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.     

基于模态应变能的结构损伤识别研究

文中应用有限元分析软件ANSYS10.0建立一个平面刚架结构模型。通过有限元模态分析获得未损伤结构与损伤结构的固有频率和振型。应用单元模态应变能法对模型进行损伤定位。结果证明这种方法对于平面刚架的损伤识别是有效的。     

Modelling the structural behaviour of frost-damaged reinforced concrete structures

A methodology is introduced to predict the mechanical behaviour of reinforced concrete structures with an observed amount of frost damage at a given time. It is proposed that the effects of internal frost damage and surface scaling can be modelled as changes of material and bond properties, and geometry, respectively. These effects were studied and suggestions were made to relate the compressive strength and dynamic modulus of elasticity, as the indicators of damage, to the response of the damaged concrete in compression and tension, and to the bond behaviour. The methodology was applied to concrete beams affected by internal frost damage, using non-linear finite element analyses. A comparison of the results with available experimental data indicated that the changes in failure mode and, to a rather large extent, the effect on failure load caused by internal frost damage can be predicted. However, an uncertainty was the extension and distribution of the damaged region which affected the prediction of the load capacity.     

Studies on damage and FRP strengthening of reinforced concrete beams by vibration monitoring

In this paper, modal characteristics of reinforced concrete beam specimens are identified using experimental test data. Nine concrete beam specimens were gradually damaged and the changes of dynamic parameters were monitored from initial to the failure state. Six of the specimens were strengthened with externally bonded CFRP sheets when the load reached approximately half of the predicted failure load. The identification methods based on measured modal parameters were utilized and the efficiencies of these methods were investigated. These methods include frequency changes, Modal Assurance Criterion (MAC), Coordinate Modal Assurance Criterion (COMAC) and modal curvatures. The comparison of the methods shows that the frequency changes are not fully capable of detecting damage and predicting the potency of strengthening. The MAC values can reveal the changes of overall stiffness of the beams during the load steps. The change of stiffness at each degree of freedom of beams evaluated by COMAC and modal curvatures show that the damage identification of the beam specimens is best described by modal curvature method.     

Ambient vibration testing and updating of the finite element model of a simply supported beam bridge

An ambient vibration test on a concrete bridge constructed in 1971 and calibration of its finite element model are presented. The bridge is characterized by a system of post-tensioned and simply supported beams. The dynamic characteristics of the bridge, i.e. natural frequencies, mode shapes and damping ratios were computed from the ambient vibration tests by using the Eigensystem Realization Algorithm (ERA). Then, these characteristics were used to update the finite element model of the bridge by formulating an optimization problem and then using Genetic Algorithms (GA) to solve it. From the results of the ambient vibration test of this type of bridge, it is concluded that two-dimensional mode shapes exist: in the longitudinal and transverse; and these experimentally obtained dynamic characteristics were also achieved in the analytical model through updating. The application of GAs as optimization techniques showed great versatility to optimize any number and type of variables in the model.     

基于曲率模态的钢筋混凝土梁损伤检测研究

阐明了曲率模态的基本原理。对钢筋混凝土简支梁进行逐级加荷-卸荷试验,每次卸荷后进行动态检测试验,用DASP系统对试验数据进行分析,得到位移模态。利用二阶差分法,由位移模态得到了曲率模态。结果表明,曲率模态能较为准确地识别钢筋混凝土简支梁的损伤,且对微小损伤较为敏感,高阶的曲率模态对于损伤的敏感性高于低阶曲率模态。利用曲率模态能够较好地判定损伤的位置以及损伤的相对程度。     

预应力混凝土结构非线性有限元分析

提出了能反映预应力钢筋与混凝土间相对滑移和相互作用的单元模型,此模型可模拟预应力钢筋的张拉和用于无粘结预应力混凝土结构分析。采用这一单元模型建立了预应力混凝土结构的非线性分析有限元模型,非线性方面考虑了材料和几何非线性、预应力摩擦损失、钢筋松弛、混凝土收缩和徐变等因素。该有限元模型可用于有粘结和无粘结预应力混凝土结构张拉施工和工作阶段的全过程分析,分析内容包括弹塑性变形、混凝土开裂和破坏等。最后给出了有粘结和无粘结预应力混凝土连续梁的分析实例,受力变形、破坏形态等的分析结果与试验结果吻合良好,验证了该模型的合理性和有效性。     

Free vibration of non-uniformly ring stiffened cylindrical shells using analytical, experimental and numerical methods

In this research, the free vibration analysis of cylindrical shells with circumferential stiffeners, i.e. rings with non-uniform stiffeners eccentricity and unequal stiffeners spacing is investigated using analytical, experimental and finite elements (FE) methods. Ritz method is applied in analytical solution while stiffeners treated as discrete elements. The polynomial functions are used for Ritz functions and natural frequency results for simply supported stiffened cylindrical shell with equal rings spacing and constant eccentricity is compared with other's analytical and experimental results, which showed good agreement. Also, a stiffened shell with unequal rings spacing and non-uniform eccentricity with free–free boundary condition is considered using analytical, experimental and FE methods. In experimental method, modal testing is performed to obtain modal parameters, including natural frequencies, mode shapes and damping in each mode. In FE method, two types of modeling, including shell and beam elements and solid element are used, applying ANSYS software. The analytical and the FE results are compared with the experimental one, showing good agreements. Because of insufficient experimental modal data for non-uniformly stiffeners distribution, the results of modal testing obtained in this study could be as useful reference for validating the accuracy of other analytical and numerical methods for free vibration analysis.     

无粘结预应力装配梁试验研究

对4个无粘结预应力装配梁试件进行低周反复加载试验,考虑预应力筋偏心位置、锚固长度、初始预应力度等参数变化。结果表明:无粘结预应力装配梁具有令人满意的抗震特性,与现浇混凝土结构相比虽然耗能低,但延性好自恢复能力强(残余变形小),较非线性大位移下试件破坏程度轻。分析了装配梁的恢复力特性、延性、耗能等性能与试验参数的关系,为无粘结预应力装配结构在地震地区的使用提供参考。     

Damage Identification of a Composite Beam Using Finite Element Model Updating

Abstract:   The damage identification study presented in this article leveraged a full-scale sub-component experiment conducted in the Charles Lee Powell Structural Research Laboratories at the University of California, San Diego. As a payload project attached to a quasi-static test of a full-scale composite beam, a high-quality set of low-amplitude vibration response data was acquired from the beam at various damage levels. The Eigensystem Realization Algorithm was applied to identify the modal parameters (natural frequencies, damping ratios, displacement and macro-strain mode shapes) of the composite beam based on its impulse responses recorded in its undamaged and various damaged states using accelerometers and long-gage fiber Bragg grating strain sensors. These identified modal parameters are then used to identify the damage in the beam through a finite element model updating procedure. The identified damage is consistent with the observed damage in the composite beam.     

Nonlinear behaviour of unprotected composite slim floor steel beams exposed to different fire conditions

An efficient nonlinear 3D finite element model has been developed to investigate the structural performance of composite slim floor steel beams with deep profiled steel decking under fire conditions. The composite steel beams were unprotected simply supported with different cross-sectional dimensions, structural steel sections, load ratios during fire and were subjected to different fire scenarios. The nonlinear material properties of steel, composite slim concrete floor and reinforcement bars were incorporated in the model at ambient and elevated temperatures. The interface between the structural steel section and composite slim concrete floor was also considered, allowing the bond behaviour to be modelled and the different components to retain its profile during the deformation of the composite beam. Furthermore the thermal properties of the interface were included in the finite element analysis. The finite element model has been validated against published fire tests on unprotected composite slim floor steel beams. The time–temperature relationships, deformed shapes at failure, time–vertical displacement relationships, failure modes and fire resistances of the composite steel beams were evaluated by the finite element model. Comparisons between predicted behaviour and that recorded in fire tests have shown that the finite element model can accurately predict the behaviour of the composite steel beams under fire conditions. Furthermore, the variables that influence the fire resistance and behaviour of the unprotected composite slim floor steel beams, comprising different load ratios during fire, cross-section geometries, beam length and fire scenarios, were investigated in parametric studies. It is shown that the failure of the composite beams under fire conditions occurred for the standard fire curve, but did not occur for the natural fires. The use of high strength structural steel considerably limited the vertical displacements after fire exposure. It is also shown that presence of additional top reinforcement mesh is necessary for composite beams exposed to short hot natural fires. The fire resistances of the composite beams obtained from the finite element analyses were compared with the design values obtained from the Eurocode 4 for composite beams at elevated temperatures. It is shown that the EC4 predictions are generally conservative for the design of composite slim floor steel beams heated using different fire scenarios.     

An efficient two-stage approach for structural damage detection using meta-heuristic algorithms and group method of data handling surrogate model

In this study, the performance of an efficient two-stage methodology which is applied in a damage detection system using a surrogate model of the structure has been investigated. In the first stage, in order to locate the damage accurately, the performance of the modal strain energy based index for using different numbers of natural mode shapes has been evaluated using the confusion matrix. In the second stage, to estimate the damage extent, the sensitivity of most used modal properties due to damage, such as natural frequency and flexibility matrix is compared with the mean normalized modal strain energy (MNMSE) of suspected damaged elements. Moreover, a modal property change vector is evaluated using the group method of data handling (GMDH) network as a surrogate model during damage extent estimation by optimization algorithm; in this part of methodology, the performance of the three popular optimization algorithms including particle swarm optimization (PSO), bat algorithm (BA), and colliding bodies optimization (CBO) is examined and in this regard, root mean square deviation (RMSD) based on the modal property change vector has been proposed as an objective function. Furthermore, the effect of noise in the measurement of structural responses by the sensors has also been studied. Finally, in order to achieve the most generalized neural network as a surrogate model, GMDH performance is compared with a properly trained cascade feed-forward neural network (CFNN) with log-sigmoid hidden layer transfer function. The results indicate that the accuracy of damage extent estimation is acceptable in the case of integration of PSO and MNMSE. Moreover, the GMDH model is also more efficient and mimics the behavior of the structure slightly better than CFNN model.     

基于模态应变能变化率的L形管道损伤识别

为识别L形管道的局部损伤,根据局部结构的振型、刚度矩阵和固有频率,得到管道局部的模态应变能变化率指标,并利用有限元软件ABAQUS模拟不同参数模型,得到低阶模态数据以及管道各单元的模态应变能变化率。模拟结果表明：采用该损伤指标,能够较好地确定L形管道的损伤位置,并且直管单元比弯曲单元对该指标更敏感;对同一单元不同损伤程度的对比,可以反映其损伤程度的大小;对L形管道不同弯曲角度进行模拟,该指标对不同弯曲角度L形管道的损伤识别具有普遍性;对L形管道不同缺陷长度进行模拟,模态应变能变化率指标在缺陷取周向长度的1/32时达到极限。     

Operational Modal Parameter Identification from Power Spectrum Density Transmissibility

Abstract: Operational modal analysis subjected to ambient or natural excitation under operational conditions has recently drawn great attention. In this article, the power spectrum density transmissibility (PSDT) is proposed to extract the operational modal parameters of a structure. It is proven that the PSDT is independent of the applied excitations and transferring outputs at the system poles. As a result, the modal frequencies and mode shapes can be extracted by combing the PSDTs with different transferring outputs instead of different load conditions where the outputs from only one load condition are needed. A five‐story shear building subjected to a set of uncorrelated forces at different floors is adopted to verify the property of PSDTs and illustrate the accuracy of the proposed method. Furthermore, a concrete‐filled steel tubular half‐through arch bridge tested in the field under operational conditions is used as a real case study. The identification results obtained from currently developed method have been compared with those extracted from peak‐picking method, stochastic subspace identification, and finite element analysis. It is demonstrated that the operational modal parameters identified by the current technique agree well with other independent methods. The real application to the field operational vibration measurements of a full‐sized bridge has shown that the proposed PSDTs are capable of identifying the operational modal parameters (natural frequencies and mode shapes) of a structure.     

珠江大桥动力特性测试与分析

利用频域中的单模态识别法(SDOFI)对珠江大桥——大跨度预应力砼连续刚构桥的现场环境振动试验数据进行桥梁动力特性识别。利用ANSYS建立了全桥三维有限元模型并进行了理论模态分析。     

Vibration response of an elastically point-supported plate with attached masses

Experimentally determined natural frequencies and modes shapes are presented for an elastically point-supported isotropic plate with attached masses under impulsive loading. These results are compared to frequencies and to modes shapes determined from the Rayleigh–Ritz method and a finite element analysis using COMSOL. Accelerometers mounted at three locations on the plate, provide input for ME’Scope Modal Analysis Software to identify frequency peaks and modes shapes. Orthogonal polynomials, which meet free–free plate boundary conditions, are selected as the basis functions used in the Rayleigh–Ritz method. A Mindlin plate theory, adjusted for negligible transverse shear effects, is used in COMSOL. Frequencies and mode shapes for four plate configurations are presented, compared using each method, and indicate good agreement between the numerical, analytical and experimental results.     

类COMAC指标在桥梁损伤识别中的应用研究

为了研究桥梁结构损伤并探索损伤识别指标,提出基于应变频响函数的参数COMACsfrf作为损伤识别指标。在此基础上采用有限元方法,以一简支板为仿真算例,以结构模型的单元刚度衰减来模拟损伤。结果表明:CO-MACsfrf对损伤的敏感程度高于由振型、应变等推演出的特征指标;该方法可用于结构损伤定位以及定性评价多处损伤。     

轻钢-混凝土组合梁的试验研究及非线性有限元分析

针对轻钢-混凝土组合梁这种新的结构形式,本文进行了六个试件的试验研究,分析了构件的破坏形式、荷载-位移曲线、荷载-应变曲线、钢材和混凝土的应变分布及板宽度方向应变分布等。通过试验研究,初步了解了轻钢-混凝土组合梁的特点和各种截面的粘结性能。采用组合梁单元模型,对轻钢-混凝土组合梁进行了非线性有限元分析,理论计算结果与试验结果吻合较好。     

刚度分布评估的直接识别程序

基于未知刚度分布结构的有限元模型以及标准振频和振动模式,借助于逆问题运算法则,提出结构中刚度分布评估的直接识别程序。通过轴向应变和曲率模态分别确定轴向和弯曲两个独立的刚度指标。所提程序允许对破坏单元进行同步定位,精确量化受损的严重程度,而且对不同的结构类型,包括框架、梁和桁架均适用。在程序中也考虑了噪声随机测度和实际节点的影响。通过数值研究,对程序的有效性、可靠性以及应用范围进行验证。     

A direct identification procedure for assessment of stiffness distribution

An identification procedure is presented for assessment of the stiffness distribution in structures with the aid of an inverse-problem algorithm, based on an FE model of the structure with an unknown stiffness distribution and a subset of measured vibration frequencies and vibration modes. Two independent stiffness indicators–axial and flexural–are used, determined by means of the axial strain and the curvature mode shapes, respectively. The procedure permits simultaneous location of damaged elements, with accurate quantification of damage severity. Furthermore, it is applicable to a variety of structure types, including frames, beams and trusses. The effects of random measurement noise and of realistic joints are taken into consideration. The effectiveness, reliability, and range of application of the procedure are demonstrated in a numerical study.