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In order to reveal the internal dynamic property of short-term traffic flow, the nonlinear analysis method is used to identify the chaotic property of traffic flow which is the basis for the prediction of the traffic flow time series. Traffic flow time series is reconstructed in phase-space based on chaos theory. The embedding dimension and delay time are first calculated via the C-C method. The correlative dimension of attractor is then calculated with the Grassberger-Procaccia method. The largest Lyapunov exponent of traffic flow set is calculated on the basis of the improved small data set method to verify the presence of the chaos in traffic flow time series. A novel multi-step adaptive prediction method is proposed to solve the problem of adjusting the filter parameters of the chaos local adaptive prediction method during traffic flow multi-step prediction. The traffic flow time series are found to have chaotic properties in different statistical scales of 2, 4, and 5 min and show that the improved small data set method can accurately evaluate the chaotic property for traffic flow time series, and that the multi-step adaptive prediction method is capable of effectively predicting its fluctuation, which provides a useful reference for traffic guidance and control.
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Keywords:
- traffic flow /
- chaos /
- maximum Lyapunov exponent /
- multi-step adaptive prediction
[1] Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[2] Barana G, Tsuda I 1993 Phys. Lett. A 175 421
[3] Briggs K 1990 Phys. Lett. A 151 27
[4] Rosenstein M T, Collins J, Deluca C J 1993 Physica D 65 117
[5] Chen Z, Liang P 2000 J. Guizhou Normal Univ. (Natural Science) 18 58(in Chinese) [陈琢, 梁蓓 2000 贵阳师范大学学报 (自然科学版) 18 58]
[6] Zhang Y M, Qu S R, Wen K G 2009 China Civil Engineer. J. 42 119 (in Chinese) [张玉梅, 曲仕茹, 温凯歌 2009 土木工程学报 42 119]
[7] Lu Y, Chen Y H, He G G 2007 Systems Engineer. Theor. Pract. 27 85 (in Chinese) [卢宇, 陈宇红, 贺国光 2007 系统工程理论与实践 27 85]
[8] Ding T, Zhou H C 2004 Sys. Engn. Electron 26 338 (in Chinese) [丁涛, 周惠成 2004 系统工程与电子技术 26 338]
[9] Zhang J S, Xiao X C 2000 Acta Phys. Sin. 49 403 (in Chinese) [张家树, 肖先赐 2000 物理学报 49 403]
[10] Gan J C, Xiao X C 2003 Acta Phys. Sin. 52 1096 (in Chinese) [甘建超, 肖先赐 2003 物理学报 52 1096]
[11] Gan J C, Xiao X C 2003 Acta Phys. Sin. 52 2996 (in Chinese) [甘建超, 肖先赐 2003 物理学报 52 2996]
[12] Zhang J S, Dang J L, Li H C 2007 Acta Phys. Sin. 56 67 (in Chinese) [张家树, 党建亮, 李恒超 2007 物理学报 56 67]
[13] Zhang Y M, Qu S R 2010 Appl. Res. Comput. 27 4486 in Chinese) [张玉梅, 曲仕茹 2010 计算机应用研究 27 4486]
[14] Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Vol. 898) (Berlin: Springer-Verlag) p230
[15] Dong L, Gao S, Liao X Z 2007 Acta Energiae Solaris Sin. 28 1290 (in Chinese) [冬雷, 高爽, 廖晓钟 2007 太阳能学报 28 1290]
[16] Kim H S, Eykholt R, Salas J D 1999 Physica D 127 48
[17] Brock W A, Hsieh D, Lebaron A B 1991 Nonlinear Dynamics, Chaos and Instability: Statistical Theory and Economic Evidence (Cambridge: MTT Press) p217
[18] Grassberger P, Procaccia I 1983 Physica D 9 1898
[19] L J H, Lu J A, Chen S H 2002 Chaotic Time Series Analysis and Applications (Wuhan: Wuhan University Press) p116 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉: 武汉大学出版社) 第116页]
[20] Meng Q F, Zhang Q, Mu W Y 2006 Acta Phys. Sin. 55 1666 (in Chinese) [孟庆芳, 张强, 牟文英 2006 物理学报 55 1666]
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[1] Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[2] Barana G, Tsuda I 1993 Phys. Lett. A 175 421
[3] Briggs K 1990 Phys. Lett. A 151 27
[4] Rosenstein M T, Collins J, Deluca C J 1993 Physica D 65 117
[5] Chen Z, Liang P 2000 J. Guizhou Normal Univ. (Natural Science) 18 58(in Chinese) [陈琢, 梁蓓 2000 贵阳师范大学学报 (自然科学版) 18 58]
[6] Zhang Y M, Qu S R, Wen K G 2009 China Civil Engineer. J. 42 119 (in Chinese) [张玉梅, 曲仕茹, 温凯歌 2009 土木工程学报 42 119]
[7] Lu Y, Chen Y H, He G G 2007 Systems Engineer. Theor. Pract. 27 85 (in Chinese) [卢宇, 陈宇红, 贺国光 2007 系统工程理论与实践 27 85]
[8] Ding T, Zhou H C 2004 Sys. Engn. Electron 26 338 (in Chinese) [丁涛, 周惠成 2004 系统工程与电子技术 26 338]
[9] Zhang J S, Xiao X C 2000 Acta Phys. Sin. 49 403 (in Chinese) [张家树, 肖先赐 2000 物理学报 49 403]
[10] Gan J C, Xiao X C 2003 Acta Phys. Sin. 52 1096 (in Chinese) [甘建超, 肖先赐 2003 物理学报 52 1096]
[11] Gan J C, Xiao X C 2003 Acta Phys. Sin. 52 2996 (in Chinese) [甘建超, 肖先赐 2003 物理学报 52 2996]
[12] Zhang J S, Dang J L, Li H C 2007 Acta Phys. Sin. 56 67 (in Chinese) [张家树, 党建亮, 李恒超 2007 物理学报 56 67]
[13] Zhang Y M, Qu S R 2010 Appl. Res. Comput. 27 4486 in Chinese) [张玉梅, 曲仕茹 2010 计算机应用研究 27 4486]
[14] Takens F 1981 Dynamical System and Turbulence, Lecture Notes in Mathematics (Vol. 898) (Berlin: Springer-Verlag) p230
[15] Dong L, Gao S, Liao X Z 2007 Acta Energiae Solaris Sin. 28 1290 (in Chinese) [冬雷, 高爽, 廖晓钟 2007 太阳能学报 28 1290]
[16] Kim H S, Eykholt R, Salas J D 1999 Physica D 127 48
[17] Brock W A, Hsieh D, Lebaron A B 1991 Nonlinear Dynamics, Chaos and Instability: Statistical Theory and Economic Evidence (Cambridge: MTT Press) p217
[18] Grassberger P, Procaccia I 1983 Physica D 9 1898
[19] L J H, Lu J A, Chen S H 2002 Chaotic Time Series Analysis and Applications (Wuhan: Wuhan University Press) p116 (in Chinese) [吕金虎, 陆君安, 陈士华 2002 混沌时间序列分析及其应用 (武汉: 武汉大学出版社) 第116页]
[20] Meng Q F, Zhang Q, Mu W Y 2006 Acta Phys. Sin. 55 1666 (in Chinese) [孟庆芳, 张强, 牟文英 2006 物理学报 55 1666]
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