基于多重分形去趋势波动分析法的交通流多重分形无标度区间自动识别方法

发布时间：2019-06-04 00:39

【摘要】：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.
[Abstract]:Scale-free interval is a scale range in which fractal self-similarity exists in the statistical sense of time series, and it is an important part of the study of multifractal characteristics of traffic flow. In order to solve the problem that multiple fractal de-trend fluctuation analysis (multi-fractal detrended fluctuation analysis,MF-DFA) is lack of effective method to identify scale-free interval in the study of multifractal traffic flow, In this paper, based on the analysis of the abrupt point property of logarithmic curve of traffic flow fluctuation function in the process of algorithm, combined with the construction idea of traditional scale-free interval recognition method, a scale-free interval automatic recognition method based on MF-DFA algorithm is established. Taking some roads in the direction of the outer ring of the second Ring Road in Beijing as an example, the effectiveness of the new method is verified by comparing with the results of the traditional scale-free interval identification method. The results show that the proposed method can automatically identify the multifractal scale-free interval of traffic flow, and the stability is good. The case study shows that the fluctuation of traffic flow is small and the self-similarity is strong in a short time. With the prolongation of the research time, the fluctuation of traffic flow becomes larger and the self-similarity disappears gradually, which further explains the finiteness of scale-free interval of traffic flow.
【作者单位】：北京交通大学交通运输学院城市交通复杂系统理论与技术教育部重点实验室;
【基金】：国家高技术研究发展计划(批准号:2011AA110303) 国家重点基础研究发展计划(批准号:2012CB725406) 国家自然科学基金(批准号:71001006)资助的课题~~
【分类号】：O211.61;U491.112

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