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无标度区间是时间序列在统计意义上存在分形自相似性的尺度范围，是交通流多重分形特征研究中的重要组成部分. 为解决交通流多重分形研究中多重分形去趋势波动分析法（multi-fractal detrended fluctuation analysis，MF-DFA）缺乏有效识别无标度区间方法的问题，本文在分析算法过程中交通流波动函数对数曲线突变点性质的基础上，结合传统无标度区间识别方法的构建思想，建立基于MF-DFA 算法的无标度区间自动识别方法. 以北京市二环快速路外环方向的部分道路为例开展实例研究，通过与传统无标度区间识别方法的结果对比，验证新方法的有效性. 研究结果表明：本文方法能自动识别交通流多重分形无标度区间，且稳定性好；案例研究可知交通流短时间内波动较小、自相似性较强，随着研究时间段变长、交通流波动逐渐变大，自相似性逐渐消失，进一步解释了交通流无标度区间的有限性.
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关键词:
- 交通流 /
- 多重分形 /
- 无标度区间 /
- 多重分形去趋势波动分析法
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.-
Keywords:
- traffic flow /
- multi-fractal theory /
- scale-less range /
- multi-fractal detrended fluctuation analysis algorithm
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[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]
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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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