Expert Systems With Applications 91 (2018) 452–463

Contents lists available at ScienceDirect

Expert Systems With Applications

journal homepage: www.elsevier.com/locate/eswa

Lane-changes pre diction base d on adaptive fuzzy neural network

Jinjun Tang

a , Fang Liu

b , Wenhui Zhang

c , Ruimin Ke

d , Yajie Zou

e , ∗

a School of Traffic and Transportation Engineering, Central South University, Changsha, 410075, China b School of Energy and Transportation Engineering, Inner Mongolia Agricultural University, Hohhot, 010018, China c Traffic School, Northeast Forestry University, Harbin, 150040, China d Department of Civil and Environmental Engineering, University of Washington Seattle, WA 98195, USA e Key Laboratory of Road and Traffic Engineering of Ministry of Education, Tongji University, Shanghai 201804, China

a r t i c l e i n f o

Article history:

Received 16 February 2017

Revised 30 May 2017

Accepted 9 September 2017

Available online 12 September 2017

Keywords:

Lane changes

Fuzzy neural network

Steering prediction

Driving simulation

Adaptive learning algorithm

a b s t r a c t

Lane changing maneuver is one of the most important driving behaviors. Unreasonable lane changes

can cause serious collisions and consequent traffic delays. High precision prediction of lane changing

intent is helpful for improving driving safety. In this study, by fusing information from vehicle sensors, a

lane changing predictor based on Adaptive Fuzzy Neural Network (AFFN) is proposed to predict steering

angles. The prediction model includes two parts: fuzzy neural network based on Takagi–Sugeno fuzzy

inference, in which an improved Least Squares Estimator (LSE) is adopt to optimize parameters; adap-

tive learning algorithm to update membership functions and rule base. Experiments are conducted in

the driving simulator under scenarios with different speed levels of lead vehicle: 60 km/h, 80 km/h and

100 km/h. Prediction results show that the proposed method is able to accurately follow steering angle

patterns. Furthermore, comparison of prediction performance with several machine learning methods fur-

ther verifies the learning ability of the AFNN. Finally, a sensibility analysis indicates heading angles and

acceleration of vehicle are also important factors for predicting lane changing behavior.

© 2017 Elsevier Ltd. All rights reserved.

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1. Introduction

Automatic vehicles, relying on the collaboration of artificial in-

telligence, visual computing, radar monitoring device, and global

positioning system, can automatically and safely operate motor ve-

hicles in the absence of any human activities. As a key part of

Advanced Driver Assistance System (ADAS), this technology can

largely improve the driving safety and avoid traffic accidents. Fur-

thermore, it can also help to rationalize driving behavior, improve

travel efficiency and further relive traffic pressures. The whole driv-

ing process generally contains several maneuvers, such as, lane

changing, overtaking, car following and so on. In fact, due to the

impact of many external factors, the behavior of a driver is com-

plicated and mainly depends on human’s physiological status and

psychological activity. In addition, modeling driving behavior is a

complex problem which involves control theory, robotics, and psy-

chology. As one of most common and challenging behavior, drivers

should not only consider the safety distance from the front vehicle

on the current lane but also the safety space between the front

and latter vehicles on target lane during lane changing process.

∗ Corresponding author.

E-mail addresses: jinjuntang@cus.edu.cn (J. Tang), liufang@imau.edu.cn

(F. Liu), zhangwenhui@nefu.edu.cn (W. Zhang), ker27@uw.edu (R. Ke),

zouyajie@tongji.edu.cn (Y. Zou).

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http://dx.doi.org/10.1016/j.eswa.2017.09.025

0957-4174/© 2017 Elsevier Ltd. All rights reserved.

raffic accidents caused by unreasonable lane-changing behavior

ill result in personal injury and deterioration of traffic condition.

herefore, exploring the intent recognition and analyzing the route

atterns are definitely conducive to improving the safety of lane

hanging behavior ( Hou, Edara, & Sun, 2015; You et al., 2015 ).

.1. Related works

Currently, one practical solution is sole turn signal. It is an ap-

arent indicator to reflect lane-changing intention of drivers. How-

ver, this signal can be also used for other behavior, such as spe-

ific direction turning. Furthermore, many researchers ( Deutscher,

007; Lee, Olsen, & Wierwille, 2004; Ponziani, 2012; Schmidt, Beg-

iato, Hoffmann, & Krems, 2014 ) have conducted experiments to

stimate the sensitivity of the turn signal as indicator for lane

hange. They found that this method lacked sensitivity and speci-

city to predict lane changing behavior. Another method is con-

idered as using data from multi-sensor installed on the vehi-

le to predict the behavior of lane changing. Morris, Doshi, and

rivedi (2011) introduced several data source to be implemented

or route or path prediction, which include driver behavior ob-

ervation (e.g., eye-tracking, electrocardiogram), sensor information

bout the environment (e.g., safe distance detection, GPS data) and

ehicle parameters (e.g., vehicle speed, acceleration, steering wheel

ngle). By integrating these data source, various methods are pro-

J. Tang et al. / Expert Systems With Applications 91 (2018) 452–463 453

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osed to predict lane changing behaviors. They can be classified

nto following five categories: (1) Hidden Markov Model (HMM)

Kuge, Yamamura, & Shimoyama, 20 0 0; Liu & Pentland, 1997;

entland & Liu, 1999; Sathyanarayana, Boyraz, & Hansen, 2008 );

2) Neural Networks (NN) ( Cheng, Xiao, & LeQuoc, 1992; Ding,

ang, Wang, & Baumann, 2013; Macadam & Johnson, 1996; Tomar,

erma, & Tomar, 2010 ); (3) Regression Model (RM) ( Henning,

eorgeon, & Krems, 20 07; Olsen, 20 03 ); (4) Cognitive Model

CM) ( Baumann & Krems, 2007; Pickering, 2001; Salvucci, 2006;

alvucci, Mandalia, Kuge, & Yamamura, 2007 ); (5) Fuzzy Logic Sys-

em (FLS) ( Errampalli, Okushima, & Akiyama, 2008; Hessburg &

omizuka, 1995; Kim, 2002; Okushima & Akiyama, 2005; Shi &

hang, 2013 );

(1) For the Hidden Markov Model (HMM), HMM can in-

er unobservable (hidden) states from observable actions, and

tudies in this part mainly focus on constructing probabilis-

ic model to predict driving routes. Kuge et al. (20 0 0) intro-

uced a driver behavior recognition model based on HMM con-

idering driver characteristics by using driving simulation data.

athyanarayana et al. (2008) proposed a hierarchical framework to

odeled driver behavior signals, in which the first layer considered

solated maneuver recognition and second layer models the entire

oute based on HMM. (2) For the Neural Networks (NN), due to

ts strong generalization and learning ability as well as adaptabil-

ty, NN is also a popular approach selected by scholars to finish

ane-changing prediction. To overcome the disadvantage that exist-

ng lane change models do not consider the uncertainties and per-

eptions in the human behavior, Tomar et al. (2010) constructed

neural network with multilayer perceptron to predict the lane

hanging trajectory in future steps based on field data from the

ext Generation Simulation (NGSIM). Ding et al. (2013) devel-

ped a Back-Propagation (BP) neural network to predict lane-

hanging trajectory, and they also compared prediction results be-

ween BP neural network and Elman Network using the data col-

ected from driving simulator data and NGSIM. (3) For the Re-

ression Model (RM), because of its simple structure and fast cal-

ulation speed, researches used this approach to fit the relation-

hip between input variables (vehicle speed, acceleration, safe dis-

ance and so on) and output variables (steering wheel angle or

ane changing routes). In order to model lane changing process

ith slow lead vehicle, Olsen (2003) applied a logistic regression

odel considering the distance to the front and rear adjacent ve-

icle, forward time-to-collision (TTC), and turn signal activation.

enning et al. (2007) used regression model to predict the inten-

ion of lane changes considering some environmental and behav-

oral indicators: glance to the left outside mirror, turn signal, and

ane crossing. (4) For the Cognitive Model (CM), it can be used to

pproximate human cognitive processes for the purposes of com-

rehension and prediction. Salvucci (2006) introduced an Adaptive

ontrol of Thought-Rational cognitive architecture and proposed an

ntegrated driver model to accomplish processes of control, mon-

toring and decision making in a multilane highway environment.

aumann and Krems (2007) introduced some major preconditions

f safe driving in drivers’ cognitive process. (5) For the Fuzzy Logic

ystem (FLS), it is built on a probabilistic reasoning process that

ses fuzzy input parameters. Through optimizing parameters in

uzzy membership functions, FLS can be used to accurately pre-

ict driving trajectories in lane changing process. Errampalli et al.

2008) introduced fuzzy reasoning in lane changing model to re-

listically indicate uncertainties and perceptions in driving behav-

or, and they compared simulation results with traditional multi-

omial logit model to validate its effectiveness. Shi and Zhang

2013) adopted fuzzy logic to analyze multi lane change behavior,

n which several indicators are considered as input variables and

teering wheel angle is set as output variable to evaluate the effi-

iency of lane change process.

.2. Aims of study

Abundant works focused on lane changing behavior prediction

ave been obtained in previous researches, however, there still ex-

sts some issues need to be solved in emulating the complex and

ulti-ruled behavior of the driver and incorporating the uncer-

ainties of driver’s perception and decisions. Fuzzy logic is a kind

f method that can deal with the transformation between quali-

ative and quantitative information. By implementing fuzzy com-

rehensive judgment, it deals with some problems with fuzzy in-

ormation that are difficult to be solved by traditional methods.

uzzy logic is good at expressing the qualitative knowledge and

xperience with uncertainty. In the process of lane changing, the

ecision-making behavior of the driver obviously contains fuzzy or

ncertain process. So, it is effective and feasible to use fuzzy logic

heory to analyze the behavior of the lane changing. However, ac-

ording to current studies, there are several disadvantages: (1) the

ules used in fuzzy inference are not comprehensive; (2) lacking

daptive learning mechanism will result in unsatisfactory predic-

ion performance; (3) indicators or factors considered in fuzzy in-

ut variables are limited.

Aim to aforementioned three deficiencies, this study proposes

fuzzy neural network with adaptive learning ability to predict

ane changing behavior. The main work includes following three

arts. (1) Establish FNN model, determine the input and output

ariables, and construct the rule base and inference mechanism.

2) Introduce an adaptive learning process, in which the predic-

ion errors are used to adjust structure of fuzzy membership func-

ion, and then improve fuzzy reasoning process by enriching the

ule base. (3) Consider the effects of various information in in-

ut variables for driving behavior, which includes vehicle parame-

ers: vehicle speed, acceleration, heading angles, and distance from

he front vehicle in the horizontal axis and vertical axis, the out-

ut variables is determined as driving steering angle. Finally, using

he data collected from driving simulator, the effectiveness of this

tudy is validated based on statistical analysis of prediction results.

The remainder of the paper is organized as follows.

ection 2 briefly introduces the models used in study. The car-steer

odeling based on FNN is provided in Section 3 . Section 4 dis-

usses the experiment results and compares prediction accuracy

etween different models. Section 5 provides the conclusion of the

aper.

. Lane-changing driving behavior

For the vehicle model, we consider a simplified movement

odel of a four wheeled vehicle as following:

x (k + 1) = x (k ) + v (k ) · �s · cos [ θ (k ) ] y (k + 1) = y (k ) + v (k ) · �s · sin [ θ (k ) ] θ (k + 1) = θ (k ) + v (k ) · �s · tan α(k ) /l

}

(1)

here θ is the heading of the vehicle, x and y represent the posi-

ion of vehicle, x 0 and y 0 represent the centroids of vehicle, which

re determined on the basis of vehicle rear wheel, α is the steering

ngle, ν indicates the instantaneous velocity, l means the wheel-

ase, �s is the computation sampling time, and k is the simulation

tep, see Fig. 1 a. Define t 0 as the starting time, T as the ending

ime when subject vehicle finishes the lane changing maneuver,

he k ∈ [ t 0 , T ]. Therefore, according to the values of x, y and θ , we

an determine vehicle attitude. Fig. 1 b shows lane changing ma-

euver. Lag vehicle 2 is the subject vehicle, lead vehicle 2 is the

ead vehicle in the current lane, and the lag vehicle 1 and lead ve-

icle 1 represent the following vehicle and lead vehicle in the tar-

et lane, respectively. The acceleration ( acc ) can be calculated as:

454 J. Tang et al. / Expert Systems With Applications 91 (2018) 452–463

Fig. 1. Vehicular lane-changing model.

Fig. 2. Structure of prediction system.

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acc(k + 1) =

v (k + 1) − v (k )

�s (2)

Once driver decides to change lane, his/her goal will be to make

a smooth transition from the current lane to the desired lane with-

out colliding with the other vehicles around it. He/she should con-

sider several factors, the safe space on target lane, and the dis-

tance from the lead vehicle on current lane. In an ideal situation,

the lateral location of subject vehicle, y t , is the middle of the tar-

get lane, the heading, θ t , equals to 0, and horizontal location, x t ,

can vary with a certain range. This range is limited by some con-

straints, which are the safety of the lag vehicle and the lead ve-

hicle. In other words, there should be enough space to move into

the lag vehicle’s front area without colliding with the lead vehicle.

Due to the diversity of drivers, including different driving habits

and experiences, their lane changing trajectories express different

patterns shown in Fig. 1 b.

3. Lane-changing behavior prediction

3.1. System structure

The prediction system proposed in this study mainly includes

following three parts, see Fig. 2 .

1) Data collection from driving simulator. In this part, we collected

vehicle parameters, the locations of subject vehicle and lead ve-

hicle in horizontal and vertical coordinates, instantaneous ve-

locity, acceleration, heading and steering wheel angles. The de-

tailed description about experiment and data collection is pro-

vided in Section 4.1 .

2) Fuzzy Neural Network (FNN). In this part, we design its struc-

ture including four sub layers: input variables (distance be-

tween subject vehicle and lead vehicle, relative velocity, head-

ing and acceleration in the current lane), membership func-

tions, fuzzy reasoning mechanism and output variable (steering

wheel angles, α). We will introduce this part in Section 3.2 .

3) Adaptive learning algorithm. According to the prediction errors

(Root Mean Square Error: RMSE) between estimated ˆ α and ob-

served values α, the fuzzy membership functions will be auto-

matically split and then fuzzy rules will be updated. Based on

new FNN, ˆ α is updated and the new RMSE is then calculated. If

the value of RMSE is lower than a preset threshold ε, then the

prediction process is stopped and final prediction results can be

obtained. Otherwise, the learning process will be implemented

until achieving satisfactory prediction results.

.2. FNN based prediction model

The structure of an FNN contains five layers as shown in Fig. 2 .

he first layer is the input layer, in which the input variables are

tored and each node represents a variable. During the lane chang-

ng process, the driver needs to consider the relative traveling state

rom the lead vehicle and subject vehicle’s operating conditions.

herefore, we identified three relative indicators: the distance be-

ween the subject vehicle and lead vehicle in the horizontal and

ertical coordinates in the current lane ( �x and �y ), the relative

J. Tang et al. / Expert Systems With Applications 91 (2018) 452–463 455

Fig. 3. Driving simulator.

Fig. 4. Example of lane-changing route and data samples collected in the scenario with speed of 60 km/h.

Table 1

Prediction results of models in scenario with different speed.

Driving speed Errors indicators Prediction methods

AFNN SVM NN HMM MLR

60 km/h RMSE 3.5452 4.2356 4.9739 6.5389 8.7299

MAE 2.5989 3.1184 3.8044 4.7545 6.3193

MPAE (%) 5.3405 13.0394 15.2897 17.7280 22.6091

80 km/h RMSE 3.0328 3.9652 4.4112 5.2001 7.1378

MAE 2.3931 3.3412 3.6687 3.9358 4.9817

MPAE (%) 6.0714 9.33831 11.6137 12.1526 14.5196

100 km/h RMSE 2.8993 3.8893 4.3430 5.0286 6.8353

MAE 2.3148 3.3325 3.6392 4.0846 5.0810

MPAE (%) 8.2763 10.3062 12.9601 13.1356 17.5457

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elocity between subject vehicle and lead vehicle ( �v ) (Here, it

hould be noted that three relative indicators are calculated on

he basis of lead vehicle in the coordinate system), and two in-

icator of subject vehicle: traveling heading ( θ ) and acceleration

acc ). In the second layer, the input values can be transformed into

uzzy values or membership degrees to which they belong to the

embership functions. Each node in the second layer represents

membership function. The third layer represents rule reasoning

rocess, in which a Takagi–Sugeno type fuzzy inference is adopted.

he fourth layer represents fuzzy quantification of the output vari-

bles. As the control and adjustment of the driver to subject vehi-

le in the lane changing process are accomplished by fusing infor-

ation of the external environment and operating steering wheel,

he steering wheel angle is the direct indicator reflecting driver’s

ehavior. So, the output variable in this layer is determined as the

teering wheel angle. This layer integrates contributions of differ-

nt rules. Finally, the fifth layer represents the real values of the

utput variable.

In the FNN, we used a Takagi–Sugeno type fuzzy inference sys-

em to construct fuzzy rules. For each input sample, X = [ �x , �y ,

v , θ , acc ], has n memberships describing the degree, the number

f rules is equal to n 5 . The i th rule is shown as follows:

R i : IF ( �x and is A i ) and ( �y is B i ) and ( �v and is C i ) and

( θ is D ) and ( acc is E ) THEN y is f ( �x, �y, �v , θ, acc )

i i i i

456 J. Tang et al. / Expert Systems With Applications 91 (2018) 452–463

Fig. 5. Initial membership functions of five input variables.

w

b

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α

w

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i

where A, B, C, D, E indicate a fuzzy set defined by its membership

function, X i is the antecedent variable, and f i is the inference con-

sequence of variable y when the i th rule is employed. In this study,

the fuzzy membership functions are selected to be trapezoid type.

The reason is that the drivers will not quickly change their driving

behavior due to slight changes of external environment during lane

changing process. Compared to the triangle function or Gaussian

function, the values of membership degree in trapezoid function

can remain constant when input variables distribute in a certain

range. So, the trapezoid function with four parameters is defined

as follows:

m (x ) =

⎧ ⎪ ⎨

⎪ ⎩

x − a/b − a a ≤ x < b 1 b ≤ x < c d − x/d − c c ≤ x < d 0 x < a or d < x

(3)

here, m is defined as membership function of input variables, a,

, c, d are the parameters to determine the type of function. Over-

ll, the total number of membership functions is 5n . In the model,

e use a first-order Takagi–Sugeno type ( Takagi & Sugeno, 1985 )

o complete fuzzy inference system. The function f i ( �x , �y , �v, θ ,

cc ), i = 1,2,…K, K = n 5 , is a linear function. So, for an input data

oint X

0 = [ �x 0 , �y 0 , �v 0 , θ0 , acc 0 ], the inferring results of the sys-

em, ˆ α0 , can be calculated as the weighted average of outputs from

ach rule:

ˆ 0 =

∑ K i =1 w i · f i (�x 0 , �y 0 , �v 0 , θ0 , ac c 0 ) ∑ K

i =1 w i

(4)

here, w i is the membership degree achieved for the i th rule,

i =

∏ l j=1 m ( X j ) , j = 1,2,…, l, l = 5, and m ( X j ) represents the mem-

ership degree of input variable X j activated in the i th rule. For

he parameter estimation, we used a least squares estimator (LSE)

n ( Goodwin & Sin, 1984; Hsia, 1977 ) to train the linear functions.

J. Tang et al. / Expert Systems With Applications 91 (2018) 452–463 457

Fig. 6. Convergence of training errors.

E

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w

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X

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E

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t⎧⎨⎩w

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ach of the linear function can be described as follows:

= β0 + β1 X (1) + β2 X (2) + ... + βl X (l) (5)

The training dataset included p data pairs, {([ X (1, i ), X (2, i ),…,

( l,i )], y i ), i = 1,2,…, p }, X ( l,i ) means the i th data sample of the l th

nput variable. The dataset was used to calculate the coefficients

= [ β0 β1 β2 …β l ] T via the following equation based on LSE:

B = P A

T y

P = ( A

T A) −1 (6)

here

=

⎛

⎜ ⎜ ⎝

1 X (1 , 1) X (2 , 1) · · · X (l, 1) 1 X (1 , 2) X (2 , 2) · · · X (l, 2) . . .

. . . . . .

. . . . . .

1 X (1 , p) X (2 , p) · · · X (l, p)

⎞

⎟ ⎟ ⎠

nd

= [ y 1 y 2 y 3 . . . y p ] T

Define the k th row vector of matrix A in Eq. (6) to be r T k = [1

(1, k ) X (2, k ) … X ( l,k )] and denote the k th element of y as y k .

hen the vector of coefficient B can be iteratively calculated by

q. (7) shown in the following. The calculation process uses a re-

ursive, improved LSE method [25,26] to complete the optimiza-

ion.

B k +1 = B k + P k +1 r k +1 ( y k +1 − r T k +1

B k )

P k +1 =

1

λ( P k −

P k r k +1 r T k +1

P k

λ + r T k +1

P k r k +1

) k = t, t + 1 , . . . , p − 1

(7)

here λ is the forgetting factor and its value is generally between

.8 and 1.0, B t and P t are the initial values of B and P , which can be

alculated in Eq. (6) by using the first t data pairs from the train-

ng dataset. Here, we define the g as the split ratio, if p represents

he total number of training samples, then g ∗p is the number of

amples used in first step and (1 − g ) ∗p indicates the number of

amples used in second step. In this study, we set g as 0.5 and λs 0.85.

.3. The learning algorithm

In the FNN, the rule base and rule inference are the most im-

ortant parts to determine the effect of prediction. Generally, we

rstly preset rules and set up inference mechanism, then optimize

he system parameters, and finally obtain prediction result. How-

ver, due to the rules are preset, the rules may be inaccurate or

nadequate, which will seriously affect prediction performance. In

his section, we design an adaptive learning algorithm. According

o the prediction errors, it can adaptively adjust membership func-

ion and improve the rule inference mechanism, and prediction ac-

uracy can be enhanced eventually.

The prediction errors of FNN can be defined as the difference

etween estimated and the actual steering angles:

= α − ˆ α (8)

Given a set of N training data samples, the Root Mean Squared

rror (RMSE) is defined as the:

MSE =

√

1

N

N ∑

i =1

( αi − ˆ αi ) 2

(9)

The process of learning algorithm includes following several

teps:

Step 1: Calculate prediction error RMSE in Eq. (9) ;

Step 2: Compare the error: if RMSE ≤ ε then quit, otherwise go

to the next step;

Step 3: Find out all the rules are used in FNN, and identify

the rule make greatest contribution for the output values in

Eq. (4) , in other word, determine the corresponding fuzzy

rule with highest weights, max( w ), and identify the fuzzy

sets involved in membership function of all input variables;

Step 4: Equally divide these fuzzy sets into two parts, which

means split fuzzy area and replace each fuzzy set with two

new one, for each run of the learning algorithm, 2 5 new

rules are created in the rule base;

Step 5: Construct new Takagi–Sugeno inference system, use im-

proved LSE method in Eq. (7) to update optimal parameters,

and then predict new values of steering angles in FNN, then

go to the Step1 and Step 2.

. Experiments

.1. Data collection

The experiments are conducted in a driving simulator shown in

ig. 3 , which is installed sensors to collect dynamic data of sub-

ect vehicle, such as acceleration, braking and steering. The sim-

lator is also equipped with a sound system which can simulate

ounds from vehicle engine, tires. The body of the simulator is

upported by hydraulic cylinders to allow six degrees of freedom.

hree screens projecting the virtual environments are placed in

ront of the cab with a visual angle of 48 ° wide and 36 ° high. Two

dditional screens are located behind the cab so that subjects can

iew vehicles traveling behind them by scanning the mirror. The

rojector has a resolution of 1280 × 768 pixels and a frame rate

f 60 Hz to ensure a smooth and delicate simulating environment.

total of 47 experienced drivers (22 female and 25 male) ranging

rom 29 to 47 years old are recruited for the experiments. Each ex-

erienced driver has held a driving license more than 5 years with

n average annual driving distance of at least 80 0 0 km.

A van (6915 mm in length, 2150 mm in width and 2260 mm

n height) serves as the lead vehicle. The driving behavior takes

lace on a simulated road with two lanes, and each lane is 3.5 m

n width. In addition, traffic signs, buildings, guardrails and trees

458 J. Tang et al. / Expert Systems With Applications 91 (2018) 452–463

Table 2

Sensibility analysis of variables to prediction results.

Speed variables removed 60 km/h 80 km/h 100 km/h

RMSE MAE MPAE (%) RMSE MAE MPAE (%) RMSE MAE MPAE (%)

4.8687 3.9752 15.5852 4.8433 3.5254 15.6263 4.4918 3.3484 11.3987

Acc 4.7698 3.5490 13.5736 4.1347 3.0127 13.7168 4.1277 3.2724 10.6726

θ and acc 5.4451 4.5543 16.4923 5.9743 4.5707 19.9665 5.3622 4.1475 15.0216

Fig. 7. Final membership functions of five input variables after four times iterations.

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are designed to construct a realistic driving environment. In the

simulation of lane change, a lead vehicle is traveling in the front

of subject vehicle with constant speed, and the experiments are

conducted under different speed levels of lead vehicle: 60 km/h,

80 km/h and 100 km/h respectively.

Before the experiment, every subject needs to fill out a ques-

tionnaire about their age, date when they have had a drivers’ li-

ense and driving mileage. Then, a member of our research team

resents the driving simulator and the driving task. A practice ses-

ion is conducted prior to the experiments to ensure subjects be-

oming familiar with the driving simulator. Then each subject will

irectly finish the driving task in scenarios where the lead vehicle

uns at speed levels of 60 km/h, 80 km/h and 100 km/h respectively.

or each scenario, drivers need to successfully complete three valid

J. Tang et al. / Expert Systems With Applications 91 (2018) 452–463 459

Fig. 8. Prediction results of steering angles for four drivers in scenario with speed of 60 km/h.

l

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ane changing tasks. Finally, we can obtain totally 141 lane chang-

ng data samples under each scenario. Fig. 4 shows an actual data

ample. Fig. 4 a expresses a lane changing trajectory in a relative

oordinate system, dash line represents the center of lanes, and the

aximum left position is near the center line of left lane. Fig. 4 b,

, d, e, f show the distribution of five input variables: �x , �y , �v,

, acc . Fig. 4 g expresses data distribution of output variable: steer-

ng angle α. As the data were recorded with a frequency of 60 Hz,

hus, 1 time step in this study equals 0.017 s. In the simulation, the

ead vehicle is stationary before the experiment starts, and it will

ccelerate to the designed speed and keep unchanged until the ex-

p

eriment ends. The subject vehicle firstly follows the lead vehicle

t a safe and comfortable distance. Based on the previous designed

asks, the subject vehicle then will accelerate to finish lane chang-

ng behavior on the premise of ensuring safety.

.2. Model validation and results discussion

In the validity test of the model, we divide lane changing data

amples into two parts: two-thirds of samples from each driver are

ntegrated as the training dataset, and the other one-third of sam-

les are composed as testing dataset. Additionally, we define three

460 J. Tang et al. / Expert Systems With Applications 91 (2018) 452–463

Fig. 9. Prediction results of steering angles for four drivers in scenario with speed of 80 km/h.

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indicators as the criteria for evaluating the effect of the prediction:

mean absolute error (MAE), the mean absolute percentage error

(MAPE) and the root mean square error (RMSE), the definition of

RMSE can be seen in Eq. (9) .

MAE =

N ∑

i =1

| αi − ˆ αi | N

(10)

MAPE =

1

N

N ∑

i =1

| αi − ˆ αi | αi

× 100% (11)

Here, we take the lane-changing data samples collected in the

cenario with speed of 60 km/h as an example to introduce the

earning process and prediction results of the proposed method.

ig. 5 shows the initial membership function for the five input

ariables, and the μ indicates degree of membership. For each in-

ut variable, we define three fuzzy subsets to represent its val-

es from low level to high level. As we mentioned before, all the

uzzy subsets use trapezoid function to present membership de-

ree. Fig. 6 shows the distribution of training errors using the pro-

osed learning algorithm. We use the RMSE to evaluate errors. The

umber of iterations represents the running number of learning

J. Tang et al. / Expert Systems With Applications 91 (2018) 452–463 461

Fig. 10. Prediction results of steering angles for four drivers in scenario with speed of 100 km/h.

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lgorithm introduced in Section 3.3 . As the figure shows, with the

ncrease of the number of iterations, the training error decreases.

urthermore, this decreasing pattern contains two parts: when the

umber of iterations is less than four, the error declines rapidly;

hen the number of iterations is higher than four, the error de-

reases slowly and gradually tends to be stable. We can conclude

hat the improvement of model predicting ability is limited af-

er learning algorithm implementing four iterations. Therefore, we

hoose the model with four learning iteration as optimal system

o predict steering angles. Fig. 7 provides the distribution of the

embership function of five input variables after four iterations,

nd the μ indicates degree of membership. In each iteration, an

nvolved fuzzy subset will be split into two sets. There are two

umbers in the bracket for each subset. The first one indicates the

umber of iterations, and the second one represents the number

f the divided subset. For example, x 1 (4,1) means the first part of

uzzy subset x 1 belongs to variable �x was split in the fourth it-

ration. Fig. 8 shows the prediction results of steering driver using

rained AFNN model, and we only display perdition performance of

our drivers. In the figure, black line represents the actual data col-

ected from simulator, and the red line means the predicted steer-

ng angles. As we can see, the prediction model proposed in this

tudy can successfully and accurately follow the pattern of actual

ata, which indicates strong predicting ability of AFNN model.

462 J. Tang et al. / Expert Systems With Applications 91 (2018) 452–463

(

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Similarly, we also show the results of four individual drivers

in the environments with speed of 80 km/h and 100 km/h in

Figs. 9 and 10 . The numbers of iterations for these two experi-

ments are 3 and 4 respectively. Stable and accurate prediction re-

sults also verify the effectiveness of the proposed method. As the

AFNN model belongs to Machine Learning Method, we compare

predicting performance of proposed method with several conven-

tional methods to express learning ability of AFNN: Neural Net-

work (NN), Support Vector Machine (SVM), Hidden Markov Model

(HMM) and Multivariable Linear Regression (MLR). For all other

methods, we use the same input and output variables, same train-

ing and testing dataset with the AFNN. Table 1 shows prediction

accuracy of the four methods under different speed conditions ac-

cording to the three error indicators. As can be seen from the table,

because of simple structure and weak learning ability, the predic-

tion accuracy of MLR is lower than the other three methods. Com-

pared to SVM and NN, AFNN improves the results, which because

of the learning mechanism used in this study. For one thing, an im-

proved LSE method is adopted to enhance the optimization effect

of parameter in Takagi–Sugeno model of FNN. For another thing,

through applying adaptive learning algorithm, the fuzzy member-

ships are updated, the fuzzy rules are enriched, and finally the ra-

tionality and accuracy of rule reference are improved. Taking RMSE

as example, the prediction accuracy of AFNN increases by approxi-

mately 40% compared to NN and about 20% compared to SVM.

In previous studies, researchers generally consider the relative

indicators between subject vehicle and other vehicles to analyze

lane changing behavior. In this study, the input variables of predic-

tion model include not only relative indicators: �x , �y , �v , but

also parameters of subject vehicle: θ , acc . Accordingly, we employ

a sensitivity analysis to further study the influence of subject ve-

hicle parameters on prediction results. Table 2 provides the pre-

diction results of AFNN by removing input variables θ and acc . It

can be observed firstly that the removal of any one parameter will

result in the deterioration of prediction performance, which shows

that the heading and acceleration are two important factors need

to be considered in the process of lane change. We can also find

that the prediction results of model removing acc is worse than

that of model removing θ , which shows that heading angles, as a

key information for the lane change, is more important than accel-

eration in steering angle prediction. It can be imagined that vehicle

heading plays a significant role when driver controls the steering

wheel to finish lane-changing behavior.

5. Conclusion

In this paper, we introduced an adaptive fuzzy neural network

to predict driver’s lane-changing behavior. In the prediction model,

we define the distance between the subject vehicle and lead vehi-

cle in the horizontal and vertical coordinates in the current lane

( �x and �y ), the relative velocity between subject vehicle and

lead vehicle ( �v ), traveling heading ( θ ) and acceleration ( acc ) as

input variables and steering wheel angles ( α) as output variable.

The trapezoid function is used as membership function. Further-

more, a first-order Takagi–Sugeno model is used to finish fuzzy in-

ference, in which an improved LSE method is applied to optimize

modeling parameters. In the adaptive learning algorithm, according

to the prediction errors, membership functions and fuzzy inference

are updated to improve prediction performance.

In the experiments, data of input and output variables were col-

lected through vehicle simulator. Three different scenarios were

designed with different speed of lead vehicle: 60 km/h, 80 km/h

and 100 km/h. Total 47 drivers took part in the experiments, and

141 valid lane changing data samples were collected to train and

validate prediction model. In the results analysis, we define three

indicators to evaluate prediction performance: mean absolute error

MAE), the mean absolute percentage error (MAPE) and the root

ean square error (RMSE). The prediction results indicate effec-

iveness and stability of the proposed model. Moreover, we fur-

her compare the AFNN with three traditional machine learning

ethods: Neural Network (NN), Support Vector Machine (SVM)

nd Multivariable Linear Regression (MLR), and the comparison re-

ults show that the AFNN can achieve higher prediction accuracy

han the other three methods for its strong learning ability. Finally,

hrough sensibility analysis of subject vehicle parameters heading

θ ) and acceleration ( acc ), we find that these two input variables

lay an important role in prediction of steering angles and they are

wo key factors need to be considered in lane-changing process.

he works from this study will be helpful to improve the practical

ffects of ADAS and enhance lane changing safety.

While, in the future research, we will improve the current work

rom following several aspects: Firstly, for the vehicle model, we

nly use a simplified movement model of a four wheeled vehicle.

owever, in a real environment, the traveling status vehicle will

e more complex; Secondly, in the simulation experiments, all the

rivers are experienced, and the novice drivers are not considered.

herefore, future research may consider difference of lane changing

ehavior between experienced and novice drivers; Thirdly, more

nformation extracted from different data source ( Tang, Liu, Wang,

Wang, 2015, Tang, Zhang, Wang, Wang, & Liu, 2015, Tang, Zou,

t al., 2016, Tang, Jiang, et al., 2016, Tang, Liu, Zou, Zhang, & Wang,

017; Yan, Zhang, Tang, & Wang, 2017; Zhang, Tang, Wang, Wang,

An, 2017; Zou, Yang, Zhang, Tang, & Zhang, 2017, Zou, Tang, Wu,

enrickson, & Wang, 2017 ) can help to enhance prediction perfor-

ance. Finally, in the input variables of prediction model, we con-

ider the relative indicators between the subject vehicle and lead

ehicle. However, lane change process is complex, and we should

ot only consider the safety distance in the current lane but also

he safe space in the target lane. In the next step, theses important

ndicators should be taken into account in the prediction model.

cknowledgments

This research was funded in part by the Foundation of Central

outh University (grant nos. 502045002 ) and National Natural Sci-

nce Foundation of China (grant nos. 71403068 and 61573009 ).

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