Investigating adaptive-ECMS with velocity forecast ability for hybrid electric vehicles

Applied Energy xxx (2016) xxx–xxx

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Investigating adaptive-ECMS with velocity forecast ability for hybrid electric vehicles Chao Sun, Fengchun Sun, Hongwen He ⇑ National Engineering Laboratory for Electric Vehicles, Collaborative Innovation Center of Electric Vehicles in Beijing, Beijing Institute of Technology, China

h i g h l i g h t s
The convergence principle of equivalence factor searching for the adaptive-ECMS is modified and its oscillation is solved.
A radial basis function neural network based velocity predictor is constructed, its accuracy and sensitivity is studied.
The developed velocity predictor is incorporated with the adaptive-ECMS to improve the fuel economy by comparison study.
The fuel consumption is decreased by over 3% compared with traditional adaptive-ECMS when no velocity forecast is employed.

a r t i c l e

i n f o

Article history: Received 14 August 2015 Received in revised form 18 January 2016 Accepted 3 February 2016 Available online xxxx Keywords: Adaptive ECMS Velocity forecast Neural network Fuel economy Hybrid electric vehicles

a b s t r a c t Energy management strategy is crucial in improving the fuel economy of hybrid electric vehicles (HEVs). This paper targets at evaluating the role of velocity forecast in the adaptive equivalent consumption minimization strategies (ECMS) for HEVs. A neural network based velocity predictor is constructed to forecast the short-term future driving behaviors by learning from history data. Then the velocity predictor is combined with adaptive-ECMS to provide temporary driving information for real-time equivalence factor (EF) adaptation. Compared with traditional adaptive-ECMS, which uses historical driving profile for EF estimation, the proposed strategy is able to foresee the change of the driving behaviors and adjust the EF more reasonably. Simulation results show that, compared with traditional adaptive-ECMS, the proposed improvement with velocity forecast incorporated is able to achieve better fuel economy and more stable battery state of charge (SOC) trajectory, with a fuel consumption reduction by over 3%. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction 1.1. HEV and energy management HEVs are equipped with at least two different energy sources for propulsion purposes [1,2]. The additional degrees of freedom provided by powertrain hybridization enable reduced fuel consumption and tailpipe emissions over conventional internalcombustion-engine (ICE) vehicles [3]. The increased configuration complexity, however, poses a challenge for efficiently controlling the power flow between multiple on-board energy sources. Sophisticated control methods have been investigated to provide better fuel consumption performances in HEVs [4]. Among them, the equivalent consumption minimization strategy (ECMS) is an instantaneous approach derived from the Pontryagin’s Minimum Principle (PMP) [5]. Due to fast computation and no

⇑ Corresponding author.

requirement for the global power request of the driving profile, ECMS is potentially implementable in practice [6]. Generally speaking, ECMS is able to identify a series of solution candidates for the HEV energy management problem, by establishing a set of necessary conditions from PMP [7]. The solution candidates not only must satisfy these necessary conditions, but also are restricted by the defined state constraints. Being interacted by the above two principles, the optimal control strategy can be found by trial-and-error. However, in ECMS, the optimal control solution can be achieved only with a perfect tuning of the equivalence factor (EF) [8]. The EF is used to scale between the electrical cost and fuel cost in the Hamiltonian function defined according to the minimum principle, and cannot be pre-determined a prior. Additionally, ECMS is very rigid. Slight deviations from the optimal EF values may lead to unacceptable operations of the vehicle outside the SOC boundaries. Based on the above concern, real-time tuning of the equivalence factor is proposed as a superior application of ECMS, which is also called the adaptive-ECMS. An adaptive-ECMS approach is

E-mail address: [email protected] (H. He). http://dx.doi.org/10.1016/j.apenergy.2016.02.026 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Sun C et al. Investigating adaptive-ECMS with velocity forecast ability for hybrid electric vehicles. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2016.02.026

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developed in Ref. [9] to facilitate the ECMS method. The main idea is to estimate the EF over the current driving cycle block in real-time, and the adjusted EF is implemented to the next cycle block. Thus, the adaptive-ECMS energy management strategy operates along a set of block-EFs sequentially, and consequently is able to achieve fuel performance close to the global optimum solution. This procedure involves the acquirement of current driving profile information, which introduces the discussion over velocity forecast. 1.2. Velocity forecast As the gradient information can be pre-measured and stored in 3-D maps, we assume the road grade equals to zero for simplicity. To periodically estimate the block-EFs, current driving profile information needs to be provided for the optimal EF searching in real-time. Considering that the computed block-EF is to be implemented in the next driving cycle block, the best case is that the next cycle block profile is perfectly known and used for EF estimation. However in real driving circumstance, the next cycle block profile is very difficult to obtain. To compromise, employing historical driving cycle profile for current block-EF estimation has been proposed and studied [9]. There is literature reporting that driving cycle forecast is required in adaptive-ECMS [10]. Nevertheless, no detailed study on combining online velocity forecast technique with the adaptive-ECMS and exploiting its performance has been proposed to the authors’ best knowledge. There are several vehicle velocity forecast methods existed in literature, and are mainly used in model predictive control of HEVs and intelligent vehicle areas. Exponentially varying velocity forecast in Ref. [11] and stochastic Markov-chain velocity forecast in Refs. [12,13] are typically used in predictive energy management of HEVs. Artificial neural network (ANN) based velocity forecast is compared with the above two methods by the authors, and the conclusion is that the velocity predictor formulated based on ANN performances the best accuracy [14]. SUMO simulator model is a well-known microscopic traffic simulator and can also be used for velocity forecast in intelligent transportation systems [15]. The intelligent driver model (IDM) is developed in Ref. [16], and relies on the computation of a desired distance between the ego-vehicle and the vehicle in front. The SUMO and IDM velocity forecast methods require the front vehicle information and will increase the hardware cost of the vehicle. Thus we consider the velocity forecast approaches in which no additional sensor information is needed, then the velocity forecast problem will be a time series forecasting problem [17]. In Ref. [14], the velocity predictors are compared for model predictive control of HEVs. However, this paper intends to further study the effectiveness of velocity forecast method in improving the performance of adaptive-ECMS. Based on the study in [14], we select radial basis function neural network (RBF-NN) for the vehicle prediction purpose in this paper. 1.3. Main contributions In this paper, the neural network velocity forecast technique is firstly introduced to the adaptive-ECMS energy management of HEVs in the literature. The target is to further improve the adaptive-ECMS fuel economy by using the predicted velocity profiles for EF adaptation. Specifically, a RBF-NN based velocity forecast model is formulated. By learning the driving behaviors from the sample driving profiles, the velocity predictor is able to forecast the future velocity with acceptable errors. The second contribution and novelty of this paper is that the EF adaptation law in adaptiveECMS is further modified to reduce the iteration oscillation in the optimal EF searching. The stability of the EF adaptation is improved. The role of velocity forecast in adaptive-ECMS for HEV

energy management is investigated by comparing it with when historical driving information is used for EF estimation, and when future driving information is known a prior. Although the foregoing contributions are made specifically for energy management of HEVs, the proposed approach extends to plug-in HEVs with proper modification. The remainder of the paper is organized as follows. In Section 2, the configuration of a power-split HEV and basic ECMS are formulated. Section 3 develops a modified adaptive-ECMS approach, and studied the importance of future driving profile. In Section 4, the velocity forecasting performance is analyzed, and the best forecast length is determined. Simulation results are illustrated in Section 5, followed by key conclusions in Section 6. 2. Energy management problem formulation 2.1. Control-oriented powertrain model Power-split HEV is selected as the study object in this paper, since it has advantages of both series and parallel configurations [18], and is one of the most commercially successful HEV powertrains [19]. Planetary gear sets are often used to implement the power splitting functionality. The engine and generator (M/G1) are connected to the planet carrier and the sun gear, respectively. A torque coupler is used to combine the ring gear with the motor (M/G2) to power the final drive. Fig. 1 demonstrates the structure and lever diagram of the planetary gear system, from which the kinematic constraint of the angular speeds of the ring gear, sun gear and planet carrier can be derived as,

xs S þ xr R ¼ xc ðS þ RÞ

ð1Þ

where S and R are the radii of the sun gear and the ring gear, respectively. Angular speeds of the ring, sun, and carrier gears are denoted as xr ; xs and xc , respectively. M/G1 is used to transform the engine power into electricity, which can further charge the battery or directly supply M/G2. By neglecting the inertia of pinion gears and assuming that all the powertrain shafts are rigid, inertial dynamics of the powertrain can be derived as,

J M=G1

dxM=G1 ¼ T M=G1 þ FS dt

dxeng ¼ T eng  FðS þ RÞ dt dxM=G2 J M=G2 ¼ T M=G2  ðT axle =g f Þ þ FR dt

J eng

ð2Þ ð3Þ ð4Þ

where JM=G1 ; Jeng and JM=G2 are inertias of M/G1, engine and M/G2, respectively; T eng ¼ T c is the engine torque; T M=G1 ¼ T s and T M=G2 ¼ T r are M/G1 and M/G2 torques (positive in motoring mode), respectively; F represents the internal force on pinion gears; g f is the gear ratio of the final drive; T axle is the torque produced from powertrain on the drive axle. To reduce the complexity of the dynamics for a control-oriented model, inertial losses on the left side of Eqs. (2)–(4) are ignored. The rotation speed of M/G2 and the axis torque requirement are obtained by,

xM=G2 ¼ m

gf V Rwheel

dV T axle þ T brake 1 ¼  mg sinðhÞ  qAC d V 2  C r mg cosðhÞ dt 2 Rwheel

ð5Þ ð6Þ

where Rwheel is the wheel radius; V is the vehicle velocity; m is the vehicle mass; T brake is the friction brake torque; g is gravitational acceleration; h denotes the road grade and is assumed to be zero; 1 qAC d is the aerodynamic drag resistance; C r represents the rolling 2 resistance coefficient.

Please cite this article in press as: Sun C et al. Investigating adaptive-ECMS with velocity forecast ability for hybrid electric vehicles. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2016.02.026

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Ring Gear ωc

Sun Gear

ωr

ωs

Tr, ωr

Ring Gear

max Imin batt 6 I batt 6 I batt ;

S

Tc, ωc

Pinion Gear

T min eng

Carrier

Sun Gear

6 T eng 6

T min M=G1 R

Carrier

SOCmin 6 SOC 6 SOCmax ;

Ts, ωs

Fig. 1. Structure and lever diagram of the planetary gear system equipped in a power-split HEV.

T max eng ;

6 T M=G1 6

max Pmin batt 6 P batt 6 P batt ; max xmin eng 6 xeng 6 xeng ; min xM=G1 6 xM=G1 6 xmax M=G1 ;

T max M=G1 ;

max T min M=G2 6 T M=G2 6 T M=G2 ;

ð17Þ

max xmin M=G2 6 xM=G2 6 xM=G2 ;

SOCðTÞ ¼ SOCð0Þ: According to PMP, several necessary conditions are satisfied if the control law u ðtÞ is optimal,
u ðtÞ minimizes the Hamiltonian of the optimal control problem at each time instance,

At each time instant, the supervisory controller tries to find the optimal split between the engine, M/G1 and M/G2 so as to minimize the fuel consumption. The fuel rate of the engine and operation efficiencies of M/G1 and M/G2 are extracted from empirical maps, indexed by angular speeds torques,

_ fuel ¼ w1 ðxeng ; T eng Þ m

ð7Þ

gM=G1 ¼ w2 ðxM=G1 ; T M=G1 Þ

ð8Þ

gM=G2 ¼ w3 ðxM=G2 ; T M=G2 Þ

ð9Þ

where w1 ; w2 and w3 are corresponding empirical maps. The battery in a power-split HEV is connected through an inverter to supply power for or recuperate energy from electrical machines. An internal resistance model is used to describe the battery dynamics [20,21]. The state of charge (SOC) is calculated by,

Pbatt ðtÞ ¼ VIbatt ðtÞ 

I2batt ðtÞR

Ibatt ðtÞ _ SOCðtÞ ¼ Q

ð10Þ ð11Þ

Meanwhile, the battery power requirement is formulated as,

Pbatt ¼ PM=G1 =ðgM=G1 ginv ÞkM=G1 þ PM=G2 =ðgM=G2 ginv ÞkM=G2

ð12Þ

where P M=G1 and PM=G2 are shaft powers of M=G1 and M=G2, respectively; ginv is the inverter efficiency;




ki ¼

if Pi > 0

1

1 if Pi 6 0

;

for i ¼ fM=G1; M=G2g:

ð13Þ

Eqs. (1)–(13) describe the control-oriented model used in the energy management strategy. More detailed can be found in Ref. [14]. 2.2. Equivalent consumption minimization ECMS is capable to solve the optimal control problem derived from the energy management of HEVs, by applying the Pontryagins Minimum Principle (PMP). For HEVs, the battery is requested to work under a charge-sustaining mode [22]. That is, the terminal battery SOC should be equal or close to the initial battery SOC. The objective of the energy management of an HEV is to minimize its fuel consumption over the global driving task. Assume SOC is the state variable x, engine torque and motor torque are the control variables u, the cost function is formulated as,

Z

T

Jðx; uÞ ¼

_ f ðuÞdt m

ð14Þ

t0

x_ ¼ f ðx; uÞ

ð15Þ

yðtÞ ¼ gðx; uÞ

ð16Þ

subject to constraints

Hðx;u; kÞ P Hðx; u ;kÞ; where Hðx;u; kÞ _ f ðuÞ ¼ kf ðx; uÞ þ m

ð18Þ


The auxiliary variable k satisfies,

@H @f ðx; uÞ k_ ¼  ¼ @x @x

ð19Þ

Each solution that satisfies the above conditions is a candidate of the optimal control law. By minimizing the Hamiltonian at each time step, the PMP can help us find a set of solution candidates. Particularly, the co-state k determines the equivalence factor between the fuel energy usage and the electric energy usage. Intuitively, an equivalence factor can be derived from k, which is,

sðtÞ ¼ kðtÞ 

Q lhv Ebatt

ð20Þ

where Q lhv indicates the lower hearing value of the fuel used, and Ebatt means the battery energy capacity. Fig. 2 shows the battery SOC trajectories of a power-split HEV solved by ECMS with different EFs attempted. The test driving cycle is standard NEDC. As we can see, when EF equals to 348.5, the terminal battery SOC falls to the requested 0.6. The optimal state variable trajectory is thus found, as well as the optimal control decisions. However, if the given initial EF varies from 348.5, the powertrain behavior would not follow the optimal strategy, and neither the terminal battery SOC can return to 0.6. Such as when the EF is set as 378.5, the terminal SOC goes to as high as 0.75, and the fuel economy is much worse than the 348.5 situation. The EF defined above acts as an important tuning parameter in ECMS. The fuel economy of the powertrain for an assigned driving task is extremely sensitive to the EF. For each driving mission, an optimal EF exists and leads to the optimal solution. Usually, a trial and error process is needed to find the optimal or suboptimal EF. Meanwhile, the driving cycle velocity information is also required to be known a prior for the EF tuning (assume road grade is always zero). However, both of these two requirements are very difficult to satisfy in practical application, as elaborated in Section 1. 3. Adaptive-ECMS and its modification 3.1. Adaptive-ECMS The EF tuning problem of ECMS draw out the adaptive-ECMS, which intends to adjust the EF value in real-time. Firstly, a current driving cycle block is defined, which is much shorter than the overall driving cycle, and only represents the occurring driving behavior. Secondly, the controller estimates the optimal/suboptimal EF regarding the current driving cycle block. Thirdly, the adaptiveECMS implements the estimated EF to the coming driving cycle block, and the energy management continues along the driving

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0.8 EF=−378.5

Battery SOC

0.7 EF=−358.5 0.6

EF=−348.5

0.5

EF=−338.5

0.4

EF=−318.5

0

200

400

600

800

1000

1200

1400

1200

1400

40

Velocity (m/s)

NEDC Standard 30 20 10 0

0

200

400

600

800

1000

Time (s)

sðk þ 1Þ ¼ sðkÞ þ cECMS ðxðt0 Þ  xðt T ÞÞ

ð21Þ

where sðk þ 1Þ indicates the next iteration result of EF, based on the current iteration result sðkÞ; cECMS is an adjustable weight to get balance control of the SOC. A comparison simulation of adaptive-ECMS with ECMS for driving cycle Urban Dynamometer Driving Schedule (UDDS) is demonstrated in Fig. 3. Adaptive-ECMS 350 and 400 mean that the initial EF is set as 350 and 400, respectively. As we can see in Fig. 3A, the overall battery SOC trajectories of the two adaptive-ECMS examples are very different from the well-tuned ECMS, especially in the first 600 s. Particularly, the well-tuned ECMS is able to satisfy the battery SOC constraint, forcing the terminal SOC back to 0.6. Yet in the developed adaptive-ECMS, the terminal SOC drops to 0.58 and 0.57, respectively. Fig. 3B exhibits the EF adaptation results. Clearly, the EF for well-tuned ECMS is a constant optimal value 336.5. The initial EFs we tested for adaptive-ECMS are 350 and 400. The EF iteration times are restricted within 10 considering the computation burden. As can be seen, although the initial EF is 400, which is highly deviated from the optimal value, adaptiveECMS is capable to converge the block-EF back to the optimal EF value. However, due to the length limit of driving cycle block defined in adaptive-ECMS, it’s very difficult for the block-EF to be exactly the same as the optimal EF value, yet resulted with vibrations around it.

Adaptive−ECMS −350 Adaptive−ECMS −400 Well−tuned ECMS

A

0.65

0.6

0.55 0

Velocity (m/s)

task ‘block by block’. Eventually, the adaptive-ECMS manages the control decision making processes by computing a series of optimal/suboptimal block-EFs instead of one optimal EF compared with ECMS. Numerically, the block-EF can be estimated by enforcing the battery SOC equal to the initial set value at the end of each cycle block. This constraint is reasonable for an HEV, as it works under charge sustaining mode. In Ref. [10], the moving block is defined as 120 s long. Because of the lack of future driving profile, the past 120-s historical driving profile is employed for the current block-EF estimation. The EF computation process is usually defined as iterative searching based on battery SOC feedback, such as,

Battery SOC

Fig. 2. SOC trajectories derived from basic ECMS with different EF values.

200

400

600

800

1000

1200

200

400

600

800

1000

1200

B −300 −350 −400 0

Time (s) Fig. 3. SOC trajectories derived from adaptive-ECMS with different initial EF values. The normalized consumed fuel of adaptive-ECMS 350, adaptive-ECMS 400 and the well-tuned-ECMS is 237 g and 232 g and 219 g, respectively.

3.2. Modified EF adaptation law In this section, we propose a modified EF convergence principle for adaptive-ECMS to enhance the EF searching stability. Additionally, the role of velocity forecasting for adaptive-ECMS is studied, and a velocity predictor is modeled for further comparison. In basic adaptive-ECMS, the EF convergence principle stands very important. The adaptation law defined in Eq. (21) is widely used. However, this adaptation law is unable to solve the blockEF oscillation problem. Fig. 4 exhibited a typical EF oscillation problem happened in cycle segment (841–960 s) from NEDC. Fig. 4A clearly shows the EF oscillation. The initial EF starts from 350, and then it evolves to 411.8 in the second loop according to adaptation law Eq. (21). The estimation process continues to the third loop, and ends with and EF candidate 224.1, which is even further from the optimal 391.5. Unfortunately, the oscillation begins, and the EF can hardly converge to a stable value.

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−150

0.9

−250 −300 −350

EF−SOC Curve EF Estimation Gradient

0.7 0.6 0.5

−400 −450

B 0.8

Battery SOC

−200

EF Values

EF Oscillation Optimal EF

A

2

4

6

8

10

0.4 −500

−400

Convergence Loops

−300

−200

−100

EF Values

Velocity (m/s)

30 Cycle Segment from NEDC

C 20 10 0 840

860

880

900

920

940

960

Time (s) Fig. 4. EF estimation oscillation problem in NEDC 841–960 s segment. A: Estimated EFs along the convergence loops. B: Cycle block/segment selected from NEDC. C: Corresponding terminal SOC of the selected cycle block with different EFs.

The main reason of EF estimation oscillation is demonstrated in Fig. 4B. The gradient of the block-EF value and corresponding terminal SOC switched suddenly at around 390. A linear adaptation law as Eq. (21) is not suitable to resolve this piecewise function problem. Another reason that the terminal battery SOC can hardly be close to the expected value is that the terminal SOC becomes much more sensitive from 398 to 390. The slope is extremely high. We can notice that although several EF candidates are quite close to 391.5, the terminal SOC error remains huge. Due to this characteristics, a minor difference of EF would result with huge deviation from the expected 0.6 terminal SOC, and eventually generates poor estimation of the block-EF. In this paper, we employ the bisection method to solve the EF oscillation problem. The EF convergence principle is modified to follow the below procedure,
Obtain the target cycle block, initialize the EF. Implement the initial EF value, gain the terminal SOC, and evolve the EF under Eq. (21) for three loops (note that the ‘three’ convergence loop number can be changed to other options).
Based on the obtained three EF candidates from the above step, examine if there exists an oscillation problem by evaluating the terminal battery SOC under,

If



     SOC1c  SOC0  SOC2c  SOC0 < 0 or SOC1c  SOC0    SOC3c  SOC0 < 0 Oscillation:

else; No Oscillation: where SOC0 is the initial battery SOC and also the target reference SOC; SOC1c ; SOC2c ; SOC3c indicate the first, second and third EF trial SOC result, respectively.
If no oscillation is observed, the convergence process continues with Eq. (21). If an oscillation is detected, the adaptation law switches to,

sðk þ 1Þ ¼

sðkÞ þ sðk  nÞ 2

ð22Þ

where sðk  nÞ is the EF candidate whose terminal SOC error sign is contrary with sðkÞ. The modified EF convergence principle is able to solve the EF estimation oscillation problem. Fig. 5 demonstrates the EF estimation performance of the modified convergence principle. From Fig. 5A, the first three estimation loops remains the same with Fig. 4A. After the oscillation problem is examined, the estimation algorithm changes its adaptation law from Eqs. (21) and (22), and then the EF successfully evolves to the optimal 391.5. The terminal battery SOC results in Fig. 5A perform the same result with the EF estimation in Fig. 5B. Gradually, the terminal SOC converges to the expected reference 0.6. 3.3. Foreseeability importance study In real implementation of adaptive-ECMS, the accurate future driving profile is very difficult to be known in advance, and historical driving profile is generally used for the EF searching during each cycle block. This part intends to compare the fuel economy between when accurate future profile is used and when historical profile is used, thus to exploit the importance of foreseeability to adaptive-ECMS. Set the cycle block length as 120 s, the resultant battery SOC and EF trajectories from adaptive-ECMS are shown in Fig. 6. The testing cycle is NEDC. We can see that during the first 800 s, the battery SOC is able to be restricted near the initial 0.6 in both scenarios. However, after 800 s, the battery SOC deviates heavily from 0.6 and finally reaches 0.78 when historical driving profile is used. This phenomenon is undesired in HEV energy management. As expected, when the future driving profile is perfectly known to adaptive-ECMS, the terminal battery SOC is able to return to 0.6 easily. The bottom figure shows the comparison of the block-EF estimation results. Both of the EFs in these two scenarios are initialized

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−150

0.9 EF Convergence Optimal EF

A −200

0.8

−250

Battery SOC

EF Values

EF−SOC Curve EF Estimation Gradient

B

−300 −350

0.7

0.6

0.5

−400 −450

2

4

6

8

10

0.4 −500

−400

−300

Convergence Loops

−200

−100

EF Values

Fig. 5. EF estimation under the modified convergence principle for NEDC 841–960 s segment. A: Estimated EFs along the convergence loops. B: Corresponding terminal SOC of the selected cycle block.

a1 ¼ exp 

Battery SOC

0.8 No Foreseeability Full Foreseeability

0.7

400

200

400

600

800

1000

1200

600

800

1000

1200

EF

−300 −350 −400 −450 0

2

;

ð23Þ

n ¼ Wa þ b;

0.5 200

2b

!

0

0.6

0 −250

kn  ck2

Time (s) Fig. 6. Battery SOC and block-EF trajectory from the adaptive-ECMS. No foreseeability means historical driving profiles are used for EF estimation; Full foreseeability assumes that the future driving profile is fully known.

with 400. Less variation of the block-EF is observed from when future driving profile is assumed known compared with when historical driving profile is used. The normalized fuel consumptions are 238.3 g and 221.6 g, respectively. Eventually, the adaptiveECMS when future driving profiles are known in advance performs better fuel economy, and the improvement is as high as 7%.

where a1 and a0 are neural outputs of the current layer and prior layer, respectively; n is the accumulator output; c is the neural net center; b is the spread width; W is the neuron weight. Both c and b can be fit using a gradient descent method [25]. Intuitively, the future driving behavior is related to the historical velocity profile. The aim of RBF-NN is to mathematically learn and reproduce this relationship. We define the inputs of the RBFNN are historical velocity sequences, and the outputs are predicted future velocity sequences. The input–output pattern for velocity forecast is illustrated in Fig. 7. Each input–output pattern is composed of a moving window of fixed length, which can be expressed as

½V kþ1 ; V kþ2 ; . . . ; V kþHp  ¼ f nn ðV kHh þ1 ; . . . ; V k Þ;

ð24Þ

where Hh is the dimension of the input velocity sequence; f nn represents the nonlinear map function of an RBF-based predictor; Hp indicates the length of the output future velocity sequence and should equal to the cycle block length. The RBF-NN needs to learn from existing driving profiles to grasp the driving behavior features. Usually, this is called training. With the historical velocity sequence injected into a trained RBF-NN, the predictor is able to forecast reasonably accurate short-term future driving trends. Details of the ANN-based velocity forecast technique can be found in [14]. 4.2. Velocity forecast result analysis

4. Velocity forecast technique 4.1. Artificial neural network based forecast This section introduces an ANN based vehicle velocity forecast technique. To reduce the hardware cost, we assume that no telemetric equipments are used in the forecast technique, and thus this problem falls into the time series forecasting area. ANN has demonstrated strong ability in the time series forecasting [23]. A data-driven velocity predictor can be established based on the radial basis function neural network (RBF-NN) [24]. The radial basis function in the hidden layer is defined with Gaussian function and the output layer is defined with a linear function, formulated as

Standard driving cycles UDDS, US06, JN1015, NEDC, WVUINTER and HWFET are used as the training database. A velocity forecast result for a real collected driving cycle is given in Fig. 8. The forecast output length is 10 and 30 s, and the forecast process is conducted at each time instant. To reduce the problem complexity, the input length is set the same as the output length. To fully examine the forecast performance, the real collected driving cycle is different from the cycles in the train database. At each time instant, the historical driving profile is input into the trained RBF-predictor, and a possible future velocity profile is produced as output (plotted as1 red lines in Fig. 8, the blue line indicates 1 For interpretation of color in Fig. 8, the reader is referred to the web version of this article.

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Predicted velocities

Past Future Real velocities

Hh

Hp

tk Weights-1

Weights-2 V(tk+1)

Historical V(tk) velocity sequence V(t )

...

k-1

Future velocity V(tk+2) sequence

...

... ...

V(tk-H +2)

V(tk+H -1) p

h

V(tk+H )

V(tk-H +1)

p

h

Input Layer

Hidden Layer

Output Layer

Fig. 7. Input–output pattern for ANN based velocity forecast.

Velocity forecast length is 10s

Velocity (m/s)

30 Actual Velocity Predicted Velocity 20

10

0 0

100

200

300

400

500

600

700

800

900

700

800

900

Velocity forecast length is 30s

Velocity (m/s)

30

20

10

0 0

100

200

300

400

500

600

Time (s) Fig. 8. Velocity forecast result of RBF-NN predictors with 10-s and 30-s output length for a real collected driving cycle.

the actual driving profile and is used for comparison). As can be seen from Fig. 8, in most cases, the forecast result would continue the acceleration or deceleration trend delivered from the historical velocity profiles. When the forecast output length is 10 s, the produced future driving profiles are quite similar to the actual driving cycle. However, when the forecast output length grows up to 30 s, the forecast results are more complicated compared with the 10-s case. The velocity predictor generates a series of possible acceleration or deceleration actions, trying to catch the future driving style. The root mean squared error of the forecast results would generally grow when the forecast driving profile is longer. It’s difficult to observe and analyze the detailed forecast behavior from Fig. 8. Four individual velocity forecast results are randomly selected and plotted in Fig. 9, together with corresponding accelerations. In case one, when time step is at 502, the actual future velocity decreases gradually to 5 m/s in the next 30 s. Yet the forecast velocity result maintains relatively high. This is partly because the vehicle acceleration is still positive. When at time step

503 in case two, the acceleration changes from positive to negative, thus the forecast velocity result declines to about 12 m/s instead, but then returns to 15 m/s. The reason could be at this time, the deceleration action is very slight, and there still is a big possibility that the velocity would increase. Compared with case four, when time step is 511, the deceleration action becomes greater, and then the forecast velocity result also decelerates as the actual profile does. The final velocity decreases to 6 m/s. Case three is similar to case one, the acceleration becomes smaller compared with the previous time step but is still positive, the forecast velocity result tries to maintain the original velocity level and declines little by little. However at this time, the forecast result is quite close to the actual one. Based on the above results and analysis, we can see that each velocity forecast case represents a small part of the overall driving characteristics from the sample database. The RBF-predictor successfully learned these nonlinear characteristics and repeated them in a new driving cycle.

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V(m/s)

At time step 502 15

15

10

10 Predicted Velocity 5 Actual Velocity

5

2

a(m /s)

At time step 503

Actual acceleration1 Previous and Current 0 Value

1 0 −1 −2 490

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At time step 492 15

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500

510

520

530

At time step 511

15

−2 480

510

520

−2 500

510

Time(s)

520

530

540

Time(s)

Fig. 9. Four randomly selected velocity forecast results by RBF-NN, the red stars indicated the previous and current time step acceleration. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

25

4.3. Forecast length determination

20

Velocity (m/s)

The velocity forecast length, also noted as the cycle block length Hp , varies from seconds to as long as minutes. It impacts the performance of adaptive-ECMS greatly. Generally speaking, the fuel economy of adaptive-ECMS increases when the block length is set longer. However, the velocity forecast error will also grow in this case. A study on the velocity forecast error distribution over the velocity prediction length is necessary, and is beneficial for the forecast length determination. The velocity forecast results of RBF-predictors with 10-s, 30-s, 60-s and 90-s output lengths for WVUSUB at time step 695 are shown in Fig. 10. The neuron numbers of all the velocity predictors are maintained as 250 for fair comparison. The input length is set as the same with the output length. When the output length is 10-s long, the forecast result is close to the actual velocity profile with a minor root mean squared error (RMSE) 0.4396. As the output length grows, the forecast error ascends as expected. From the 30-s and 60-s length results we can see that the predicted velocity profile is able to basically follow the driving trend, yet the RMSE grows up to 1.79 and 2.08, respectively. Interestingly, the RMSE of 30-s predictor is close to the 60-s one. As for the 90-s situation, it is obvious that the forecast result deviates heavily from the actual driving profile from time step 760 to 785. Due to the poor performance of the time period 760–785, the 90-s velocity forecast RMSE increases up to 5.7754. Five driving cycles UDDS, US06, JN1015 and HWFET are used to train the RBF-NN predictor, and three driving cycles NEDC, WVUSUB and a real collected urban cycle are used for testing. The average RMSEs and standard deviations of velocity forecast with different output lengths are shown in Fig. 11. As can be seen, the average velocity forecast RMSE grows rapidly from 1.5 m/s to 3.3 m/s when the output length is below 30-s. After then the average RMSE is stabilized around 3.4 m/s till the 60-s length. From 60s to 150-s length, the average RMSE continues growing gradually up to nearly 5.5 m/s.

True Velocity of WVUSUB 10−s Output RMSE 0.4396 30−s Output RMSE 1.7999 60−s Output RMSE 2.0871 90−s Output RMSE 5.7754

15

10

5

0 680

700

720

740

760

780

800

Time (s) Fig. 10. Velocity forecast results of RBF-predictors with 10-s, 30-s, 60-s and 90-s output lengths for cycle WVUSUB.

The standard deviations of the computed forecast RMSEs are also demonstrated in Fig. 11. We can see that in the 10-s forecast situation, the standard deviation is relatively small, about 0.5. Then it slowly increases to nearly 0.9 at when the output length is 70-s. After the 90-s situation, the standard deviation grows much faster to as large as 2.1 when the output length is 150-s. Considering the above average RMSE and standard deviation results, we conclude that when the output length is longer than 70 s, the forecast performance becomes much worse and is not suitable for hybrid electric vehicle energy management in our case. Eventually, we set the velocity forecast length as 60 s for the EF adaptation purpose.

5. Results and discussion The RBF-NN based velocity forecast technique is implemented in adaptive-ECMS in this section. The parameters of the HEV pow-

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0.8

Battery SOC

Velocity Forecast RMSE Standard Deviation

6

RMSE (m/s)

5

No With Forecast Full Foreseeability

A 0.7 0.6

4

0.5

3

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0

200

400

600

200

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600

800

1000

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800

1000

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B 500

1 0

EF

2

0 −500

30

60

90

120

150

Velocity Predictor Output Length (s) Fig. 11. Average RMSE and standard deviation of the velocity forecast results under different output lengths.

ertrain is from Ref. [14]. The length of the moving cycle block is set as 60 s according the study in Section 4.3. Standard driving cycles UDDS, US06, JN1015 and HWFET are used to train the RBF-NN for velocity forecast. Standard driving cycles NEDC, WVUSUB, WVUINTER, and a real collected urban cycle are used for test. The energy management procedure is as, 1. Collect appropriate sample driving cycles, and use it to train the RBF-NN offline; 2. While in a driving task, the RBF-NN predicts future driving profiles in real-time; 3. The velocity forecast result is given to adaptive-ECMS for current block-EF searching; 4. The block-EF is updated, and a standard ECMS energy management proceeds; 5. System feeds back, the vehicle drives to the next cycle block and the energy manager returns to step 2. Three situations are considered and compared. The first situation is a basic adaptive-ECMS approach, where the past 60-s driving profile is used for EF searching. The second situation is adaptive-ECMS with velocity forecast ability enabled. The trained RBF-NN is combined with adaptive-ECMS, and the predicted driving profile is used for EF searching. The third situation is adaptiveECMS when future 60-s driving profile is perfectly known in advance. The comparison of the resultant battery SOC and blockEF trajectories for WVUINTER over these three situations are shown in Fig. 12. As we can see from Fig. 12A, when no velocity forecast is used, the battery SOC deviates from the reference 0.6 much greater than the other two situations. On the contrary, full foreseeability ensures that the battery SOC is always around 0.6 including at the end of the trip. In the velocity forecast situation, the battery SOC trajectory basically follows the full foreseeability case, and much less variation is observed compared with when no velocity forecast is incorporated. Only two obvious SOC deviations happened at around 100 and 500 s in the velocity forecast case. Another way to evaluate the energy management performance is to compare the terminal SOC values. As expected, full foreseeability satisfies this constraint well. However, when no velocity forecast is used, the terminal battery SOC is as high as 0.65. While in the velocity forecast situation, the battery terminal SOC is 0.61, which is much better than the no forecast case. Fig. 12B shows the block-EF trajectories derived from the above three situations. A number of huge jumps are observed in the no

−1000 0

Time (s) Fig. 12. Battery SOC and block-EF trajectory comparison for the WVUINTER driving cycle.

Table 1 Fuel economy comparison. Type

WVUSUB

WVUINTER

NEDC

Real cycle

Normalized average (%)

Without forecast With forecast DP optimal

226.3 214.6 185.2

514.4 507.3 490.7

232.8 218.6 203.4

236.4 228.0 216.9

89.58 93.33 100

11.7

7.1

14.2

8.4

Improvement

3.75

Improvement indicates the fuel economy improvement of adaptive-ECMS when velocity forecast is incorporated.

forecast scenario, compared with only three in the forecast situation and one jump in the full foreseeability situation. It would take time for the block-EF to recover from the jumps, and these errors eventually causes the deviation of the terminal battery SOC and the increase of overall fuel consumption. The normalized fuel economy is assessed by comparing with the optimal benchmark result calculated from dynamic programming (DP) [26]. As we can see from Table 1, the velocity forecast ability can improve the global fuel economy by over 3% on average compared with when historical driving profile is employed for EF searching, without increasing any hardware costs of the vehicle. The reason that the adaptiveECMS fuel economy is improved is that: although the velocity forecast method cannot perfectly predict the future velocity profile, it is good enough that the basic driving trend in the short-term future is predicted, and the EF estimation would be more reasonable and accurate.

6. Conclusions This paper investigated the role of velocity forecast ability in improving the adaptive-ECMS fuel economy performance for HEV energy management. The main conclusions are: First, the adaptation law of the block-EF searching is modified to resolve the EF estimation oscillation problem; Second, a RBF-NN velocity predictor is constructed, its forecast accuracy is analyzed and the best output length is determined; Third, the developed velocity predictor is incorporated with adaptive-ECMS, and the fuel economy is increased by over 3%. This study validated the effectiveness of velocity forecast in improving the performance of adaptive-ECMS in HEV energy

Please cite this article in press as: Sun C et al. Investigating adaptive-ECMS with velocity forecast ability for hybrid electric vehicles. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2016.02.026

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management. The computation of the forecast process is small, thus the on-board controller is able to accomplish the additional calculation burden. Experimental results will be presented in the future study.

Acknowledgment This work was supported in part by Chinese National Science & Technology Pillar Program (2015BAG01B01) and the Higher School Discipline Innovation Intelligence Plan (‘‘111” plan).

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Please cite this article in press as: Sun C et al. Investigating adaptive-ECMS with velocity forecast ability for hybrid electric vehicles. Appl Energy (2016), http://dx.doi.org/10.1016/j.apenergy.2016.02.026