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.     

Structural damage detection using time domain responses and an optimization method

An efficient method is proposed to determine the location and severity of structural damage using time domain responses and an optimization method. The time domain responses utilized here are the nodal accelerations measured at the limited points of a structure subjected to an impulse load. The nodal accelerations of the structure are obtained by Newmark time integration method. Firstly, using nodal accelerations extracted for the damaged structure and an analytical model of the structure, an objective function is defined for optimization. Then, the optimization-based damaged detection problem is solved via a differential evolution algorithm for finding the location and severity of damage. In order to assess the accuracy of the proposed method, four numerical examples are considered. Simulation results reveal the efficiency of the method for properly identifying damage with considering measurement noise.     

Efficiency of Jaya algorithm for solving the optimization-based structural damage identification problem based on a hybrid objective function

A Jaya algorithm was recently proposed for solving effectively both constrained and unconstrained optimization problems. In this article, the Jaya algorithm is further extended for solving the optimization-based damage identification problem. In the current optimization problem, the vector of design variables represents the damage extent of elements discretized by the finite element model, and a hybrid objective function is proposed by combining two different objective functions to determine the sites and extent of damage. The first one is based on the multiple damage location assurance criterion and the second one is based on modal flexibility change. The robustness and efficiency of the proposed damage detection method are verified through three specific structures. The obtained results indicate that even under relatively high noise level, the proposed method not only successfully detects and quantifies damage in engineering structures, but also shows better efficiency in terms of computational cost.     

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。     

Optimization-based method for structural damage localization and quantification by means of static displacements computed by flexibility matrix

This article presents an effective method for structural damage identification. The damage diagnosis problem is introduced as an optimization problem which is based on computing static displacements by the flexibility matrix. By utilizing this matrix, the complexity of the static displacement measurements in real cases can be overcome. The optimization problem is solved by a fast evolutionary optimization strategy, named the cuckoo optimization algorithm. The performance of the presented method was demonstrated by studying the benchmark problem provided by the IASC-ASCE Task Group on Structural Health Monitoring, and a numerical example of a frame. Moreover, the robustness of the presented approach was investigated in the presence of some prevalent modelling errors, and also when noisy and incomplete modal data are available. Finally, the efficiency of the proposed method was verified by an experimental study of a five-storey shear building structure. All the obtained results show the good performance of the presented method.     

基于不完备实测模态数据的结构损伤识别方法研究

在传统的基于模型修正的损伤识别中,由于实测模态信息有限而待识别参数过多,往往导致损伤识别方程出现较大误差,从而限制了该方法在复杂结构中的应用。为解决这一问题,对结构的自由度进行了分解,将损伤结构中模态振型的未测量部分表达为已测量到的模态振型、模态频率以及结构其它参数的函数。将损伤视为结构单元刚度的减小,利用完好结构的计算模态数据以及损伤结构扩充后的实测模态数据,建立了结构的损伤识别方程。运用信赖域优化算法对具有双重约束条件的目标函数进行最小化,识别出了结构各单元的刚度损伤参数。通过两个损伤识别数值仿真算例及实验验证,结果表明,在测点数量有限及测试噪声等不利因素影响下,所提方法只需运用少量的实测模态信息,即可实现结构损伤位置及程度的准确识别,同时算法具有较好的鲁棒性。     

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.     

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 identification by the eigenparameter decomposition of structural flexibility change

The use of changes in dynamically measured flexibility matrices to detect structural damage has received considerable attention during the last years. A new flexibility‐based method is proposed in this study to provide an insight to the characterizations of structural damage. The presented method makes use of the eigenparameter decomposition of structural flexibility change and approaches the damage identification problem in a decoupled manner. First, a theory is developed to determine the number of damaged elements according to the number of non‐zero eigenvalues of structural flexibility change. With the number of damaged elements determined, the localization and quantification algorithms are then developed. The proposed method is applied to three numerical examples and its efficiency is demonstrated through damage simulations. Copyright © 2008 John Wiley & Sons, Ltd.     

Eigenfrequecy-based damage identification method for non-destructive testing based on topology optimization

Non-destructive testing (NDT) detects damage according to a difference in a physical phenomenon between a normal structure and damaged structure. As a solution avoiding human errors in NDT, a numerical method based on a dynamical numerical analysis model and a structural optimization algorithm was proposed. This method automatically derives a structure with a response that is equal to that of a damaged structure through an optimization procedure. Among structural optimization methods, topology optimization can optimize the structure fundamentally by changing the topology and not just the shape of a structure. Thus, topology optimization is employed together with eigenfrequency analysis, which is the most fundamental methodology of NDT. The proposed method derives a structure that has the same eigenfrequencies as a damaged structure employing topology optimization. The shape and location of damage can be identified through the optimal shape obtained.     

基于柔度投影法和遗传算法的结构损伤识别方法研究

结构的健康监测对于结构的安全运营和维持结构的性能非常重要。近年来，基于动态测试技术的结构损伤识别方法引起了工程界的广泛关注。损伤识别属于结构工程中的反问题。损伤识别需要解决三类问题：第一，判断结构有无损伤；第二，确定结构的损伤位置；第三，确定结构的损伤程度。将柔度投影法和遗传算法相结合，提出了一种结构损伤定位和定量评估的两阶段法。第一阶段，用柔度投影法进行损伤定位。柔度投影法能够仅用结构的低阶振动测试数据进行准确定位。第二阶段，将确定结构的损伤程度问题表达成优化问题，用遗传算法进行求解。文中给出了一种用于遗传搜索的新的目标函数形式。最后，用一平面桁架桥模型进行了数值模拟，验证了所提出的方法的有效性。此外，为了使所提出的方法更加成熟，文中进行了深入探讨，给出了一些结论，有益于今后的进一步研究。     

基于Bayesian估计的整体和局部信息融合的损伤识别

在结构损伤识别中,如何充分利用整体和局部传感器测试得到的信息来增加结果的准确性是一个值得研究的问题。该文提出基于Bayesian 理论的结构整体局部信息融合的损伤识别方法。首先根据Bayesian理论建立了关于频率、位移模态和应变模态结构损伤的概率模型,静态应变信息提供了Bayesian理论的先验信息,使该概率模型充分利用了各种传感器信息;然后为了减少计算量,采用分步损伤识别的方法,在采用模态应变能指标初步定位损伤范围的基础上,用该文提出的逐个单元消去法定位损伤单元。最后对20 跨刚桁架模型进行试验研究证明了该方法的有效性,并且比较考虑与不考虑应变传感器信息的损伤识别结果。     

Sensitivity-based damage identification method for structures exposed to ground excitation

The purpose of this paper is to present a sensitivity-based finite element model (FEM) updating method using earthquake displacement response in the frequency domain and the frequency response function of structure due to ground excitation. The obtained sensitivity equation is solved by linear least square method through defining constraints on the design variables. Numerical examples of a plane truss and a plane frame support the fact that the proposed method is capable of reliable damage detection. In order to assess the effects of measurement and mass modelling errors on achieved results, model updating is conducted by adding random errors to numerically extracted displacement response and assigned mass properties. The issue of underlying soil foundation influences on obtained results is discussed and the proposed formulation is extended to more accurately capture the soil–structure behaviour. Results indicate that the proposed method is capable of identifying damage properties under different soil conditions with acceptable precision.     

《一种基于柔度的结构损伤定位新方法》

针对现有基于柔度变化的损伤定位方法在理论上仍存在错误定位的可能,从结构刚度矩阵与柔度矩阵的正交性出发,结合矩阵摄动理论及有限元理论,提出一种新的基于柔度变化的结构损伤指标,此方法仅需要结构的前几阶模态参数即可实现准确的损伤定位。通过一平面桁架结构的数值模拟证明该方法的有效性、优越性,该方法有望用于复杂结构的损伤定位分析中。     

Structural damage detection using improved particle swarm optimization

An approach based on an improved particle swarm optimization (PSO) algorithm is proposed for structural damage detection in this study. A disturbance is introduced in the evolution process to avoid the occurrence of premature. The present algorithm focuses on the mutation of global or individual best known positions to guide the swarm to escape from the local minimum. The feasibility and robustness of the modified PSO are verified by three different structures, including a beam, a truss and a plate. The results show that the method is efficient and effective for structural damage identification when measurement noise is considered.     

基于局部静力测试的约束子结构修正法

针对局部子结构为修正对象的情况,提出只利用整体结构中局部子结构部分的静力位移即可精确修正子结构模型的约束子结构方法。首先利用静力测试获得局部子结构所对应的局部柔度矩阵,通过在子结构边界处施加虚拟固定支座,把子结构从整体结构中隔离出来成为约束子结构,同时构造出该约束子结构相应的柔度矩阵。然后利用柔度扰动新方法优化修正约束子结构,即等同于修正相应的子结构模型,从而可对该子结构的损伤状况作出评估。以一个平面桁架结构为例对所提方法进行了验证。结果表明,所提方法合理可靠,计算简单快捷且精度良好。     

Resonant frequency range utilized electro-mechanical impedance method for damage detection performance enhancement on composite structures

One of the problems when using EMI method on composite structures with large surface areas can lead to unsuccessful damage detection due to a vague change in the impedance signature. In addition, a threshold value is usually defined to differentiate a damaged case from an intact case. Therefore, the change in the impedance signature subjected to damage must be significant enough to overcome the effects from other factors which can also cause a change in the impedance signature. In this study, a concept of enhancing the damage detection ability of EMI method using a piezoceramic (PZT) material is reported. The proposed technique eliminates the trial-and-error approach when determining a suitable frequency range by using a resonant frequency range acquired in the lower frequency range below 80 kHz, covering a large sensing area. The main idea is to create peaks in the impedance signature in a peak free zone by sacrificing the sensing area in order to significantly increase the sensitivity of the damage detection ability. The major advantages of the proposed technique is the utilization of the lower frequency range for damage identification using EMI method, while eliminating the time consuming problem of the trial-and-error method.     

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。     

基于应变模态分析的桁架结构损伤检测

选用桁架结构作为研究对象,应用应变模态分析方法对桁架结构的损伤进行检测。由位移模态振型推导应变模态进而用应变模态差值作为桁架结构损伤检测指标,提出了一种基于3σ准则的损伤阈值。通过应变模态差值与损伤阈值的对比来判别损伤有无并对损伤进行定位,用损伤前后应变差值的突变大小来初步确定桁架结构的损伤程度。对一具体桁架结构的单处和多处不同程度损伤工况,结合有限元软件进行了数值模拟。实际桁架的损伤检测实验验证了该方法的有效性。     

基于实测频响函数主成分的在役网架损伤识别方法

鉴于从实际网架动测中得到的频响函数已受到噪声的污染,会使模态分析出现较大的误差,提出了基于实测频响函数和主成分分析的网架损伤识别方法:用网架实测的频响函数数据作为损伤识别的基本变量,建立损伤识别矩阵,通过主成分分析和变量重构对频响函数进行减消噪处理,利用重构的频响函数前几阶主成分,在低维空间中对损伤信息进行分析、提取,并通过多元控制图,来识别网架的损伤。该方法不需要模态参数,避开了模态参数误差所引起的损伤识别不准问题,不需建立力学模型,对网架边界约束条件和结构型式没有特别的限制。为了验证该方法的可靠性,在试验室完成了足尺网架模型在不同损伤情况下动测试验。结果表明,所提出的损伤识别方法简便可行,结果可靠,尤其对噪声环境下和具有一定非线性网架的损伤识别有良好的适应性。