Wavelet‐Based Detection of Beam Cracks Using Modal Shape and Frequency Measurements

Abstract: When a structure is subjected to dynamic or static loads, cracks may develop and the modal shapes and frequencies of the cracked structure may change accordingly. Based on this, a new method is proposed to locate beam cracks and to estimate their depths. The fault‐induced modal shape and frequency changes of cracked structures are taken into account to construct a new hybrid crack detection method. The method includes two steps: crack localization and depth estimation. The locations of the cracks are determined by applying the wavelet transform to the modal shape. Using the measured natural frequencies as inputs, the depths of the cracks are estimated from a database established by wavelet finite element method. The effectiveness of the proposed hybrid two‐step method is demonstrated by numerical simulation and experimental investigation of a cantilever beam with two cracks. Our analyses also indicate that the proposed method performed reasonably well at certain level of noise.     

Crack identification method for tapered cantilever pipe-type beam using natural frequencies

A method to detect location and size of a crack in tapered cantilever pipe-type beam using changes in natural frequencies is presented. The boundary conditions of cantilever beam are applied to a general solution for vibrating tapered beam. Then, an equivalent bending stiffness for cracked beam is used to obtain the natural frequencies. Numerical simulations are carried out to construct a set of training patterns of a neural network, and committee of neural networks is employed to identify the crack. Crack identifications are carried out for the 16 damage cases numerically and for the 3 damage cases experimentally. The identified crack locations and sizes agree reasonably well with the exact values.     

Pipe crack identification based on the energy method and committee of neural networks

A crack identification method using an equivalent bending stiffness for cracked beam and committee of neural networks is presented. The equivalent bending stiffness is constructed based on an energy method for a straight thin-walled pipe, which has a through-the-thickness crack, subjected to bending. Several numerical analysis for a steel cantilever pipe using the equivalent bending stiffness are carried out to extract the natural frequencies and mode shapes of the cracked beam. The extracted modal properties are used in constructing a training patterns of a neural network. The input to the neural network consists of the modal properties and the output is composed of the crack location and size. Multiple neural networks are constructed and each individual network is trained independently with the different initial synaptic weights. Then, the estimated crack locations and sizes from different neural networks are averaged. Crack detection is carried out for 16 damage cases using the proposed method, and the identified crack locations and sizes agree reasonably well with the exact values.     

Neural Network for Rapid Depth Evaluation of Shallow Cracks in Asphalt Pavements

Abstract:   Rapid and nondestructive evaluation of pavement crack depths is a major challenge in pavement maintenance and rehabilitation. This article presents a computer-based methodology with which one can estimate the actual depths of shallow, surface-initiated fatigue cracks in asphalt pavements based on rapid measurement of their surface characteristics. It is shown that the complex overall relationship among crack depths, surface geometrical properties of cracks, pavement properties, and traffic characteristics can be learnt effectively by a neural network (NN). The learning task is facilitated by a database that includes relevant traffic and pavement characteristics of Florida's state highway network. In addition, the specific data used for the NN model development also contained laser-scanned microscopic surface geometrical properties of cracks in 95 pavement sections and pavement core samples scattered within five counties of Florida. Relatively advanced training algorithms were investigated in addition to the Standard Backpropagation algorithm to determine the optimal NN architecture. In terms of optimizing the NN training process, the "early stopping method" was found to be effective. The crack depth evaluation model was validated based on an unused portion of the database and fresh core samples. The results indicate the promise of NN usage in nondestructive estimation of shallow crack depths based on crack-surface geometry and pavement and traffic characteristics .     

Vibration-based crack prediction on a beam model using hybrid butterfly optimization algorithm with artificial neural network

Vibration-based damage detection methods have become widely used because of their advantages over traditional methods. This paper presents a new approach to identify the crack depth in steel beam structures based on vibration analysis using the Finite Element Method (FEM) and Artificial Neural Network (ANN) combined with Butterfly Optimization Algorithm (BOA). ANN is quite successful in such identification issues, but it has some limitations, such as reduction of error after system training is complete, which means the output does not provide optimal results. This paper improves ANN training after introducing BOA as a hybrid model (BOA-ANN). Natural frequencies are used as input parameters and crack depth as output. The data are collected from improved FEM using simulation tools (ABAQUS) based on different crack depths and locations as the first stage. Next, data are collected from experimental analysis of cracked beams based on different crack depths and locations to test the reliability of the presented technique. The proposed approach, compared to other methods, can predict crack depth with improved accuracy.     

土体的裂隙描述和表征单元体积研究

裂隙描述是研究裂隙对土体力学和渗透特性影响作用的基础工作,用裂隙度描述土体裂隙是一种较为合理的方法。裂隙的存在使得土体成为不连续介质,等效连续介质模型是较为成熟的用于不连续介质的模型,而确定表征单元体积的大小是运用等效连续介质模型的一个关键问题。本文建立了用摄影测定裂隙度的方法,使得裂隙度的获得更为简便和可靠。并在此基础上,建立了基于裂隙度估算表征单元体积的方法。研究表明:裂隙度是描述土体裂隙的综合指标,能够较好的反映裂隙的发育程度。用摄影法测定土体裂隙度和表征单元体积简单可行。     

中低速冲击载荷下巷道内裂纹的动态响应

 由于爆破开挖,巷道内常含有径向裂隙,并影响巷道的稳定性,为了详细地研究含径向裂纹巷道在冲击载荷作用下的动态断裂行为,采用砂岩材料制作巷道模型试样进行中低速冲击动态断裂试验,并采用AUTODYN有限差分软件进行数值模拟分析。分析巷道对称轴线上的径向裂纹在冲击荷载作用下的扩展特性及止裂现象,并采用试验–数值–解析法计算出裂纹的起裂韧度及扩展速度等参数。研究结果表明：(1) 巷道围岩在静力载荷作用和动力载荷作用下的破坏行为有较大差异,动力载荷下破坏仅是裂纹尖端处的起裂、扩展;而静力载荷下破坏除了发生在裂纹尖端处,也会在巷道拱肩、拱脚及两侧帮处发生破坏。(2) 巷道对称轴线上的裂纹在冲击载荷下的扩展路径大致沿着裂纹的原方向扩展,扩展路径中存在明显的止裂现象。(3) 采用试验–数值–解析法能够较好地计算出裂纹的起裂速度及扩展速度,进一步采用位移外推法能够求解出巷道内裂纹的动态应力强度因子时程曲线,利用测试的裂纹起裂时间确定起裂韧度。     

某框架结构梁早期裂缝成因分析与防治

针对某框架梁跨中出现梁侧垂直裂缝和梁底水平裂缝,分别从设计、材料、施工、使用四个方面分析了裂缝产生的原因,提出采用表面处理法、粘贴碳纤维加固法等对梁加固修复,并对如何防止此类裂缝产生提出预防措施,对同类工程问题有一定的借鉴作用。     

Theoretical and numerical studies of crack initiation and propagation in rock masses under freezing pressure and far-field stress

Water-bearing rocks exposed to freezing temperature can be subjected to freezeethaw cycles leading tocrack initiation and propagation, which are the main causes of frost damage to rocks. Based on theGriffith theory of brittle fracture mechanics, the crack initiation criterion, propagation direction, andcrack length under freezing pressure and far-field stress are analyzed. Furthermore, a calculation methodis proposed for the stress intensity factor （SIF） of the crack tip under non-uniformly distributed freezingpressure. The formulae for the crack/fracture propagation direction and length of the wing crack underfreezing pressure are obtained, and the mechanism for coalescence of adjacent cracks is investigated.In addition, the necessary conditions for different coalescence modes of cracks are studied. Using thetopology theory, a new algorithm for frost crack propagation is proposed, which has the capability todefine the crack growth path and identify and update the cracked elements. A model that incorporatesmultiple cracks is built by ANSYS and then imported into FLAC3D. The SIFs are then calculated using aFISH procedure, and the growth path of the freezing cracks after several calculation steps is demonstratedusing the new algorithm. The proposed method can be applied to rocks containing fillings such asdetritus and slurry.
2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.     

钢筋UHPC受弯构件裂缝宽度计算方法研究

为建立钢筋UHPC受弯构件的裂缝宽度计算方法,对6根钢筋UHPC梁进行四点抗弯试验,分析试验梁的裂缝发展过程和分布规律,以此为基础评估了现有规范公式计算钢筋UHPC受弯构件裂缝宽度的适用性,给出考虑UHPC抗拉贡献的钢筋UHPC受弯构件的钢筋应力计算方法和裂缝宽度建议计算公式,并通过国内16根钢筋UHPC梁的97组有效裂缝宽度试验结果对给出的裂缝宽度建议公式的适用性进行验证。研究结果表明：①UHPC梁表面裂缝宽度小于0.25mm时,裂缝宽度基本呈线性规律扩展,裂缝数量不断增加,裂缝间距逐渐减小;裂缝宽度超过0.25mm后,裂缝宽度迅速扩展并形成主裂缝,裂缝数量基本不变,裂缝间距趋于稳定,裂缝分布密而细,呈现出多元开裂现象。②直接采用GB 5010-2010规范和CECS 38-2004规范的裂缝宽度公式计算钢筋UHPC受弯构件的裂缝宽度误差较大。③基于UHPC材料特性,提出考虑UHPC抗拉作用的钢筋UHPC受弯构件开裂截面的钢筋应力计算方法,可较好地预测钢筋UHPC受弯构件开裂截面的钢筋应力。④结合试验数据和分析,对GB 50010-2010规范中平均裂缝间距、钢筋应变不均匀系数、构件受力特征系数进行修正,给出钢筋UHPC受弯构件裂缝宽度计算公式,修正后的建议公式计算值与文章试验值吻合良好,且与法国UHPC规范公式预测结果相比离散性更小。⑤建议公式的裂缝宽度计算值与收集的裂缝宽度试验数据库的试验值之比的平均值为0.99,标准差为0.19,表明建议公式适用性良好,可为UHPC结构设计规范的编制提供参考。     

Buckling analysis of cracked plates using hierarchical trigonometric functions

The present paper deals with the estimation of buckling loads of plates with cracking damages. The hierarchical trigonometric functions are used to define the displacement function of the cracked plate. Selective choosing of the trigonometric functions satisfies the various boundary conditions of a plate bounded by support members in a continuous plated structure. Moreover, the analysis of the cracked plate can be carried out with a minimum number of equations accurately. In the present paper, the buckling loads of plates with various types of cracks, such as edge crack and central crack, are estimated under uniaxial compressive load, biaxial compressive load and in-plane shear load. The results are found to correlate well with those obtained using a finite element method.     

钢筋混凝土梁式结构裂缝特征与损伤评估方法试验研究

服役中大量钢筋混凝土梁式桥的结构性能急待采取行之有效的方法对其进行评估 ,以便研究进一步采取的措施。本文基于四片板梁和四片T梁模型室内试验结果 ,并由开裂截面的几何关系和裂缝开展理论 ,经回归分析及结构非线性分析 ,建立了以裂缝特征统计参数推测结构配筋率的方法 ,达到有效评估结构性能的目的 ,将结构外观检查的定性评估升级为定量评估 ,具有重要的使用价值。该方法简便可行、费用低廉     

结构型纤维对开裂混凝土渗透性能的影响

为研究结构型聚丙烯纤维和结构型钢纤维对带裂缝混凝土渗透性能的影响,通过圆饼试件的反馈劈拉试验预制不同宽度等级的裂缝,借助数码显微镜（supereyes）对不同位置处的裂缝宽度进行测量,利用自行设计的常水头渗透实验装置对带裂缝圆饼试件的渗透率进行测定,利用激光扫描仪对试件开裂面形态进行测量。对比分析了结构型聚丙烯纤维和结构型钢纤维对开裂混凝土渗透性能的影响。研究表明：素混凝土试件在劈拉试验中发生脆性破坏,而掺入结构型聚丙烯纤维和结构型钢纤维的试件开裂后均表现出较好的韧性,裂缝宽度得到较好的控制;随着裂缝宽度的增大,开裂混凝土的渗透率增大;结构型聚丙烯纤维和结构型钢纤维提高了试件开裂面的曲折度和粗糙度,与同等裂缝宽度的素混凝土试件相比,掺加结构型聚丙烯纤维和结构型钢纤维试件的渗透率有不同程度的降低。修正后的泊肃叶定律（Poiseuille law）可以反映结构型聚丙烯纤维和结构型钢纤维对开裂混凝土渗透率的影响。     

不同模态振型在梁结构裂缝识别中的差异

采用Gaus2小波对多裂缝梁的不同模态振型进行小波变换,分析了不同模态振型在梁结构裂缝检测中的差别。同时,还采用最小二乘法算出各裂缝处的Lipschitz指数,进而分析了各模态振型函数在裂缝处的奇异性程度。结论表明:梁结构裂缝识别的效果主要由裂缝处的小波系数的模的大小决定。     

Crack Detection from the Slope of the Mode Shape Using Complex Continuous Wavelet Transform

Abstract: A new method for cracks detection in beams is proposed by using the slope of the mode shape to detect cracks, and by introducing the angle coefficients of complex continuous wavelet transform. This study is aimed at detecting the location of the nonpropagating transverse crack. A series of beams with cracks that are simulated by rotational springs with equivalent stiffness are analyzed. The mode shape and the slope of this lumped crack model are calculated. Through complex continuous wavelet transform of the slope of the mode shape using Complex Gaus1 wavelet (CGau1), the locations of cracks are detected from the modulus line and the angle line of wavelet coefficients. By comparison, the singularity is much more apparent from the angle line of complex continuous wavelet transform. This demonstrates that the proposed method outperforms the existing method of wavelet transform of the mode shape with real wavelets. Also, this method can detect cracks in beams with different boundary conditions. The influence of crack locations and crack depth on crack detection is discussed. Finally, the noise effect is studied. Through the multiscale analysis, the locations of cracks may be detected from the angle of wavelet coefficients.     

利用基本模态振型对梁结构裂缝识别的小波方法研究

文章首先讨论了含裂缝梁结构的柔度矩阵的变化;其次,通过选择不同模态振型函数进行小波变换分析,总结了不同模态振型在梁结构裂缝检测中的不同规律;最后,文章以悬臂梁为例,选用Gaus2小波对悬臂梁基本振型进行小波变换,进而对悬臂梁中的裂缝进行识别,裂缝深度与Lipschitz指数进行拟合。     

多裂纹相互作用下混凝土断裂参量的有限元数值分析

基于虚拟裂纹闭合技术（VCCT），采用有限元分析方法对具有预制中心裂纹的三点弯曲混凝土梁的能量释放率G和应力强度因子K进行了分析计算，应力强度因子的计算结果和相关的理论结果具有较好的一致性，验证了该方法的有效性。然后，考虑2条对称的副裂纹，分析计算了混凝土梁的副裂纹长度对主裂纹应力强度因子的作用效果，获得了副裂纹长度对主裂纹应力强度因子的影响规律。最后，固定主裂纹和副裂纹的长度，改变副裂纹的位置，在多裂纹相互作用下，对混凝土梁副裂纹与主裂纹之间的相对位置对主裂纹应力强度因子的影响进行了计算，得出了副裂纹位置变化对主裂纹应力强度因子的影响规律。该数值方法的建立，对处理和计算混凝土的多裂纹断裂问题具有较好的工程应用前景。     

层状裂隙岩体蠕变柔量估计的合理方法

基于Taylor模型方法和粘弹性断裂力学理论，推导了层状裂隙岩体的单轴、剪切以及体积蠕变柔量，并合理考虑了裂隙相互作用效应的影响，分析了层状裂隙岩体单轴蠕变和剪切蠕变的各向异性。计算分析指出，裂隙岩体的单轴蠕变柔量随裂隙密度参数的增加而增大，随裂隙倾角的增加而减小。考虑裂隙相互作用效应时，层状裂隙岩体的蠕变柔量明显大于不考虑裂隙相互作用的情况。该方法为通过室内岩石流变实验了解实际工程中裂隙岩体的蠕变特性提供了一种可能。     

采用混杂纤维ECC的叠合板#br# 组合梁负弯矩受力性能试验研究

基于一种新型混杂纤维ECC材料研发一种钢 混凝土-ECC组合桥面结构,用于连续组合桥梁的负弯矩区以提升其抗裂性能,可代替其他复杂的工程措施。完成2根钢-混凝土-ECC叠合板组合梁和1根钢-混凝土叠合板组合梁的静力单调加载试验。通过对承载力、刚度与裂缝发展的分析,初步论证混杂纤维ECC用于钢-混凝土组合梁的可行性和优势。试验表明：在纵向受拉钢筋配筋率相等的情况下,采用ECC后浇层的叠合板组合梁在正常使用阶段的承载力略高于对比梁,刚度则高于对比梁且裂缝数量减少、宽度减小;在采用界面拉毛处理后,后浇ECC与混凝土之间的黏结性能良好,界面未出现滑移破坏。基于试验数据和规范方法,提出了含ECC构件的受弯裂缝宽度计算公式,公式计算值与相关试验吻合较好。     

HRB500级钢筋混凝土框架梁开裂性能试验研究

为了研究HRB500级钢筋作为受力主筋的混凝土框架梁开裂性能,对3榀1层2跨的混凝土框架结构进行静力试验,量测了在跨中集中荷载作用下梁端与跨中截面的裂缝宽度、位移、转角以及混凝土和钢筋应变。结果表明：框架梁端裂缝宽度实测值一般大于采用现行混凝土结构设计规范公式的计算值。研究了框架梁端裂缝的开展机理,基于黏结-滑移理论,提出把裂缝处钢筋与混凝土之间的滑移分为在节点内滑移和在梁端内滑移两部分,建立框架梁抵抗负弯矩的纵向钢筋在节点区的黏结-滑移模型和相应的最大裂缝宽度计算式,并根据对试验结果的统计分析,校准了黏结-滑移模型的参数。框架梁端最大负弯矩作用下的裂缝宽度计算式可供工程实践和规范修订参考。