基于改进的G-P算法的相空间嵌入维数选择  

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

作　　者：高俊杰[1] 王豪[1] 

机构地区：[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

出　　处：《计算机工程与应用》2014年第9期107-110,共4页Computer Engineering and Applications

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。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 algo-rithm 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 duplicat-ed 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.

关 键 词：混沌 相空间重构 嵌入维数 饱和关联维数法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]