Design of an Improved Fuzzy Logic Based Model for Prediction of Car ...

Proceedings of the 2011 IEEE Intemational Conference on Mechatronics April 13-15, 2011, Istanbul, Turkey

Design of an Improved Fuzzy Logic Based Model for Prediction of Car Following Behavior Alireza Khodayari

#l¥

"4 #2 #3 , Reza Kazemi , Ali Ghaffari , Reinhard Braunstingl

#Mechanical Engineering Department, K. N. Toosi University o/Technology Tehran, Iran

'[email protected] '[email protected]

"

'[email protected]

Institute 0/ Mechanics, Graz University o/Technology Graz, Austria '[email protected]

¥

Currently works as a visiting student in Institute of Mechanics, Graz University of Technology, Graz, Austria.

Abst ract

Nowadays, car following models, as the most popular

-

microscopic traffic Dow modeling, are increasingly being used by transportation experts to evaluate new Intelligent Transportation System (ITS) applications. This paper presents a car following model that was developed using a fuzzy inference system (FIS) to simulate and predict the future behavior of a Driver-Vehicle­ Unit (DVU). This model was developed based on a new idea for estimating the instantaneous reaction of DVU, as an input of fuzzy model. The model's performance was evaluated based on field data.

The

instantaneous

results

reaction

showed that fuzzy model based on delay

outperformed

the

other

car

following models. The proposed model can be used in Driver Assistant Devices, Safe Distance Keeping Observers, Collision Prevention Systems and other ITS applications.

Keywords-car following, fuzzy logic, modeling, prediction, instantaneous reaction delay.

I.

INTRODUCTION

Intelligent transportation systems (ITS) are a multidisciplinary area with its focus on incorporating up-to­ date information technologies of all kinds in the field of transportation. Recent advances in intelligent and automated vehicles, and continuous improvements of information-based road infrastructures, have propelled research to understand their interactions and to evaluate them on a large scale. This evaluation will, in return, provide valuable feedback not only on how to improve the road-based information and control systems but on how to design vehicle-based intelligent systems. Simulation has become a cost-effective option for the evaluation of infrastructure improvements, on-road traffic management systems, and in vehicle driver support systems due to the fast evolution of computational modeling techniques. Moreover, a rapid development of sophisticated microscopic simulation models over the past decade has led to a tide of applications of microscopic simulation in transportation engineering [1].

Microscopic traffic flow modeling has gained lots of attention in the past 50 years. Microscopic Models are increasingly being used by transportation experts to evaluate new ITS application. A variety of applications including car navigation systems, Adaptive Cruise Control systems, Lane Keeping Assistance Systems and Collision Prevention Systems Directly use the Microscopic traffic flow Models [2]. Driving behavior differs among drivers. Every human driver follows his specific patterns while driving. This fact is observable in ordinary driving behaviors such as hitting the gaslbrake pedals, turning the steering wheel and distance keeping while following a vehicle. ITS applications are consequently expected to be customized and specialized for individual drivers according to their specific driving styles. Many Driver Assistant Systems require a model representing the typical driving patterns of the target driver in order to cooperate in the driving behavior. Driver Models can be trained either in offline or online manners and Driver Assistant Systems can use appropriate models for a certain driver through driver identification [3]. Car following models are among the most popular microscopic traffic flow modeling approaches aiming to describe the process of following a leader car by a vehicle. As shown in Fig. 1, car following describes the longitudinal action of a driver when he follows another car and tries to maintain a safe distance to the leading car. The majority of available car following models assume that the driver of the follower vehicle (FV) responds to a set of variables like relative velocity and relative distance between the leader vehicle (LV) and the FV, velocity of the FV, and/or desired distance and/or velocity of the target driver. The response is typically considered to be as acceleration or velocity changes of the following vehicle [4].

978-1-61284-985-0/11/$26.00 ©2011 IEEE 200

,

FoUOWtl'VtlllrIt

Ltadtl' Vtlllclt

Fig. 1, Car following behavior

_

J

(LV and FV) [4].

To develop microscopic traffic simulation of high fidelity, researchers are often interested in imitating human's real driving behavior at a tactical level. That is, without describing the detailed driver actions, nvus in the simulation are modeled to replicate their states in reality, i.e., the profiles of vehicle position, velocity, acceleration, and steering angle. Fig. 2 shows the model structure of a nvu in which the detailed driver actions become internal [1]. Vehicle system noise

Observation noise Obsen'ation inputs

!

Ji\ �q7

Human actions

l

p(t) (1 , ati) W

State

outputs

Vehicle dynamics 1-,-.

Control feedhark.�

Fig. 2, Structure of a DVU model [1].

A number of factors have been found to influence car following behavior, and these include individual differences of age, gender, and risk-taking behavior [5, 6]. Regarding literatures, car-following models can be classified into 14 groups as follows: Gazis-Rerman-Rothery [7], collision avoidance/safe distance [8], linear model! ReIly [9], action point [10], fuzzy logic-based model [11], desired spacing [12], capacity drop and hysteresis theory [13], neural network [14], optional velocity [15], adaptive neural fuzzy inference system [4], emotional learning fuzzy inference system [16], local­ linear neural fuzzy [17], local quadratic neural fuzzy [18] and genetic algorithm based optimized least squares support vector machine [19]. All models presented for car following behavior are evaluated based on their ability to predict or estimate of increase or decrease of FV acceleration. In a general classification, car following behavior microscopic models can be divided into 2 groups: mathematical equation-based and input-output based. The most important point in mathematical models is calculation and obtaining model parameters. Therefore, these parameters

were always chosen by average of experiment values and regarding them as a constant value of nyu. Because these parameters are a function of time, results of these models are match test cases only and are not reliable. In input-output models, by considering the fixed nvu reaction time, output values are applied to input. Since the nvu reaction time is not actually constant, other parameters vary with time. So an error in modeling results because of the difference between real data and data used for modeling [4]. The highly nonlinear nature of car following behavior necessitates the development of intelligent algorithms to describe, model and predict this phenomenon. Fuzzy logic can be a potential method dealing with structural and parametric uncertainties in the car following behavior. Integration of human expert knowledge expressed by linguistic variables is a powerful tool enabling fuzzy models to deal with uncertainties and inaccuracies [20]. In this paper, we are going to focus on fuzzy inference system design for modeling and prediction of car following behavior in real traffic flow, considering the effects of driver's behaviors. The presented model can be utilized in several applications of intelligent transportation systems. II. DESIGN AN IMPROVED FuZZY CAR FOLLOWlNG MODEL A more accurate representation of car following behavior should take into account the non-linearity of human response and limitations of human perception system, i.e. drivers may not be able to perceive relative speed and headway accurately, and the decision process (acceleration control) could be highly non-linear. A fuzzy inference system (PIS) can map between variables the driver can perceive and variables the driver can directly control with arbitrary accuracy based on 'fuzzy reasoning'. This makes the system natural and suitable to model a human-in-the-Ioop system [21]. Fuzzy systems are established on fuzzy logic which is based on the idea that sets are not crisp but some are fuzzy, and these can be described in linguistic terms such as fast, slow and medium. Fuzzy sets have boundaries that are not precise and are described by membership functions that are curves defining how each point in the input space is mapped to a membership grade. The transition from non-membership to membership is gradual rather than abrupt. The value of the membership is between 0 and 1. A membership degree of 1 represents certainty with respect to an entity belonging to a particular set. Fuzzy inference systems use IF-THEN-ELSE rules to relate linguistic terms defined in output space and input space. Every linguistic term corresponds to a fuzzy set. A PIS could then be used to represent the open loop mapping in car following processes, which is able to approximate any nonlinear function with arbitrary accuracy and therefore is able to identify car following behavior more accurately [21]. To design the fuzzy model, as shown in Fig. 3, it is assumed that the fuzzy inference system applied for the prediction model has four inputs and one output, whose inputs are instantaneous reaction delay, relative speed, relative distance and velocity of FV, and output is acceleration of FV.

201

xx

In4m!1

in4mQ

in4mn

RelativeOlslance

xx

CarFollowingModel

flu)

RelaliveSpeed

xx

(sug,no)

FVsV,'oo�

xx

FVsAcceleration

InstantaneousReadionDelav

0.2

0.6

04

0.8

Fig. 3, Designed car following fuzzy model.

We use Gaussian membership function for every fuzzy set. There are three membership functions for each input, as shown in Fig. 4 which inputs are relative distance (a), relative speed (b), velocity of FV (c) and instantaneous reaction delay (d). Inlmfl

inlmf3

inlm�

II

13

12

15

14

16

17

18

14

16

18

22

(d) Fig. 4, Inputs of fuzzy model, (a) relative distance, velocity of FV and (d) instantaneous reaction delay.

(b) relative speed, (c)

At fIrst, the rule base contains 81 fuzzy if-then rules of Takagi-Sugeno's type in the fuzzy car following model [22]. We total got 53 fuzzy rules, which have some corresponding relationship with the common sense when driving a car. For example, rule 1 means "if relative distance is much too close and relative speed is closing fast and FV speed is high and instantaneous reaction delay is large, then the negative acceleration is strong". The fuzzy surface is illustrated in Fig.5.

4DG

19

300 � lii 200 li c 0

(a) In2mfl

1.2

in2m�

()

in2ml3

�(j) 1'00 >. LL.

!J

·rnsta[1laneousReactionDela,(

RelaliveDistanGe

(a)

·2

(b) In3mfl

in3m!3

in3mf2

:z

N

"-

InstantaneQusReactionDelay.

20

JO

40

511

60

70

80

90

1l1li

Rel8tiveSpeect

(b)

liD

(c)

202

In June 2005, a dataset of trajectory data of vehicles travelling during the morning peak period on a segment of Interstate 101 highway in Emeryville (San Francisco), California has been made using eight cameras on top of the 154m tall 10 Universal City Plaza next to the Hollywood Freeway US-lO1. On a road section of 640m, as shown in Fig. 6, 6101 vehicle trajectories have been recorded in three consecutive IS-minute intervals. This dataset has been published as the "US-lOl Dataset". The dataset consists of detailed vehicle trajectory data on a merge section of eastbound US-lOl. The data is collected in 0.1 second intervals. Any measured sample in this dataset has 18 features of each driver-vehicle InstantaneousReae:tionDelay FVsVeloctty unit in any sample time, such as longitudinal and lateral (c) position, velocity, acceleration, time, number of road, vehicle class, front vehicle and etc. Fig. 5, The fuzzy surface of model for FV acceleration output [Takagi­ The trajectory data seem to be unfiltered and exhibit some Sugeno's parameter], (a) relative distance and instantaneous reaction delay, (b) relative speed and instantaneous reaction delay, (c) velocity of FV and noise artefacts, so we have applied a moving average filter to instantaneous reaction delay. all trajectories before any further data analysis. Comparison of unfiltered and filtered data is shown in Fig. 7. III. DISCUSSION AND RESULTS 4r----,-----,---,-,

In order to evaluate the competence of fuzzy estimator system based on the instantaneous reaction delay idea, another fuzzy estimator system without instantaneous reaction delay input was designed. And also, that car following behavior model was simulated and verified using actual measured values as inputs. Real car following data from US Federal Highway Administration's Next Generation Simulation (NGSIM) dataset [23] is used to validate the model and to assess its performance.

10

15

20

Time(sec)

35

40

Fig. 7, Comparison of unfiltered and filtered data.

To estimate driver reaction delays from real data, several approaches have been proposed. Now the reaction time of the two actions, acceleration and deceleration, are analyzed using the observed data of many LV-FV in the actual traffic flow. Fig. 8 indicates how the DVU instantaneous reaction delay can be calculated by using the proposed idea [4]. This idea is based on the fact that the delay time is the time between stimulus and reaction. In car following behavior, the variation of relative velocity and acceleration of FV is the concept of the stimulus and reaction. Variations in relative velocity and FV acceleration are the maximums or minimums of velocity trajectory or FV acceleration, respectively. DVU instantaneous reaction is the time difference between two subsequent variations: relative velocity as stimulus and FV acceleration as reaction. The reaction time of each action is collected from the observed data in the range from 3.5 sec to -1.5 sec. If the calculated reaction time might be negative, reaction time is assumed to be null in the simulation.

Fig. 6, A segment of Interstate 101 highway in Emeryville, San Francisco, California [23].

203

Relative Velocity(m's) - AcceleratiorVDeceleration(mls2)

absolute percentage error (MAPE), according to equation (1), shows the mean absolute error can be considered as a criterion for model risk for using it in real world conditions. Root mean squares error (RMSE), according to equation (2), is a criterion for comparing error dimension in various models. Standard deviation error (SDE), according to equation (3), indicates the persistent error even after calibration of the model. In these equations, xi shows the real value of the variable being

•••••.

, ,

, ,

modeled (observed data),

Xi

shows the real value of variable

modeled by the model and x is the real mean value of the variable and N is the number of test observations [24]. Tim:(sec)

Fig. 8, Calculation nyu instantaneous reaction delay based our new idea [4].

Fig. 9 shows the performance results for FlS estimator for DVU car following behavior based on instantaneous reaction delay as input to estimate the FV acceleration. As seen in this figure, the trajectories of real driver and fuzzy model are quite the same. Fig. 10 shows the performance of FlS estimator for DVU in car following behavior without instantaneous reaction delay input to estimate the FV acceleration. 2.5,----.".---,----,---,...., Real , 2 -Model",

MAPE

=

RMSE

=

lOot IXi -Xi I N

1

i=1

-

N

N

(x." -x.) L i=1 A

RESULT OF ERROR FOR FuZZY CAR FOLWWING MODEL Fuzzy Car Following Model

�0.5

·

1

·1.5 ·

o

with instantaneous reaction delay input instantaneous without reaction delay input

,

- -1-

-

-1---

,

2 L-_-L__�__L-_-L__�__L-_�__�

15

20 TiJre(s)

25

30

35

40

RMSE

SDE

0.2392

0.3247

0.0298

0.5449

0.4863

0.0486

IV. CONCLUSION

Fig. 9, Results for fuzzy estimator with instantaneous reaction delay input.

In this paper, a fuzzy model for DVU in car following was studied. This model uses instantaneous reaction delay for DVU as an input. In this model, the stimulus and reaction should be considered as an input and output with respect to accurate instantaneous reaction time. Satisfactory performance of the proposed model is demonstrated through comparisons with real traffic data and also the results of other fuzzy model. The simulation results show the efficiency of the proposed model in driver modeling and prediction of the driver's actions comparing with other model. The proposed model can be used in driver assistant devices, safe distance keeping observers, collision prevention systems and other ITS applications.

3 .'-"Real - Model

51 " o ro

l:o�

Error Criteria MAPE

Fuzzy car following model based on instantaneous reaction delay has a lower error value comparing with fuzzy model in all 3 criteria. This result shows that this new model has a strong capability with respect to other models.

- _1- _ _

10

(3)

TABLE I

e

o

2 )

Errors in modeling with considering MAPE, RMSE and SDE are summarized in Table I.

�I

�'{).5

(2)

100

1.5

]

2

MAPE

·····

0 -

(1)

Xi

10 -'--15 -'--20 -'--25 30 -'35 "---40 "---' _ _. -'----'---

REFERENCES

TiJre(s)

[I]

Fig. 10, Results for fuzzy estimator without instantaneous reaction delay input.

To examine the performance of developed models, various criteria are used to calculate errors. The criterion mean

[2]

204

x. Ma, I. Andreasson, "Behavior Measurement, Analysis, and Regime Classification in Car Following", IEEE Transactions on Intelligent Transportation Systems, vol. 8, no. 1, pp. 144-156, 2007. P. Y. Li and A. Shrivastava, "Traffic flow stability induced by constant time headway policy for adaptive cruise control vehicles", Transportation Research Part C, (2002).

[3]

[4]

[5]

[6]

[7]

[8]

[9]

C. Miyajima, Y. Nishiwaki, K. Ozawa, T. Wakita, K. Itou, K. Takeda, and F. Itakura, "Driver Modeling Based on Driving Behavior and Its Evaluation in Driver Identification", Proceedings of the IEEE, Vol.95, No.2, 2007. A. Khodayari, A. Ghaffari, R. Kazemi, N. Manavizadeh, "ANFIS Based Modeling and Prediction Car Following Behavior in Real Traffic Flow Based on Instantaneous Reaction Delay", 13th International IEEE Conference on Intelligent Transportation Systems (ITSC 2010), Portugal, pp. 599-604, 2010. S. Panwai, H. Dia, "Neural Agent Car.Following Models", IEEE Transactions on Intelligent Transponation Systems, vol. 8, no. 1, pp. 60.70, 2007. A. Khodayari, A. Ghaffari, S. Ameli, J. Falahatger, "A Historical Review on Lateral and Longitudinal Control of Autonomous Vehicle Motions", the 2010 IEEE International Conference on Mechanical and Electrical Technology (ICMET 2010), Singapore, pp. 421-429, 2010. K. I. Ahmed, "Modeling divers. acceleration and lane changing behavior", Sc.D. Dissenation, Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, Cambridge, Massachusetts, 1999. R. Tatchikou, S. Biswas, F. Dion, "Cooperative Vehicle Collision Avoidance using Inter-vehicle Packet Forwarding", IEEE Global Telecommunications Conference (GWBECOM'05), vol. 5, pp. 27622766, 2005. T. H. Yang, C. W. Zu, "Linear dynamic car-following model", Fifth

[24]

World Congress on Intelligent Control and Automation (WCICA04),

[10]

[11]

[12]

[13]

[I4]

[I5]

[I6]

[17]

[18]

[I9]

[20]

[21]

[22] [23]

vol. 6, pp. 5212- 5216, 2004. W. Wang, W. Zhang, D. Li, K. Hirahara, K. Ikeuchi, "Improved action point model in traffic flow based on driver's cognitive mechanism., IEEE Intelligent Vehicles Symposium, pp. 447- 452, 2004. P. Zheng, M. McDonald, "Application of Fuzzy Systems in the Car­ Following Behavior Analysis", Lecture Notes in Computer Science, Springer, book: Fuzzy Systems and Knowledge Discovery, vol. 3613/2005, pp. 782-791, 2005. P. Hidas, "Modeling vehicle interactions in microscopic simulation of merging and weaving", Transponation Research Pan C: Emerging Technologies, vol. 13, no. 1, pp. 37.62, 2005. Z. Li, F. Liu, Y. Liu, "A Multiphase Car-Following Model of Traffic Flow and Numerical Tests", IEEE International Conference on Automation and Logistics, pp. 6-10, 2007. S. Panwai, H. Dia, "A Reactive Agent-Based Neural Network Car Following Model", the 8th International IEEE Conference on Intelligent Transponation Systems, pp. 375- 380, 2005. M. Kanai, K. Nishinari, T. Tokihiro, "Stochastic optimal velocity model and its long-lived metastability", Phys. Rev. E, vol. 72, no. 3, 2005. A. Ghaffari, R. Zarringhalam, M. Abdollahzade, ''ELFIS based Modeling and Prediction of Driver-Vehicle-Unit.s Behavior in Real Traffic Flow", Elsevier, Engineering Applications of Anificial Intelligence (in press), 2010. A. Ghaffari, R. Zarringhalam, M. Abdollahzade, "Predicting the Future States of a Vehicle in a Car-Following Scenario Using Locally Linear Neuro-Fuzzy Models and LOLIMOT Learning Algorithm", IS 2008 . IEEE International Conference on Intelligent Systems, 2008. R. Zarringhalam, .Modeling, "Prediction, and Control of Traffic Flow Regarding the Driver.s Microscopic Behavior", M.Sc. Thesis in Mechanical Engineering, K. N. Toosi University of Technology, Iran, 2008. A. Ghaffari, R. Zarringhalam, M. Abdollahzade, "GA-LSSVM: an inventive method and its application in simulation and prediction of microscopic traffic flow", Elsevier, Simulation Modeling Practice and Theory (in press), 2010. A. Khodayari, A. Ghaffari, R. Kazemi, N. Manavizadeh, "Modeling and Intelligent Control Design of Car Following Behavior in Real Traffic Flow", IEEE International Conference on Cybernetics and Intelligent Systems (CIS201O), Singapore, pp. 261-266, 2010. P. Zheng, M. McDonald, "Application of Fuzzy Systems in the Car­ Following Behaviour Analysis", Fuzzy Systems and Knowledge Discovery, Springer, vol. 3613, pp. 782-791, 2005. B. Kosko, "Neural Networks and Fuzzy Systems", Prentice-Hall, 1991. US Department of Transportation, ''NGSIM - Next Generation Simulation", ngsim.jhwa.dot.gov, 2009.

205

J. R. Taylor, "An introduction to error analysis: the study of uncertainties in physical measurements", University Science Books, Mill Valley, CA, 1982.