A frequency‐domain noniterative algorithm for structural parameter identification of shear buildings subjected to frequent earthquakes

System identification is the key technique for damage detection in application of structural health monitoring. In contrast to modal parameters, changes in structural parameters (stiffness and damping) are more sensitive and straightforward for damage detection of a building under severe environments such as earthquakes. In this study, we first present the fundamental theory for direct identification of structural parameters by using the frequency‐domain responses of a shear building in frequent earthquakes. Shear buildings are widely adopted for structural analysis of low‐ and middle‐rise buildings in practice. Modal information, in terms of spectrum ratios, is implicitly used in the proposed noniterative algorithm to greatly improve the estimation accuracy as well as to avoid any human intervention. The fundamental theory is validated by the numerical and physical examples. The numerical examples are further used to verify the high efficiency, accuracy, and robustness of the proposed algorithm against noised responses. The proposed algorithm is highly efficient because no iterative computation is necessary, while the necessary Fourier transform of the dynamic responses is not very time consuming. Furthermore, the proposed algorithm is highly accurate and robust because (a) the fundamental theory behind the algorithm is straightforward: the identification values should have the same value irrespective of circular frequencies, according to the theory; (b) error in modal parameter identification is completely avoided because it is unnecessary to identify the exact values of the frequencies as in many existing methods.     

Damage location and assessment along structural elements using damage submatrices

A new method to locate and determine the magnitude of damage, expressed as the loss of stiffness, along structural elements of buildings, called Damage Submatrices Method is presented. The method uses information related to the stiffness of both states of the structure: undamaged and damaged, utilizing iterative eigenvalue computations. The novelty of the method relies on its capability to identify damage in specific zones of structural elements depending on how the undamaged model of the structure was discretized. Another advantage of the proposed method is its convergence. This paper also contributes a new approach to simulate noise perturbing stiffness matrices. This technique can be useful for realistic damage detection investigations. Also, the proposed technique used to expand condensed damaged stiffness matrices, to global coordinates, may be useful for system identification projects. Two examples taken from the literature are studied involving limited modal measurements and noise effects to calibrate the method and corroborate its capability for damage assessment. Application of the proposed method to these structures corroborates its efficiency for identifying stiffness degradation of structural elements.     

Wavelet-Based Structural Health Monitoring of Earthquake Excited Structures

Abstract:   The article presents a wavelet-based structural health monitoring technique for structures subjected to an earthquake excitation utilizing the instantaneous modal information. The instantaneous mode shape information is first extracted from the vibration response data collected during an earthquake event by using a wavelet packet sifting process. A confidence index (CI) is proposed to validate the results obtained. The identified normalized instantaneous mode shapes in conjunction with the corresponding CIs can be effectively used to monitor damage development in the structure. The effectiveness of the proposed approach is illustrated for two damage scenarios, sudden stiffness loss and progressive stiffness degradation, and different base excitations including three real earthquake signals and a random signal. Consistently good results were obtained in all cases. Issues related to robustness of the method in the presence of a measurement noise and sensitivity to damage severity are discussed.     

A Two‐Step Model Updating Algorithm for Parameter Identification of Linear Elastic Damped Structures

A Frequency Response Functions (FRFs)‐based two‐step algorithm to identify stiffness, mass, and viscous damping matrices is developed in this work. The proposed technique uses the difference between the experimentally recorded FRF and their analytical counterparts by minimizing the resultant error function at selected frequency points. In the first step, only mass and stiffness matrices are updated while keeping the uncalibrated viscous damping matrix constant. In the second step, the damping matrix is updated via changes on the selected unknown modal damping ratios. By using a stacking procedure of the presented error function that combines multiple data sets, adverse effects of noise on the estimated modal damping ratios are decreased by averaging the FRF amplitudes at resonant peaks. The application of this methodology is presented utilizing experimentally obtained data. The presented algorithm can perform an accurate structural identification via model updating, with a viscous damping matrix that captures the variation of the modal damping ratios with natural frequencies as opposed to other conventional proportional damping matrix formulations.     

Identification of modal damping ratios of four‐flue chimney of a thermoelectrical plant using pseudo‐inverse matrix method

Some computational issues related to the identification of modal parameters of structures are presented in this paper. Optimal estimation of modal parameters often requires the solution of an overdetermined linear system of equations. Hence the computation of a pseudo‐inverse matrix is involved. In this paper the numerical performance of different algorithms for Moore–Penrose pseudo‐inverse computation have been tested for modal analysis of a four‐flue chimney of a thermoelectrical plant. The computational scheme herein adopted for parameter identification is based on well‐known modal properties and has a fast rate of convergence to solution. The computation of the Rayleigh damping coefficients a and b is an important step in the area of the modal superposition technique. The proposed approach can accurately predict damping ratios and all the eigenvectors without evaluating mass and stiffness matrices. Copyright © 2007 John Wiley & Sons, Ltd.     

基于最小秩方法的结构损伤识别

针对结构损伤识别中的最小秩方法存在的问题,经过研究发现,对测试模态进行关于质量矩阵的正交归一化可保证反演后刚度矩阵的对称性;提出了一种迭代修正算法,可保持反演结果的稀疏性;基于模态力余量,定义了一种损伤指标来预先判定结构损伤单元的位置,并可据此选取合适的测试模态阶数进行反演计算。数值试验结果表明,改进后的方法在考虑测试模态误差的情况下可对结构的损伤进行精确的定位和标定。     

Dynamic reduction-based structural damage detection of transmission tower utilizing ambient vibration data

This paper reports a feasibility study of utilizing ambient vibration data measured from a limited number of sensors in the structural damage detection of transmission towers, which are large-scaled three-dimensional spatial structures. To develop a practical and efficient structural damage detection methodology, the characteristics of transmission towers are considered in the development stage, including the most common types of damage, accessible locations for installing sensors, the technique needed to identify a reliable set of modal parameters utilizing ambient vibration data, a method to divide the transmission tower into sub-structures for structural damage detection, a way to formulate the damage detection problem, and the corresponding solution method. The proposed methodology is numerically verified by simulated noisy data from a three-dimensional transmission tower sample under both single and multiple damage cases. Very encouraging results are obtained, showing that the proposed methodology can identify the damaged sub-structure by estimating the ‘equivalent’ stiffness reduction even in the presence of both measurement noise and modeling error.     

Long-Term Monitoring and Identification of Bridge Structural Parameters

Abstract:   Vibration of a new concrete bridge was monitored and change in the bridge structural stiffness was identified accordingly over a 5-year period. This three-span 111-m long bridge is instrumented with 13 acceleration sensors at both the superstructure and the columns. The sensor data are transmitted to a server computer wirelessly. Modal parameters of the bridge, that is, the frequencies and the modal shapes were identified by processing 1,707 vibration data sets collected under traffic excitations, based on which the bridge structural parameters, stiffness and mass, and the soil spring values were identified by employing the neural network technique. The identified superstructure stiffness at the beginning of the monitoring was 97% of the stiffness value based on the design drawings. In the identified modal frequencies, a variation from −10% to +10% was observed over the monitoring period. In the identified stiffness values of the bridge superstructure, a variation from −3% to +3% was observed over the monitoring period. Based on the statistical analysis of the collected data for each year, 5% decrease in the first modal frequency and 2% decrease in the superstructure stiffness were observed over the 5-year monitoring period. Probability density functions were obtained for stiffness values each year. Stiffness threshold values for the collapse of the bridge under the operational loading can be determined. Then the number of years can be assessed for which the area under the proposed probability density functions is greater than the threshold value. So the information obtained in this study is valuable for studying aging and long-term performance assessment of similar bridges.     

Modal Flexibility Analysis of Cable-Stayed Ting Kau Bridge for Damage Identification

Abstract:   The cable-stayed Ting Kau Bridge has been permanently instrumented with more than 230 sensors for long-term structural health monitoring. In this article, the feasibility of using the measured dynamic characteristics of the bridge for damage detection is studied. Making use of a validated three-dimensional (3D) finite element model (FEM), modal flexibility matrices of the bridge are constructed using a few truncated modes and incomplete modal vectors at the sensor locations. The relative flexibility change (RFC) between intact and damage states is then formulated as an index to locate damage. The applicability of this flexibility index for damage location in the cable-stayed bridge is examined by investigating various damage scenarios including those at stay cables, longitudinal stabilizing cables, bearings and supports, longitudinal girders and cross girders, and taking into account measurement noise in modal data. The influence of two ambient factors, that is, temperature change and traffic loading, on the damage detectability is also analyzed by approximately considering an equivalent alteration in the material and structural behaviors. It is revealed that in the absence of ambient effects the RFC index performs well for locating damage of different severities in single-damage cases. In multi-damage cases the RFC index may provide false-negative identification for damage at the members with low sensitivity. Eliminating ambient effects is requisite for reliable detection of damage at stay cables and cross girders. The capability of the RFC index for locating damage at cross girders is significantly dropped in the presence of measurement noise.     

Modal Identification Study of Vincent Thomas Bridge Using Simulated Wind-Induced Ambient Vibration Data

Abstract:   In this article, wind-induced vibration response of Vincent Thomas Bridge, a suspension bridge located in San Pedro near Los Angeles, California, is simulated using a detailed three-dimensional finite element model of the bridge and a state-of-the-art stochastic wind excitation model. Based on the simulated wind-induced vibration data, the modal parameters (natural frequencies, damping ratios, and mode shapes) of the bridge are identified using the data-driven stochastic subspace identification method. The identified modal parameters are verified by the computed eigenproperties of the bridge model. Finally, effects of measurement noise on the system identification results are studied by adding zero-mean Gaussian white noise processes to the simulated response data. Statistical properties of the identified modal parameters are investigated under an increasing level of measurement noise. The framework presented in this article will allow us to investigate the effects of various realistic damage scenarios in long-span cable-supported (suspension and cable-stayed) bridges on changes in modal identification results. Such studies are required to develop robust and reliable vibration-based structural health monitoring methods for this type of bridge, which is a long-term research objective of the authors.     

Damage Detection in a Girder Bridge by Artificial Neural Network Technique

Abstract:   Vibration-based damage identification (VBDI) techniques rely on the fact that damage in a structure reduces its stiffness and alters its global vibration characteristics. Measurement of changes in the vibration characteristics can therefore be used to determine the damage in the structure. Although VBDI offers several advantages, most of the available damage identification algorithms fail when applied to practical structures due to the effect of measurement errors, need to use incomplete mode shapes, mode truncation, and the nonunique nature of the solutions. This article presents a new robust two-step algorithm that uses the modal energy-based damage index to locate the damage and an artificial neural network technique to determine the magnitude of damage. The proposed algorithm is applied to detect simulated damage in a finite element model of a girder and a similar model of a real bridge named Crowchild Bridge located in Alberta, Canada. The results show that the proposed algorithm is quite effective in identifying the location and magnitude of damage, even in the presence of measurement errors in the input data.     

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。     

EMD-based random decrement technique for modal parameter identification of an existing railway bridge

Vibrational measurement data are often nonstationary and modal parameter identification based on these data is of practical value for structural health monitoring and condition assessment. The empirical mode decomposition (EMD) is a most recent tool for analysis of nonstationary signals. An EMD-based random decrement (RD) technique is presented to identify modal parameters from monitoring vibrational data. The nonstationary measurement data are first decomposed into a series of quasi-stationary intrinsic mode functions (IMFs) by EMD. The RD technique is then applied to the selected IMFs to obtain the free-decay response. The modal frequencies and damping ratios are finally identified from the free-decay response by minimizing the error between the measured free-decay responses and the predicted responses from a parametric model. The present method is applied to extract the modal parameters of the Nanjing Yangtze River Bridge from the measured responses. The identification result is compared to those from finite element analysis as well as from the experimental result identified with the peak-picking (PP) method. In addition, the modal frequencies of the bridge loaded with heavy trains are also identified and compared to the ‘empty’ bridge. The EMD-based random decrement (RD) technique provides an effective and promising tool for modal parameter identification for large bridges and other structures.     

Modal identification of non-classically damped structures using generalized sparse component analysis

Modal identification method based on blind source separation (BSS) technique has gained extensive attentions for civil structures. Developing the complex modes estimation method is important in practical applications because the assumption of proportional damping is not always satisfied. Sparse component analysis (SCA) performs well in underdetermined BSS problems. However, SCA is confined to the situation of proportional damping. In this study, a generalized SCA method is proposed to extend the original SCA method to both real and complex modes identification. First, the general formulation of complex modes is extended by the analytic form to eliminate the complex conjugate part in the BSS model. A new single-source-point detection method that is available to handle real and complex modes is proposed. Local outlier factor method is adopted to remove the outliers in single source points. Subsequently, complex-valued modal matrix is calculated by the clustering technique. Then, modal responses are recovered using the complex version of smoothed zero norm method, where modal frequencies and damping ratios can be extracted. Finally, the effectiveness of the proposed method is demonstrated for identification of real and complex modes, close modes, and underdetermined problem. The application to a benchmark structure demonstrates the effectiveness for practical applications.     

Nonlinear Damping Identification in Precast Prestressed Reinforced Concrete Beams

Abstract:  This article presents a damage detection method for prestressed reinforced concrete (PRC) elements based on free vibration tests and nonlinear damping identification. Integrated static and dynamic experiments were carried out on three precast PRC beam specimens. The static loading induced different levels of damage to the beams. At each damage level, impulsive loading was applied to the beams and the free vibration response was measured. The dynamic response data were processed using different methods including the multi-input multi-output (MIMO) curve fitting and the Hilbert transform techniques. A strong correlation is observed between the level of concrete damage (cracks) and the amount of nonlinear energy dissipation that can be modeled by means of quadratic damping. The nonlinear damping can be extracted from the free vibration response for each vibration mode. The proposed method is suited for quality control when manufacturing precast PRC members, and can be further extended for in situ detection of damage in concrete structures under ambient vibration.     

Performance of Vibration-Based Damage Detection Methods in Bridges

Abstract:   The important advances achieved in the modal identification, sensors, and structural monitoring of bridges have motivated the bridge engineering community to develop damage detection methods based on vibration monitoring. Some of these methods have already been demonstrated under certain conditions in bridges with deliberate damage. However, the performance of these methods for damage detection in bridges has not been fully proven so far and more research needs to be done in this direction. In this article, six damage detection methods based on vibration monitoring are evaluated with two case studies. First, the dynamic simulation and modal parameters of a cracked composite bridge are obtained. Here, the damage detection methods are evaluated under different crack depth, extension of the damage, and noise level. Second, damage is identified in a reinforced concrete bridge. This bridge was deliberately damaged in two phases. In this example, damage detection methods, which do not require comparison between different structural conditions, were applied. In the first case study, evaluated damage detection methods could detect damage for all the damage scenarios; however, their performance was notably affected when noise was introduced to the vibration parameters. In the second case study, the evaluated methods could successfully localize the damage induced to the bridge.     

Structural parameter identification and damage detection for a steel structure using a two-stage finite element model updating method

A two-stage eigensensitivity-based finite element (FE) model updating procedure is developed for structural parameter identification and damage detection for the IASC-ASCE structural health monitoring benchmark steel structure on the basis of ambient vibration measurements. In the first stage, both the weighted least squares and Bayesian estimation methods are adopted for the identification of the connection stiffness of beam-column joints and Young’s modulus of the structure; then the damage detection is conducted via the FE model updating procedure for detecting damaged braces with different damage patterns of the structure. Comparisons between the FE model updated results and the experimental data show that the eigensensitivity-based FE model updating procedure is an effective tool for structural parameter identification and damage detection for steel frame structures.     

Real-time structural health monitoring of a supertall building under construction based on visual modal identification strategy

This paper presents a real-time structural health monitoring technique for a supertall building under construction, Lotte World Tower (LWT), the tallest building in Korea. To evaluate the state and safety of the supertall building under construction, this study presents a visual modal identification method to identify mode shape and damping ratio based on modal responses from the monitoring system. In the method, mode shape and damping are visually identified from the time history plotting of well-filtered modal responses in real time. Since the presented method does not include a kind of complex calculation for measured data required in the previous SI methods, it can avoid time consuming in system identification (SI) as well as variation in value of modal parameter extracted from measurement. An ambient vibration test on the LWT under construction was performed in 2015. Using the test data, the presented method identified the mode shapes and damping of the LWT visually with small variations without any complicated computations. Further, this study presents a model updating method with a simplified pseudo frame model to construct a baseline model for the LWT under construction using measured modal responses. The validity of the updated model for the LWT was verified through estimations of mode shape and structural responses.     

超高层建筑结构加强层耗能减震技术及连接节点设计研究

在框架-核心筒结构体系中,加强层可显著提高结构抗侧刚度、减小结构侧移,但会带来结构刚度、内力突变等不利影响。以某超高层建筑为工程背景,研究了黏滞阻尼器在伸臂桁架体系中的应用及在多遇地震和罕遇地震作用下的减震效果,研究了设置黏滞阻尼器的环带桁架在超高层建筑中的较优位置和减震效率。结果表明：黏滞阻尼器在伸臂桁架结构中的设置可以减小核心筒剪力墙的塑性损伤,减小结构的动力响应;设置黏滞阻尼器的环带桁架宜布置在层间相对速度大的位置,随超高层结构高度增加,阻尼器的减震效率降低。通过对伸臂桁架与外框柱、核心筒连接节点的设计及构造的分析,提出了连接节点的设计建议。     

Two-stage damage diagnosis approach for steel braced space frame structures

In order to diagnose the location and extent of damage in steel braced space frame structures, a two-stage damage diagnosis approach is proposed. This approach is comprised of the damage locating vectors method and eigensensitivity analysis. By deriving formulas used to calculate characterizing stresses in space frame members, and by defining characterizing stresses in connections, the damage locating vectors method is extended to locate damage in space frame members and connections. In addition, the simplified calculation of modal mass-normalization constants for damaged structures is improved. The first- and second-order sensitivities of the modal parameter discrepancies with respect to the structural model parameters and the stiffness matrix of beam elements with one damaged end are utilized. To verify the effectiveness of the proposed approach, numerical simulation analysis and experimental testing of a steel braced space frame model are performed. Ten and seven damage patterns are simulated in the numerical example and experimental testing, respectively. Modal parameters of the undamaged and damaged structures are extracted from the acceleration data using the natural excitation technique (NExT) and the eigensystem realization algorithm (ERA). The extended damage locating vectors method is utilized to determine potentially damaged elements. Based on the identified modal information, the extent of damage of the potentially damaged elements is estimated using the second-order eigensensitivity analysis. It is demonstrated that the two-stage damage diagnosis approach is effective when the damage of the members or connections in steel braced space frame structures reaches a certain level.