【作者】 王东；

【导师】 舒勤；

【作者基本信息】 四川大学 ， 信号与信息处理， 2023， 硕士

【摘要】 混沌作为非线性科学的重要分支之一,自20世纪下半叶以来,已在物理、化学、气象、通信、生物医学、控制和工程等领域得到广泛研究与应用。混沌信号即由具有不规则行为的确定性非线性系统所产生的具有非周期、随机时间演化和宽频谱等特性的信号。实际观测到的混沌信号往往受到噪声干扰,而噪声的存在破坏了混沌信号在相空间中的奇异吸引子的结构特征,掩盖了信号原本的混沌动力学特性,进而影响到混沌特征量的准确计算,使得对数据的分析偏离实际,给后续的研究和应用带来困难。因此对混沌信号进行有效的降噪是后续各种处理的前提。混沌信号的特性使得传统线性滤波方法的降噪性能下降,而基于相空间重构(Phase Space Reconstruction,PSR)的降噪方法是一类十分有效的方法,它充分利用观测信号的混沌特性,可以最大程度地保留奇异吸引子的形状。本文对基于相空间重构的混沌信号降噪方法进行了研究,在白噪声的背景下,针对现有方法的不足提出改进,并将其用于仿真混沌信号与实测ECG(electrocardiogram)信号的降噪处理当中。文章主要工作如下:1)论述了混沌信号降噪的研究背景及意义,概述了基于相空间重构的混沌信号降噪方法在国内外的研究现状。介绍了混沌与混沌信号处理的基本理论,并重点阐述了相空间重构理论以及坐标延迟重构法中均匀嵌入方法的参数选取问题。2)针对局部投影(Local Projection,LP)方法在不同噪声水平下局部邻域难以选取以及当原始动力系统未知时局部子空间难以划分的问题,提出一种基于模糊递归图(Fuzzy Recurrence Plot,FRP)和最优硬阈值(Optimal Hard Threshold,OHT)准则改进的局部投影方法:首先利用核平均互信息量(Kernel Average Mutual Information,KAMI)法与Cao方法选取嵌入参数对观测信号进行相空间重构,利用重构相空间的FRP选取相点邻域。然后利用奇异值分解(Singular Value Decomposition,SVD)对相点邻域矩阵进行分解,采用OHT准则对奇异值进行自适应截断,从而实现局部邻域信号子空间与噪声子空间的划分。仿真实验结果表明该方法降噪效果优于原始LP方法和其他同类方法,不仅具有更好的自适应性,而且相比LP方法迭代次数更少。3)针对FRP计算量大以及SVD对异常值敏感的问题,提出一种基于连续变分模态分解(Successive Variational Mode Decomposition,SVMD)的局部鲁棒主成分分析(Robust Principal Component Analysis,RPCA)的方法:首先利用SVMD对信号进行分解得到本征模态函数(Intrinsic Mode Function,IMF),计算各IMF的多尺度扩散熵(Multiscale Dispersion Entropy,MDE)并筛选出噪声对应的IMF分量,进而估算出噪声的统计参数。接着利用改进的C-C方法选取嵌入参数进行相空间重构。为了抑制信号的畸变,采用在重构相空间轨线两端补充邻近相点的方法。然后综合考虑相点染噪前后距离的变化规律和相空间轨线的时间演化信息,结合前面估计出的噪声统计参数,得到初始邻域半径估计值。最后针对高维相空间中吸引子轨线与噪声在局部邻域的低秩性与稀疏性,采用RPCA方法进行降噪处理。仿真实验结果表明该方法降噪性能优于其他文献所提同类方法。对比前述FRP-OHT-LP方法,虽然在高信噪比情形下略差于FRP-OHT-LP方法,但其在低信噪比情形下降噪效果更好,并且消耗更少的计算资源。更多还原

【Abstract】 As one of the important branches of nonlinear science,chaos has been widely studied and applied in physics,chemistry,meteorology,communications,biomedicine,control and engineering since the second half of the 20 th century.Chaotic signal is a signal generated by a deterministic nonlinear system with irregular behavior,which has the characteristics of aperiodic,random time evolution and broadband spectrum.The actual observed chaotic signal is often disturbed by noise,and the existence of noise destroys the structure of the strange attractor of the chaotic signal in the phase space,conceals the original chaotic dynamic characteristics of the signal,and then affects the accurate calculation of the chaotic characteristic quantity,which makes the analysis of the data deviate from the reality,and brings difficulties to the subsequent research and application.Therefore,effective noise reduction of chaotic signals is the premise of subsequent processing.The characteristics of chaotic signal degrade the noise reduction performance of traditional linear filtering methods,while the noise reduction method based on phase space reconstruction(PSR)is a very effective method.It makes full use of the chaotic characteristics of the observed signals and can preserve the shape of strange attractors to the maximum extent.In this paper,the noise reduction method of chaotic signal based on phase space reconstruction is studied.Under the background of white noise,improved methods is proposed to overcome the shortcomings of existing methods,and it is used in the noise reduction processing of simulated chaotic signal and measured electrocardiogram(ECG)signal.The main work of this paper is as follows:(1)The background,significance and research status of chaotic signal denoising methods based on phase space reconstruction are summarized,and the basic theory of chaos and chaotic signal processing are introduced with emphasis on phase space reconstruction theory and the parameter selection methods of the uniform embedding in the coordinate delay reconstruction.(2)In order to solve the difficulties in selection of local neighborhoods under different noise levels and partition of local subspaces when the original dynamic system is unknown in local projection(LP)methods,a local projection method based on fuzzy recurrence plot(FRP)and optimal hard threshold(OHT)criteria was proposed: firstly,the kernel average mutual information(KAMI)method and Cao method are used to select embedding parameters to reconstruct the phase space,and the FRP is used to select the neighborhood of the phase point.Then the singular value decomposition(SVD)is performed on neighborhood matrix,and the OHT criterion is used to truncate the singular value,so as to realize the adaptive division of signal subspace and noise subspace in local neighborhood.The simulation results show that the noise reduction effect of the method is better than that of the original LP method and other similar methods.It not only has better adaptability,but also has fewer iterations compared with the LP method.(3)Aiming at the problems of large calculation of FRP and SVD’s sensitivity to outliers,a local robust principal component analysis(RPCA)method based on successive variational mode decomposition(SVMD)is proposed: firstly,SVMD is used to decompose the signal into intrinsic mode function(IMF),the multi-scale dispersion entropy(MDE)of each IMF are calculated to screen out the IMF corresponding to the noise,and then the statistical parameter of the noise is estimated.Then,the improved C-C method is used to select the embedding parameters for phase space reconstruction.In order to suppress the signal distortion,the method of supplementing adjacent phase points at both ends of the trajectory is adopted.Then,combined with the previously estimated noise statistical parameters,the initial neighborhood radius is obtained by comprehensively considering the distance change before and after the phase point containing noise and the time evolution information of the trajectory.Finally,aiming at the low rank of attractor trajectories and the sparsity of noise in the local neighborhood of high dimension phase space,RPCA method is used for noise reduction.The simulation results show that the noise reduction performance of this method is better than that of similar methods proposed in other literatures.Compared with the FRP-OHT-LP method,although it is slightly worse than the FRP-OHT-LP method in the case of high signal-to-noise ratio,its noise reduction effect is better in the case of low signal-to-noise ratio,and it consumes fewer computing resources.更多还原