基于小波分析的梁裂缝识别研究

利用小波分析对筒支梁的裂缝进行识别。将带裂缝筒支梁的基本振型用Mexican Hat小波进行连续小波变换，从小波系数在裂缝处出现模极大值可以识别出裂缝位置，利用由小波系数计算得到的Lipschitz指数来识别裂缝深度，Lipschitz指数随着裂缝深度的增加而减小。通过分析和仿真计算获得满意结果，在仿真算例中分析了裂缝位置对Lipschitz指数的影响很小，可以忽略；振型的测点距离越大，Lipschitz指数越大。同时指出噪声对Lipschitz指数有影响但在噪声不很大时仍能较好地识别裂缝。该方法同样适用于多条裂缝的识别和其他构件的裂缝识别。     

基于模态振型和平稳小波变换的悬臂梁微小缺陷识别研究

结构损伤识别方法有很多种,通常结构振动模态振型对缺陷的损伤识别较为敏感,振型体现结构的固有属性及结构局部的特征,可以用于检测缺陷的存在及其位置。但是缺陷比较微小时,仅仅通过振型难以进行损伤识别。因此本文通过对振型进行平稳小波变换处理来检测悬臂梁的微小缺陷。通过有限元模态分析获得含不同缺陷深度、不同缺陷宽度、不同缺陷位置的悬臂梁模型的振型并利用平稳小波变换进行分析处理。结果表明:该方法可以准确判断缺陷的存在及其位置,并且平稳小波细节系数突变峰值随着缺陷深度增大而增大,随着缺陷宽度增大而增大;另外,该方法受振型节点影响,在工程实际应用时应综合前几阶次振型进行缺陷识别。     

辅助质量块—单裂纹悬臂梁耦合系统固有频率的理论研究及其应用

论文研究了辅助质量块—单裂纹悬臂梁耦合系统的固有频率,用无缺陷悬臂梁固有振型叠加一个多项式来近似拟合含单裂纹悬臂梁的振型,由动力学方法推导了辅助质量块—单裂纹悬臂梁系统的固有频率方程的解析形式,系统频率随着质量块在梁上位置改变而改变,即可得到固有频率曲线,此频率曲线包含了缺陷信息,因此可对固有频率曲线进行平稳小波变换来识别梁上的缺陷.同时用有限元计算结果对上述固有频率理论推导进行验证,有限元结果与论文理论推导结果相一致.最后论文数值计算了质量块大小、缺陷深度、位置等因素对系统固有频率的影响,也探讨了平稳小波变换用于识别损伤,结果验证了该理论推导的可靠性和损伤识别的准确性.     

含双裂纹圆截面悬臂梁的损伤识别研究

裂纹的萌生和扩展直接影响构件的振动响应，对构件的安全可靠性具有重要影响．本文以圆截面悬臂梁为对象，结合转角模态振型和模态频率等高线，研究了一种双裂纹识别技术．首先，基于应力强度因子和卡氏定理推导了无裂纹梁单元和含裂纹梁单元的刚度矩阵；在此基础上，建立了含裂纹圆截面悬臂梁的有限元动力学方程；然后，结合裂纹对梁转角模态振型和模态频率的影响，提出了双裂纹识别策略．最后，通过算例讨论了双裂纹识别策略的可行性．结果表明，圆截面悬臂梁的模态转角在裂纹位置出现突变，裂纹深度越大转角突变值越大；将识别出的裂纹位置作为已知参数，通过模态频率等高线法，可以准确地识别出双裂纹的深度．     

基于SBFEM和深度学习的裂纹状缺陷反演模型

结构内部缺陷的识别是结构健康监测的重要研究内容, 而当前以无损检测为主的结构安全检测多以定性分析为主, 定量识别缺陷的尺度较困难. 本文将比例边界有限元法(scaled boundary finite element methods, SBFEM)和深度学习相结合, 提出了基于Lamb波在结构中传播时的反馈信号定量识别结构内部裂纹状缺陷的反演模型. 通过随机生成缺陷信息(位置、大小), 采用SBFEM模拟Lamb波在含不同缺陷信息的结构中的信号传播过程, SBFEM仅需对结构边界离散可最小化网格重划分过程, 大大提高了计算效率. Lamb波在含裂纹状缺陷结构中传播时观测点的反馈信号包含大量的裂纹信息, 基于这一特性可为深度学习模型提供足够多的反映问题特性的训练数据. 建议的缺陷反演模型规避了传统反分析问题的目标函数极小化迭代过程, 在保证计算精度的前提下大大减少了计算成本. 对含单裂纹和多裂纹板的数值算例进行分析, 结果表明: 建立的缺陷识别模型能够准确地量化结构内部的缺陷, 对浅表裂纹亦有很好的识别效果, 且对于含噪信号模型仍具有较好的鲁棒性.      

一种不完备测试数据下的结构损伤识别方法

在单元刚度损伤系数和振型扩阶的基础上,建立了单元的损伤控制方程,提出了一种不完备测试自由度下的损伤识别方法。该方法以单元刚度损伤系数作为识别量,通过计算结构损伤前后频率和振型的改变,然后利用控制方程反解出损伤系数,从而确定出结构损伤位置和大小。悬臂梁桁架结构的数值模拟表明,在一定的噪声水平下可以同时成功地识别出的损伤位置和程度,而且对噪声有较强的鲁棒性。     

小波分析在圆柱壳结构损伤检测中的应用研究

为了检测出圆柱壳中的裂纹引起的损伤,利用sym4小波,对含裂纹圆柱壳的应变能曲线进行连续小波变换和多分辨分析,从小波系数出现局部模极大值来识别损伤的存在以及裂缝位置。通过分析和计算获得满意结果,表明此方法在圆柱壳结构损伤诊断中具有较高的应用价值。     

铝板中激光Lamb波信号的模态分析与缺陷检测研究

激光激励的Lamb波信号具有较宽的频带,且包含多个模态信息。本文采用二维傅里叶变换和时频分析等信号分析技术用于检测信号中的模态成分及缺陷信息识别。首先,对200组激光Lamb波信号进行二维傅里叶变换,得到信号的频率-波数图,可识别出激光Lamb波信号中的低阶A0、S0和高阶模态,并且A0模态能量高,可用于缺陷检测。随后对有、无缺陷状态下Lamb波信号进行连续小波变换,从时频图中识别出缺陷信号的频率成分,进一步提取特定频率下的小波系数幅值信号,实现了缺陷信息的识别。结果表明,二维傅里叶变换能较好地识别激光Lamb波的模态成分,而提取出的连续小波变换系数图,能准确实现缺陷定位。     

一种新的小波及其在结构损伤检测中的应用

结构受冲击将引起某些部位的震荡、裂纹甚至断裂,从而导致结构刚度下降.此时振动信号会出现奇异性或携带突变信息,而这些突变信息反映了结构的损伤情况.加之冲击信号测试环境一般较为复杂,环境噪声对测试存在一定的影响.然而,利用合理的小波变换技术去噪可以识别出损伤情况.本文通过对冲击振动的信号特性进行分析构造了一种新的基本小波,并论证了该小波的基本特征.最后运用小波分析的信号奇异检测理论结合实例将该小波用于冲击振动仿真分析中.计算结果表明,利用该小波进行结构损伤信号分析能清晰地识别结构损伤的时刻.采用该小波函数的构造方法,可避免通常采用Daubechies系列小波作为信号分析而要繁琐地选择不同小波函数的过程.     

用频率识别平面刚架结构裂纹的遗传算法

给出含单个裂纹结构的动力有限元方程,根据结构前５阶频率的变化,来识别裂纹的位置和深度。将识别转化为多峰值的全局优化问题,给出跗算法解法此识别的运算步骤。以结构含单一裂纹的两处算例,作裂纹识别的数值试验,计算结果表明此方法是可行的,对裂纹参数的识别有较好的精神和可靠性。     

Crack identification in beams using wavelet analysis

In this paper a simple method for crack identification in beam structures based on wavelet analysis is presented. The fundamental vibration mode of a cracked cantilever beam is analyzed using continuous wavelet transform and both the location and size of the crack are estimated. The position of the crack is located by the sudden change in the spatial variation of the transformed response. To estimate the size of the crack, an intensity factor is defined which relates the size of the crack to the coefficients of the wavelet transform. An intensity factor law is established which allows accurate prediction of crack size. The viability of the proposed method is investigated both analytically and experimentally in case of a cantilever beam containing a transverse surface crack. In the light of the results obtained, the advantages and limitations of the proposed method as well as suggestions for future work are presented and discussed.     

Wavelet-based crack identification of bridge beam from operational deflection time history

A new method for crack identification of bridge beam structures under a moving load based on wavelet analysis is presented. Crack is modeled through rotational springs whose compliance is evaluated using linear elastic fracture mechanics. Dynamic behavior of the cracked beam subject to moving load is analyzed using mode superposition. The response obtained at a single measuring point is analyzed using continuous wavelet transform and the location of the cracks is estimated. The locations of the cracks are determined from the sudden changes in the spatial variation of the transform responses. To estimate the relative depth of the cracks, a damage factor is established which relates the size of the cracks to the coefficients of the wavelet transform. The proposed method is validated by both simulation and experiment. Locations of multiple damages can be located accurately, and the results are not sensitive to measurement noise, speed and magnitude of moving load, measuring location, etc.     

基于裂纹附加模态Timoshenko梁的裂纹损伤识别

将梁中横向裂纹等效为无质量扭转弹簧，并忽略其对梁剪切变形的影响，得到的具有任意裂纹数目Timoshenko 梁自振模态的统一显示解析表达式．将裂纹梁的自振模态分为基本模态和裂纹附加模态，利用最小二乘拟合，建立了利用裂纹附加模态函数的梁裂纹损伤识别方法．通过数值模拟开展了简支单裂纹梁以及悬臂和固支双裂纹梁等的裂纹损伤识别，考察了测量误差对损伤识别的影响，数值结果表明本文所提出的裂纹损伤识别方法对裂纹位置的识别精度高于对裂纹损伤程度的识别精度；随着测量误差的增加，裂纹位置及裂纹损伤程度的识别误差增加，但仍在可接受的范围内，故该裂纹损伤识别方法在实际工程中具有一定的应用价值．     

CRACK IDENTIFICATION IN STEPPED CANTILEVER BEAM COMBINING WAVELET ANALYSIS WITH TRANSFORM MATRIX

This paper illustrates the crack identification method combining wavelet analysis with transform matrix. Firstly, the fundamental vibration mode was applied to wavelet analysis. The crack location was found by the peaks of the wavelet coefficients. Secondly, based on the identified crack locations, a simple transform matrix method requiring only the first two tested natural frequencies was used to further identify the crack depth. The present method can be used for crack identification in a complex structure. Numerical results of crack identification of a stepped cantilever beam show that the suggested method is feasible.     

不确定边界条件下悬臂梁裂纹参数识别方法研究

基于Bernoulli-Euler梁振动理论,以等效弹簧来模拟裂纹引起的局部软化效应和由非完全固支边界条件引起的转角效应。推导了悬臂梁在不确定边界条件下确定其振动频率的特征方程,直接利用该特征方程,提出一种有效估计裂纹参数的优化方法,通过计算测量频率和理论频率之间的误差目标函数最小化即可识别裂纹参数-裂纹位置和深度。最后,应用两个实例-理想固支边界条件下和非完全固支边界条件下的悬臂梁实验来说明本文方法的有效性。实验结果表明:只需梁结构前三阶频率即可识别裂纹位置和深度。对于理想边界条件下的裂纹参数识别,在测量频率存在小误差情况下,该方法仍能给出比较满意的结果,对于非完全固支边界条件下的裂纹参数识别,利用本文方法能得到比Narkis的方法更精确的裂纹位置识别结果。同时本文方法还能给出比较满意的裂纹深度识别结果。     

A NEW APPROACH TO FREE VIBRATION ANALYSIS OF A BEAM WITH A BREATHING CRACK BASED ON MECHANICAL ENERGY BALANCE METHOD

In this paper, a new approach to free vibration analysis of a cracked cantilever beam is proposed. By considering the effect of opening and closing the crack during the beam vibration, it is modeled as a fatigue crack. Also, local stiffness changes at the crack location are considered to be a nonlinear amplitude-dependent function and it is assumed that during one half a cycle, the frequencies and mode shapes of the beam vary continuously with time. In addition, by using the experimental tests, it is shown that the local stiffness at the crack location varies continuously between the two extreme values corresponding to the fully closed and the fully open cases of the crack. Then, by using the mechanical energy balance the dynamic response of the cracked beam is obtained at every time instant. The results show that for a specific crack depth, by approaching the crack location to the fixed end of the beam, more reduction in the fundamental frequency occurs. Furthermore, for a specific crack location, the fundamental frequency diminishes and the nonlinearity of the system increases by increasing the crack depth. In order to validate the results, the variations of the fundamental frequency ratio against the crack location are compared with experimental results.     

Waveform fractal dimension for mode shape-based damage identification of beam-type structures

Mode shape-based structural damage identification has been a research focus during the last couple of decades. Most of the existing methods need a numerical or measured baseline mode shape serving as a reference to identify damage, and this requirement extremely limits the practicability of the methods. Recently, waveform fractal dimension such as Katz’s waveform fractal dimension (KWD) has been explored and applied to mode shape for crack identification without a baseline requirement. In this study, different from the popular KWD, an approximate waveform capacity dimension (AWCD) is formulated first, from which an AWCD-based modal abnormality algorithm (AWCD-MAA) is systematically established. Then, the basic characteristics of AWCD-MAA on abnormality detection of mode shapes, e.g., crack localization, crack quantification, noise immunity, etc., are investigated based on an analytical crack model of cantilever beams using linear elastic fracture mechanics. In particular, from the perspective of isomorphism, a mathematical solution on the use of applying waveform fractal dimension to higher mode shapes for crack identification is originally proposed, from which the inherent deficiency of waveform fractal dimension to identify crack when implemented to higher mode shapes is overcome. The applicability and effectiveness of the AWCD-MAA is validated by an experimental program on damage identification of a cracked composite cantilever beam using smart piezoelectric sensors/actuators (i.e., Piezoelectric lead–zirconate–titanate (PZT) and polyvinylidene fluoride (PVDF)). The proposed AWCD-MAA provides a novel, viable method for crack identification of beam-type structures without baseline requirement, and it largely expands the scope of fractal in structural health monitoring applications.     

Modal identification of multi-degree-of-freedom structures based on intrinsic chirp component decomposition method

Modal parameter identification is a mature technology. However, there are some challenges in its practical applications such as the identification of vibration systems involving closely spaced modes and intensive noise contamination. This paper proposes a new time-frequency method based on intrinsic chirp component decomposition(ICCD)to address these issues. In this method, a redundant Fourier model is used to ameliorate border distortions and improve the accuracy of signal reconstruction. The effectiveness and accuracy of the proposed method are illustrated using three examples: a cantilever beam structure with intensive noise contamination or environmental interference, a fourdegree-of-freedom structure with two closely spaced modes, and an impact test on a cantilever rectangular plate. By comparison with the identification method based on the empirical wavelet transform(EWT), it is shown that the presented method is effective,even in a high-noise environment, and the dynamic characteristics of closely spaced modes are accurately determined.     

悬臂梁中开闭裂纹的损伤识别

利用裂纹诱导弦挠度函数,建立了悬臂Euler-Bernoulli 中开闭裂纹位置、深度、初始张开角等损伤参数的识别方法．为此,首先将梁中开闭裂纹等效为单向扭转弹簧,给出了考虑裂纹缝隙效应的裂纹梁等效抗弯刚度,并得到悬臂Euler-Bernoulli 开闭裂纹梁弯曲挠度的显式闭合解及裂纹诱导弦挠度函数,证明了裂纹诱导弦挠度的分段线性函数．其次,基于单向扭转弹簧的性质,建立了通过多步加载进行梁中开闭裂纹参数及其上下侧属性的识别方法．最后,通过数值算例验证了本文所建立的开闭裂纹损伤识别方法的适用性和可靠性,考察了裂纹分布位置、深度和初始张开角以及裂纹识别区间和挠度测量误差等参数对识别结果的影响,结果表明：当裂纹处于张开状态时,裂纹处裂纹诱导弦挠度斜率改变量随着施加荷载的增加而增加;当裂纹闭合时,其裂纹诱导弦挠度斜率改变量将保持为常量;裂纹损伤参数的识别误差随测量误差的增加而增加,但整体识别结果具有较高的精度,较好的鲁棒性．