改进的谐波小波包变换及其在弱故障特征提取中的应用

通过引入频谱幅值修正系数改进了通常的谐波小波包变换。改进的谐波小波包变换使得信号分解前后各子带的频谱幅值保持不变,能精确提取相应子带故障调制信号的强度与频率,为机械故障诊断带来了方便。仿真实验和轴承故障诊断实例不仅表明谐波小波包具有一般正交小波包无法比拟的完美的带通滤波性能和极强的微弱特征信号提取能力,而且还表明改进的谐波小波包变换确实使得信号分解前后各子带的频谱幅值保持不变,能精确提取相应子带故障调制信号的强度与频率,有一定的工程应用价值。     

基于粒子群优化的多小波图像降噪

提出一种基于粒子群优化的多小波图像降噪方法.该方法首先根据图像降噪的特点,采用粒子群算法优化CL多小波的前置滤波器,实现了图像多小波变换的自适应预滤波;接着对一幅含噪声图像进行多小波分解,根据多小波分解后的能量分布特性,对小波系数进行阈值处理;后经多小波反变换,得到重构图像.实验表明,本文方法的客观性能(PSNR)和主...     

提升静态小波与自适应PCNN相结合的图像融合算法

提出了一种新的基于提升静态小波变换与自适应PCNN相结合的图像融合算法.该方法定义一种图像单个像素的清晰度作为PCNN的链接强度,使得PCNN能根据像素清晰度的变化来自适应地调整链接强度的大小,接着对图像经提升静态小波分解得到的低频子带系数的改进拉普拉斯能量和及高频子带系数的单个像素的灰度值,分别作为自适应PCNN神经元的外部输入,并根据点火次数来确定图像融合系数.最后由提升静态小波变换的逆变换得到融合图像.实验表明,该方法在视觉效果和客观评价指标上都优于传统的基于小波变换、提升静态小波变换、提升静态小波-PCNN的图像融合算法.     

一种医学超声图像降噪方法

提出一种基于小波变换的医学超声图像降噪方法。图像进行三次小波分解,对变换后不同尺度的高频子图像进行小波半软阈值处理,最后通过小波逆变换和指数变换重构图像。     

采用小波变换的功率测量方法

根据国家电能质量标准和国际相关标准对电能质量的要求 ,提出了一种基于小波变换的非正弦波电流 (电压 )有效值和功率的计算方法。此方法利用子带滤波器对非正弦信号进行多分辨率分解 ,得到各个不同频带的小波分解系数 ,在小波域上用小波系数计算基波、谐波电流 (电压 )的有效值及功率 ;同时利用快速小波变换算法对短时间信号进行分析 ,得到了很好的测量结果 ,为工程实践中快速、精确地测定电网的功率参数提供了一种有效的方法。     

基于小波变换的STM图像处理

根据扫描隧道显微镜(STM)的特点,阐述了将小波变换应用于扫描隧道显微镜的降噪、增强及融合的方法,对于STM扫描获得的石墨原子图像,选用不同的小波基函数和分解层数进行分解和重构,结果表明,利用小波变换对扫描隧道显微镜图像进行处理是有效的、可行的,图像质量得到了明显提高。     

基于经验模态分解的图像拼接

对待拼接图像分别进行经验模态分解,对分解得到的第一个固有模态函数与第二个固有模态函数的叠加进行特征点提取、特征点匹配与变换矩阵的估计以实现图像的拼接,文中提出的方法有效提高了特征点匹配的正确率,具有很强的鲁棒性。在图像融合方面文中提出一种新的基于余弦关系变换的加权融合技术,在实现图像无缝拼接的同时,可有效去除拼接图像重叠区域的重影与鬼影现象。     

多义图像合成算法研究

提出了一种基于小波变换的多义图像合成算法。该算法首先通过视角来选择小波分解级对两幅目标图像进行小波分解,然后根据可选的小波融合规则和权值变量融合并重构出在两个视角下的多义图像;对小波算法与现有两种算法进行了分析比较,通过试验证明该算法合成的结果多义特性更好,合成图视觉效果醒目并充分保留原目标图像的色彩和细节特征。合成结果采取了均值降噪。     

基于NSCT和PCNN的红外与可见光图像融合方法

提出了一种基于非采样Contourlet变换(NSCT)和脉冲耦合神经网络(PCNN)的红外与可见光图像融合方法.首先用NSCT对已配准的源图像进行分解,得到低频子带系数和各带通子带系数;其次对低频子带系数采取一种基于边缘的方法以得到融合图像的低频子带系数;对各带通子带系数提出了一种改进的基于PCNN的图像融合方法来确定融合图像的各带通子带系数;最后经过NSCT逆变换得到融合图像.实验结果表明,本文方法优于Laplaeian方法、小波方法和传统的NSCT方法.     

多聚焦宫颈细胞图像融合方法

由于显微镜物镜焦深范围小,随着放大倍数的增大,景深会相应减小,只有那些在聚焦平面或其附近的物体才是可见的.本文提出了一种基于小波分解的多聚焦宫颈细胞图像融合算法,利用小波变换获取原始图像的小波系数,利用不同的融合规则和融合算子构造融合图像的小波系数,利用一致性校验得到最终的融合结果,解决了宫颈细胞不能在一幅图像中完全聚焦清晰的问题.     

Introduction to wavelets in engineering

The aim of this paper is to provide an introduction to the subject of wavelet analysis for engineering applications. The paper selects from the recent mathematical literature on wavelets the results necessary to develop wavelet-based numerical algorithms. In particular, we provide extensive details of the derivation of Mallat's transform and Daubechies' wavelet coefficients, since these are fundamental to gaining an insight into the properties of wavelets. The potential benefits of using wavelets are highlighted by presenting results of our research in one- and two-dimensional data analysis and in wavelet solutions of partial differential equations.     

自适应冗余提升小波降噪分析及其在轴承故障识别中的应用

为有效识别机械设备中滚动轴承的微弱故障信息,本文提出一种自适应冗余提升小波降噪方法。根据待分解低频尺度系数所含的不同特征,应用范数准则来自适应地选取最匹配于该尺度系数特征的小波函数。同时,引入多孔算法,用以通过冗余性来保证逐层分解后各尺度系数和小波系数所含有的丰富的信息量。接下来,对各层小波系数采用变尺度阈值降噪算法,并对降噪后的系数进行重构及包络谱分析,进而提取滚动轴承的故障特征。应用上述方法分别对轴承实验台轴承混合故障信号和现场实际信号进行分析,均较好地实现了故障识别,验证了本文方法的有效性。     

基于半正交B样条小波的任意控制顶点数曲线光顺

目前,小波分析应用于逆向工程时,对控制顶点有特殊要求,只能处理2j r个控制顶点的图形,为此提出了一种可以光顺任意控制顶点B样条曲线的小波分析新方法。在介绍B样条定义的基础上,从小波分析的定义出发,用严格的数学证明推导了任意控制顶点曲线的小波分解与重构具体算法。最后,该算法成功应用于B样条曲线的小波光顺,实例表明,该算法准确、结果稳定,效率理想。     

Wavelet packet based channel equalization

Recently, considerable amount of attention is being given to the field of wavelets and wavelet packets. It has found numerous applications in signal representation, image compression and applied mathematics. In this paper, we present a channel equalization method based on wavelet packets. The proposed equalizer structure is based on the fact that for sufficiently narrowband sequences, a non-ideal channel can be modelled as an attenuation and delay. If the data sequence is used to modulate a set of narrowband wavelet packets, then no equalization is required at the receiver end. The equalization problem reduces to that of determining the delay introduced by the channel for each of the wavelet packets. A minimum square variance algorithm for adaptively choosing the delay has been proposed. This algorithm has been shown to perform as desired analytically in a simple delay channel case. Simulations have been used to study its performance in the non-ideal channel’s case and the results corroborate theoretical predictions.     

A second generation wavelet based finite elements on triangulations

In this paper we have developed a second generation wavelet based finite element method for solving elliptic PDEs on two dimensional triangulations using customized operator dependent wavelets. The wavelets derived from a Courant element are tailored in the second generation framework to decouple some elliptic PDE operators. Starting from a primitive hierarchical basis the wavelets are lifted (enhanced) to achieve local scale-orthogonality with respect to the operator of the PDE. The lifted wavelets are used in a Galerkin type discretization of the PDE which result in a block diagonal, sparse multiscale stiffness matrix. The blocks corresponding to different resolutions are completely decoupled, which makes the implementation of new wavelet finite element very simple and efficient. The solution is enriched adaptively and incrementally using finer scale wavelets. The new procedure completely eliminates wastage of resources associated with classical finite element refinement. Finally some numerical experiments are conducted to analyze the performance of this method.     

Surface wavelets: a multiresolution signal processing tool for 3D computational modelling

In this paper, we provide an introduction to wavelet representations for complex surfaces (surface wavelets), with the goal of demonstrating their potential for 3D scientific and engineering computing applications. Surface wavelets were originally developed for representing geometric objects in a multiresolution format in computer graphics. These wavelets share all of the major advantages of conventional wavelets, in that they provide an analysis tool for studying data, functions and operators at different scales. However, unlike conventional wavelets, which are restricted to uniform grids, surface wavelets have the power to perform signal processing operations on complex meshes, such as those encountered in finite element modelling. This motivates the study of surface wavelets as an efficient representation for the modelling and simulation of physical processes. We show how surface wavelets can be applied to partial differential equations, stated either in integral form or in differential form. We analyse and implement the wavelet approach for a model 3D potential problem using a surface wavelet basis with linear interpolating properties. We show both theoretically and experimentally that an O(h) convergence rate, h_n being the mesh size, can be obtained by retaining only O((logN) ^7/2N) entries in the discrete operator matrix, where N is the number of unknowns. The principles described here may also be extended to volumetric discretizations. Copyright © 2001 John Wiley & Sons, Ltd.     

图论在无比例工程图中的应用

利用CAD进行工程设计,最终呈现给用户的是各种各样的工程图。无比例工程图一直是工程CAD软件中无法很好满足用户要求的部分。本文仔细讨论了工程图中各个元素之间的相互关系,给出了一种基于图论的无比例工程出图方法,并将其应用到钢结构节点祥图中,取得了很好的效果。     

Hat interpolation wavelet‐based multi‐scale Galerkin method for thin‐walled box beam analysis

The objective of the present work is to propose a new adaptive wavelet‐Galerkin method based on the lowest‐order hat interpolation wavelets. The specific application of the present method is made on the one‐dimensional analysis of thin‐walled box beam problems exhibiting rapidly varying local end effects. Higher‐order interpolation wavelets have been used in the wavelet‐collocation setting, but the lowest‐order hat interpolation is applied here first and a hat interpolation wavelet‐based Galerkin method is newly formulated. Unlike existing orthogonal or biorthogonal wavelet‐based Galerkin methods, the present method does not require special treatment in dealing with general boundary conditions. Furthermore, the present method directly works with nodal values and does not require special formula for the evaluation of system matrices. Though interpolation wavelets do not have any vanishing moment, an adaptive scheme based on multi‐resolution approximations is possible and a preconditioned conjugate gradient method can be used to enhance numerical efficiency. Copyright © 2001 John Wiley & Sons, Ltd.     

A spline wavelet finite‐element method in structural mechanics

The wavelet‐based methods are powerful to analyse the field problems with changes in gradients and singularities due to the excellent multi‐resolution properties of wavelet functions. Wavelet‐based finite elements are often constructed in the wavelet space where field displacements are expressed as a product of wavelet functions and wavelet coefficients. When a complex structural problem is analysed, the interface between different elements and boundary conditions cannot be easily treated as in the case of conventional finite‐element methods (FEMs). A new wavelet‐based FEM in structural mechanics is proposed in the paper by using the spline wavelets, in which the formulation is developed in a similar way of conventional displacement‐based FEM. The spline wavelet functions are used as the element displacement interpolation functions and the shape functions are expressed by wavelets. The detailed formulations of typical spline wavelet elements such as plane beam element, in‐plane triangular element, in‐plane rectangular element, tetrahedral solid element, and hexahedral solid element are derived. The numerical examples have illustrated that the proposed spline wavelet finite‐element formulation achieves a high numerical accuracy and fast convergence rate. Copyright © 2005 John Wiley & Sons, Ltd.     

一种紧支集双正交小波基的构造

基于对偶尺度函数及对偶小波，提出了一种构造紧支集双正交小波基的算法，并给出严密的证明和推导过程。应用该算法，结合函数优化方法，构造出一系列包括样条小波、接近正交的双正交小波及其它具有特殊性质的双正交小波。该构造算法丰富了小波理论，可以广泛应用于信号分析、图像处理等领域。