混沌时间序列的平均周期计算方法

The Calculating Method of the Average Period of Chaotic Time Series

在研究制造质量信息系统的混沌特性,使用小数据量法求解时间序列的Lyapunov指数时,使用文献中推荐的方法计算得到的平均周期不可信。针对这个问题,对比分析了六种平均周期计算方法,及其与时间序列长度、经过FFT变换后的幅值及功率之间的关系。在此基础上,以华南智信的日产品生产合格率数据及Lorenz系统产生的混沌时间序列为原始数据,计算这两个混沌时间序列的六个平均周期。实际生产数据与Lorenz系统数据进行对比后,发现六种平均周期对于平均周期计算来说,大小变化是一致的;再结合生产合格率数据的物理意义,对计算结果进行分析,综合前述理论分析,得到的结论是以功率加权计算得到的平均周期的在实际使用过程中有意义。

In the process of studying the chaotic characteristic of manugacturing quality information system,small data sets method was used for calculating the Lyapunov exponents of the time series,the average period of the time series calculated by the document recommended method was unreliable.Six average period calculating methods were compared and analyzed in term of the time series length,swing and power under FFT.Then the daily product qualified rate of HuananZhixin and time series produced by Lorenz system were used as the chaotic time series. Six kinds of average periods were calculated for the two chaotic time series. The variances of the six average periods are consistent between the two chaotic time series.The results combining with the physical meaning of product qualified rate was analyzed.It is concluded that the power weighted method is meaningful in calculating the average period.