一种识别关联维数无标度区间的新方法  

A novel method to identify the scaling region of correlation dimension

作　　者：周双[1,2] 冯勇[1] 吴文渊[1] 

机构地区：[1]中国科学院重庆绿色智能技术研究院,自动推理与认知重庆市重点实验室,重庆400714 [2]中国科学院大学,北京100049

出　　处：《物理学报》2015年第13期28-33,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11301524);重庆市科技攻关项目(批准号:cstc2012gg B40004);中国科学院西部之光联合学者资助的课题~~

摘　　要：在计算关联维数过程中,为了减少人为因素识别无标度区间带来的误差,提出一种基于模拟退火遗传模糊C均值聚类识别无标度区间的新方法.该方法根据无标度区间对应曲线的二阶导数在零附近波动的变化特征,利用分类算法进行识别.首先对双对数关联积分的离散数据进行二阶差分;然后利用模拟退火遗传模糊C均值聚类方法对该数据进行分类,选出在零附近波动的数据;再剔除粗大误差保留有效数据;最后进行统计分析识别出线性度最好的作为无标度区间.应用新方法对两个著名的混沌系统Lorenz和Henon进行了仿真,计算结果与理论值非常符合.实验表明,所提出的新方法与主观识别、K-means和2-means方法比较,可以有效自动识别无标度区间,减少误差,计算结果更加精确.A random fractal exhibits self-similarity over the scaling region, this is different from the regular fractal. The scaling region obtained by the proper method for the exact fractal dimension is very important. And the correlation dimension is one of the fractal dimensions which is used widely in many fields. Therefore, it is necessary and timely to identify the scaling region that plays a critical role in calculating the correlation dimension accurately in various chaotic systems. Visual identification is widely used to determine the scaling region as a quick and simple subjective method. However, this method may lead to an inaccurate result in Grassberger Procaccia algorithm. In order to reduce the error caused by human factors from computing the correlation dimension, a novel method of identifying the scaling region based on simulated annealing genetic fuzzy C-means clustering algorithm is proposed. This new method is based on the fluctuating characteristics that the second-order derivative of the curve within the scaling region is zero or nearly zero. Firstly, the second-order differential of the double logarithm correlation integral discrete data is calculated. Secondly, the simulated annealing genetic fuzzy C-means clustering method is used for dividing the data into three groups： positive fluctuation data , zero fluctuation data, and negative fluctuation data. The zero fluctuation data are selected to retain, the rest is excluded. Thirdly, the 3 σ criteria are used for excluding gross errors to retain those valid from the zero fluctuation data. Fourthly, the data of the consecutive nature point interval are chosen from the retained data. Finally, the regression analysis and statistical test are used to identify the scaling region from the data valid. In order to verify the effectiveness of the proposed method, it is used to simulate the Lorenz and Henon systems. The calculated results are in good agreement with the theoretical values. Experimental results show that the proposed new approach is easy to o

关 键 词：关联维数 无标度区间 分形 模糊聚类 

分 类 号：TP311.13[自动化与计算机技术—计算机软件与理论]