Identification of complex sound sources produced by gear units

Noise source visualisation represents an important tool for technical acoustics. Many techniques of noise source visualisation have been developed, based on a specific noise source in a specific type of acoustic environment. A new visualisation method of complex noise sources is presented, using an acoustic camera and a new algorithm. Different transient acoustical phenomena can be noted. Additionally, a new family of biorthogonal wavelets is applied to determine fault in gears. The new wavelets are a generalisation of biorthogonal wavelet systems. Smoothness is controlled independently in the analysis. For the optimisation of the synthesis bank, discrete finite variation is used. Differentiability is measured, for which a large number of vanishing wavelet moments is necessary, in favour of a smoothness measure based on the fact that a finite depth of the filter bank tree is in most case related to practical applications.     

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。     

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.     

小波包——自回归谱分析及在振动诊断中的应用

概叙了小波、小波包理论，由此提出一种称之为小波包－－自回归谱分析的新方法，它将小波包和自加归模型结合起来，该方法在机械诊断中，实现不同频道范围内，不同零部件故障信息分离和提取，并以挖掘机提升系统龄轮箱的振动信号为例，说明该方法是提取弱故障信息并进行早期诊断的有效方法。     

基于SVDD和距离测度的齿轮泵故障诊断方法研究

提出了一种基于支持向量域描述和距离测度的齿轮泵故障诊断方法。该方法首先对齿轮泵各种工况下的振动信号进行小波包分解,提取各频带能量百分比作为特征向量;然后仅利用正常工况下的特征向量训练SVDD超球模型,通过定义绝对距离测度检测齿轮泵状态是否出现异常;最后针对每类工况下的特征向量单独训练SVDD超球模型,通过定义相对距离测度准确定位齿轮泵的不同故障工况。试验结果表明,采用小波包频带能量降低了数据维数,有效浓缩了故障信息;基于绝对距离测度和相对距离测度的SVDD故障诊断方法既能检测异常状态,又能区分各种故障工况,达到了状态监测和故障分类识别的目的。     

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.     

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.     

基于BLCD和小波域双谱的齿轮故障诊断方法

本文对固有时间尺度分解(Intrinsic time-scale decomposition,简称ITD)方法进行了改进,提出了基于B样条的局部特征尺度分解方法(B spline-based Local characteristic-scale decomposition,简称BLCD),在此基础上将BLCD与小波域双谱相结合应用于齿轮故障诊断。首先将BLCD方法和ITD方法进行对比分析,验证BLCD方法的优越性。然后采用BLCD方法将齿轮振动信号进行分解,得到若干个ISC分量(Intrinsic scale component,简称ISC),再对ISC分量进行小波域双谱分析,通过双谱中峰值个数和耦合频率的成分来判断齿轮是否发生了故障。实验数据的分析结果表明,基于BLCD和小波域双谱的齿轮故障诊断方法能有效地应用于齿轮的故障诊断。     

基于双正交小波变换的资源二号卫星与多光谱影像融合方法研究

针对基于Darbechies等正交小波函数的遥感影像融合时引起失真的现象,引入双正交小波函数,提出了基于双正交小波变换的融合方法,对资源二号卫星和TM的多光谱影像的融合进行研究,并把融合结果与主成分、IHS和Brovey等融合结果进行比较。通过对光谱特征曲线、相关系数、光谱扭曲程度等分析和空间细节的对比,说明双正交小波融合方法除了提高空间分辨率外,最好地保持了多光谱影像的光谱特征,有利于专题信息的提取。     

基于复解析小波变换的瞬时频率分析方法

提出了利用基于复解析小波变换的瞬时频率分析的新方法。复解析小波变换将Hilbert变换与小波分析紧密结合在一起，具有自适应分析能力。对信号作复小波解析变换得到信号的瞬时频率，通过瞬时频率的功率谱分析就可提取信号特征。通过对齿轮故障振动信号的分析，表明该方法能有效地诊断齿轮局部故障，且与传统的频域方法相比具有更好的分析效果。     

基于扭振分析方法的齿轮传动系统故障辨识

通过分析齿轮啮合过程的数学模型及典型故障,论证了扭振分析方法在齿轮系统故障诊断上的优越性,并提出一种测量齿轮轴上扭振信息的新方法。在此基础上搭建了齿轮传动系统,通过采用永磁旋转(角)加速度传感器检测齿轮系统各个运行状态下不同轴上的扭振信号;然后,分别对齿轮传动系统轴上的扭振信号和平台的振动信号采用小波包分解,提取各个节点的能量作为特征向量;最后,结合以径向基函数(RBF)为核函数的支持向量机(SVM)分别进行故障的辨识。实验结果表明:轴上的扭振信号在齿轮系统故障诊断上的效果要优于平台振动信号的诊断效果。     

基于双正交小波信道估计改进的TR-UWB系统

针对超宽带（UWB）信号因脉冲持续时间短、时域分辨率高、在传播中出现密集多径现象的特点,利用小波函数和超宽带脉冲之间的相似特性,提出了一种基于双正交小波基的高效估计多径衰落幅度和时延等信道参数的信道估计算法,以便接收机能捕获足够的信号能量。通过滑动相关实现了同尺度上信号与小波的内积运算,避免了峰值搜索过程,简化了估计器的结构。同时,基于由信道冲激响应估计值合成的本地相关模板信号,提出了改进的发射-参考超宽带（TR—UWB）系统。Monte—Carlo仿真结果表明,该算法的归一化均方误差较小,改进的TR—UWB系统能有效抑制参考符号中噪声的影响,系统性能优于传统TR接收机。     

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。     

Parallel implementation of the biorthogonal multiresolution time-domain method

The three-dimensional biorthogonal multiresolution time-domain (Bi-MRTD) method is presented for both free-space and half-space scattering problems. The perfectly matched layer (PML) is used as an absorbing boundary condition. It has been shown that improved numerical-dispersion properties can be obtained with the use of smooth, compactly supported wavelet functions as the basis, whereas we employ the Cohen-Daubechies-Fouveau (CDF) biorthogonal wavelets. When a CDF-wavelet expansion is used, the spatial-sampling rate can be reduced considerably compared with that of the conventional finite-difference time-domain (FDTD) method, implying that larger targets can be simulated without sacrificing accuracy. We implement the Bi-MRTD on a cluster of allocated-memory machines, using the message-passing interface (MPI), such that very large targets can be modeled. Numerical results are compared with analytical ones and with those obtained by use of the traditional FDTD method.     

行星齿轮箱振动信号特征提取新方法

与轴承、定轴齿轮箱相比,提取行星齿轮箱的故障特征更加困难,且传统方法对行星齿轮箱的诊断效果不好。针对行星齿轮箱故障振动信号的非线性、复杂性等特性,提出一种基于小波包样本熵和均方根值的故障特征提取新方法。该方法首先对原始信号进行连续等长度截取,获得样本信号,再利用小波包变换分解样本信号,计算分解后各频段的样本熵和均方根值,并进行归一化处理。将归一化参数作为加权平均的权重,计算加权平均的样本熵和均方根值。最后将两参数做商得到新参数。故障诊断及抗噪试验结果表明,新特征提取方法能增大行星齿轮箱不同故障特征的区分度且有较好的稳定性,同时新参数具有一定的抗噪性。     

机械故障诊断中的小波基及算法研究

针对小波分析在机械故障诊断应用中的小波基选择和快速算法存在的问题,对常用的正交、半正交、双正交小波提取信号特征的能力进行了分析比较,表明半正交Ｂ样条小波因具有线性相位和采用较长的分解序列而具有较好的频率局部化特性和较小的变换误差,具有比较好的综合性能。推导了正交小波包的图形显示算法。利用该算法解决了小波变换快速算法中存在的数据长度随分解层数倍减小的问题。研究结果为故障诊断中小波基的选择和信号的深层     

Fault mode analysis and detection for gear tooth crack during its propagating process based on dynamic simulation method

Gearbox is one of the most important parts of rotating machinery, therefore, it is vital to carry out health monitoring for gearboxes. However, it is still an unsolved problem to disclose the impact of gear tooth crack fault on gear system vibration features during the crack propagating process, besides effective crack fault mode detection methods are lacked. In this study, an analytical model is proposed to calculate the time varying mesh stiffness of the meshing gear pair, and in this model the tooth bending stiffness, shear stiffness, axial compressive stiffness, Hertzian contact stiffness and fillet-foundation stiffness are taken into consideration. Afterwards, the vibration mechanism and effects of different levels of gear tooth crack on the gear system dynamics are investigated based on a 6 DOF dynamic model. Then, the crack fault vibration mode is studied, and a parametrical-Laplace wavelet method is presented to describe the crack fault mode. Furthermore, based on the maximum correlation coefficient (MCC) criterion, the optimized Laplace wavelet base is determined, which is then designed as a health indicator to detect the crack fault. The results show that the proposed method is effective in fault diagnosis of severe tooth crack as well as the early stage tooth crack.     

Spatial Wavelet Approach to Local Matrix Crack Detection in Composite Beams with Ply Level Material Uncertainty

Wavelet coefficients based on spatial wavelets are used as damage indicators to identify the damage location as well as the size of the damage in a laminated composite beam with localized matrix cracks. A finite element model of the composite beam is used in conjunction with a matrix crack based damage model to simulate the damaged composite beam structure. The modes of vibration of the beam are analyzed using the wavelet transform in order to identify the location and the extent of the damage by sensing the local perturbations at the damage locations. The location of the damage is identified by a sudden change in spatial distribution of wavelet coefficients. Monte Carlo Simulations (MCS) are used to investigate the effect of ply level uncertainty in composite material properties such as ply longitudinal stiffness, transverse stiffness, shear modulus and Poisson’s ratio on damage detection parameter, wavelet coefficient. In this study, numerical simulations are done for single and multiple damage cases. It is observed that spatial wavelets can be used as a reliable damage detection tool for composite beams with localized matrix cracks which can result from low velocity impact damage.     

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。     

基于小波分析和模糊神经网络的齿轮故障诊断研究

建立齿轮故障信号采集模拟试验台,结合小波分析特征提取方法和模糊神经网络对齿轮故障进行了诊断,通过实验仿真,取得了很好的诊断结果。相比于传统的BP神经网络诊断方法,无论在诊断速度还是诊断精度上,模糊神经网络更具有优势。