相空间重构中嵌入维和时间延迟的选择.pdf

38 　4 西　安　交　通　大　学　学　报 Vol.38　№4 2004 4 　JOURNAL OF XI ′AN JIAOTONG UNIVERSITY Apr.2004 1 2 2 1 2 2 马红光, 李夕海 , 王国华 , 韩崇昭, 许剑锋, 朱小菲 (1. , 710049, ;2. , 710025, ) :提出了一种用 相空间重构的嵌入维和时间延迟自动算法, 它利用混沌时间序列的去偏复自相关函 数的零点来确定时间延迟,有效地降低了平均位移法跟踪平均位移量斜率变化的随意性所造成的计算误差, 并借助 复自相关法和 Γ-te t 的迭代计算求得准最佳的嵌入维和时间延迟参数.该算法具有较充分的理论 依据,其计算复杂度不大, 对数据长度的依赖性不强.仿真实验结果表明,用该算法计算标准混沌时间序列关 联维的相对误差由传统算法的4.4%降低到1.06%,有效地提高了计算相空间重构中不变量的精度. :相空间重构;嵌入维;时间延迟;复自相关 :TN751　:A 　:0253-987X (2004)04-0335-04 Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction 1 2 2 1 2 2 MaHongguang , LiXihai , Wang Guohua , Han Chongzhao , XuJianfeng , ZhuXiaofei (1.School of Electronic and Information Engineering, Xi′an Jiaotong Univer ity, Xi′an 710049, China ; 2.Re earch In titute of High Technology, Xi′an 710025, China) Abstract:A new algorithm i propo ed for computing the embedding dimen ion and delay time in pha e pace recon- truction.It make u e of the zero of non-bia multiple autocorrelation function of the chaotic time erie to determine the time delay, which efficiently depre e the computing error cau ed by tracing the lope varying of average di placement (AD )arbitrarily in AD algorithm.Thereafter, by mean of the iterative algorithm of multiple autocorrelation and Γ-te t, the near-optimum parameter of embedding dimen ion and delay time are e timated.Thi algorithm provide with a ound theoretic ba i , and it computing complexity i relatively lower and not trongly depended on the data length.The imu- lated experimental re ult indicate that the relative error of the correlation dimen ion of tandard chaotic time erie i de- crea ed from