相空间重构延迟时间互信息改进算法研究

针对改进互信息算法利于快速可靠获得时间序列相空间重构的延迟时间问题,通过等边缘分布2、4等分Lorenz时间序列构成平面分析Cellucci互信息算法缺陷;用大小顺序值代替原序列数值、判断新序列数值所在等边缘概率区间获得概率分布矩阵、修正概率分布矩阵最末行与列改进Cellucci互信息算法;以改进算法所得最佳延迟时间进行Lorenz时间序列相空间重构并以小数据量法得出其最大Lyapunov指数,对比雅可比矩阵法所得最大Lyapunov指数以确认改进算法的有效性。结果表明,时间序列长度不能整除划分区间数时Cellucci互信息算法会获得错误的最佳延迟时间;所提改进算法能消除Cellucci算法缺陷,且计算速度快于Fraser算法;数据序列长度较大时改进算法结果更稳定;由两种最大Lyapunov指数计算方法所得结果间误差较小,表明改进的互信息算法有效、可靠。

Improved mutual information algorithm for phase space reconstruction

Improvement of mutual information algorithm is good for gaining time delay in phase space reconstrution of time series rapidly and reliably. Firstly, fault of Cellucci’s mutual information algorithm is analyzed based on respectively partitioning plane, which constructed by a pair of Lorenz series with the same size, into four and sixteen grids with equal distribution probability in elements on each axis. Then improved mutual information algorithms is promoted based on the original probability matrix that shows the distribution of points corresponding to data pairs of Lorenz series on the plane by sorting two series respectively, replacing each numerical value with its order number in its own series so as to judge the element in which data sets are located and revising the last column and row of the matrix. Finally, after reconstructing phase space with the optimal time delay, comparison between the maximal Lyapunov exponent calculated by Rosenstein’s algorithm from time series and that gained by Jaccobi matrix from Lorenz equation is used to confirm the validity of the new mutual information algorithms. The results show that Cellucci’s mutual information algorithm will lead to wrong optimal time delay when series size is not a multiple of elements. The new algorithm, whose result is steadier when large numbers of data pairs are used, can not only eliminate the default of Cellucci’s algorithm but also is faster than Fraser’s algorithm. Besides, the lesser error of the maximal Lyapunov exponents from the comparison shows that the new mutual information algorithm is available and feasible.