Research on Vehicle Lane-Change Driving Behavior Based on Optimal Velocity Model

Vehicle lane-change driving behavior affects the safety of vehicle driving and the stability of traffic flow, and it has great significance to establish a reasonable lane-change driving behavior model for studying lane-change driving characteristics and developing driver assistance system. The influence of the associated vehicle driving state on the lane-change behavior during the changing process is analyzed, and the driving behavior model based on optimal velocity model is established by using the vehicle following theory. The Theil`s U objective function is used to calibrate the model parameters, the prediction results of the model are compared with the actual measured results. The study shows that the lane-change behavior can be approximately described as the two kinds of car following behavior in the original lane and the target lane to the front car. The lane-change model established can truly describe the lane-change driving characteristics.


Introduction
Vehicle lane-change driving is a common behavior in multi-lane traffic flow. It has a direct impact on the safety of vehicle driving and the stability of traffic operation. Studying vehicle lane-change driving behavior and building reasonable modeling method are of great significance for the design and development of the driver's auxiliary system and the vehicle automatic driving system to ensure the safety of the road traffic.
Scholars at home and abroad have studied vehicle driving behavior from different angles. For example, Gipps [1] established a decision structure model of urban road change early, which took into account the influence of traffic signals, obstacles and vehicle types on the changing behavior; Zhang Y. et al [2] established the MRS changing model and concluded that the changing motive was mainly determined by the characteristics of the driver and the stimulus from the external driving environments; Kesting et al. [3] proposed a lane changing model to judge vehicle lane changing behavior and avoid risk by using longitudinal acceleration; Zheng Z. [4] put forward the vehicle changing rule through studying the traffic simulation model; Talebpour [5] proposed a vehicle routing model based on game theory and verified it by experimental data; and Shi [6], combining the vehicle following process with the changing process, established the longitudinal acceleration model in the process of the vehicle arbitrariness based on the full velocity difference model. Wang [7] put forward a car following model with two front cars based on two models of the full velocity difference following and the probability lane changing. There have more researched on the lane changing rules [8,9], while study on the comprehensive influence of the driving state of the associated vehicle and the lateral displacement of the changing vehicle on the change of the driving behavior is so less that the lane changing characteristics under the typical lane-change case cannot be well reflected.
In this paper, vehicle lane-change driving behavior is analyzed, and the classic vehicle-following model that only considering the influence of single car information on the following car is extended to the a new, which considering the influence of driving states on original lane and target lane on the changing vehicle. A model of driving behavior based on the optimal velocity following model is established, also a reasonable model of parameter calibration is put forward to verify the correctness of the lane-changing model.

Vehicle Changing Behavior
According to the different driving motivation, the behavior of vehicle changing can be divided into mandatory and random characters [10], no matter what the changing behavior should be realized through the driver's perceptiondecision -execution. The driver should make a series of decisions in a short time [11,12]. Figure 1 shows a typical sketch of the vehicle lane change.

Change of the Weight Coefficient in Lane-Changing
The

The Establishment of Vehicle Change
Behavior Model

Optimal Velocity Following Model
Vehicle following refers to the process of following the forward vehicle when the vehicle is lined up in a single lane without overtaking. The typical vehicle following process is shown in Figure 3. Vehicle following model is an important microscopic traffic flow model to study vehicle following behavior. In 1995, Bando et al [13] put forward the Optimal Velocity model based on the speed optimization function of vehicle spacing. It is expressed as: Where α represents the reaction sensitivity coefficient of drivers; ( ) Where max v represents the maximum vehicle speed; c h represents the safe distance between vehicles.

The Establishment of a Lane-Changing Model
During changing lane, the driving behavior of lane-changing vehicle is divided into three stages: perception-decision-execution. In the perception stage, lane changing drivers perceive the driving state of the current vehicle and the surrounding vehicles. The perception variables usually include the location, speed, acceleration of the vehicle, the location, speed and acceleration of the surrounding vehicles, as well as the distance between the vehicle and the surrounding vehicle, the relative speed, etc. In the decision stage, lane changing drivers make decisions on perceived variables according to different rules and driving behavior models, and the decision variables are generally the acceleration or speed of the vehicle. At the execution stage, the driver adjusts the driving state according to the driving decision [14]. Taking the acceleration of lane changing vehicle as the decision variable, the schematic diagram of the lane changing model is shown in Figure 4.

Changing Rules of Weight Coefficient
In the process of changing the lane, taking the left lane-change as an example, the lateral position of the lane-change vehicle is restricted. The longitudinal direction of the vehicle is x axis and the lateral migration is y axis. The shadow part in Figure 5 shows the start and terminal range of the lane-changing vehicle. Where ω represents the width of the vehicle, H represents the width of the lane.  Put formula (1) and (2) into formula (3), the model of lane-change driving behavior based on the optimal velocity following model is established, then it is expressed as: The determined parameters of the lane-change driving behavior model are: 0

Parameter Calibration of Vehicle Lane-Change Driving Behavior Model
The purpose of parameter calibration is to keep the traffic simulation data from the model to be consistent with the actual traffic data. By constructing the objective function, it is used to reflect the difference between the simulation data of the model and the real data, and then to find the parameters that make the objective function minimum, that is, the value of the calibrated parameter.

The Determination of the Objective Function
The constraint condition of objective function is the effective range of parameters in the model. We use the following general formula to express the parameter calibration problem in microscopic traffic model. Then, it is expressed as:

Parameter Calibration of Lane-Changing Model
The Binhai Road of Huangdao Development Zone in Qingdao is selected as the data collection point, and the driving states of 50 vehicles at different time are randomly recorded. The test data are processed according to the real-time monitoring video and running track of the vehicle to to determine the changing behaviors and the starting and stopping points of the vehicles. For vehicle n, r n (t) represents the vehicle location at any time t, ∆t represents data sampling time interval, r n (t i ) represents the vehicle location at the time of data sampling t i .  Table 1. 50 groups of lane changing data were randomly divided into two groups: training and testing. The training data is used to calibrate the parameters of the model by solving the minimum value problem of the objective function, and the testing data is used to examine the calibration results of the model parameters. The minimum value of the objective function is solved by genetic algorithm [15]. The calibration results of model parameters are shown in Table 2. The calibration index of model parameters is expressed by the Mean Absolute Error of the predicted values and the measured values at each sampling point. Then, it is expressed as MAD reflects the range of driver uncertainty in vehicle trajectory data to a certain extent. It is generally believed that if the MAE error of the calibration parameter is within the range of MAD error, the parameter calibration results can reach the acceptable range [16]. The expression of MAD is as follows: According to the calibration results and testing data of model parameters, the calculation of the calibrated evaluation index of model is that MAE=1.65m/s 2 . It is known from table 1 that the calculation of the mean absolute deviation of the acceleration from the actual data is 1.70m/s 2 . It is shown that the calibrated error of the model parameters is smaller, and the calibration results of model parameters are effective.
According to the calibration result, the value of 0 κ is greater than that of 0

Comparison of Model Prediction Results
Taking the one lane-changing process of a vehicle in the experimental data as an example, comparing the actual data of changing lane with the calibrated data of model, the prediction value of the acceleration of lane-changing vehicle with time can be obtained. Figure 7 shows the acceleration predicted value of the model and the actual acceleration value along with time. It shows that the predicted value of the lane-change model based on the optimal velocity following model is consistent with the real value of the actual lane-change driving, and the correctness of the model is also proved. But at the same time, there are still great differences between the predicted value and the true value in some parts, which is due to the large difference between the driving behavior characteristics of different drivers, and the driving behavior is influenced by the driver's age, sex, driving age and education. The model prediction results can only be statistically as close to the overall characteristics of the sample population as possible, but cannot ensure that the predicted results of each sample are fully consistent with the actual values.

Conclusion
The behavior of lane-change vehicle in the changing process is affected by the driving state of the surrounding related vehicles and the lateral migration itself, based on the classic vehicle-following theory, which can be approximately divided into several combinations of the following behavior. The model of vehicle lane-change driving behavior by using the Their`s U target function and experimental data to effectively calibrate the parameters of the changing model, is proved that can accurately reflect the vehicle driving behavior characteristics. Hope provide reference for design and development of driver assistance system and vehicle automatic driving system to ensure road safety.