简单非线性多次降噪过程中的异常状态

Abnormal state in the process of simple nonlinear noise repeated reduction

为了降低电子制造企业的产品合格率时间序列中的噪声,采用了简单非线性降噪算法对时间序列进行多次局部降噪.在降噪过程中,在某一邻域半径的重构相空间中出现了大部分点变成了孤立点的异常状态.通过对异常状态与正常状态的对比研究,发现异常状态下的时间序列是不变的,而且该时间序列的最大Lyapunov指数为恒定值,其大小已经接近该降噪过程能够达到的最大Lyapunov指数.在重构相空间中的降噪过程中出现异常状态的意义在于:这种状态下的系统在重构相空间中已经进入一种基本有序的状态,重构相空间中的大部分点之间只存在时间相关性,所以出现异常状态后的时间序列正是降噪所要寻找的最佳混沌时间序列.

In order to reduce the noise of electronic plant＇s product qualified ratio time series, the simple nonlinear noise reduction method is applied by multiple noise reduction. In the process of noise reduction, most of the points in the reconstructed phase space turn into isolated points in a specific radius neighborhood, or an abnormal state. Compared with the normal state, an unchanged time series is found in the abnormal state, and the biggest Lyapunov exponent of this unchanged time series is a constant which approaches the biggest Lyapunov exponent in the noise repeated reduction process. The meaning of the abnormal state in the roconstructed phase space is： the system of this abnormal state is approximately ordered in the reconstructed phase space, and most of the points in the reconstructed phase space are only time related. So the time series of the abnormal state is just the optimal time series which is sought by the noise reduction procedure.