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

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.

Multi-fractal detrended fluctuation analysis algorithm based identification method of scale-less range for multi-fractal charateristics of traffic flow

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