基于小波变换在线结构损伤检测分析研究

传统的傅立叶变换只能确定一个函数奇异性的整体性质,而难以确定奇异点在空间的位置及分布情况.小波变换具有空间局部化性质,利用小波变换来分析信号的奇异性及奇异性位置和奇异度的大小是比较有效的.在结构发生损伤时,结构的刚度发生了变化,因此结构动力响应的在线监测信号相应的发生了间断点,由于小波分析具有刻划信号局部特征的作用,通过对结构响应进行小波分解以后可以确定结构是否出现损伤以及确定损伤发生的时刻.     

THE WAVELET TRANSFORM OF PERIODIC FUNCTION AND NONSTATIONARY PERIODIC FUNCTION

Some properties of the wavelet transform of trigonometric function, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with this equation agrees well with the function.     

Crack detection of structure for plane problem with spatial wavelets

In this paper, the structure damage detection with spatial wavelets is approached. First, a plane stress problem, a rectangular plate containing a short crack under a distributed loading on the edge, is investigated. The displacement response data along the parallel and perpendicular lines at different positions from the crack are analyzed with the Haar wavelet. The peak in the spatial variations of the wavelets indicates the direction of the crack. In addition, a transverse crack in a cantilever beam is also investigated in the same ways. For these problems, the different crack positions are also simulated to testify the effectiveness of the technique. All the above numerical simulations are processed by the finite element analysis code, ABACUS. The results show that the spatial wavelet is a powerful tool for damage detection, and this new technique sees wide application fields with proad prospects. The project supported by the National Natural Science Foundation of China     

基于应变模态小波变换的框架结构损伤识别研究

采用应变模态的小波变换方法研究了框架结构的损伤识别问题。以有限元分析求解含裂缝平面框架应变模态为基础,利用Guass2小波对框架的应变模态进行小波变换,再用db3小波对应变模态小波变换系数进行去噪处理,最后通过对去噪处理后的小波系数模极大值点来识别框架结构裂缝的位置,建立了基于应变模态小波变换识别平面框架损伤的方法。以一层平面框架为例,分别给出了框架梁含有裂缝、框架柱含有裂缝、框架梁和柱均含有裂缝的有限元模型,计算得到结构的应变模态,并通过应变模态小波分析来识别平面框架裂缝的位置。从识别结果发现,经小波去噪处理后应变模态小波系数的模极大值点能够有效识别框架结构的损伤,数值计算验证了方法的有效性。本文研究对工程结构损伤诊断有参考价值。     

A fast algorithm for soil dynamics calculations by wavelet decomposition

Summary The article presents a fast numerical algorithm for calculating the response of a halfspace under any surface loads. Under certain conditions there exists an analytical solution to the problem in the Fourier domain. To get the desired response, a numerical inverse Fourier transform of this analytic solution has to be made. By using a wavelet decomposition, the proposed algorithm can reduce the calculation time significantly, thus allowing the computation of complex problems. As an example, the response of the beam-halfspace coupled system under moving load is presented. Received 6 March 1997; accepted for publication 20 May 1997     

小波分析在悬臂梁裂纹识别中的应用

基于空间信号的小波分析理论,将含裂纹悬臂梁前四阶振型信息直接用于小波变换,小波系数在空间域上的突变反映了裂纹的存在并指出了裂纹的位置.本文分析了前四阶振型对小波识别结果的敏感性,利用小波系数模极大值在尺度上的表现与Lipschitz指数之闻的关系建立了集中因子和裂纹深度之间的关系,以此来估计裂纹深度.鉴于实测信号往往是含噪声信号,分析了噪声对识别结果的影响规律.数值算例表明利用sym4小波对含裂纹梁的四阶振型信息进行小波分析可以准确地识别出裂纹的位置和深度;高阶振型对结构损伤较为敏感,高阶振型更适合于微裂纹和含噪声信息的处理,但高阶振型的非线性也会给裂纹识别带来一定的困难.使用本文方法进行结构裂纹参数识别,噪声对裂纹位置的影响只是指示清晰度的影响,基本不会产生错误的识别,而对裂纹深度的影响远比对位置的影响复杂,由于小波系数混入了噪声成分,从而增加了集中因子的取值,致使识别结果总是比真实结果偏大.     

连续小波变换在损伤探测中的应用

本文选取Gabor小波作为母函数，采用连续小波变换对含裂纹悬臂梁中的弯曲波进行分析，提取波动信号中某一频率分量上的入射波、反射波及透射波信号，由此可以准确地检测出悬臂梁的损伤位置，并对可其损伤程度做出定性估计。实验结果表明，这是一种行之有效的损伤检测方法，可以推广应用到复杂结构的损伤检测中去。     

大体积混凝土拆模后表层温度的Fourier震荡

将大体积混凝土拆模后很快予以保护的过程简化为大气温度的线性脉冲。研究了脉冲时间对Fourier震荡的影响。成果可以解释混凝土温度在边界层的不合理现象,指出了修正Fourier震荡的途径。     

Accumulative damage near crack tip for welded bridge members: fatigue life determination

The behavior of crack growth for the fatigue damage accumulation near tip where damage is most severe is analyzed. Fatigue life is assessed for the welded members of bridges under traffic loading. Two parts are considered. They consist of the development of a fatigue damage accumulation model for welded bridge members and a method for calculating the stress intensity factor that is needed for evaluating the fatigue life of welded bridge members with cracks. Based on the concept of continuum damage accumulation and fatigue and fatigue crack growth relations, results are obtained to describe the relationship between the cracking count rate and the effective stress intensity factor. Crack growth and fatigue life are found for two types of welded members assisted by using fatigue experimental results. The stress intensity factors are modified by correcting for the geometric shape of the welded members in order to reflect the influence of the weldment and geometry. This is accomplished via the stress intensity factor. The calculated and measured fatigue lives were generally in good agreement for the initial cracking conditions of two types of welded members widely used in steel bridges.     

Application of wavelet transform to bifuraation and chaos study

The response of a nonlinear vibration system may be of three types, namely, periodic, quasiperiodic or chaotic, when the parameters of the system are changed. The periodic motions can be identified by Poincare map, and harmonic wavelet transform (HWT) can distinguish quasiperiod from chaos, so the existing domains of different types of motions of the system can be revealed in the parametric space with the method of HWT joining with Poincar'e map. Communicated Zhang Ruqing Project supported by the National Natural Science Foundation of China     

用Fourier变换莫尔法测量流体自由表面微幅波的振幅

采用一种非接触的光学方法－傅立叶变换莫尔法（Fourier transformmethod），结合数字图像处理技术，对微幅振荡的水表面波的振幅进行测量。它是对全场中每一个像素点进行测量，比较触测量法具有更高的灵敏度。它为微幅水表面波振幅的测量提供了一种手段。通过将计算机生成的周期性光栅图像经投影机直接投影到被测物体的参考平面，经CCD摄像头、图像板捕捉存储形成数字化的光栅图像，利用傅立叶变换莫尔法处理光栅图像，从而获得包含有水表面波的振幅的相位信息，再经适当的几何变换获得振幅信息。我们在垂直振荡装置上进行了不同激励频率和不同振幅的表面波的振幅测量。     

噪声对管道超声纵向导波损伤检测的影响

在管道超声导波检测技术的基础上,对不同程度纵向缺陷的损伤检测进行了数值模拟.利用缺陷反射信号对损伤的定位,通过改变管壁局部刚度,研究了缺陷反射信号强度变化的相关规律以及超声导波对缺陷的敏感度,分析了噪声信号对损伤识别的影响,并利用小波的分解和重构算法将信噪分离.结果表明不同程度的信噪比会对超声导波检测法造成一定的影响,通过低通滤噪的方法对信号进行信噪分离,可实现高噪条件下的损伤检测.     

结构损伤的小波分形神经网络检测

用神经网络进行结构损伤检测、分析的有效性在很大程度上取决于训练样本的好坏。小波变换在时域和频域都具有表征信号局部特征的能力,小波包分析利用可以伸缩和平移的可变视窗能够聚焦到信号的任意细节,因此对有损伤的结构的非线性动力特性能进行有效的分析。利用分形几何方法不依赖于系统的数学模型的特点,将分形维数与小波分析相结合,建立了结构损伤的小波分形神经网络检测方法。研究结果表明,结构不同状态下的振动信号的各频段分形维数有明显的不同,可以将振动信号的各频段分形维数作为结构损伤检测的特征量,并用神经网络将结构的不同状态模式识别出来。     

Application of multi-dimensional wavelet transform to fluid mechanics

This paper first reviews the application research works of wavelet transform on the fluid mechanics. Then the theories of continuous wavelet transform and multi-dimensional orthogonal(discrete) wavelet transform, including wavelet multiresolution analysis, are introduced. At last the applications of wavelet transform on 2 D and 3 D turbulent wakes and turbulent boundary layer flows are described based on the hot-wire, 2 D particle image velocimetry(PIV) and 3 D tomographic PIV.     

The wavelet analysis method of stationary random processes

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基于小波分析的建(构)筑物爆破振动安全评估

基于现场实测爆破振动数据,采用小波分析技术对爆破振动信号的能量特征进行分析,得到了信号不同频带上的能量分布,根据受控结构体对爆破振动动态响应特征,探索建立了能考虑爆破振动的强度、频率和持续时间以及受控建(构)筑物本身的动态响应特性(固有频率和阻尼比)等因素的综合安全判据响应能量判据,并用工程实例验证了该判据的可行性和可靠性。响应能量判据能准确地描述爆破振动对受控建(构)筑物的影响程度,较现行的速度-频率安全判据,更能全面地反映爆破振动对建(构)筑物危害的本质。     

The Fractional Fourier Transform and Harmonic Oscillation

The ath-order fractional Fourier transform is a generalization ofthe ordinary Fourier transform such that the zeroth-order fractionalFourier transform operation is equal to the identity operation and thefirst-order fractional Fourier transform is equal to the ordinaryFourier transform. This paper discusses the relationship of thefractional Fourier transform to harmonic oscillation; both correspondto rotation in phase space. Various important properties of thetransform are discussed along with examples of commontransforms. Some of the applications of the transform are brieflyreviewed.     

Fourier analysis of Schwarz domain decomposition methods for the biharmonic equation

Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.     

基于梁连续抗弯刚度与小波变换的结构损伤识别方法研究

为了解决基于小波变换系数难以识别结构边缘损伤的问题,以及试验中损伤对周边的影响导致小波系数难以精确定位损伤位置的问题,提出了基于梁连续抗弯刚度与小波变换的结构损伤位置识别方法。该方法结合梁结构连续抗弯刚度与小波系数边缘的特点,在未知无损梁结构振动参数的情况下,能有效识别出梁结构边缘损伤且能准确定位试验中梁结构的损伤,通过损伤梁的数值模拟与试验证明了该方法的正确性。     

基于能量耗散分析的混凝土随机疲劳损伤模型

基于微-细观随机断裂模型(MMSF)发展了一类混凝土随机疲劳损伤模型。该模型将MMSF中的微弹簧视为一能量耗散单元并考察了其跨尺度的能量耗散过程。在纳观尺度,引入速率过程理论描述裂纹的扩展速度,并基于裂纹层级模型和自相似假定完成从纳观尺度到微观尺度的过渡。由此建立了微弹簧在疲劳荷载作用下的多尺度耗能描述。此外,为了考虑疲劳加载中混凝土多条裂纹的相互影响,引入了包含损伤扩展效应和损伤愈合效应的疲劳损伤因子来修正耗能表达。通过与相关试验的对比,证明了该模型能反映疲劳荷载作用下混凝土的主要力学行为,如疲劳损伤三阶段特点、疲劳寿命的离散性和疲劳寿命随加载频率的变化趋势等。