−179.615 +ΔTv
D_L5
T
v=−1050 +ΔTv
D_L6
v
=45−Δv
D_L7
Tv
=−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
0
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
0
900
1800
2700
Basic decision rules
Auxiliary decision rules
ECC of vehicle
10

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.
5

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)

11
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 Table6
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.
6

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)
E
with
−E
without
E
without
≤0.5
%
(28)
0
≤
ΔT
v≤
0.15T
v_
max
0
≤Δ
v
≤
0.15vmax
FIGURE 15 Representative driving conditions: (A) Urban
congestion condition. (B) Urban unimpeded condition. (C) Suburban
condition. (D) Highway condition
(A) (B)
(C) (D)
12

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]
T
X
i=[xi1,xi2,...,xi7]Ti=
1,2,...,334
y=SN
SD
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

13
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.
7

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
6
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
Percentage of time that the service coefficient of the vehicle
power capacity is below  0.5
20
Percentage of time that the service coefficient of the vehicle
power capacity is in  0.5 to  0.15
21
Percentage of time that the service coefficient of the vehicle
power capacity is in  0.15 to 0
22
Percentage of time that the service coefficient of the vehicle
power capacity is in 0 to 0.15
23
Percentage of time that the service coefficient of the vehicle
power capacity is in 0.15 to 0.5
24
Percentage of time that the service coefficient of the vehicle
power capacity is above 0.5
25
TABLE 9 Obtained top ten principal components
No. Variances CVCRs (%)
1 8.1322 32.5288
2 4.4802 50.4495
3 3.1453 63.0307
4 2.0813 71.3558
5 1.478 77.2677
6 1.2214 82.1533
7 0.9252 85.8542
8 0.9096 89.4927
9 0.5434 91.6664
10 0.3932 93.2391
FIGURE 17 Variation of the prediction accuracies of the GRNN
based DCR and DCR1 with σ
14

CHEN Et al.
calculated (referred to as DP based EMS). The third group
of energy consumption is derived from the developed on
line adaptive EMS. Compared with the traversal based
EMS, the energy consumption caused by the DP based
EMS almost does not increase, which once again indicates
that the introduced simple power allocation method does
FIGURE 18 Developed online adaptive EMS for the HCEP
Original energy
management issue
Simplified energy
management issue
Optimal working
mode sequences
Basic working
mode decision rules
Auxiliarywor king
mode decision rules
Online wo rking
mode decision rules
Simple power
allocation method
Representative
driving conditions
334 training
samplesGRNNbased DCR
PCA
and
GRNN
Starting
Collecting a period of
vehicle speed profile
Calculating characteristics
of the vehicle speed pr of ile
Recognizing thecurrent
driving condition
Updating Δvand ΔT
v
online
Determining target
working mode s
Determiningtarget po wer
distribution
Ending
Entering the next
control time
Translatingand
optimization
composite equipartition
Onli ne adaptive energy management of th e HCEP
DP
SVM
Cycle No.
Vehicle energy consumption (kWh)
Increasing
rate (%)
Traversal based
EMS
DP based
EMS
Developed
EMS
1 1.007 1.009 1.014 0.70
2 4.770 4.778 4.808 0.80
3 3.455 3.458 3.472 0.40
4 4.857 4.861 4.880 0.47
5 3.028 3.029 3.030 0.07
6 0.955 0.957 0.960 0.52
7 1.336 1.340 1.357 1.57
8 0.758 0.760 0.767 1.19
9 1.213 1.214 1.217 0.33
10 0.842 0.844 0.853 1.31
11 1.842 1.846 1.867 1.36
12 2.964 2.967 2.999 1.18
TABLE 10 Energy consumption
comparison for different EMSs

15
CHEN Et al.
not destroy the energy saving potential of the HCEP, and
the simplification of the energy management issue of the
HCEP is reasonable.
As expected, the energy consumption caused by the de
veloped online adaptive EMS only has a slight increase com
pared to these caused by the traversal based and DP based
EMSs. And, compared with the DP based EMS, the mode
switching times of the online adaptive EMS are greatly re
duced, as shown in Table 11. These comparisons show that
the developed online adaptive EMS can not only maintain
the energy efficiency of the HCEP, but also can significantly
reduce the mode switching frequency.
In order to further verify the effectiveness of the devel
oped online adaptive EMS, a test driving cycle including
traffic characteristics of the urban congestion, urban un
impeded, suburban, and highway is established, as shown
in Figure 19. The recognition result of the GRNN based
DCR is also shown in Figure 19. The numbers 1, 2, 3,
and 4 denote the conditions of the urban congestion, urban
unimpeded, suburban, and highway, respectively. The rec
ognition result shows that the constructed GRNN based
DCR can identify the driving condition accurately. In
addition, the energy consumption curves of the traversal
based EMS, DP based EMS, and online adaptive EMS are
drawn in Figure 20. As expected, these energy consump
tion curves are almost overlap. Moreover, the working
mode sequences of the upper and lower coupling layers
determined by the developed EMS are shown in Figures
21 and 22, respectively. In Figure 21, the numbers 1 and 2
denote modes SA and TC, respectively. In Figure 22, the
numbers 1, 2, and 3 denote modes SM1, SM2, and SC,
respectively.
FIGURE 21 Working mode sequences of the upper coupling
layer
TABLE 11 Comparison of mode switching times for different
EMSs
Cycle
No.
DP based
EMS
Developed
EMS
Decreasing
rate (%)
1 310 157 49.35
2 288 192 33.33
3 284 186 34.51
4 172 105 38.95
5 58 24 58.62
6 162 89 45.06
7 567 269 52.56
8 188 69 63.30
9 99 54 45.45
10 453 315 30.46
11 262 166 36.64
12 248 149 39.92
FIGURE 19 Test driving cycle and recognition result of the
GRNN based DCR
FIGURE 20 Comparison of energy consumption for different
EMSs
16

CHEN Et al.
8

CONCLUSION
In this paper, an online adaptive EMS is developed for the
promising HCEP. The developed EMS can not only ensure
the energy saving effect of the HCEP, but also can effec
tively avoid frequent working mode switching, as well as has
adaptive ability to different driving conditions. The research
in this paper can provide reference for the development of
EMSs for electric powertrains that simultaneously operates
in the torque coupled mode and rotational speed coupled
mode.
First, by introducing simple torque and rotation speed al
location submethods, the energy management of the HCEP
is transformed from the optimization in a three dimensional
continuous space to the optimization in a set containing only
six elements. After that, the DP is used to offline solve the
simplified energy management issue, and the optimal work
ing mode sequences of the HCEP are obtained.
Second, the online working mode decision rules of the
HCEP are established according to the obtained optimal
working mode sequences. And, the auxiliary rules in the
working mode decision rules are optimized for different
types of driving conditions.
Third, the PCA is utilized to reduce the dimension of the
characteristic parameters used to express driving conditions.
After that, the seven dimensional GRNN based DCR with
the highest prediction accuracy of 95.45% is trained. On the
basis of the trained DCR, established working mode deci
sion rules, and introduced torque and rotation speed alloca
tion submethods, an online adaptive EMS is developed for
the HCEP.
Compared with the traversal based EMS that is optimal
in term of energy saving, the energy consumptions obtained
from the developed online adaptive EMS increase only
slightly, and the increasing rate is 0.07% to 1.57% under
12 comprehensive driving cycles. Compared with the DP
based EMS which has similar energy saving effect with the
traversal based EMS, the mode switching times caused by
the developed online adaptive EMS are greatly reduced, with
a decreasing rate of 30.46% to 63.30%. These comparisons
validate the effectiveness of the developed online adaptive
EMS.
ACKNOWLEDGMENTS
This work was supported by the National Natural Science
Foundation of China under Grant 51975069 and the Natural
Science Foundation of Chongqing (China) under Grant
cstc2018jcyjAX0077.
ORCID
Hongyu Shu https://orcid.org/0000000181572892
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AUTHOR BIOGRAPHIES
Xianbao Chen graduated
as a vehicle engineer from
the School of Automotive
Engineering, Chongqing
University (2016), and is
currently a Ph.D. student
at the School of
Automotive Engineering,
Chongqing University.
His interests include elec
tric machines, electric
powertrain, especially in wheel motor powertrain.
18

CHEN Et al.
Hongyu Shu received his
Ph.D. in mechanical engi
neering from Chongqing
University, Chongqing,
China, in 1999. He is cur
rently a professor of the
State Key Laboratory of
Mechanical Transmission,
Chongqing University,
China. His research inter
ests include electric vehi
cles, mechatronics, vehi
cle noise, vibration and harshness, and vehicle system
dynamics and control. He is currently a senior member of
the Chinese Society of Mechanical Engineering.
Yitong Song graduated as a
vehicle engineer from the
College of Mechanical
and Vehicle Engineering,
Hunan University (2016),
and is currently a Ph.D.
student at the School of
Automotive Engineering,
Chongqing University.
His main interests are inte
grated chassis control
techniques for electric ve
hicles. He is currently working on integrated chassis con
trol based on four wheel steering and an active differential
braking system of electric vehicles.
How to cite this article: Chen X, Shu H, Song Y.
Development of an online adaptive energy
management strategy for the novel hierarchical
coupled electric powertrain. Energy Sci Eng.
2021;00:1– 18. https://doi.org/10.1002/ese3.931