非线性时间序列定性相空间推理方法研究

Research on Method of Qualitative Phase Space Reasoning of Non-linear Time Series

提出一种基于定性仿真的非线性时间序列重构相空间的方法,定性相空间推理是其关键一步。通过时间序列定性状态的抽象来裁减其状态空间,规约行为轨迹,重构其定性相空间图。用3变量Lorenz系统产生的数据流对算法进行验证,结果表明能够保留原始相空间图的几何形状和拓扑关系,捕捉到相空间图中存在的行为轨迹的特征。

A method of reconstructing non-linear time series of phase space based on qualitative simulation was proposed,and the key step is qualitative reasoning in phase space.The method,on the basis abstraction of qualitative state of time series,trims state space and regulates behavior trajectories to reconstruct its qualitative phase space graph.After being tested by Lorenz system with 3 variables,the result proves that the method can keep geometrical shape and topology relation,and catch characters of behavior trajectories in phase space graph.