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Time delay and optimal embedding dimension for the real measurement traffic flow series, which are used by mutual information method and false nearest-neighbor method, respectively, are determined for phase space reconstruction of the traffic flow series. The saturation correlation dimension and the largest Lyapunov exponent for traffic flow series are calculated to estimate its chaotic characteristics. Based on the least mean square (LMS) algorithm, a novel second-order Volterra model using Davidon-Fletcher-Powell method (DFPSOVF) is constructed, in which a variable convergence factor based on a posteriori error assumption, characteristic of real-time change with the input signal, is applied. DFPSOVF model can avoid some problems caused by improper selection of parameters when using LMS adaptive algorithm for coefficient adjustment in Volterra model. DFPSOVF model can also be applied to short-term traffic flow prediction with chaotic characteristics. Results show that when model memory length is consistent with embedding dimension of traffic flow series, it obtains higher prediction accuracy, which can meet the needs for traffic guidance and traffic control, and can also provide a new method, a new idea and engineering application reference for intelligent traffic control.
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Keywords:
- traffic flow /
- chaos /
- DFPSOVF model /
- prediction
[1] Li T 2005 Phys. D 207 41
[2] Low D J, Addison P S 1997 Proceeding of the 30th ISATA Conference Florence, Italy, June 16-19, 1997 p175
[3] Tong M R, Xue H X, Lin L 2008 J. of Highway and Transportation Research and Development 25 124 (in Chinese) [童明荣, 薛恒新, 林琳 2008 公路交通科技 25 124]
[4] Cirianni F, Leonardi G 2004 Air Pollution XII 14 559
[5] Wang J, Guan W 2006 Proceeding of the 10th World Multi-Conference on Systemics, Cybernetics and Informatics, Orlando, FL, USA, July 16-19, 2006 p94
[6] Smith B L, Williams B M, Oswald R K 2002 Transp. Res. C: Emerg. Technol. 10 303
[7] Zhang J S, Xiao X C 2001 Acta Phys. Sin. 50 1248 (in Chinese) [张家树, 肖先赐 2001 物理学报 50 1248]
[8] 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]
[9] Zhang J S, Xiao X C 2000 Acta Phys. Sin. 49 1221 (in Chinese) [张家树, 肖先赐 2000 物理学报 49 1221]
[10] Wei B L, Luo X S, Wang B H, Quan H J, Guo W, Fu J J 2002 Acta Phys. Sin. 51 2205 (in Chinese) [韦保林, 罗晓曙, 汪秉宏, 全宏俊, 郭维, 傅金阶 2002 物理学报 51 2205]
[11] Du J, Cao Y J, Liu Z J, Xu L Z, Jiang Q Y, Guo C X, Lu J G 2009 Acta Phys. Sin. 58 5997 (in Chinese) [杜杰, 曹一家, 刘志坚, 徐立中, 江全元, 郭创新, 陆金桂 2009 物理学报 58 5997]
[12] Sigrist Z, Grivel E, Alcoverro B 2012 Signal Process. 92 1010
[13] Mathews V J 1991 IEEE Signal Process. Mag. 8 10
[14] Zhang H J, Han C Z 2004 J. Xian Jiaotong Univ. 38 583 (in Chinese) [张华君, 韩崇昭 2004 西安交通大学学报 38 583]
[15] Takens F 1981 Lecture Notes in Mathematics 898 361
[16] Wang H Y, Lu S 2006 Nonlinear Time Series Analysis and Its Application (Beijing: Science Press) p33-40 (in Chinese) [王海燕, 卢山 2006 非线性时间序列分析及其应用(北京: 科学出版社)第33-40页]
[17] Henry D, Abarbanel N M, Rabinovich M I, Evren T 2001 Phys. Lett. A 281 368
[18] Kennel M B, Brown R, Abarbanel H D I 1992 Phys. Rev. A 45 3403
[19] Grassberger P, Procaccia I 1983 Phys. D 9 189
[20] Rosenstein M T, Collins J J, De Iuca C J 1993 Phys. D 65 117
[21] De Campos M L R, Antoniou A 1997 IEEE Trans. Circuits Syst. 44 924
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[1] Li T 2005 Phys. D 207 41
[2] Low D J, Addison P S 1997 Proceeding of the 30th ISATA Conference Florence, Italy, June 16-19, 1997 p175
[3] Tong M R, Xue H X, Lin L 2008 J. of Highway and Transportation Research and Development 25 124 (in Chinese) [童明荣, 薛恒新, 林琳 2008 公路交通科技 25 124]
[4] Cirianni F, Leonardi G 2004 Air Pollution XII 14 559
[5] Wang J, Guan W 2006 Proceeding of the 10th World Multi-Conference on Systemics, Cybernetics and Informatics, Orlando, FL, USA, July 16-19, 2006 p94
[6] Smith B L, Williams B M, Oswald R K 2002 Transp. Res. C: Emerg. Technol. 10 303
[7] Zhang J S, Xiao X C 2001 Acta Phys. Sin. 50 1248 (in Chinese) [张家树, 肖先赐 2001 物理学报 50 1248]
[8] 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]
[9] Zhang J S, Xiao X C 2000 Acta Phys. Sin. 49 1221 (in Chinese) [张家树, 肖先赐 2000 物理学报 49 1221]
[10] Wei B L, Luo X S, Wang B H, Quan H J, Guo W, Fu J J 2002 Acta Phys. Sin. 51 2205 (in Chinese) [韦保林, 罗晓曙, 汪秉宏, 全宏俊, 郭维, 傅金阶 2002 物理学报 51 2205]
[11] Du J, Cao Y J, Liu Z J, Xu L Z, Jiang Q Y, Guo C X, Lu J G 2009 Acta Phys. Sin. 58 5997 (in Chinese) [杜杰, 曹一家, 刘志坚, 徐立中, 江全元, 郭创新, 陆金桂 2009 物理学报 58 5997]
[12] Sigrist Z, Grivel E, Alcoverro B 2012 Signal Process. 92 1010
[13] Mathews V J 1991 IEEE Signal Process. Mag. 8 10
[14] Zhang H J, Han C Z 2004 J. Xian Jiaotong Univ. 38 583 (in Chinese) [张华君, 韩崇昭 2004 西安交通大学学报 38 583]
[15] Takens F 1981 Lecture Notes in Mathematics 898 361
[16] Wang H Y, Lu S 2006 Nonlinear Time Series Analysis and Its Application (Beijing: Science Press) p33-40 (in Chinese) [王海燕, 卢山 2006 非线性时间序列分析及其应用(北京: 科学出版社)第33-40页]
[17] Henry D, Abarbanel N M, Rabinovich M I, Evren T 2001 Phys. Lett. A 281 368
[18] Kennel M B, Brown R, Abarbanel H D I 1992 Phys. Rev. A 45 3403
[19] Grassberger P, Procaccia I 1983 Phys. D 9 189
[20] Rosenstein M T, Collins J J, De Iuca C J 1993 Phys. D 65 117
[21] De Campos M L R, Antoniou A 1997 IEEE Trans. Circuits Syst. 44 924
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