CAJ | 학술논문

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。
침대개진호신식산법리우쾌속가고획득시간서렬상공간중구적연지시간문제，통과등변연분포2、4등분Lorenz 시간서렬구성평면분석 Cellucci 호신식산법결함；용대소순서치대체원서렬수치、판단신서렬수치소재등변연개솔구간획득개솔분포구진、수정개솔분포구진최말행여렬개진 Cellucci 호신식산법；이개진산법소득최가연지시간진행Lorenz 시간서렬상공간중구병이소수거량법득출기최대 Lyapunov 지수，대비아가비구진법소득최대 Lyapunov 지수이학인개진산법적유효성。결과표명，시간서렬장도불능정제화분구간수시 Cellucci 호신식산법회획득착오적최가연지시간；소제개진산법능소제 Cellucci 산법결함，차계산속도쾌우 Fraser 산법；수거서렬장도교대시개진산법결과경은정；유량충최대 Lyapunov 지수계산방법소득결과간오차교소，표명개진적호신식산법유효、가고。
The mutual information algorithm was improved for gaining rapidly and reliably the time delay in phase space reconstrution of time series.The defect of Cellucci's mutual information algorithm was analyzed based on respectively partitioning the plane,constructed by a pair of Lorenz series with the same size,into four or sixteen grids with equal distribution probability in elements on each axis.The improved mutual information algorithms was then promoted based on the original probability matrix that shows the distribution of points corresponding to data pairs of Lorenz series on the plane via the process of sorting the two series,replacing each numerical value by its order number in its own series so as to judge in which data set the element is located and revising the last column and row of the matrix.Finally,after reconstructing the phase space with the optimal time delay,the comparison between the maximal Lyapunov exponent calculated by Rosenstein's algorithm from time series and that gained by Jaccobi matrix from Lorenz equation was used to confirm the validity of the new mutual information algorithm.The results show that Cellucci's mutual information algorithm may lead to wrong optimal time delay when the 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 difference between the maximal Lyapunov exponents calculated by the two algorithms shows that the new mutual information algorithm is available and feasible.