混沌特性时间序列线性变换理论方法及其应用  

Analysis and Application of the Chaos Character of Time Series after Linear Transformation

作　　者：鄂加强[1] 王春华[1] 彭雨[1] 李娟[1] 龚金科[1] 朱浩[1] 

机构地区：[1]湖南大学机械与运载工程学院,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2009年第2期36-42,共7页Journal of Hunan University:Natural Sciences

基　　金：湖南省自然科学基金资助项目(06JJ50103)

摘　　要：通过对时间序列的相空间的重构,用G-P算法、Wolf算法证明了混沌时间序列经过线性变换后其关联维数、Lyapunov指数以及Kolmogorov熵大小不变,从而得出了线性变换后混沌时间序列的混沌特性保持不变的结论.同时将这一理论和热力学中的相似实验相结合,验证了实验模型系统进入混沌则实际系统必也能够在相应时刻进入混沌状态.该结论被成功应用到对汽包水位晃荡幅值的测量当中,验证了汽包水位的晃荡幅值具有混沌特性,并成功地对该时间序列进行了预测.Based on the phase space reconstruction, the conclusion that the correlative dimension and the Lyapunov exponents of the time series remain unchanged has been proved with G-P algorithm and Wolf algorithm. And this new theory has also proved the establishment of similar experiments for chaos system. Such conclusion has been successfully applied to the analysis of the amplitude of the sloshing of the water level of drum boiler with chaos character. Meanwhile, the time series have been successfully forecasted.

关 键 词：时间序列 混沌 相空间重构 相似原理 

分 类 号：O415.5[理学—理论物理] TK223.13[理学—物理]