一种基于Logistic模型的突变过程性分析方法及其应用

摘要

传统突变检测方法往往将突变检测的关键放在“突变点”上而忽略突变事件发生、发展乃至消亡的过程。本文提出一种新的检测突变过程的方法,其基于Logistic模型推导出能够反应均值突变过程的分段函数,利用分段函数对实际时间序列进行参数提取,借助参数的物理意义,研究分析完整的突变过程,从而加深对突变过程性的理解和认识,为进一步研究突变的形成机理、影响因素乃至发展趋势奠定重要的科学基础。文章还对太平洋年代际振荡(PDO)指数进行突变过程性检测,发现1940/1942,1977,1987年开始序列发生突变,突变持续时间锁定在某些固定值,并且系统相图表明一般性系统存在三种基本的状态。%The traditional detection method of abrupt change may pay more attention on the“point of abrupt change”and neglect the process of its onset, development and extinction. This paper has proposed a new detection method to obtain the abrupt change process (ACP);it can extract suitable parameters from real time series by using a piecewise function which is based on a logistic model that reflects the ACP. With the help of parameters’ physical meaning, we researched and analyzed the whole ACP, deepened the understanding and awareness of ACP, to lay the scientific foundation for further study on the formation mechanism, affecting factors and trends of the abrupt change. Besides, by detecting the PDO time series’ ACP, we also find that the time series began to change in 1940/1942, 1977, 1987, and the duration of abrupt change is locked in some fixed values;furthesmore, the phase graph of the system showed that a normal system world have 3 basic states.