摘要
提出了一种用于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,并借助于复自相关法和Γ test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.
A algorithm is proposed for computing the embedding dimension and delay time in phase space reconstruction. It makes use of the zero of non-bias multiple autocorrelation function of the chaotic time series to determine the time delay, which efficiently depresses the computing error caused by tracing the slope varying of average displacement (AD) arbitrarily in AD algorithm. Thereafter, by means of the iterative algorithm of multiple autocorrelation and Γ-test, the near-optimum parameters of embedding dimension and delay time are estimated. This algorithm provides a sound theoretic basis for practical work, and its computing complexity is low and not strongly depends on the data length. The simulated experimental results indicate that the relative error of the correlation dimension of standard chaotic time series is decreased from 4.4% by the conventional algorithm to 1.06% by using this algorithm. The accuracy of invariants in phase space reconstruction is improved.
出处
《西安交通大学学报》
EI
CAS
CSCD
北大核心
2004年第4期335-338,共4页
Journal of Xi'an Jiaotong University
关键词
相空间重构
嵌入维
时间延迟
复自相关
Chaos theory
Correlation methods
Delay control systems
Iterative methods
Time series analysis
