多重分形降趋波动分析法和移动平均法的分形谱算法对比分析  

A comparative study of multifractal detrended fluctuation analysis and multifractal detrended moving average algorithm to estimate the multifractal spectrum

作　　者：奚彩萍[1] 张淑宁[2] 熊刚[3] 赵惠昌[1] 

机构地区：[1]南京理工大学电子工程与光电技术学院,南京210094 [2]江苏科技大学电子信息学院,镇江212003 [3]上海交通大学电子信息与电气工程学院,上海200240

出　　处：《物理学报》2015年第13期327-340,共14页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61301216,61171168)资助的课题~~

摘　　要：多重分形降趋波动分析法(MFDFA)和多重分形降趋移动平均法(MFDMA)是用来估算一维随机分形信号多重分形谱的两种算法,已被拓展应用于二维和高维分形信号的分析.本文简要介绍了MFDFA和MFDMA算法及其在一维时间序列中的应用.首次系统地从算法模型、计算统计精度、样本量的敏感性、无标度区选取的敏感性、矩选择的敏感性和计算量这六个方面对两种算法进行了对比分析,以典型多重分形信号BMC信号为例,分析两种算法的适用性和优劣性.为实际应用中,针对具体信号如何选用MFDFA或MFDMA算法,以及两种算法的参数设置提供了有价值的参考.Multifractal detrended fluctuation analysis （MFDFA） and multifractal detrended moving average （MFDMA） algo-rithm have been established as two important methods to estimate the multifractal spectrum of the one-dimensional random fractal signals. They have been generalized to deal with two-dimensional and higher-dimensional fractal signals. This paper gives a brief introduction of the two algorithms, and a detail description of the numerical experiments on the one-dimensional time series by using the two methods. By applying the two methods to the series generated from the binomial multiplicative cascades （BMC）, we systematically carry out comparative analysis to get the advantages, disadvantages and the applicability of the two algorithms, for the first time so far as we know, from six aspects： the similarities and differences of the algorithm models, the statistical accuracy, the sensitivities of the sample size, the selection of scaling range, the choice of the q-orders, and the calculation amount. For one class of signals, the larger the sample size, the more accurate the estimated multifractal spectrum. Selection of appropriate scaling range affects the statistical accuracy in comparison of the two methods for almost all examples. The presence of scale invariance should be checked by first running the two methods over a large scaling range （e.g., from 10 to （N＋1）/11 in this paper） and then plot log10（Fq （scale）） against log10（scale）. In the MFDFA-m （m is the polynomial order, and in this paper m=1） method, the scaling range can be selected from max{m＋2, 10}to N/10, N is the sample size of the time series. In the MFDMA algorithm, the scaling range should be from 10 to （N＋1）/11. It is favorable to have an equal spacing between scales and the number of the scales should be larger than 10 and usually be selected from 20 to 40. The q-orders should consist of both positive and negative q’s. When ｜q｜=5, the calculated results will not be sensitive with the increas

关 键 词：多重分形降趋波动分析法 多重分形降趋移动平均法 随机分形信号 对比分析 

分 类 号：TN911.6[电子电信—通信与信息系统]