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Scale-less range is an interval of measurement of time series in which fractional self-similarity exists statistically. In order to solve the problem of the lack of necessary steps to calculate fractal range in multi-fractal detrended fluctuation analysis algorithm (MF-DFA) in traffic flow, a new scale-less identification method based on MF-DFA is proposed through analyzing the characteristics of the mutation point in logistic curve of traffic flow wave function in steps of MF-DFA and the principles of the traditional fractal scale-less range identification method. Beijing's road network is taken for example to investigate the fractal scale-less range. Analysis results show that the identification method based on MF-DFA algorithm is valid, automatic and steady in identifying the fractal scale-less range in Beijing's traffic flow. Further, the reason why the scale-less range in traffic is limited is that small traffic flow waves account for a bigger percentage in scale-less range while big wave is bigger so that it is out of the scale-less range.
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Keywords:
- traffic flow /
- multi-fractal theory /
- scale-less range /
- multi-fractal detrended fluctuation analysis algorithm
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[16] Tang G J, Du B Q, Wang S L 2009 J. Power Engineer. 29 440 (in Chinese) [唐贵基, 杜必强, 王松玲 2009 动力工程 29 440]
[17] Du B Q, Jia Z W, Tang G J 2014 J. Vibration Shock 32 40 (in Chinese) [杜必强, 贾子文, 唐贵基 2014 振动与冲击 32 40]
[18] Jia Z W, Wang P, Fang J Y 2012 Design Res. 11 24 (in Chinese) [贾子文, 王鹏, 方俊元 2012 设计与研究 11 24]
[19] Wu H S, Ni L P, Zhang F M, Zhou X, Du J Y 2014 Control and Decision 29 455 (in Chinese) [吴虎胜, 倪丽萍, 张凤鸣, 周漩, 杜继勇 2014 控制与决策 29 455]
[20] Kantelhardt J W, Zschiegner S A 2002 Physica A 316 87
[21] Couillard M, Davison M 2005 Physica A 348 404
[22] Varotsos P A, Sarlis N V, Skordas E S 2003 Phys. Rev. E 67 021109
[23] Zhou Y, Leung Y, Yu Z G 2014 Chin. Phys. B 20 090507
[24] Gou X Q, Zhang Y J, Dong W S 2006 Acta Phys. Sin. 55 957 (in Chinese) [苟学强, 张义军, 董万胜 2006 55 957]
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[1] He G G, Ma S F, Feng W D 2002 Chin. J. Highway Trans. 15 82 (in Chinese) [贺国光, 马寿峰, 冯蔚东 2002 中国公路学报 15 82]
[2] Yin G, Chen Y F 2013 Appl. Mech. Mater. 380 1256
[3] Buendía G M, Viswanathan G M 2008 Phys. Rev. E 23 121
[4] Zhang Y 2011 Ph. D. Dissertation (Beijing: Beijing Jiaotong University) (in Chinese) [张勇 2011 博士学位论文 (北京: 北京交通大学)]
[5] Mandelbrot B B 1967 Science 156 636
[6] Quan Y, Li W, Jiang S 2011 Power Engineering and Automation Conference Wuhan, China, September 8-9, 2011 p305
[7] Luo S H, Zeng J S 2009 Acta Phys. Sin. 58 150 (in Chinese) [罗世华, 曾九孙 2009 58 150]
[8] Li T, Shang P J 2007 Acta Phys. Sin. 56 4393 (in Chinese) [李彤, 商朋见 2007 56 4393]
[9] Huo Y L, Zhang G S, L S H, Yuan P 2013 Acta Phys. Sin. 62 059201 (in Chinese) [火元莲, 张广庶, 吕世华, 袁萍 2013 62 059201]
[10] Cao G X, Cao J, Xu L B 2013 Physica A 392 797
[11] Wang D L, Yu Z G, Anh V 2012 Chin. Phys. B 21 080504
[12] Kim H S, Salas J D 1999 Physica D 127 48
[13] Wu Z C 2002 Acta Geodaet. Cartograph. Sin. 31 240 (in Chinese) [巫兆聪 2002 测绘学报 31 240]
[14] Dang J W, Shi Y, Huang J G 2003 Comput. Engineer. Appl. 23 35 (in Chinese) [党建武, 施怡, 黄建国 2003 计算工程与应用 23 35]
[15] Li H Q, Wang F Q 1993 Fractal Theory and Application in Molecular Science (Beijing: Beijing Science Press) pp53-68 (in Chinese) [李后强, 汪富泉 1993 分形理论及其在分子科学中的应用(北京: 科学出版社) 第53–68页]
[16] Tang G J, Du B Q, Wang S L 2009 J. Power Engineer. 29 440 (in Chinese) [唐贵基, 杜必强, 王松玲 2009 动力工程 29 440]
[17] Du B Q, Jia Z W, Tang G J 2014 J. Vibration Shock 32 40 (in Chinese) [杜必强, 贾子文, 唐贵基 2014 振动与冲击 32 40]
[18] Jia Z W, Wang P, Fang J Y 2012 Design Res. 11 24 (in Chinese) [贾子文, 王鹏, 方俊元 2012 设计与研究 11 24]
[19] Wu H S, Ni L P, Zhang F M, Zhou X, Du J Y 2014 Control and Decision 29 455 (in Chinese) [吴虎胜, 倪丽萍, 张凤鸣, 周漩, 杜继勇 2014 控制与决策 29 455]
[20] Kantelhardt J W, Zschiegner S A 2002 Physica A 316 87
[21] Couillard M, Davison M 2005 Physica A 348 404
[22] Varotsos P A, Sarlis N V, Skordas E S 2003 Phys. Rev. E 67 021109
[23] Zhou Y, Leung Y, Yu Z G 2014 Chin. Phys. B 20 090507
[24] Gou X Q, Zhang Y J, Dong W S 2006 Acta Phys. Sin. 55 957 (in Chinese) [苟学强, 张义军, 董万胜 2006 55 957]
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