Damage detection by the distribution of predicted constraint forces

Damage causes the deterioration of dynamic and static performance of intact structures. Regarding the measured static displacement or modal displacement data as constraints for describing damaged responses, this study derives analytical equations to estimate constraint forces in the satisfaction of constraints. The constraint forces are forces required for describing the flexural shape of the damaged beam under static and dynamic loadings. Based on the concept that the occurrence of damage causes the change of force mechanism, this work proposes an analytical method to detect damage from the distribution of constraint forces. When compared to the displacement curvature and the frequency response function (FRF) curvature methods using 2% noise, the results have shown that the proposed method is less sensitive to noise and is more effective in detecting multiple damaged areas in the beam of short span length and their intensity at low levels of damage.     

Exploiting cantilever curvature for noise reduction in atomic force microscopy

Optical beam deflection is a widely used method for detecting the deflection of atomic force microscope (AFM) cantilevers. This paper presents a first order derivation for the angular detection noise density which determines the lower limit for deflection sensing. Surprisingly, the cantilever radius of curvature, commonly not considered, plays a crucial role and can be exploited to decrease angular detection noise. We demonstrate a reduction in angular detection shot noise of more than an order of magnitude on a home-built AFM with a commercial 450 μm long cantilever by exploiting the optical properties of the cantilever curvature caused by the reflective gold coating. Lastly, we demonstrate how cantilever curvature can be responsible for up to 45% of the variability in the measured sensitivity of cantilevers on commercially available AFMs.     

基于频率变化率的结构刚度非均匀退化识别

针对不利环境作用、损伤等易造成结构局部损伤且刚度退化程度不均匀的问题,以受弯梁为研究对象,从构件动力特性入手,综合考虑损伤前后的模态挠度曲率和固有频率变化,提出了基于频率变化率的刚度非均匀退化识别方法。首先,在柔度矩阵的基础上推导模态挠度曲率,通过损伤前后模态挠度曲率的改变量识别损伤位置参数,判定损伤区域;其次,对损伤区域进行节段划分,从欧拉-伯努利梁的动力方程出发建立损伤程度、损伤区域位置参数与固有频率之间的矩阵函数,实现直接利用频率值变化评估构件不同区域损伤程度。研究结果表明,该方法能很好地识别结构局部损伤位置和损伤程度,尤其是对于结构局部刚度不均匀退化的评估具有明显的优势。     

损伤结构的曲率模态分析

基于结构有限元分析软件ANSYS得到的结构位移模态分析数据，针对具有不同损伤状况的悬臂梁进行了结构曲率模态分析。研究结果表明，曲率模态分析技术不仅能准确诊断悬臂梁损伤位置，而且可以判断悬臂梁的损伤程度。仿真结果表明，本文提出的曲率模态幅值突变系数与结构损伤程度之间具有较好的线性相关性。     

振型曲率在板类结构动力检测中的应用

以四边简支方形弹性薄板为研究对象，通过数值计算得到板损伤前后的多阶模态参数，进而得到板面内两个方向的位移振型曲率并用于板的损伤检测研究。结果表明：当布置有足够数量的振型测点时，振型曲率及板损伤前后的振型曲率差均可用于板损伤的探测与定位，并能大致判断损伤的程度；当振型测点间距过大，或测点偏离损伤区域时，均可能导致检测的失败。     

An experimental study on damage detection of structures using a timber beam

Using vibration methods for the damage detection and structural health monitoring in bridge structures is rapidly developing. However, very little work has so far been reported on timber bridges. This paper intends to address such shortcomings by experimental investigation on a timber beam using a vibration based method to detect damage. A promising damage detection algorithm based on modal strain energy was adopted and modified to locate/evaluate damage. A laboratory investigation was conducted on a timber beam inflicted with various damage scenarios using modal tests. The modal parameters obtained from the undamaged and damaged state of the test beam were used in the computation of damage index, were then applied using a damage detection algorithm utilising modal strain energy and a statistical approach to detect location of damage. A mode shape reconstruction technique was used to enhance the capability of the damage detection algorithm with limited number of sensors. The test results and analysis show that location of damage can be accurately identified with limited sensors. The modified method is less dependent on the number of modes selected and can detect damage with a higher degree of confidence.     

AGS结构的损伤定位仿真

为了检测先进复合材料格栅结构(AG S)的损伤所在位置,提出了通过计算结构在损伤前、后模态曲率差的方法,来进行计算和分析。建立了格栅结构在有约束条件下的有限元模型,通过AN SY S中的模态分析得到模态振型位移值,计算了结构损伤前、后的模态曲率差,通过这一指标对结构的损伤进行辨识,并分析了采用多阶模态的计算效果。结果表明,通过第1阶模态振型模态曲率差的计算,可对单损伤状况做出有效的检测;对于多损伤工况,需使用前3阶模态的曲率差进行分析,才能有效检测损伤的位置。     

结合模态区间分析和IARR的不确定性损伤识别

针对结构不确定性损伤识别中经典区间算法容易发生扩张的问题,提出将模态区间分析和改进解析冗余度(improved analytical redundancy reduction,简称IARR)相结合的损伤识别方法。首先,将结构静力平衡方程用约束条件方程组表示,通过改进解析冗余度使得方程组仅包含平动变量;其次,把与假定损伤单元相关的方程集中在同一子集,代入区间变量将方程扩展成区间形式,通过模态区间运算判断各约束条件的满足情况来实现损伤定位;最后,采用静载作用下的试验钢梁验证所提出的方法,结合刚度参数、挠度参数和外荷载3种随机变量,建立各梁段约束条件方程。结果表明:考虑测试误差、参数不确定性时,能通过约束条件的不满足有效定位梁的小损伤。     

钢筋混凝土简支梁超载后动力特性试验研究

基于采用动态法评估桥梁结构构件超载后损伤的目的,设计和开展了试验研究和相应理论分析。通过对钢筋混凝土简支梁进行反复超载试验,测出构件从完整到破损,以及不同超载幅值和次数对应损伤状态下的频率和阻尼比等模态参数,考查了其与构件承载力的关系,为采用结构动力参数评估结构损伤分析了频率和阻尼比随损伤状态不同的变化规律,根据试验结果得到频率和荷载等级关系的经验公式,为采用动态法评估既有桥梁提供了理论依据     

基于贝叶斯思想的框架结构损伤检测方法研究* .txt

摘要：基于单自由度体系的统计矩理论,以位移四阶矩和加速度八阶矩为损伤指标,使用贝叶斯思想和Gibbs抽样相结合方法,提出一种框架结构损伤检测新方法。以理论分析为基础选取3种典型损伤指标,在信噪比40及30 dB环境噪音的不同损伤工况下,使用贝叶斯思想和Gibbs抽样相结合方法,对某12层标准框架数值模型的不同损伤指标进行了损伤识别效果的对比研究,并在此基础上与其他相似检测方法进行对比分析,发现使用贝叶斯思想和Gibbs抽样相结合的新方法,提出的损伤指标更适合框架结构损伤检测,与标准结果偏差均在5%以内。进一步分析12层标准框架振动台试验数据,选取3个典型振动工况中所有梁柱单元及前20个振动工况累积下的典型梁柱单元分别进行损伤检测,结果表明,所提方法避免了多次采样进行贝叶斯分析的局限性,且一定程度上能反映各损伤单元随振动台试验工况累积而表现出来的损伤程度变化,有助于推动所提方法在框架结构损伤检测中的实际应用。 .txt     

大型复杂结构损伤识别两步法研究

基于模型修正技术及模态柔度曲率差方法提出了一种解决大型复杂结构损伤识别问题的两步法。首先运用基于模型修正的损伤识别方法进行模糊识别,通过建立带约束边界非线性最小二乘目标函数,极小化结构实测模态与解析模态之间的误差,将损伤识别问题转化为优化问题,并采用信赖域方法求解该优化问题,识别出损伤所属单元组。然后运用模态柔度曲率差方法,对损伤进行精确定位。对某导弹发射台骨架的数值仿真及试验研究结果表明,该损伤识别两步法识别效果较为理想,为解决大型复杂结构的损伤识别问题提供了新思路。     

基于CMSE理论和遗传算法的结构损伤检测方法研究

提供了一种基于交叉模态应变能(CMSE)的结构损伤位置和严重程度的有效检测方法。传统的模态应变能方法必须比较损伤结构和完好结构的同一阶模态信息,并且要求解析的和测量的模态在尺度上一致或者标准化,而CMSE方法没有这样的限制。在损伤位置的检测上引入了遗传算法,有利于大型复杂结构的损伤位置检测。算例采用了复合材料机翼盒段模型,结果表明,CMSE方法与遗传算法相结合是检测结构损伤的有效方法之一。     

静压圆柱导轨系统静态刚度理论模型研究

静态刚度是静压圆柱导轨系统的重要性能指标,然而到目前为止尚未见到该类导轨静态刚度的理论模型。研究建立静压圆柱导轨五自由度静态刚度模型,考虑到静压圆柱导轨系统是由导柱与静压直线轴承的串联系统,首先,给出了工作台位移与导柱变形、静压直线轴承位移之间的几何关系,并根据静压圆柱导轨五自由度静态刚度的定义,推导了各刚度系数的数学表达式;其次,基于梁弯曲变形理论,采用线性叠加原理推导导柱在轴承油膜力作用下的变形方程;再次,基于静压理论,运用高斯积分推导了考虑导柱挠曲影响的轴承油膜承载能力模型,提出了轴瓦相对导柱的位移计算方法;最后,搭建了静压圆柱导轨刚度测试装置,完成了五自由度静态刚度的测试,验证了理论模型。结果表明：建立的静压圆柱导轨五自由度静态刚度模型精度高,可为静压圆柱导轨静态特性计算奠定理论基础。     

基于小波分析的简支梁桥损伤识别

提出了基于小波子带信号能量曲率变化的损伤识别方法。分别对完好和损伤状态下结构的振动响应进行二进离散小波变换,通过信号子带分解与重构将响应分解到不同频带,使叠加的模态响应分离。定义了信号相对能量曲率差损伤指标,利用该指标对结构的损伤进行识别定位。应用此方法对一简支梁桥进行损伤数值分析,结果表明:二进离散小波变换可以对结构振动响应中叠加的多阶模态信息进行有效分离;信号相对能量曲率差指标可以对损伤进行有效识别,且不受激励位置及荷载大小影响。最后通过模型实验验证了该方法的正确性及可行性。     

Novel Laplacian scheme and multiresolution modal curvatures for structural damage identification

Modal curvature is more sensitive to structural damage than directly measured mode shape, and the standard Laplace operator is commonly used to acquire the modal curvatures from the mode shapes. However, the standard Laplace operator is very prone to noise, which often leads to the degraded modal curvatures incapable of identifying damage. To overcome this problem, a novel Laplacian scheme is proposed, from which an improved damage identification algorithm is developed. The proposed step-by-step procedures in the algorithm include: (1) By progressively upsampling the standard Laplace operator, a new Laplace operator is constructed, from which a Laplace operator array is formed; (2) by applying the Laplace operator array to the retrieved mode shape of a damaged structure, the multiresolution curvature mode shapes are produced, on which the damage trait, previously shadowed under the standard Laplace operator, can be revealed by a ridge of multiresolution modal curvatures; (3) a Gaussian filter is then incorporated into the new Laplace operator to produce a more versatile Laplace operator with properties of both the smoothness and differential capabilities, in which the damage feature is effectively strengthened; and (4) a smoothened nonlinear energy operator is introduced to further enhance the damage feature by eliminating the trend interference of the multiresolution modal curvatures, and it results in a significantly improved damage trait. The proposed algorithm is tested using the data generated by an analytical crack beam model, and its applicability is validated with an experimental program of a delaminated composite beam using scanning laser vibrometer (SLV) to acquire mode shapes. The results are compared in each step, showing increasing degree of improvement for damage effect. Numerical and experimental results demonstrate that the proposed novel Laplacian scheme provides a promising damage identification algorithm, which exhibits apparent advantages (e.g., high-noise insusceptibility, insightful in damage revealment, and visualized damage presentation) over the standard Laplace operator.     

基于互相关函数幅值向量的结构损伤检测实验研究

进行了基于互相关函数幅值向量(cross correlation function amp litude vector,CorV)的受随机激励结构损伤检测的实验研究。以一个复合材料单跨梁为实验对象,通过在梁的局部位置上安装夹板,改变夹板对结构附加刚度,来模拟结构的损伤。对结构施加随机激励,分别用加速度传感器和应变传感器采集结构的响应信号,计算结构在损伤前后的CorV,使用互相关函数幅值向量置信度准则(cross correlation function amp litude vector assurance criterion,CVAC)来度量结构受损前后CorV的变化。结果表明,结构损伤前后的CorV之间的CVAC较完好结构之间的CVAC有明显下降;分析结构损伤前后CorV中分量的相对变化,可确定损伤产生的区域。使用互相关函数幅值向量,只需要测量结构在随机激励作用下的时域响应信号,就可检测出结构损伤的存在及损伤的位置。因此本文所采用的方法可应用于环境激励下的结构健康监测。     

复合材料结构损伤联合定位法试验研究

提出了复合材料结构损伤联合定位法,该法需首先获得复合材料结构在随机激励下的振动响应信号,计算结构的互相关函数幅值向量,通过对损伤结构的互相关函数幅值向量进行光滑拟合作为参考向量,再对损伤情况下的互相关函数幅值向量和参考向量分别进行连续小波变换,得到各自的小波系数,进而求得小波系数差的模,根据小波系数差的模的极值进行损伤的定位。该方法无需进行结构建模和模态识别,在无完好结构信息的情况下就可准确进行损伤定位。最后,还通过蜂窝夹层梁和玻璃纤维层合板的损伤检测试验,验证了该方法的有效性。     

梁的破损对频率振型及振型曲率的影响

本文用欧拉梁振动理论，改变简支梁中某一小段的高度以模拟破损。仿真结果表明，破损对某些阶频率、振型的影响不大，对振型曲率的影响较大．用振型曲率监测简支梁的破损优于用频率或振型的监测方法。     

Crack detection in simply supported beams without baseline modal parameters by stationary wavelet transform

There are significant changes in the vibration responses of cracked structures when the crack depth is significant in comparison to the depth of the structure. This fact enables the identification of cracks in structures from their vibration response data. However when the crack is relatively small, it is difficult to identify the presence of the crack by a mere observation of the vibration response data. A new approach for crack detection in beam-like structures is presented and applied to cracked simply supported beams in this paper. The approach is based on finding the difference between two sets of detail coefficients obtained by the use of the stationary wavelet transform (SWT) of two sets of mode shape data of the beam-like structure. These two sets of mode shape data, which constitute two new signal series, are obtained and reconstructed from the modal displacement data of a cracked simply supported beam. They represent the left half and the modified right half of the modal data of the simply supported beam. SWT is a redundant transform that doubles the number of input samples at each iteration. It provides a more accurate estimate of the variances at each scale and facilitates the identification of salient features in a signal, especially for recognising noise or signal rupture. It is well known that the mode shape of a beam containing a small crack is apparently a single smooth curve like that of an uncracked beam. However, the mode shape of the cracked beam actually exhibits a local peak or discontinuity in the region of damage. Therefore, the mode shape ‘signal’ of a cracked beam can be approximately considered as that of the uncracked beam contaminated by ‘noise’, which consists of response noise and the additional response due to the crack. Thus, the modal data can be decomposed by SWT into a smooth curve, called the approximation coefficient, and a detail coefficient. The difference of the detail coefficients of the two new signal series includes crack information that is useful for damage detection. The modal responses of the damaged simply supported beams used are computed using the finite element method. For real cases, mode shape data are affected by experimental noise. Therefore, mode shape data with a normally distributed random noise are also studied. The results show that the proposed method has great potential in crack detection of beam-like structures as it does not require the modal parameters of an uncracked beam as a baseline for crack detection. The effects of crack size, depth and location, and the effects of sampling interval are examined.     

纳米硬度计研究多晶硅微悬臂梁的弹性模量

利用纳米硬度计通过微悬臂梁的弯曲试验来测量其力学特性是一种简便而有效的方法,具有很高的载荷分辨率,可精确测量微悬臂梁纳米级弯曲形变。运用该方法在研究微悬臂梁的弯曲形变过程中,必须考虑压头在微悬臂梁上的压入以及微悬臂沿宽度方向的挠曲。微悬臂梁采用普通的集成电路工艺(IC)制造。试验研究表明,多晶硅微悬臂梁的纯挠曲与载荷成很好的线性关系,呈现弹性变形,通过该线性关系可计算得到梁的弹性模量。测得的多晶硅微悬臂梁的弹性模量为156±(2.9%-6.3%)GPa。