基于改进IDM-GARCH模型的速度波动不确定性研究
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摘要
为定量分析跟驰行为中由驾驶人感知不确定性产生的速度波动不确定性,基于改进IDM-GARCH模型研究了后车速度波动存在的异方差性。首先,提出在经典智能驾驶模型中加入速度差刺激项和非对称系数,以增强速度波动方程残差项的实际意义。在此基础上,为度量速度波动的不确定性引入异方差的思想,并验证速度波动方程残差项的异方差性,最后运用广义自回归条件异方差模型对其异方差性建模。实证分析中,采用了美国联邦公路管理局主导下的下一代仿真项目中真实有效的跟驰数据。研究结果表明:改进的IDM模型能有效地拟合实际跟驰行为中后车的速度变化,且较经典IDM模型在精度上有了很大提高;同时,GARCH类模型估计的条件方差也能准确反映后车速度波动的趋势和幅度,以及不同驾驶人驾驶行为的差异。
To quantitatively analyze the uncertainty of velocity fluctuation caused by driver perception uncertainty in car following behavior, the heteroscedasticity of velocity fluctuation based on the improved IDM-GARCH model was studied. First, for enhancing the practical significance of the residuals of velocity fluctuation equation, the velocity difference stimulus and the asymmetry coefficient was added to the classical IDM model. On this basis, the idea of heteroscedasticity was introduced to measure the uncertainty in velocity fluctuation, and the heteroscedasticity of the residuals of the velocity fluctuation equation was proved, and the heteroscedasticity was modeled using the GARCH model. In the empirical analysis, the real and effective car following data from the next-generation simulation project(NGSIM) led by the Federal Highway Administration was adopted. The results demonstrate that the improved IDM model can effectively fit the velocity fluctuation of the following car, and the accuracy of the model is improved greatly compared with the classical IDM model. Simultaneously, the conditional variance estimated by the GARCH model can accurately reflect the trend and range of velocity fluctuation of the following car and the difference in the driving behavior among different drivers.
To quantitatively analyze the uncertainty of velocity fluctuation caused by driver perception uncertainty in car following behavior, the heteroscedasticity of velocity fluctuation based on the improved IDM-GARCH model was studied. First, for enhancing the practical significance of the residuals of velocity fluctuation equation, the velocity difference stimulus and the asymmetry coefficient was added to the classical IDM model. On this basis, the idea of heteroscedasticity was introduced to measure the uncertainty in velocity fluctuation, and the heteroscedasticity of the residuals of the velocity fluctuation equation was proved, and the heteroscedasticity was modeled using the GARCH model. In the empirical analysis, the real and effective car following data from the next-generation simulation project(NGSIM) led by the Federal Highway Administration was adopted. The results demonstrate that the improved IDM model can effectively fit the velocity fluctuation of the following car, and the accuracy of the model is improved greatly compared with the classical IDM model. Simultaneously, the conditional variance estimated by the GARCH model can accurately reflect the trend and range of velocity fluctuation of the following car and the difference in the driving behavior among different drivers.
引文
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[7] SPYROPOULOU I. Simulation Using Gipps' Car Following Model: An In-depth Analysis [J]. Transportmetrica, 2007, 3 (3): 231-245.
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[11] 王殿海,金盛.车辆跟驰行为建模的回顾与展望[J].中国公路学报,2012,25(1):115-127. WANG Dian-hai, JIN Sheng. Review and Outlook of Modeling of Car Following Behavior [J]. China Journal of Highway and Transport, 2012, 25 (1): 115-127.
[12] PAZ A, PEETA S. Information-based Network Control Strategies Consistent with Estimated Driver Behavior [J]. Transportation Research Part B, 2009, 43 (1): 73-96.
[13] CHEN D, AHN S, LAVAL J, et al. On the Periodicity of Traffic Oscillations and Capacity Drop: The Role of Driver Characteristics [J]. Transportation Research Part B, 2014, 59: 117-136.
[14] SHEU J B. Characterization of Driver Behavior During Car Following Using Quantum Optical Flow Theory [J]. Transportmetrica A, 2013, 9 (3): 269-298.
[15] SHEU J B, WU H J. Driver Perception Uncertainty in Perceived Relative Speed and Reaction Time in Car Following-A Quantum Optical Flow Perspective [J]. Transportation Research Part B, 2015, 80: 257-274.
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[18] BOLLERSLEV T. Generalized Autoregressive Conditional Heteroskedasticity [J]. Journal of Econometric, 1986, 31 (3): 307-327.
[19] YU S W, SHI Z K. An Improved Car-following Model Considering Headway Changes with Memory [J]. Physica A, 2015, 421 (1): 1-14.
[20] LIU D W, SHI Z K, AI W H. Enhanced Stability of Car-following Model upon Incorporation for Short-term Driving Memory [J]. Communications in Nonlinear Science & Numerical Simulation, 2017, 47 (2): 139-150.
[21] TREIBER M, KESTING A, HELBING D. Delays, Inaccuracies and Anticipation in Microscopic Traffic Models [J]. Physica A, 2006, 360 (1): 71-88.
[22] YANG L H, ZHANG X Q, Gong J K, et al. The Research of Car-following Model Based on Real-time Maximum Deceleration [J]. Mathematical Problems in Engineering, 2015, 2015 (6): 1-9.
[23] SAIFUZZAMAN M, ZHENG Z D, HAQUE M, et al. Revisiting the Task-capability Interface Model for Incorporating Human Factors into Car-following models [J]. Transportation Research Part B, 2015, 82 (12): 1-19.
[24] LIU L, ZHU L L, YANG D. Modeling and Simulation of the Car-truck Heterogeneous Traffic Flow Based on a Nonlinear Car-following Model [J]. Applied Mathematic & Computation, 2016, 273 (1): 706-717.
[25] CHEN C Y, LI L, HU J M, et al. Calibration of MITSIM and IDM Car-following Model Based on NGSIM Trajectory Datasets [C] // IEEE. IEEE International Conference on Vehicular Electronics and safety. New York: IEEE, 2010: 48-53.
[26] 杨达.考虑后车的车辆跟驰行为建模与分析[D].成都:西南交通大学,2009. YANG Da. Modeling and Analysis of the Car-following Behavior Considering the Following Vehicle [J]. Chengdu: Southwest Jiaotong University, 2009.
[27] 柴锐.车联网环境下的驾驶行为特性研究[D].北京:北京理工大学,2016. CHAI Rui. Research on Driving Behavior Characteristic Based on Internet of Vehicles [D]. Beijing: Beijing Institute of Technology, 2016.
[28] 陆建.城市道路驾驶人跟驰行为[M].北京:科学出版社,2013. LU Jian. Driving Behavior on City Road [M]. Beijing: Science Press, 2013.
[29] JIANG R, WU Q S, LIU Z J. Full Velocity Difference for Car-following Theory [J]. Physical Review E, 2001, 64 (2): 17-101.
[30] YU S W, ZHAO X M, XU Z G, et al. An Improved Car-following Model Considering the Immediately Ahead Car's Velocity Difference [J]. Physica A, 2016, 461: 446-455.
[31] WEI D L, LIU H C. Analysis of Asymmetric Driving Using a Self-learning Approach [J]. Transportation Research Part B, 2013, 47 (1): 1-14.
[32] YEO H, SKABARDONIS A. Understanding Stop-and-go Traffic in View of Asymmetric Traffic Theory [J]. Transportation & Traffic Theory Golden Jubilee, 2009 (7): 99-115.
[33] LI C G, JIANG X B, WANG W H, et al. A Simple Car-following Model Based on the Artificial Potential Field [J]. Procedia Engineering, 2016, 137: 13-20.
[34] HARIS N, HANEEN F. Latent Class Model for Car Following Behavior [J]. Transportation Research Part B, 2012, 46 (5): 563-578.
[35] VINCENZO P, MARIA T B, BIAGIO C. On the Assessment of Vehicle Trajectory Data Accuracy and Application to the Next Generation Simulation (NGSIM) Program Data [J]. Transportation Research Part C, 2011, 19 (6): 1243-1262.
[36] SUN Z, JIN W L, STEPHEN G R. Simultaneous Estimation of States and Parameters in Newell's Simplified Kinematic Wave Model with Eulerian and Lagrangian Traffic Data [J]. Transportation Research Part B, 2017, 104: 106-122.
[2] HERMAN R, MONTROLL E W, POTTS R B. Traffic Dynamics: Analysis of Stability in Car Following [J]. Operations Research, 1959, 7 (1): 86-106.
[3] PIPES L A. An Operational Analysis of Traffic Dynamics [J]. Applied Physics, 1953, 24 (3): 274-283.
[4] GAZIS D C, HERMAN R, ROTHERY R W. Nonlinear Follow-the-leader Models of Traffic Flow [J]. Operations Research, 1961, 9 (4): 545-567.
[5] NEWELLS G F. Nonlinear Effects in the Dynamics of Car Following [J]. Operations Research, 1961, 14 (4): 595-606.
[6] GIPPS P G. A Behavioral Car-following Model for Computer Simulation [J]. Transportation Research Part B, 1981, 15 (2): 105-111.
[7] SPYROPOULOU I. Simulation Using Gipps' Car Following Model: An In-depth Analysis [J]. Transportmetrica, 2007, 3 (3): 231-245.
[8] BANDO M, HASEBE K, NAKAYAMA A, et al. Dynamical Model of Traffic Dynamics [J]. Physical Review E, 1998, 58 (1): 133-138.
[9] TREIBER M, HENNECKE A, HEKBING D. Congested Traffic States in Empirical Observation and Microscopic Simulations [J]. Physical Review E, 2000, 62 (2): 1805-1824.
[10] TREIBER M, HELBING D. Memory Effects in Microscopic Traffic Models and Wide Scattering in Flow Density Data [J]. Physical Review E, 2003, 68 (4): 6119-6126.
[11] 王殿海,金盛.车辆跟驰行为建模的回顾与展望[J].中国公路学报,2012,25(1):115-127. WANG Dian-hai, JIN Sheng. Review and Outlook of Modeling of Car Following Behavior [J]. China Journal of Highway and Transport, 2012, 25 (1): 115-127.
[12] PAZ A, PEETA S. Information-based Network Control Strategies Consistent with Estimated Driver Behavior [J]. Transportation Research Part B, 2009, 43 (1): 73-96.
[13] CHEN D, AHN S, LAVAL J, et al. On the Periodicity of Traffic Oscillations and Capacity Drop: The Role of Driver Characteristics [J]. Transportation Research Part B, 2014, 59: 117-136.
[14] SHEU J B. Characterization of Driver Behavior During Car Following Using Quantum Optical Flow Theory [J]. Transportmetrica A, 2013, 9 (3): 269-298.
[15] SHEU J B, WU H J. Driver Perception Uncertainty in Perceived Relative Speed and Reaction Time in Car Following-A Quantum Optical Flow Perspective [J]. Transportation Research Part B, 2015, 80: 257-274.
[16] 高铁梅.计量经济分析方法与建模[M].北京:清华大学出版社,2009. GAO Tie-mei. Econometric Analysis Method and Modeling [M]. Beijing: Tsinghua University Press, 2009.
[17] ENGLE R. Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation [J]. Econometric, 1982, 50 (4): 987-1007.
[18] BOLLERSLEV T. Generalized Autoregressive Conditional Heteroskedasticity [J]. Journal of Econometric, 1986, 31 (3): 307-327.
[19] YU S W, SHI Z K. An Improved Car-following Model Considering Headway Changes with Memory [J]. Physica A, 2015, 421 (1): 1-14.
[20] LIU D W, SHI Z K, AI W H. Enhanced Stability of Car-following Model upon Incorporation for Short-term Driving Memory [J]. Communications in Nonlinear Science & Numerical Simulation, 2017, 47 (2): 139-150.
[21] TREIBER M, KESTING A, HELBING D. Delays, Inaccuracies and Anticipation in Microscopic Traffic Models [J]. Physica A, 2006, 360 (1): 71-88.
[22] YANG L H, ZHANG X Q, Gong J K, et al. The Research of Car-following Model Based on Real-time Maximum Deceleration [J]. Mathematical Problems in Engineering, 2015, 2015 (6): 1-9.
[23] SAIFUZZAMAN M, ZHENG Z D, HAQUE M, et al. Revisiting the Task-capability Interface Model for Incorporating Human Factors into Car-following models [J]. Transportation Research Part B, 2015, 82 (12): 1-19.
[24] LIU L, ZHU L L, YANG D. Modeling and Simulation of the Car-truck Heterogeneous Traffic Flow Based on a Nonlinear Car-following Model [J]. Applied Mathematic & Computation, 2016, 273 (1): 706-717.
[25] CHEN C Y, LI L, HU J M, et al. Calibration of MITSIM and IDM Car-following Model Based on NGSIM Trajectory Datasets [C] // IEEE. IEEE International Conference on Vehicular Electronics and safety. New York: IEEE, 2010: 48-53.
[26] 杨达.考虑后车的车辆跟驰行为建模与分析[D].成都:西南交通大学,2009. YANG Da. Modeling and Analysis of the Car-following Behavior Considering the Following Vehicle [J]. Chengdu: Southwest Jiaotong University, 2009.
[27] 柴锐.车联网环境下的驾驶行为特性研究[D].北京:北京理工大学,2016. CHAI Rui. Research on Driving Behavior Characteristic Based on Internet of Vehicles [D]. Beijing: Beijing Institute of Technology, 2016.
[28] 陆建.城市道路驾驶人跟驰行为[M].北京:科学出版社,2013. LU Jian. Driving Behavior on City Road [M]. Beijing: Science Press, 2013.
[29] JIANG R, WU Q S, LIU Z J. Full Velocity Difference for Car-following Theory [J]. Physical Review E, 2001, 64 (2): 17-101.
[30] YU S W, ZHAO X M, XU Z G, et al. An Improved Car-following Model Considering the Immediately Ahead Car's Velocity Difference [J]. Physica A, 2016, 461: 446-455.
[31] WEI D L, LIU H C. Analysis of Asymmetric Driving Using a Self-learning Approach [J]. Transportation Research Part B, 2013, 47 (1): 1-14.
[32] YEO H, SKABARDONIS A. Understanding Stop-and-go Traffic in View of Asymmetric Traffic Theory [J]. Transportation & Traffic Theory Golden Jubilee, 2009 (7): 99-115.
[33] LI C G, JIANG X B, WANG W H, et al. A Simple Car-following Model Based on the Artificial Potential Field [J]. Procedia Engineering, 2016, 137: 13-20.
[34] HARIS N, HANEEN F. Latent Class Model for Car Following Behavior [J]. Transportation Research Part B, 2012, 46 (5): 563-578.
[35] VINCENZO P, MARIA T B, BIAGIO C. On the Assessment of Vehicle Trajectory Data Accuracy and Application to the Next Generation Simulation (NGSIM) Program Data [J]. Transportation Research Part C, 2011, 19 (6): 1243-1262.
[36] SUN Z, JIN W L, STEPHEN G R. Simultaneous Estimation of States and Parameters in Newell's Simplified Kinematic Wave Model with Eulerian and Lagrangian Traffic Data [J]. Transportation Research Part B, 2017, 104: 106-122.