一种基于奇异值分解的自适应降噪方法

根据信号处理基本理论和方法．针对奇异值分解方法中有关的Hankel矩阵有效秩难以确定的难题,提出了一种奇异值分解方法,即主分量分解方法．并通过试验数据进行了验证。仿真信号和海上实录信号的降噪实验研究表明．提出的方法比基本的LMS滤波和奇异值分解降噪效果更加优越,能有效提高信噪比并去除噪声。     

基于双树复小波和奇异差分谱的齿轮故障诊断研究

针对故障齿轮振动信号的非平稳特征和包含强烈噪声,很难提取故障特征频率的情况,提出了基于双树复小波和奇异差分谱的故障诊断方法。首先将非平稳的故障振动信号通过双树复小波分解为几个不同频段的分量;由于噪声的影响,从各个分量的频谱中难以准确地得到故障频率。然后对包含故障特征的分量构建Hankel矩阵并进行奇异值分解,求奇异值差分谱曲线,确定奇异值个数进行SVD重构降噪,由此实现对故障特征信息的提取。最后再求希尔伯特包络谱,便能准确地得到故障频率。实验结果和工程应用表明,该方法可以有效地提取齿轮的故障特征信息,验证了方法的可行性和有效性。     

基于SVD降噪的经验模式分解及其工程应用

提出了一种基于奇异值分解降噪的机械设备振动型号经验模式分解方法,该方法首先对原始振动信号进行相空间重构和奇异值分解,然后根据分解奇异值的奇异熵确定降噪阶次,最后利用经验模式分解法提取降噪后振动信号的基本模式分量。对滤波前和滤波后的工业现场振动信号进行了经验模式分解,分析结果表明奇异值分解能够有效地提高信噪比,突出原始振动信号的故障特征,使得降噪后的振动信号分解出的基本模式分量具有更明确的物理意义,有利于对设备故障进行精确诊断。     

基于最优Morlet小波和SVD的滤波消噪方法及故障诊断的应用

分析了传统的小波去噪方法和小波变换的滤波特性.利用小波变换技术、奇异值分解技术和Morlet小波良好的时域和频域特性,提出了基于最优Morlet小波和SVD的滤波消噪方法.首先,采用最小Shannon熵方法确定出最优Morlet小波;然后,利用奇异值分解技术确定出最佳变换尺度a;最后对信号进行滤波消噪处理,从而提取信号中的有用成分.实验结果表明,该方法具有良好的去噪性能,用于故障特征提取是有效的.     

延伸奇异值分解包及其在高速列车轮对轴承故障诊断中的应用

结合多分辨奇异值分解包的分解结构和对滚动轴承故障信号的Hankel矩阵的奇异值分布特性研究,提出了延伸奇异值分解包。该算法的核心包括矩阵递推构造和矩阵重构。以分量信号能量为指标,提出了有效分量信号的筛选准则,并基于该准则,进一步提出了延伸奇异值分解包的快速算法。仿真结果表明,延伸奇异值分解包对信号中共振频带分量信号具有很好的分解能力,方法具有强鲁棒性,同时极大地改善了奇异值分解包中出现的模态混叠。应用高速列车轮对轴承试验数据对该方法进行试验验证,结果表明,该方法能有效分离高速列车轮对轴承复合故障信号的不同共振频带信号,对筛选的有效分量信号进行包络分析,可有效提取不同类型的故障特征频率及其谐波,对共振频带的聚集性和故障的表征力相比奇异值分解包均有显著提高。     

Fractional M-band dual tree complex wavelet transform for digital watermarking

In this paper, a novel digital watermarking scheme using fractional M-band dual tree complex wavelet transform (Fr-M-band-DT-CWT) is proposed. High frequency channels have wide bandwidth and low frequency channels have narrow bandwidth. These characteristics are suitable for analysing low frequency signal, but not for relatively high frequency signal. The images often contain many edges, which may cause rich middle and high frequency components in the 2-band wavelet domain. Therefore, the ordinary 2-band dual tree complex wavelet transform (DT-CWT) is not well-suited for analysing the image. So, the M-band DT-CWT with the FrFT called Fr-M-band-DT-CWT is proposed in this paper to address this problem. Further, we integrate the Fr-M-Band-DT-CWT with singular value decomposition (SVD) in order to enhance the performance. Experimental results of the proposed watermarking scheme are compared with the previously available watermarking algorithms, fractional Fourier transform (FrFT), fractional wavelet transform (FrWT). Further, the proposed watermark extraction scheme is also tested on different attacks. The results of the present investigations show that the proposed watermarking scheme is superior as compared to other existing watermarking schemes.     

抗印刷/扫描彩色图像零水印方案

针对印刷/扫描对图像特征的影响规律,设计了一种基于离散小波变换及奇异值分解的抗印刷/扫描鲁棒性零水印方案,用于印刷品的防伪认证。将彩色图像转换到CIE Lab色彩空间,对亮度分量做一次小波分解,再对其低频子图进行分块奇异值分解,以其最大奇异值矩阵构造零水印。仿真及印刷实验结果表明:该方案具有较好的抗印刷/扫描鲁棒性。     

一种基于小波变换与奇异值分解对振动系统模态频率进行识别的新方法

针对从受噪声污染的脉冲响应信号和快速正弦扫频响应信号中识别振动系统的单模态和密集多模态的频率问题，将小波变换与奇异值分解（SVD）滤波相结合，利用基于小波变换的能量分布函数，为了提高对密集模态和含有噪声信号的识别效果，对该能量分布函数求n次方，再进行奇异值分解后，根据奇异值，求出主要分量，然后通过主要分量对应的n次方尺度图或频率计算公式，识别出模态的频率。仿真结果证明了该方法的有效性和可行性。     

Medical images compression for remote diagnosis using modified SPIHT data organization and fidelity enhancement filter

In this work, an 8 × 8 Discrete Cosine Transform (DCT) approach is adopted to perform DCT shrinkage, followed by modified set partitioning in hierarchical trees (SPIHT) data organization and fidelity enhancement filter for reducing the memory required to store a remote diagnosis and rapidly transmit it. The DCT shrinkage has the ability to retain the detailed characteristics of an image. By means of a simple transformation to gather the DCT spectrum data with the same frequency domain, the DCT shrinkage exploits all the characteristics of individual blocks to a global framework. In this scheme, insignificant DCT coefficients that correspond to the same spatial location in the high‐frequency sub‐bands can be used to reduce the redundancy by a combined function proposed in association with the modified SPIHT. Meanwhile, quad‐tree decomposition and a set of morphological filters for reducing the artifacts are presented. This set of filters employs 8 predefined morphological operations, namely 4 structuring elements (SE), each of which includes both dilation and erosion operations. The voting strategy is used to select the most suitable morphological filter for each block. Simulation results show that the image compression reduced the computational complexity to only a half of the wavelet based sub‐band decomposition and improved the quality of the reconstructed medical image in terms of both the peak signal‐to‐noise ratio (PSNR) and the perceptual results close to JPEG2000 and the original SPIHT at the same bit rate. © 2007 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 17, 49–61, 2007     

基于ITD-SVD和MOMEDA的故障特征提取方法

为提高滚动轴承故障诊断的准确性,提出一种基于固有时间尺度分解(ITD)、奇异值分解(SVD)和多点最优最小熵反褶积(MOMEDA)相结合的故障特征提取方法。首先,采用ITD分解故障振动信号,并构建基于峭度和相关系数的组合权重指标筛选准则,从而完成分量信号的筛选与重构。其次,对其进行SVD滤波降噪。最后,利用MOMEDA提取降噪后信号中的周期性冲击成分,并通过Hilbert包络谱分析得到诊断结果。经过实验数据分析,结果表明所提出的方法不仅能滤除噪声干扰,增强故障特征信息,而且能准确提取出故障特征。     

Estimation of attractor dimension of EEG using singular value decomposition

This paper describes a novel application of singular value decomposition (SVD) of subsets of the phase-space trajectory for calculation of the attractor dimension of a small data set. A certain number of local centres (M) are chosen randomly on the attractor and an adequate number of nearest neighbours (q=50) are ordered around each centre. The local intrinsic dimension of a local centre is determined by the number of significant singular values and the attractor dimension (D ₂) by the average of the local intrinsic dimensions of the local centres. The SVD method has been evaluated for model data and EEG. The results indicate that the SVD method is a reliable approach for estimation of attractor dimension at moderate signal to noise ratios. The paper emphasises the importance of SVD approach to EEG analysis.     

基于VMD和SVD的柴油机气门间隙异常特征提取研究

为有效地从柴油机缸盖表面振动信号中提取气门间隙故障特征,提出一种基于变分模态分解(VMD)和奇异值分解(SVD)的特征提取新方法。采用VMD算法对缸盖振动信号进行分解,利用所得的模态分量构建特征矩阵;接着应用SVD理论将特征矩阵转变为表征频率特性的奇异值序列,探讨了稳定工况下的奇异值序列与不同气门间隙状态之间的关系;由于转速、负荷等工况的改变对信号特征层的影响与故障所引起的信号特征的改变可能非常相似,因此将奇异值序列作为特征参数,输入到随机森林分类器中,构建分类模型,对柴油机变工况下的气门间隙故障进行诊断。实验结果表明:该方法能有效识别气门间隙故障,突出故障敏感特征;与传统基于Hankel矩阵和小波包系数矩阵的SVD特征提取方法相比,该方法所提特征参数在柴油机变工况条件下具有更高的识别率。     

基于自适应VMD的高速列车轴箱轴承故障诊断

以尺度空间对信号频谱中共振频段的识别能力为基础,结合变分模态分解(VMD)对信号的自适应分解能力,提出了预估惩罚因子的尺度空间引导VMD算法。该算法的核心包括以尺度空间对信号频段的共振频段划分从而确定VMD中的本征固有模态个数,并根据共振频段边界预估VMD各个本征固有函数的初始中心频率与相应的惩罚因子取值,从而提高VMD的自适应性以及准确性。仿真结果表明,该方法能够正确识别低信噪比条件下的故障信号的共振频带,并对信号进行准确的分解。应用高速列车轴箱轴承实验数据对该方法进行实验验证,能够有效分解信号中包含的不同故障冲击;与选择不同惩罚因子的VMD算法相比,能够更准确地提取出信号中的不同故障冲击,对VMD分解的自适应性与准确性有着显著提高。     

Sub‐band coding of digital images

Abstract

An efficient sub‐band coding method for encoding images is presented in this paper. In this method a frequency band decomposition of the image is carried out by means of two‐dimensional separable quadrature mirror filters (QMF's), which split the image spectrum into sixteen uniform sub‐bands. In the coding process, we employ special quantizers and encoding algorithms which are designed according to the characteristics (including the visual perceptual property) of the sub‐bands to quantize and to encode these subimages, separately. The simulation results are presented in terms of average bit rates and the quality (in subjective as well as mean squared senses) of the reconstructed images. These results indicate that a good quality reproduction can be achieved at high compression rates. The paper also shows that a seven‐band decomposition has very high performance in quality, compression rate, and economy.     

基于重分配配算法和奇异值分解的多小波脊线提取

小波脊线能较好地揭示信号瞬时频率变化情况。针对目前多小波脊线提取方法存在的问题,提出了一种多小波脊线提取的新方法。该法通过连续小波变换得到小波尺度谱后,利用重分配算法对其进行处理,再通过奇异值分解降噪,然后通过求小波系数的模极大值点来提取各分量的小波脊线。与其它方法相比,该法更加适合于某些分量具有较大载波频率的低信噪比多分量AM-FM信号的小波脊线提取。在齿轮故障特征提取中的应用结果也验证了所提方法的有效性和实用性。     

A singular‐value decomposition (SVD)‐based generalized finite difference (GFD) method for close‐interaction moving boundary flow problems

In this paper, we present a study on a singular‐value decomposition (SVD)‐based generalized finite difference (GFD) method and a nodal selection scheme for moving body/boundary flow problems formulated on a hybrid Cartesian cum meshfree grid system. The present study shows that the SVD‐based method is more robust and accurate than the conventional least‐squares‐based GFD scheme. A nodal selection scheme is also introduced to overcome the problem of numerical instability associated with the clustering of computational nodes. Such nodal clustering occurs dynamically when moving bodies or boundaries approach within close proximity of each other, resulting in the overlap of their meshfree grids. The nodal scheme is applied to close‐interaction flow problems as exemplified by the squeezing action of a circular cylinder through a very narrow slot and the close proximity bypass interaction of two oscillating circular cylinders. Copyright © 2008 John Wiley & Sons, Ltd.     

EMD和二进正交小波分解对旋转机械振动信号处理效果的研究

二进正交小波分解通过一组高、低通正交镜像滤波器，以二分频形式把信号分解到各个频段中，经验模式分解（EMD）具有类似性质。但由于分解原理问的差异，对同一信号有不同处理效果。以故障滚动轴承振动信号处理为例，对比分析两种方法的处理效果，表明对于旋转机械，由于故障信号往往表现为调幅形式，而且相互间具有不同的载波与调制波频率，EMD方法是以信号的真实物理意义实现自适应二分频分解，能完整保留各个调幅信号，二进正交小波变换严格按照数学意义分解信号，势必破坏调幅信号完整性，影响故障定位，对比处理效果，EMD提取故障特征频率的效果要比二进正交小波分解好。     

Optical watermark scheme based on singular value decomposition ghost imaging and particle swarm optimization algorithm

An optical image watermarking algorithm, based on singular value decomposition (SVD) ghost imaging and multiple transforms, is designed. The watermark image is first encrypted by applying an SVD ghost imaging system, then the encrypted watermark is embedded into the cover image with the help of multiple transforms, including lifting wavelet transform (LWT), discrete cosine transform (DCT), discrete fractional angular transform (DFAT) and SVD. Four sub-band images are produced from the host image by LWT and DCT. The improved DFAT, whose scaling factors and parameter are optimized by particle swarm optimization algorithm, is operated in the new matrix. Afterwards, SVD is executed in the two-part image and the encrypted watermark is embedded in the host image by mutual operation of different matrices. Simulation results validate that the proposed watermark scheme is superior in the aspects of security, robustness and imperceptibility.     

Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure

The direct methods for the solution of systems of linear equations with a symmetric positive‐semidefinite (SPS) matrix A usually comprise the Cholesky decomposition of a nonsingular diagonal block A _???? of A and effective evaluation of the action of a generalized inverse of the corresponding Schur complement. In this note we deal with both problems, paying special attention to the stiffness matrices of floating structures without mechanisms. We present a procedure which first identifies a well‐conditioned positive‐definite diagonal block A _???? of A , then decomposes A _???? by the Cholesky decomposition, and finally evaluates a generalized inverse of the Schur complement S of A _????. The Schur complement S is typically very small, so the generalized inverse can be effectively evaluated by the singular value decomposition (SVD). If the rank of A or a lower bound on the nonzero eigenvalues of A are known, then the SVD can be implemented without any ‘epsilon’. Moreover, if the kernel of A is known, then the SVD can be replaced by effective regularization. The results of numerical experiments show that the proposed method is useful for effective implementation of the FETI‐based domain decomposition methods. Copyright © 2011 John Wiley & Sons, Ltd.     

基于改进奇异值分解和经验模式分解的滚动轴承早期微弱故障特征提取

针对滚动轴承早期微弱故障特征难以提取的问题,提出了改进奇异值分解(SVD)和经验模式分解(EMD)的滚动轴承早期微弱故障特征提取方法。首先用多分辨奇异值分解将信号分成具有不同分辨率的近似和细节信号,然后对近似信号用奇异值差分谱进行消噪,对消噪后的信号进行经验模态分解,将得到的各本征模函数分量进行希尔伯特包络解调,从而获得滚动轴承故障特征信息,最后通过对滚动轴承早期内圈故障的诊断实验证明了该方法的有效性