一种改进的Lyapunov指数谱算法及应用研究

Improved Method of Computing Lyapunov-spectrum and Its Application

提出了改进的Darbyshire-Broomhead(D-B)Lyapunov指数谱算法,通过互信息函数确定嵌入延迟,利用伪近邻法(False Nearest Neighbors,FNN)确定最佳嵌入维,从而确定了Lyapunov指数的个数,克服了原算法排除可疑指数过程中容易引起过多或过少的指数的缺点,然后再根据简化D-B理论计算出整个序列的Lyapunov指数。分别对含有噪声和不含有噪声的Lorenz时间序列仿真对比验证了该算法的有效性及稳定性。最后利用该算法对输油管道压力时间序列进行了Lyapunov指数的计算并分析出该时间序列具有混沌特征。

A new method of computing the Lyapunov-spectrum based on Darbyshire-Broomhead＇s arithmetic （D-B） was given, in which the delay was computed based on mutual-information function, and the optional embedding was obtained based on false nearest neighbors （FNN） that would get the number of Lyapunov exponents also and Lyapunov-spectrum of time series including noise was evaluated based on the Darbyshire-Broomhead＇s Lyapunov- spectrum theory. This method could avoid the step of removing spurious exponents. A comparison for Lyapunov exponents of Lorenz time series with and without noise was done. The results show the validity and convergence. At last, Lyapunov-spectrums of experiential datasets of press time series for oil pipeline were computed by the method proposed. Chaos character was found from the result.