﻿ 驾驶员驾驶行为的统计学特性
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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (6): 832-841.  DOI: 10.11908/j.issn.0253-374x.2019.06.013 0

### 引用本文

LIU Rui, MA Zhixiong, WU Biao, ZHU Xichan. Driving Behavior Statistical Characteristics of the Driver[J]. Journal of Tongji University (Natural Science), 2019, 47(6): 832-841. DOI: 10.11908/j.issn.0253-374x.2019.06.013

### 文章历史

Driving Behavior Statistical Characteristics of the Driver
LIU Rui , MA Zhixiong , WU Biao , ZHU Xichan
School of Automotive Studies, Tongji University, Shanghai 201804, China
Abstract: In this paper, the driving behavior statistical characteristics of the driver are studied by using the naturalistic driving data. The longitudinal acceleration, lateral acceleration, yaw rate, and velocity of the vehicle were chosen as the characteristic parameters which were employed to describe the driving behavior of the driver. Firstly, the convergence of the driving behavior of the driver was discussed. The kernel density estimation was used to achieve the probability distribution of the driving behavior characteristic parameters. And the kullback-liebler divergence was applied to describe the distribution distinction between datasets which were composed of different amount of data. Next, the distribution characteristics of the driving behavior characteristic parameters were proposed by using the convergent dataset. In the last, the conditional distribution of the driving behavior characteristic parameters were used to study the interaction between these parameters. The conclusions can be summarized as: The forward acceleration, brake deceleration, lateral acceleration, and yaw rate approximately follow the Pareto distribution. The steering maneuver of the driver tends to be more intense when brake deceleration or forward acceleration increases, and vice versa. The steering, braking, and accelerating maneuvers of the driver become more intense and then become less intense when the velocity increases.
Key words: driving behavior    naturalistic driving studies    Pareto distribution    kernel density estimation    kullback-leibler divergence

1 自然驾驶数据采集

 图 1 测试车、数据采集系统以及摄像头图像信息 Fig.1 Test vehicle, data acquisition systems, and videos information from the camera
2 驾驶行为特征参数分布的收敛性

2.1 核密度估计

 ${\hat f_n}(x) = \frac{1}{n}\sum\limits_{i = 1}^n {\frac{1}{h}} K\left( {\frac{{x - {x_i}}}{h}} \right)$ (1)

 $K(x)=\frac{1}{\sqrt{2 \pi}} \exp \left(-\frac{x^{2}}{2}\right)$ (2)

2.2 相对熵

 $\begin{array}{l}{D_{\mathrm{KL}}\left[\hat{f}_{n+m}(x)| | \hat{f}_{n}(x)\right]=} \\~~~~~ {\int_{-\infty}^{\infty} \hat{f}_{n+m}(x) \log \frac{\hat{f}_{n+m}(x)}{\hat{f}_{n}(x)} \mathrm{d} x}\end{array}$ (3)

 $\forall \mathit{\Gamma } \le n \le \mathit{\Omega }, \left\| {{D_{KL}}\left[ {{{\hat f}_{n + m}}(x)||{{\hat f}_n}(x)} \right]} \right\| < \varepsilon$ (4)

2.3 数据处理过程及结果

(1) 选取1×105组观测数据作为初始数据集.

(2) 将1×105组新的观测数据加入到之前数据集中.旧数据集中包含k×105组观测数据，新的数据集中包含(k+1)×105组观测数据.

(3) 计算旧数据集与新数据集的核密度函数，并计算这两个数据集的相对熵DKL.

(4) 若DKL不满足式(4)，跳转到第(2)步；若DKL满足式(4)且Ω-k>50×105，成功并结束，并令Γ=k；若DKL满足式(4)且Ω-k < 50×105，失败并结束，数据库需要更大的数据量.

 $\mathit{\Gamma } = \max \left\{ {{\mathit{\Gamma }_x}|x \in \left\{ {{a_x}, {a_y}, v, \omega } \right\}} \right\}$ (5)

 图 2 不同数据量时纵向加速度的核密度函数 Fig.2 Kernel density function of the longitudinal acceleration with different amount of data
 图 3 不同数据量时侧向加速度的核密度函数 Fig.3 Kernel density function of the lateral acceleration with different amount of data
 图 4 不同数据量时速度的核密度函数 Fig.4 Kernel density function of the velocity with different amount of data
 图 5 不同数据量时横摆角速度的核密度函数 Fig.5 Kernel density function of the yaw rate with different amount of data

 图 6 驾驶行为特征参数的相对熵 Fig.6 Kullback-Leibler divergence of the driving behavior characteristic parameters

 $\begin{array}{l} \mathit{\Gamma } = \max \left\{ {{\mathit{\Gamma }_{{a_x}}}, {\mathit{\Gamma }_{{a_y}}}, {\mathit{\Gamma }_v}, {\mathit{\Gamma }_\omega }} \right\} = \\ \begin{array}{*{20}{l}} {\max \left\{ {23 \times {{10}^5}, 45 \times {{10}^5}, 897 \times {{10}^5}, 22 \times {{10}^5}} \right\} = }\\ {897 \times {{10}^5}} \end{array} \end{array}$ (6)

3 驾驶行为特征参数的分布特性

 $C_{\mathrm{AIC}}=2 r-2 \ln L$ (7)
 $L=\hat{f}(x | \boldsymbol{\theta}, \boldsymbol{M})$ (8)

 $C_{\mathrm{BIC}}=r \ln n-2 \ln L$ (9)
 $L=\hat{f}(x | \boldsymbol{\theta}, \boldsymbol{M})$ (10)

 图 7 不同统计分布侧向加速度拟合效果 Fig.7 Fitting results of the lateral acceleration of different statistical distributions

4 驾驶行为特征参数之间的相互影响

4.1 加速度之间的相互影响

 图 8 不同纵向加速区间的侧向加速度的概率密度 Fig.8 Density of the lateral acceleration in different longitudinal acceleration intervals

 图 9 不同纵向加速度区间的侧向加速度百分位 Fig.9 Percentile of the lateral acceleration in different longitudinal acceleration intervals

 图 10 纵向加速度与侧向加速的联合分布[8] Fig.10 The multivariate distribution of the longitudinal acceleration and lateral acceleration[8]

 图 11 不同侧向加速度区间的前向加速度百分位 Fig.11 Percentile of the forward acceleration in different lateral acceleration intervals

 图 12 不同侧向加速度区间的制动减速度百分位 Fig.12 Percentile of the brake deceleration in different lateral acceleration intervals

4.2 速度对驾驶行为特征参数的影响

 图 13 不同速度区间的侧向加速度的概率密度 Fig.13 Density of the lateral acceleration in different velocity intervals

 图 14 不同速度区间的前向加速度百分位 Fig.14 Percentile of the forward acceleration in different velocity intervals
 图 15 不同速度区间的制动减速度百分位 Fig.15 Percentile of the brake deceleration in different velocity intervals
 图 16 不同速度区间的侧向加速度百分位 Fig.16 Percentile of the lateral acceleration in different velocity intervals
 图 17 不同速度区间的横摆角速度百分位 Fig.17 Percentile of yaw rate in different velocity intervals

5 结论

 [1] MARINIK A, BISHOP R, FITCHETT V, et al. Human factors evaluation of level 2 and level 3 automated driving concepts[R]. Washington D C: NHTSA, 2014. [2] KHOSRAVANI S, KHAJEPOUR A, FIDAN B, et al. Development of a robust vehicle control with driver in the loop[C]//American Control Conference. Portland: IEEE, 2014: 3482-3487. https://ieeexplore.ieee.org/document/6858845/ [3] LI R, LI S, GAO H, et al. Effects of human adaptation and trust on shared control for driver-automation cooperative driving[C/CD]//SAE Technical Paper Series. Detroit: SAE Publication Group, 2017. 2017-01-1987. [4] LEE J D, SEE K A. Trust in automation: designing for appropriate reliance[J]. Human Factors, 2004, 46(1): 50 DOI:10.1518/hfes.46.1.50.30392 [5] ZHANG Y, ANTONSSON E K, GROTE K. A new threat assessment measure for collision avoidance systems[C]//Intelligent Transportation Systems Conference. Toronto: IEEE, 2006: 968-975. https://ieeexplore.ieee.org/document/1706870/ [6] DUGOFF H, FRANCHER P S, SEGEL L. Tire performance characteristics affecting vehicle response to steering and braking control inputs[R]. Ann Arbor: University of Michigan, 1969. [7] BOSETTI P, DA LIO M, SAROLDI A. On the human control of vehicles: an experimental study of acceleration[J]. European Transport Research Review, 2013, 6(2): 157 [8] LIU R, ZHU X. Driving data distribution of human drivers in urban driving condition[C]//International Conference on Intelligent Transportation Systems. Yokohama: IEEE, 2017: 1-6. https://www.researchgate.net/publication/323792440_Driving_data_distribution_of_human_drivers_in_urban_driving_condition [9] REYMOND G, KEMENY A, DROULEZ J, et al. Role of lateral acceleration in curve driving: driver model and experiments on a real vehicle and a driving simulator[J]. Human Factors, 2001, 43(3): 483 DOI:10.1518/001872001775898188 [10] VANWINSUM W, GODTHELP H. Speed choice and steering behavior in curve driving[J]. Human Factors, 1996, 38(3): 434 DOI:10.1518/001872096778701926 [11] BUTAKOV V A, IOANNOU P. Personalized driver/vehicle Lane change models for ADAS[J]. IEEE Transactions on Vehicular Technology, 2015, 64(10): 4422 DOI:10.1109/TVT.2014.2369522 [12] BISHOP C M. Pattern recognition and machine learning[M]. New York: Springer, 2006 [13] JONES M C, MARRON J S, SHEATHER S J. Progress in data-based bandwidth selection for Kernel density estimation[J]. Computational Statistics, 1996, 11(3): 337 [14] SILVERMAN B W. Density estimation for statistics and data analysis[M]. Boca Raton: CRC Press, 1986 [15] BOTEV Z I, GROTOWSKI J F, KROESE D P. Kernel density estimation via diffusion[J]. Annals of Statistics, 2010, 38(5): 2916 [16] SHEATHER S J, JONES M C. A reliable data-based bandwidth selection method for kernel density estimation[J]. Journal of the Royal Statistical Society Series B-Methodological, 1991, 53(3): 683 [17] RUDEMO M. Empirical choice of histograms and kernel density estimators[J]. Scandinavian Journal of Statistics, 1982, 9(2): 65 [18] BOWMAN A W. An alternative method of cross-validation for the smoothing of density estimates[J]. Biometrika, 1984, 71(2): 353 DOI:10.1093/biomet/71.2.353 [19] HALL P, MARRON J S, PARK B U. Smoothed cross-validation[J]. Probability Theory and Related Fields, 1992, 92(1): 1 [20] MACKAY D J C. Information theory, inference and learning algorithms[M]. Cambridge: Cambridge University Press, 2003 [21] WANG Wenshuo, LIU Chang, ZHAO Ding. How much data are enough? a statistical approach with case study on longitudinal driving behavior[J]. IEEE Transactions on Intelligent Vehicle, 2017, 2(2): 85 [22] ZHAO D, LAM H, PENG H, et al. Accelerated evaluation of automated vehicles safety in lane-change scenarios based on importance sampling techniques[J]. IEEE Transactions on Intelligent Transportation Systems, 2017, 18(3): 595 DOI:10.1109/TITS.2016.2582208 [23] WIT E, VAN DEN HEUVEL E, ROMEIJN J W. All models are wrong...': an introduction to model uncertainty[J]. Statistica Neerlandica, 2012, 66(3): 217 DOI:10.1111/j.1467-9574.2012.00530.x [24] AHO K, DERRYBERRY D, PETERSON T. Model selection for ecologists: the worldviews of AIC and BIC[J]. Ecology, 2014, 95(3): 631 DOI:10.1890/13-1452.1 [25] FOSS S, KORSHUNOV D, ZACHARY S. An introduction to heavy-tailed and subexponential distributions[M]. New York: Springer, 2011