Damage detection by the topology design formulation using modal parameters

The feasibility of using the topology design method for structural damage identification is investigated for the first time. The finite element model of an undamaged structure and some point‐frequency response functions of a damaged structure are assumed to be available. To carry out the feasibility study, the topology optimization formulation suitable for structural damage detection is newly set up, where both resonances and anti‐resonances are used as the damage indication modal parameters. An idea to progressively reduce the candidate damaged elements is also developed to improve the accuracy and efficiency of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.     

Damage assessment in plate-like structures using a two-stage method based on modal strain energy change and Jaya algorithm

The paper presents an effective two-stage approach based on modal strain energy change and Jaya algorithm for damage assessment in plate-like structures. In the first stage, a newly developed damage indicator, named as normalized modal strain energy-based damage index (nMSEBI), is proposed to help locate potential damage elements more effectively. After eliminating most of the healthy elements, the actual damaged sites and its extent in plate structure are determined in the second stage by minimizing an objective function, which is solved using Jaya algorithm. For finding a suitable objective function used in optimization process, two different objective functions are considered to examine their effects on the performance of the utilized optimization algorithm. The efficiency and accuracy of the proposed two-stage damage detection method are investigated by two numerical examples comprising a concrete plate and a four-layer (0°/90°/90°/0°) laminated composite plate with multiple damage locations. All of the obtained results indicate that even under measurement noise, the proposed method can identify the actual damage sites and estimate the extent of damage with high precision. In addition, the numerical results also show that the computational cost of the optimization process using the objective function based on modal flexibility change is much lower than that using the objective function based on mode shapes change.     

A damage identification method for truss structures using a flexibility-based damage probability index and differential evolution algorithm

An efficient method for the multiple damage detection of truss systems using a flexibility-based damage probability index (FBDPI) and differential evolution algorithm (DEA) is proposed. In the first step, a new FBDPI is introduced to find the potentially damaged elements of truss systems. The proposed FBDPI is based on the changes of elemental strain, due to damage, computed by the flexibility matrix of the structure. The flexibility matrix of the structure is dynamically estimated using modal analysis data. In the second step, the reduced damage problem is transformed into a standard optimization problem having few damage variables. Then, the DEA is employed to solve the optimization problem for determining the actual location and severity of damaged elements. Simulation results considering measurement noise demonstrate the high efficiency of the proposed method for the damage detection of truss structures.     

Flexibility-based structural damage identification using Gauss–Newton method

Structural damage will change the dynamic characteristics, including natural frequencies, modal shapes, damping ratios and modal flexibility matrix of the structure. Modal flexibility matrix is a function of natural frequencies and mode shapes and can be used for structural damage detection and health monitoring. In this paper, experimental modal flexibility matrix is obtained from the first few lower measured natural frequencies and incomplete modal shapes. The optimization problem is then constructed by minimizing Frobenius norm of the change of flexibility matrix. Gauss–Newton method is used to solve the optimization problem, where the sensitivity of flexibility matrix with respect to structural parameters is calculated iteratively by only using the first few lower modes. The optimal solution corresponds to structural parameters which can be used to identify damage sites and extent. Numerical results show that flexibility-based method can be successfully applied to identify the damage elements and is robust to measurement noise.     

连续梁结构损伤识别的改进柔度阵方法

传统柔度阵方法难以指示多跨连续梁这样一些复杂连续体结构在支撑处的损伤,提出以结构柔度阵某些自由度对应的对角元素的变化率作为损伤指示函数,对多跨连续梁结构进行更为有效的损伤识别。识别的机理是利用损伤指示函数对于单元损伤因子灵敏度矩阵的对角占优特性,产生对损伤因子分布的“覆盖效应”,从而反映出结构损伤的状态特征。文中给出有关计算公式,进行了数值模拟并比较几种状态的损伤识别结果,显示了本文方法的合理性。     

Combining interface damage and friction in a cohesive‐zone model

A new method to combine interface damage and friction in a cohesive‐zone model is proposed. Starting from the mesomechanical assumption, typically made in a damage‐mechanics approach, whereby a representative elementary area of the interface can be additively decomposed into an undamaged and a fully damaged part, the main idea consists of assuming that friction occurs only on the fully damaged part. The gradual increase of the friction effect is then a natural outcome of the gradual increase of the interface damage from the initial undamaged state to the complete decohesion. Suitable kinematic and static hypotheses are made in order to develop the interface model whereas no special assumptions are required on the damage evolution equations and on the friction law. Here, the Crisfield's interface model is used for the damage evolution and a simple Coulomb friction relationship is adopted. Numerical and analytical results for two types of constitutive problem show the effectiveness of the model to capture all the main features of the combined effect of interface damage and friction. A finite‐step interface law has then been derived and implemented in a finite‐element code via interface elements. The results of the simulations made for a fibre push‐out test and a masonry wall loaded in compression and shear are then presented and compared with available experimental results. They show the effectiveness of the proposed model to predict the failure mechanisms and the overall structural response for the analysed problems. Copyright © 2006 John Wiley & Sons, Ltd.     

结构损伤检测的人工鱼群算法

结构损伤检测实际上属于系统识别的问题,其最终目标是识别结构损伤前后物理参数的变化。可利用实测结构模态参数建立方程求解得到结构物理参数,该过程在数学上往往转化为求解约束优化问题。由此,尝试采用人工鱼群算法来求解这类大型土木工程约束优化问题,首先介绍了算法的参数定义、行为描述及算法流程,然后利用经典测试函数对算法计算性能进行测试,最后给出了结构损伤识别这类约束优化问题的目标函数并通过数值仿真验证了该算法的有效性和鲁棒性。考虑测量噪声影响并通过不同损伤工况的数值仿真,研究结果表明,人工鱼群算法能有效地检测出损伤单元所处位置和损伤程度,因而将其应用到结构损伤检测领域是可行的。     

框架结构损伤定位的比例柔度矩阵分解法试验研究

提出了基于比例柔度矩阵LU分解的结构损伤定位方法。该方法从结构振动响应入手,首先识别出结构前几阶模态振型和频率,构建结构比例柔度矩阵;然后对损伤前后的比例柔度矩阵差进行LU分解;最后基于U矩阵和曲率方法构建损伤指标对损伤进行定位。基于某20层框架结构进行了数值模拟损伤定位研究;并在实验室设计、建造一个6层集中质量剪切型框架模型,基于该模型分别进行了振动台试验和脉冲激励试验。模拟和试验下的单损伤和多损伤工况结果均表明:提出的方法能准确地对结构损伤进行定位。该方法只需要损伤前后测点的振动响应数据,不需要结构有限元模型,避免了复杂的结构有限元模型建模和模型修正工作;并且构建一个满足精确度的比例柔度矩阵只需要结构的前几阶低阶模态参数,而低阶参数的识别准确性相对较高,这些优点均为该方法的工程应用奠定了基础。     

A coupled approach of optimization,uncertainty analysis and configurational mechanics for a fail‐safe design of structures

In this contribution, a novel method for a fail‐safe optimal design of structures is proposed, which is a coupled approach of optimization employing a genetic algorithm, the structural analysis conducted in the framework of fracture mechanics and uncertainty analysis. The idea of fail‐safe structures is to keep their functionality and integrity even under damage conditions, for example, a local failure of substructures. In the present work, a design concept of a substructure exhibiting a damage accumulating function due to the application of crack arresters is introduced. If such a substructure is integrated within a system of coupled substructures, it will accumulate the damage arising from the boundary conditions change induced by the failure of certain neighbouring structural elements and hinder further damage escalation. The investigation of failure of the damage accumulating substructure is introduced within a finite element framework by a combination of discrete fracturing and configurational mechanics based criteria. In order to design a structure, which will fail safely according to a predefined scenario, uncertainties are taken into account. The developed approach optimizes the configuration of crack arresters within the damage accumulating substructure so that the uncertain crack propagation is hindered and only a local failure of this element occurs. Copyright © 2016 John Wiley & Sons, Ltd.     

Damage identification in framed structures using natural frequencies

A novel procedure for damage identification of framed structures is proposed, where both the location and the extent of structural damage in framed structures can be correctly determined using only a limited number of measured natural frequencies. No knowledge of the modal shapes of the damaged structure is required. On the basis of the characteristic equations for the original and the damaged structure, a set of equations is generated. Two computational techniques, the direct iteration (DI) technique and the Gauss–Newton least-squares (GNLS) technique, are utilized to determine structural damage from the derived equations. Finally, different numerical examples are used to demonstrate the effectiveness of the proposed method. © 1997 John Wiley & Sons, Ltd.     

基于柔度差曲率矩阵的结构损伤识别方法

柔度是较频率和位移模态更敏感的结构损伤标示量。提出利用结构损伤前、后的柔度矩阵,先后对柔度矩阵差的列、行进行两次差分,求得柔度差曲率矩阵(δFlexibility Curvature Matrix),并以其对角元素作为检测结构损伤指标(δFCMD)的新方法。该方法仅需低阶模态参数即可进行损伤检测,不论对简支梁、悬臂梁、固支梁,或多跨连续梁,单一位置损伤、支撑处损伤、轻微损伤,还是多种损伤共存,均具有损伤定位的能力、并能定性反映损伤程度。通过与已有的柔度差、柔度变化率、均匀荷载面曲率差等柔度指标的数值模拟分析研究,显示了该指标检测损伤的有效性和优越性。     

摇摆构件摇摆前分析模型

该文为更合理地解释角部损伤后的摇摆构件在摇摆运动前的变形,参考已有的类似弥散塑性模型建立了新的损伤后摇摆构件摇摆前分析模型。同时通过用新的有效刚度系数考虑计算中的塑性变形,提出了一个损伤影响系数来考虑角部缺陷对摇摆构件整体的影响。通过ABAQUS实体有限元模型和已有的试验对提出的分析模型进行验证,结果表明,该文提出的理论模型准确预测了损伤前后的摇摆构件在摇摆前的变形情况。该文使用的随接触面正应力分布而变化的有效刚度系数经验证适用于摇摆构件摇摆前的分析。通过调整该文提出的损伤影响系数可合理反映出不同程度的角部损伤对摇摆构件刚度的影响。     

基于时间序列模型自回归系数灵敏度分析的结构损伤识别方法

该文在分析了时间序列模型的自回归系数对结构单元刚度灵敏度的基础上,提出了一种采用随机载荷作用下结构的时域响应数据进行损伤识别的新方法。该方法首先根据随机载荷作用下的结构响应拟合适用的时序模型;然后建立基于自回归系数的损伤灵敏度矩阵,通过该矩阵可以建立由单元损伤导致的自回归系数的变化与损伤系数变化之间的关系;最后通过求解损伤系数向量来识别损伤位置和损伤程度。对一悬臂梁结构损伤识别的数值结果表明:在计入1%和2%测量噪声的情况下,该方法仅利用单个传感器的时域测量数据,就能够较好地识别单个单元和多个单元损伤;如果对基于多个传感器的识别结果进行综合,识别结果则更加准确、可靠。     

Two-Stage Multi-damage Detection Method Based on Energy Balance Equation

In order to solve structural multi-damage identification problem, a two-stage damage detection method based on energy balance equation and evidence fusion is presented. First, a Frequency Change Identification (FCI) method and Modal Strain Energy Dissipation Ratio (MSEDR) method are utilized to preliminarily identify structural damage locations, and then a Fusion Damage Localization (FDL) method based on evidence theory is proposed to precisely detect damage locations. The FDL method mainly utilizes evidence theory to combine both the FCI localization information and the MSEDR localization information. Thus, more precise damage localization information can be acquired. After the damaged locations are determined, an Energy Balance Equation (EBE) index is presented to identify structural damage extent. Considering that strain energy dissipation should be equal to the change of modal strain energy, a quartic EBE equation is deduced, and structural damage extent can be obtained through the solution of the equation. An average quantification index is also proposed to improve identification precision. The simulation results demonstrate that the FDL method can perfectly detect structural damage locations, and the EBE index and average index can identify structural damage extent.     

Damage identification in plates based on the ratio of modal strain energy change and sensitivity analysis

A two-step method based on modal strain energy is presented for damage identification in thin plates. In the first step, damage is localized with the modal strain energy change ratio approach. A method is proposed to weaken the ‘Vicinity Effect’, thus reduces the false alarms in the localization of damage. In the second step, the damage extents of the suspected damaged elements are obtained iteratively with modal strain energy change sensitivity-based finite element model updating approach. Model reduction is introduced to eliminate the measurement of rotation degrees-of-freedom in the mode shapes. Two numerical examples are studied to demonstrate the effectiveness and robustness of the proposed method. Both single damage and multiple damage cases are studied and good identification results are obtained. The effect of measurement noise on the identification results is investigated.     

基于受控结构振型的损伤定位分步识别方法

提出了基于神经网络技术和受控结构振型数据的损伤定位分步识别方法。首先采用状态反馈控制的方法,有目的地对结构进行极点配置,得到设置的受控结构的动力特性数据。将结构划分为若干个子区域,以受控结构损伤前后振型差作为输入参数,利用概率神经网络确定结构损伤所在的子区域,然后用多损伤定位确信准则对结构损伤子区域中的具体损伤位置进行识别。数值仿真表明,利用概率神经网络能有效地确定结构损伤子区域,采用分步识别的策略能大大缩小具体损伤单元的识别范围,而利用受控结构的动力特性参数可提高识别指标对损伤的敏感度,进而提高损伤识别的准确性。     

损伤叶片动力参数变化规律的数值模拟与试验研究

风力发电机叶片的结构动力特性是叶片结构设计时考虑的重要方面,其动力特性对于整个风力机的安全运行具有重要意义。为了研究损伤引起的结构自振频率的变化规律,从有限元模拟以及试验两方面结合进行了研究。通过对比两种研究方法所得的固有频率值的变化规律,找出他们的共性,从而互相印证结果的正确性。结果表明,叶片的固有频率值受损伤位置、损伤大小以及叶片转速的影响。加权柔度曲率损伤指标在损伤位置处产生突变,从而可判断其损伤位置,根据突变值的大小确定其损伤程度。     

基于人工鱼群算法的结构模型修正与损伤检测

提出结构模型修正结构损伤检测的人工鱼群算法。将结构模型修正与结构损伤检测结构动力学逆问题转化为约束优化数学问题,并尝试用人工鱼群算法求解。介绍人工鱼群算法基本原理,定义关键参数并描述觅食、聚群、追尾及随机等行为;据模型修正原理利用结构损伤前后模态特性数据定义优化问题目标函数;通过两层刚架不同损伤工况数值仿真、三层框架试验数据验证方法的有效性。结果表明,基于人工鱼群算法的结构模型修正与损伤检测方法能有效修正结构有限元模型,在不同噪声水平及各种结构损伤工况下不仅能准确定位结构损伤且能精确识别损伤程度。     

基于互相关函数幅值向量的结构损伤定位方法研究

在利用互相关函数幅值向量（Correlation Function Amplitude Vector，CorV）进行结构损伤检测的方法基础上，进一步提出了利用互相关函数幅值向量来确定受损结构的损伤位置的方法。通过在随机激励下不同测点的时域响应求得结构互相关函数幅值向量后，对损伤前后结构的互相关函数幅值向量进行二阶差分处理，根据差分处理后的互相关函数幅值向量分布图可以直观地判别出结构损伤的位置。用一个四边固支板和一个四层楼房基准模型的损伤定位为算例，验证了所提出方法的有效性和准确性。算例表明，用所提出的方法只需要测量结构受随机激励的时域响应，就可同时确定多处结构损伤的位置，且具有较好的抗测量噪声能力。因此，所提出的方法可应用于环境随机激励下的结构健康监测技术。     

Assessment and rehabilitation of the damaged historic Cenabı Ahmet Pasha Mosque

Historic structures form a very important part of our cultural heritage and are supposed to be preserved properly. Therefore, full comprehension of the structural behavior of historic structures is of prior importance. In this study, a damaged single domed mosque of 16th century classical Ottoman Architecture has been investigated. Serious damage was recorded at various locations and structural elements including the dome and the structural masonry walls, as a result of which the structure was recently closed to worshippers and visitors. The mosque was constructed in the 16th century on silty–clay soil. Due to local drought conditions in the last couple of decades, the water table has changed excessively, causing soil displacements that have especially affected the masonry structure. The main objective of the present study is to explore the reasons for the structural damage and to propose a rehabilitation method suitable for the amelioration of the observed damage. The results of the structural analyses conducted have been compared with the observed damage and some rehabilitation methods have been proposed accordingly. These methods include mini-pile application proceeding as far as the firm soil (rock) in order to prevent the soil displacement. Furthermore, as the cracks on the masonry walls would be repaired using materials that would be in conformity with the structure's historical texture, it has been proposed that a steel ring be fitted suitably around the damaged dome's base in order to contain further propagation of cracks.