摘要:
对于一个稳定的动力系统而言,系统变量的概率密度具有较为稳定的分布型,而当系统的动力学结构发生变化后可能会导致系统变量的分布型发生不同程度的变化.鉴于此,本文从识别系统变量的概率密度分布的微小变化角度出发,将描述时间序列概率分布特征的偏度系数和峰度系数应用于时间序列的突变检测中.数值试验结果表明,偏度系数和峰度系数对突变信号具有很好的识别能力,进而揭示了一条检测突变的新途径.进一步的研究表明,新方法的检测结果对于子序列长度的选择具有较小的依赖性.
Abstract:
For a stable dynamic system,probability density distribution（PDD） of a system variable is relatively stable,and if there is a change in dynamic structure of a system,the PDD of the system variable will have some change correspondingly.According to this characteristic of PDD of a dynamic system,in this paper we present two new methods,namely,skewness index and kurtosis index,to detect an abrupt change in a time series by means of identifying some small changes in PDD.Tests on model time series indicate that skewness index and kurtosis index can be used to identify an abrupt change,such as abrupt change in parameter of an equation and abrupt dynamic change.Thus,we provide a new approach to detecting abrupt change in time series based on PDD.Further studies show that the detected results of the skewness index and kurtosis index are almost independence of the length of a subseries.
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