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.     

Damage detection method for large structures using static and dynamic strain data from distributed fiber optic sensor

A method for damage detection applicable to large slender steel structures such as towers of large-scale wind turbines, long-span bridges, and high-rise buildings is presented. This method is based on continuous strain data obtained by distributed fiber optic sensor (FOS) and neural network (NN) analysis. An analytical model for cracked beam based on an energy balance approach was used to train a NN. The continuous static strains and the natural frequencies obtained from the distributed FOSs were used as the input to the trained NN to estimate the crack depths and locations. An experimental study was carried out on a cracked cantilever beam to verify the present method for damage identification. The cracks were inflicted on the beam, and static and free vibration tests were performed for the intact case and the damage cases. The distributed FOSs were used to measure the continuous strains. The damage estimation was carried out for the 5 damage cases using the NN technique. It has been found that the identified crack depths and locations agree reasonably well with the inflicted cracks on the structure.     

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。     

Crack detection in beam-like structures

Sensibility analysis of experimentally measured frequencies as a criterion for crack detection has been extensively used in the last decades due to its simplicity. However the inverse problem of the crack parameters (location and depth) determination is not straightforward. An efficient numerical technique is necessary to obtain significant results. Two approaches are herein presented: The solution of the inverse problem with a power series technique (PST) and the use of artificial neural networks (ANNs). Cracks in a cantilever Bernoulli–Euler (BE) beam and a rotating beam are detected by means of an algorithm that solves the governing vibration problem of the beam with the PST. The ANNs technique does not need a previous model, but a training set of data is required. It is applied to the crack detection in the cantilever beam with a transverse crack. The first methodology is very simple and straightforward, though no optimization is included. It yields relative small errors in both the location and depth detection. When using one network for the detection of the two parameters, the ANNs behave adequately. However better results are found when one ANN is used for each parameter. Finally, a combination between the two techniques is suggested.     

悬臂系统振动特性的研究

本文研究悬臂系统,包拓悬臂弹性梁及其附带的质块的振动特性.本文首先导出了该系统频率和振型的分析表达式,并利用计算机辅助设计软件,分别讨论了质块质量及弹簧常数对系统频率的影响.上述系统的不同参数,对系统的固有频率的影响是不同的,为此我们研究了在若干特定参数下,系统固有频率对质块位置的敏感度,并得到相应的结论.     

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.     

A new approach for free vibration analysis of nonuniform tall building structures with axial force effects

Dynamic analysis of beam‐like structures is significantly important in modeling actual cases such as tall buildings and several other related applications as well. This article studies free vibration analysis of tall buildings with nonuniform cross‐section structures. A novel and simple approach is presented to solve natural frequencies of free vibration of cantilevered tall structures with variable flexural rigidity and mass densities. These systems could be replaced by a cantilever Timoshenko beam with varying cross‐sections. The governing partial differential equation for vibration of a nonuniform Timoshenko beam under variable axial loads is transformed with varying coefficients to its weak form of integral equations. Natural frequencies can be determined by requiring the resulting integral equation, which has a nontrivial solution. The presented method in this study has fast convergence. Including high accuracy for the obtained numerical results as well. Numerical examples including framed tube as well as tube‐in‐tube structures are carried out in the study and compared with available results in the literature, and also with the results obtained from finite element analysis in order to show the accuracy of the proposed method in the study. Obtained results indicate that the presented method in this study is powerful enough for the free vibration analysis of tall buildings.     

Fourier p-elements for curved beam vibrations

Several Fourier p-elements for in-plane vibration of thin and thick curved beams are presented. Fourier trigonometric functions are used as enriching functions to avoid the ill-conditioning problems associated with high order polynomials. The element matrices are analytically integrated in closed form. With the additional Fourier degrees of freedom, the accuracy of the computed natural frequencies is greatly improved. Furthermore, the elements with enriching shape functions can avoid membrane and shear locking. The vibration of a thin ring, whose exact solutions are available, is analyzed by the present elements. The present elements can compute accurately high natural modes as the higher mode shapes synchronize with the Fourier functions nicely. The free vibration analysis of a number of hinged circular arches with various subtended angles and the tapered cantilever arches having uniform and non-uniform cross-section is carried out as numerical examples. The condition numbers for polynomial p-elements and Fourier p-elements are compared to show the superior numerical stability of the method.     

工字形截面楔形梁的有限元分析

针对钢结构中常用的工字形截面楔形构件 ,推导出了楔形梁的位移模式 ,并在此基础上 ,用有限元原理 ,通过符号计算软件 ,求得相应的形函数与刚度矩阵。最后 ,给出了一悬臂梁的比较算例。     

Quantification and localisation of damage in beam-like structures by using artificial neural networks with experimental validation

This paper presents a damage detection algorithm using a combination of global (changes in natural frequencies) and local (curvature mode shapes) vibration-based analysis data as input in artificial neural networks (ANNs) for location and severity prediction of damage in beam-like structures. A finite element analysis tool has been used to obtain the dynamic characteristics of intact and damaged cantilever steel beams for the first three natural modes. Different damage scenarios have been introduced by reducing the local thickness of the selected elements at different locations along finite element model (FEM) of the beam structure. The necessary features for damage detection have been selected by performing sensitivity analyses and different input–output sets have been introduced to various ANNs. In order to check the robustness of the input used in the analysis and to simulate the experimental uncertainties, artificial random noise has been generated numerically and added to noise-free data during the training of the ANNs. In the experimental analysis, two steel beams with eight distributed surface-bonded electrical strain gauges and an accelerometer mounted at the tip have been used to obtain modal parameters such as resonant frequencies and strain mode shapes. Finally, trained feed-forward backpropagation ANNs have been tested using the data obtained from the experimental damage case for quantification and localisation of the damage.     

A preliminary research on wireless cantilever beam vibration sensor in bridge health monitoring

According to specific bridge environment, optimal design piezoelectric cantilever beam structure by using results of theoretical calculations and simulation, verify natural frequencies of piezoelectric cantilever beam and production ability of data by experiment, thus formed a complete set of design method of piezoelectric cantilever beam. Considering natural frequency of vibration and intensity of the beam body, design a new type of piezoelectric cantilever beam structure. Paper analyzes the principle of sensor data acquisition and transmission, design a hardware integration system include signal conversion module, microcontroller module and wireless transmission module, test local read and wireless transmission for the combination structure of cantilever beam and data collection card, experimental verification of the radio piezoelectric vibrating cantilever vibration response is intact, the beam produced signal by vibration, acquisition card converts and wireless transmit data, this proved a good and intuitive linear response in simulation of bridge vibration test. Finally, the paper designed a kind of new wireless sensor of vibration cantilever beam, suitable for small bridge health monitoring based on Internet of things.     

再生混凝土悬臂梁阻尼性能与损伤关系的试验研究

再生混凝土结构构件非弹性阶段阻尼性能与其损伤程度密切相关。以再生粗骨料取代率 及其粒级为主要参数,采用悬臂梁低周反复加载和自由衰减振动的交叉试验,研究再生混凝土 悬臂梁在不同损伤阶段的阻尼性能,建立悬臂梁阻尼比与损伤指数的定量关系,探讨悬臂梁裂 缝发展对其阻尼和损伤演变的影响。研究结果表明：再生混凝土悬臂梁阻尼比随损伤指数先增 大后减小,峰值阻尼比是初试弹性阶段阻尼比的2~3倍;损伤指数相同时,再生混凝土悬臂梁阻 尼比随再生粗骨料取代率的增加而增大,随再生粗骨料粒径的减小而增大;再生粗骨料的基本 性质、取代率及其粒级对再生混凝土结构构件的阻尼比和损伤指数影响显著;再生混凝土悬臂 梁阻尼性能和损伤指数的演变与悬臂梁裂缝数量、开展高度及宽度的发展密切相关。     

Approximate analysis of tall buildings using sandwich beam models with variable cross‐section

In this paper an approximate method is carried out for determining the natural periods of multistory buildings subjected to earthquake. The building resists lateral forces through a combination of lateral resisting systems. These systems could be replaced by a cantilever Timoshenko or a sandwich beam with varying cross‐section that characterizes three kinds of stiffnesses: the global bending stiffness, the local bending stiffness and the shear stiffness. Using appropriate transformations, the differential equations for flexural and shear free vibration of a cantilever beam with variably distributed mass and stiffness are reduced to Bessel's equations and ordinary differential equations. The frequency equations can be solved by selecting suitable expressions such as exponential and power functions for stiffness and mass distribution along the height of the building. The calculated frequencies are combined appropriately by using approximate methods. Based on the fact that shear and bending deformations are all considered, the free vibration frequency of the structure could be calculated. The capability and accuracy of the proposed method are demonstrated by a numerical example in which finite element results are compared with the proposed methodology and other approximate methods. Copyright © 2007 John Wiley & Sons, Ltd.     

大跨度空间网格结构的损伤定位

本文建立了基于模态曲率法和人工神经网络技术相结合的、适用于大跨度空间网格结构的损伤定位新方法,即首先应用模态曲率法判断结构是否发生损伤并识别发生损伤的局部结构,然后对发生损伤的局部结构利用人工神经网络技术识别损伤的准确位置。通过分析和比较发现,以模态曲率为基础的损伤参数比较适合于大跨度空间网格结构的损伤定位,三种以模态曲率为基础的损伤定位参数按有效性进行排序,从低到高依次为模态曲率、模态曲率差、模态曲率变化率;针对天津奥林匹克中心体育场大跨度悬挑管桁结构进行了不同损伤状况的数值模拟,验证了所建立的损伤定位方法的适用性和有效性。研究结果表明:利用模态曲率变化率识别损伤发生的大致位置,当单榀桁架发生损伤时,识别的准确率达到100%,当多榀桁架同时发生损伤时,识别的准确率达93.7%;采用人工神经网络技术识别损伤桁架的准确损伤位置时,在无测量噪声影响下,损伤定位的准确率达到97.0%,且测量噪声对损伤定位准确率的影响很大。     

Crack detection of the cantilever beam using new triple hybrid algorithms based on Particle Swarm Optimization

The presence of cracks in a concrete structure reduces its performance and increases in the size of cracks result in the failure of the structure. Therefore, the accurate determination of crack characteristics, such as location and depth, is one of the key engineering issues for assessment of the reliability of structures. This paper deals with the inverse analysis of the crack detection problems using triple hybrid algorithms based on Particle Swarm Optimization (PSO); these hybrids are Particle Swarm Optimization-Genetic Algorithm-Firefly Algorithm (PSO-GA-FA), Particle Swarm Optimization-Grey Wolf Optimization-Firefly Algorithm (PSO-GWO-FA), and Particle Swarm Optimization-Genetic Algorithm-Grey Wolf Optimization (PSO-GA-GWO). A strong correlation exists between the changes in the natural frequency of a concrete beam and the crack parameters. Thus, the location and depth of a crack in a beam can be predicted by measuring its natural frequency. Hence, the measured natural frequency can be used as the input parameter of the algorithm. In this paper, this is applied to identify crack location and depth in a cantilever beam using the new hybrid algorithms. The results show that among the proposed triple hybrid algorithms, the PSO-GA-FA and PSO-GWO-FA algorithms are much more effective than PSO-GA-GWO algorithm for the crack detection.     

两类呼吸裂缝模型及其动力响应对比分析

结构构件开裂产生的非线性振动响应是结构损伤识别的重要依据,而选择合理的模型对准确计算这种非线性振动响应至关重要。根据振动过程中裂缝处结构刚度的变化规律,对现有呼吸裂缝模型进行了分析总结,并选取具有典型代表的两种模型,以带裂缝悬臂梁受迫简谐振动为例,对比分析了两种模型在不同激励频率和不同裂缝深度下结构响应的频谱特性。结果表明:相同条件下双线型呼吸裂缝模型较曲线型呼吸裂缝模型更易出现高频分量和谐振现象,能更好地表征裂缝在振动过程中的呼吸效果。     

Bending and buckling of inflatable beams: Some new theoretical results

The non-linear and linearized equations are derived for the in-plane stretching and bending of thin-walled cylindrical beams made of a membrane and inflated by an internal pressure. The Timoshenko beam model combined with the finite rotation kinematics enables one to correctly account for the shear effect and all the non-linear terms in the governing equations. The linearization is carried out around a pre-stressed reference configuration which has to be defined as opposed to the so-called natural state. Two examples are then investigated: the bending and the buckling of a cantilever beam. Their analytical solutions show that the inflation has the effect of increasing the material properties in the beam solution. This solution is compared with the three-dimensional finite element analysis, as well as the so-called wrinkling pressure for the bent beam and the crushing force for the buckled beam. New theoretical and numerical results on the buckling of inflatable beams are displayed.     

Vibrational analysis of single-walled carbon nanotubes using beam element

Vibrational analysis of single-walled carbon nanotubes (SWCNTs) is performed using a finite element method (FEM). To this end, the vibrational behavior of bridge and cantilever SWCNTs with different side lengths and diameters is modeled by three-dimensional elastic beams and point masses. The beam element elastic properties are calculated by considering mechanical characteristics of the covalent bonds between the carbon atoms in the hexagonal lattice. The mass of each beam element is assumed as point masses at nodes coinciding with the carbon atoms. Implementing the atomistic simulation approach, the natural frequencies of zigzag and armchair SWCNTs are computed. It is observed that the findings are in good agreement with the molecular structural mechanics data available in the literature. Then, the computational results are adopted to develop a predictive equation to propose a quick tool for estimating natural frequencies of the SWCNTs with different boundary conditions and geometrical parameters.     

基于压电主动传感技术的高温后PVA-ECC梁冲击损伤监测研究

研究了低速冲击荷载作用下具有高温损伤的聚乙烯醇纤维增强水泥基复合材料（PVA-ECC）梁的损伤特征,对比分析不同温度损伤与室温下的PVA-ECC梁,在同一跌落高度和落锤质量上进行了一系列的落锤低速冲击试验,模拟冲击能量对梁的影响结果。采用压电陶瓷智能骨料传感器的主动监测方法和扫频波信号,监测落锤低速冲击作用下PVA-ECC梁的裂纹产生、发展、断裂全过程与波衰减的规律。基于小波包能量法分析重复冲击试验下的PVA-ECC梁裂缝发展演化。建立了PVA-ECC梁三维有限元模型,通过有限元分析得出300 ℃高温加热后的PVA-ECC梁低速冲击裂纹开展全过程,并与实测结果进行对比。结果表明:高温损伤造成PVA-ECC梁的抗冲击性能减弱;室温下的PVA-ECC梁有一定抗冲击能力,但当温度达到PVA纤维的熔点（230 ℃）时,PVA-ECC梁中的PVA纤维消失,产生孔隙,形成素水泥砂浆梁,不具有抗冲击能力;高温损伤造成PVA-ECC丧失了高强度、韧性、耐疲劳的能力特性。     

框支剪力墙和落地剪力墙共同工作时的自振周期

本文将框支剪力墙和落地剪力墙合并成一个弹性支座上的Timoshenko悬臂粱,考虑截面的剪切和转动惯量的影响,求得了其水平振动时的自振周期计算公式。还讨论了各种因素的影响及简化的计算公式。