基于相空间重构和奇异值分解的混沌时间序列局部降噪

Local Noise Reduction in Chaotic Time Series Based on Phase Space Reconstruction and the Singular Value Decomposition

针对混沌时间序列的局部降噪问题,提出了一种相空间重构和奇异值分解(SVD)相结舍的方法,即对重构相空间中第一个相点及其邻近点组成的矩阵进行局部SVD,并以提取主要信息后的矩阵更新原矩阵,再逐次向后完成全部相点的迭代。对Lorenz系统和实测日产品合格率混沌时间序列进行仿真,并从两个方面对降噪效果进行评价,结果验证了该方法的有效性,并且局部SVD的降噪优势明显优于全局;但是一次局部SVD降噪在实测数据的极值点处会失效,这正是局部降噪的细腻性,可能会挖掘出实际生产运营中隐含的问题,随后通过不断减小邻域半径进行多次迭代局部SVD最终减小了孤立点对降噪效果的影响。

In this paper, a local method integrates the phase space reconstruction with the singular value decomposition （SVD） is proposed to reduce noise in chaotic time series which means conduct local SVD to the matrix of the first point and its adjacent points of the reconstructed phase space, then update the original matrix with new matrix which extracted main information, after that we iterate all following points successively. Applied this method to the white Gaussian Lorenz system and measured product qualified rate of chaotic time series, evaluated the effects in two aspects, the simula- tion results verify the effectiveness and reveals that the local SVD advantage is more excellent than global. In addition, local SVD will fail in extreme points of the measured data which may dig out the hidden problems in the actual production and operation. Finally we weaken the influence of isolated points on the noise reduction eventually by many times iteration of decreasing-radius local SVD.