【摘要】 重构相空间是非线性分析的基础,利用关联积分导出的C-C方法是估计相空间重构参数延迟时间τd和延迟时间窗τw的有效方法。由于混沌系统的初值敏感性和实际序列长度有限并带噪,使得C-C方法估计出的τd和τw具有波动性。为了降低估值偏差,借鉴谱估计中平均法的思想,提出一种不同于已有文献利用整段序列估算τd和τw,而采用对序列分段估值后取平均的方法,并重点讨论了带噪序列的τd和τw估值及序列长度对估值的影响。数值仿真证明这种平均处理方法对τd和τw的估值具有较好的有效性和可靠性。更多还原

【Abstract】 State space reconstruction is the basis of nonlinear analysis and the C-C method derived from the correlation integral is an efficient way to estimate the two parameters for state space reconstruction,the delay time τ_d and delay time window τ_w.For chaotic systems are sensitive to initial conditions,and measured data with finite number are noise-corrupted,the estimates of τ_d and τ_w with C-C method are fluctuant.In order to reduce estimate deviations,similar to the average method in spectral estimation,a time series was divided into several segments and each one was used to estimate corresponding values and the averages were taken as the estimates of τ_d and τ_w.This method differs from the ones in literature which used the entire series for estimate.The estimates with noise-corrupted data and the effects of series length on the estimates were discussed.Numerical simulation showed that method is effective and reliable for estimates of τ_d and τ_w.更多还原