Computer Engineering and Applications ›› 2014, Vol. 50 ›› Issue (9): 107-110.

Previous Articles     Next Articles

Determination of embedding dimension for phase space based on improved G-P method

GAO Junjie, WANG Hao   

  1. Department of Automation, School of Electronic Information and Electrical Engineering, Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai Jiaotong University, Shanghai 200240, China
  • Online:2014-05-01 Published:2014-05-14

基于改进的G-P算法的相空间嵌入维数选择

高俊杰,王  豪   

  1. 上海交通大学 电子信息与电气工程学院 自动化系,系统控制与信息处理教育部重点实验室,上海 200240

Abstract: This paper makes a study on the determination of embedding dimension for phase space reconstruction. A new algorithm is proposed based on the improved G-P method modifying the origin G-P method in four aspects. New algorithm realizes automatic calculation of dimension through self-adaptive choice of neighborhood radius, evenly changing step size and identification of non-scale range by rapid automatic judgement based on BDS statistic. By deleting duplicated and complex computing, proposed algorithm greatly speeds up solving rate. The MATLAB simulation results show that the algorithm proposed in this paper is more accurate and efficient.

Key words: chaos, phase space reconstruction, embedding dimension, saturation correlation dimension method

摘要: 对混沌时间序列相空间重构中嵌入维数的选择进行了研究,针对饱和关联维数算法(G-P算法)存在的四点不足,提出了一种计算最佳嵌入维数的改进算法。通过对邻域半径区间的自适应选择,采用均匀变化步长的方式;对无标度区间利用基于BDS统计限定范围的快速自动判定法进行识别,实现了系统维数的自动计算;针对原算法存在的重复运算、繁杂计算问题,从算法原理和程序结构上进行了改良,大大加快求解速率。在理论分析的基础上,用新算法进行试验,仿真结果表明设计的算法对嵌入维数的选择更准确更高效。

关键词: 混沌, 相空间重构, 嵌入维数, 饱和关联维数法