Evolution of modal characteristics of a mid-rise cold-formed steel building during construction and earthquake testing

Vibration-based structural identification is an essential technique for assessing structural conditions by inferring information from the dynamic characteristics of structures. However, the robustness of such techniques in monitoring the progressive damage of real structures has been validated with only a handful of research efforts, largely due to the paucity of monitoring data recorded from damaged structures. In a recent experimental program, a mid-rise cold-formed steel building was constructed at full scale atop a large shake table and subsequently subjected to a unique multi-hazard scenario including earthquake, post-earthquake fire, and finally post-fire earthquake loading. Complementing the simulated hazard events, low-amplitude vibration tests, including ambient vibrations and white noise base excitation tests, were conducted throughout the construction and the test phases. Using the vibration data collected during the multi-hazard test program, this paper focuses on understanding the modal characteristics of the cold-formed steel building in correlation with the construction and the structural damage progressively induced by the simulated hazard events. The modal parameters of the building (i.e., natural frequencies, damping ratios, and mode shapes) are estimated using two input–output and two output-only time-domain system identification techniques. Agreement between the evolution of modal parameters and the observations of the progression of physical damage demonstrates the effectiveness of the vibration-based system identification techniques for structural condition monitoring and damage assessment.     

Automatic modal parameter identification of high arch dams: feasibility verification

Modal parameters, including fundamental frequencies, damping ratios, and mode shapes, could be used to evaluate the health condition of structures. Automatic modal parameter identification, which plays an essential role in realtime structural health monitoring, has become a popular topic in recent years. In this study, an automatic modal parameter identification procedure for high arch dams is proposed. The proposed procedure is implemented by combining the density-based spatial clustering of applications with noise (DBSCAN) algorithm and the stochastic subspace identification (SSI). The 210-m-high Dagangshan Dam is investigated as an example to verify the feasibility of the procedure. The results show that the DBSCAN algorithm is robust enough to interpret the stabilization diagram from SSI and may avoid outline modes. This leads to the proposed procedure obtaining a better performance than the partitioned clustering and hierarchical clustering algorithms. In addition, the errors of the identified frequencies of the arch dam are within 4%, and the identified mode shapes are in agreement with those obtained from the finite element model, which implies that the proposed procedure is accurate enough to use in modal parameter identification. The procedure is feasible for online modal parameter identification and modal tracking of arch dams.

     

曲率模态小波法用于网壳结构损伤的识别和定位

工程结构损伤的识别与定位研究以往主要针对梁、框架等结构形式,根据大跨度空间结构杆件和节点繁多等特点,提出用曲率模态和小波混合方法对空间结构的损伤进行识别和定位.以跨度100 m的Schwedler网壳结构损伤前、后的曲率模态作为标识量,分别通过离散和连续小波变换,判断网壳结构有无损伤和损伤位置,统计了小波系数差与结构损伤的图形关系,计算了各种损伤工况下该方法判断损伤的准确程度.结果发现基于曲率模态和小波方法的大跨度网壳结构损伤定位精度很高,充分证明该方法对此类结构损伤定位具有有效性和实用性.     

Uncertainty analysis of strain modal parameters by Bayesian method using frequency response function

Structural strain modes are able to detect changes in local structural performance, but errors are inevitably intermixed in the measured data. In this paper, strain modal parameters are considered as random variables, and their uncertainty is analyzed by a Bayesian method based on the structural frequency response function (FRF). The estimates of strain modal parameters with maximal posterior probability are determined. Several independent measurements of the FRF of a four-story reinforced concrete frame structural model were performed in the laboratory. The ability to identify the stiffness change in a concrete column using the strain mode was verified. It is shown that the uncertainty of the natural frequency is very small. Compared with the displacement mode shape, the variations of strain mode shapes at each point are quite different. The damping ratios are more affected by the types of test systems. Except for the case where a high order strain mode does not identify local damage, the first order strain mode can provide an exact indication of the damage location.     

基于应变模态的结构损伤定位方法

针对简支梁的单一位置及其多位置损伤，利用结构有限元分析软件计算得到简支梁的位移模态，再通过应变和位移之间具有一阶导数的关系，对简支梁进行了应变模态分析。结果表明，应变模态对损伤比较敏感而位移模态对损伤不够敏感；当损伤发生在应变模态的节点处时，损伤不易被识别，但是可以结合多阶应变模态进行损伤识别。最后对应变模态法的工程实用性进行了评价。     

Dynamic characterization of a long span bridge: A finite element based approach

Aging bridges coupled with increasing traffic loads are producing a severe toll on the nation's infrastructure. This has made it necessary to take a closer look at the health of existing bridges and develop automated damage identification methods if possible. Recent works in the field of structural dynamics have shown that damage detection techniques utilizing parameters like mode shapes, modal frequencies and damping ratios can be used to identify damage in structural systems. It is, however, important to be able to establish a baseline model for the structure first, and then a model updating technique can be utilized to evaluate the condition of the structure from time to time. It is with this goal in mind that the authors have decided to establish the process for obtaining a baseline model for a long span bridge. Based on the actual design drawings of a bridge, finite element (FE) models of the bridge in question are developed using SDRC-IDEAS. Three models of the bridge are simulated using Normal Mode Dynamics solver in SDRC-IDEAS to obtain the modal parameters of interest, in this case the modal frequencies and the mode shapes. A modal assurance criteria (MAC) is utilized to compare the different simulated mode shapes and, finally, the modal frequencies that have been obtained from the FE analysis are compared to frequencies that have been obtained from some preliminary field tests.     

基于摄动有限元方法对梁结构损伤的识别

结构损伤的定量识别是工程技术中急待解决的问题。利用矩阵摄动和结构有限元动力学理论推出梁结构损伤程度定量识别的公式和方法,该方法仅需要在役结构的固有频率测量值就可识别结构的损伤位置和损伤程度,而且可以识别结构的老化程度,避免了由模态振型识别损伤,因测量自由度不足带来的误差,通过对一钢悬臂梁损伤识别的数值仿真,证明了该方法的有效性。该方法具有较大的工程应用价值。     

基于类柔度差曲率和频率摄动的结构损伤识别

为提高梁式结构损伤诊断的效率,提出一种基于类柔度差曲率和频率摄动的结构损伤识别方法。首先根据结构振动理论,研究广义柔度矩阵计算公式;再利用模态柔度对结构损伤灵敏性高的优点,改进基于柔度差曲率的损伤定位指标,定义类柔度差曲率LCFC损伤指标,并初步识别损伤;最后基于矩阵摄动进行结构损伤识别结果确认。考虑多种损伤工况,对一简支梁结构进行损伤识别数值模拟验证。结果表明:仅使用一阶模态,建立的类柔度差曲率LCFC指标对梁式结构损伤定位具有良好的诊断效果,且计算工作量小;对于含边界损伤单元的多损伤工况,当损伤程度大于10%时,LCFC指标识别有效;当损伤程度不大于25%时,各工况二阶摄动识别结果精度较高,相对误差较一阶摄动结果明显降低,证明了该方法的实用性、有效性和精确性。     

Algorithms for time synchronization of wireless structural monitoring sensors

Dense networks of wireless structural health monitoring systems can effectively remove the disadvantages associated with current wire‐based sparse sensing systems. However, recorded data sets may have relative time‐delays due to interference in radio transmission or inherent internal sensor clock errors. For structural system identification and damage detection purposes, sensor data require that they are time synchronized. The need for time synchronization of sensor data is illustrated through a series of tests on asynchronous data sets. Results from the identification of structural modal parameters show that frequencies and damping ratios are not influenced by the asynchronous data; however, the error in identifying structural mode shapes can be significant. The results from these tests are summarized in Appendix A. The objective of this paper is to present algorithms for measurement data synchronization. Two algorithms are proposed for this purpose. The first algorithm is applicable when the input signal to a structure can be measured. The time‐delay between an output measurement and the input is identified based on an ARX (auto‐regressive model with exogenous input) model for the input–output pair recordings. The second algorithm can be used for a structure subject to ambient excitation, where the excitation cannot be measured. An ARMAV (auto‐regressive moving average vector) model is constructed from two output signals and the time‐delay between them is evaluated. The proposed algorithms are verified with simulation data and recorded seismic response data from multi‐story buildings. The influence of noise on the time‐delay estimates is also assessed. Copyright © 2004 John Wiley & Sons, Ltd.     

基于模态曲率法的大跨度斜拉桥损伤识别

大跨度斜拉桥是重要的交通结构,研究其在主梁损伤条件下的损伤定位问题具有重要的工程价值。合理选择设计参数并对其进行敏感性分析,根据现场实测的桥梁动力特性数据,通过调整选定的设计参数对初始的有限元模型进行修正。在基准有限元模型的基础上,通过模拟不同位置和不同程度的主梁损伤,探讨了模态曲率法对结构损伤识别的有效性。结果表明,模态曲率法能够对大跨斜拉桥进行初步的损伤定位,确定主梁单处损伤和多处损伤的损伤位置;对于单处损伤,在噪声水平3%的情况下仍具有较好的适用性。从而为后期更为精确的桥梁结构损伤检测提供依据。     

环境激励下基于波动能量法的结构损伤识别

目前作为结构健康监测系统核心的损伤识别大多是基于模态参数变化而进行的,但模态参数对局部损坏不敏感,导致损伤识别精度不够。波在结构中的传播状态可以更好地反映局部损伤状况,波动能量可以作为损伤识别的有效指标。为了提高环境激励下结构损伤识别的精度,采用S变换分析了结构输出信号,建立波动能量指标,从而使波动能量指标的使用领域扩展到非平稳信号范围。最后通过三层钢框架试验及弹性分层剪切梁的数值模型对该方法进行了验证,结果表明:该方法不仅能够有效识别结构损伤位置,而且能够识别出损伤程度。     

A Taylor basis for kinematic nonlinear real-time simulations. Part II: The Taylor basis

Real-time simulations are used to a significant extent in many engineering fields. However, if nonlinearities are included, the real-time requirement significantly limits the size and complexity of numerical models. The present work constitutes the second of two papers where a general basis method to simulate kinematic nonlinear structures more efficiently is introduced. The advantage of the basis formulation is that it enables the number of basis vectors to be increased without increasing the number of unknown basis co-ordinates. This allows for larger numerical kinematically nonlinear models to run in real time. The basis is organized from a Taylor series that includes the system mode shapes and their complete first-order modal derivatives derived in Part I. The Taylor series predicts fixed linear relations between the modal co-ordinates of the system mode shapes and the modal derivatives, respectively. Thus, the full solution is known solely by determining the modal co-ordinates of the mode shapes, which significantly minimizes the computational costs. Furthermore, it is illustrated that the stability of the Taylor basis formulation is dependent on the mode shape frequencies only, allowing the applied time steps to be significantly larger than in standard nonlinear basis analysis. An example illustrates a case where the computational time can be decreased by one order of magnitude using a Taylor basis formulation compared with a standard basis formulation including identical basis vectors.     

Rotation effects on measurements of lateral motion

Inertial transducers that measure horizontal movement are affected by rotation of the measurement location. In this paper, the effect of rotation is expressed quantitatively as a fraction of the translational signal amplitude and is shown to depend inversely on the effective radius of rotation of the measurement location and the square of the frequency component of the signal. Correction procedures are presented for various cases that arise in the determination of modal amplitudes and mode shapes for tower structures, suspension bridges and frame building structures. Specific numerical results are included for the CN Tower and the Commerce Court Building in Toronto, Canada, and the Lions' Gate Suspension Bridge in Vancouver, British Columbia. Rotational effects on signals obtained from horizontal transducers can be significant for very low frequency tower structures and suspension bridges, but are not likely to be of importance for frame buildings.     

Bridge health monitoring system based on vibration measurements

A bridge health monitoring system is presented based on vibration measurements collected from a network of acceleration sensors. Sophisticated structural identification methods, combining information from the sensor network with the theoretical information built into a finite element model for simulating bridge behavior, are incorporated into the system in order to monitor structural condition, track structural changes and identify the location, type and extent of damage. This work starts with a brief overview of the modal and model identification algorithms and software incorporated into the monitoring system and then presents details on a Bayesian inference framework for the identification of the location and the severity of damage using measured modal characteristics. The methodology for damage detection combines the information contained in a set of measurement modal data with the information provided by a family of competitive, parameterized, finite element model classes simulating plausible damage scenarios in the structure. The effectiveness of the damage detection algorithm is demonstrated and validated using simulated modal data from an instrumented R/C bridge of the Egnatia Odos motorway, as well as using experimental vibration data from a laboratory small-scaled bridge section.     

Response‐only modal identification of structures using strong motion data

Dynamic characteristics of structures — viz. natural frequencies, damping ratios, and mode shapes — are central to earthquake‐resistant design. These values identified from field measurements are useful for model validation and health‐monitoring. Most system identification methods require input excitations motions to be measured and the structural response; however, the true input motions are seldom recordable. For example, when soil–structure interaction effects are non‐negligible, neither the free‐field motions nor the recorded responses of the foundations may be assumed as ‘input’. Even in the absence of soil–structure interaction, in many instances, the foundation responses are not recorded (or are recorded with a low signal‐to‐noise ratio). Unfortunately, existing output‐only methods are limited to free vibration data, or weak stationary ambient excitations. However, it is well‐known that the dynamic characteristics of most civil structures are amplitude‐dependent; thus, parameters identified from low‐amplitude responses do not match well with those from strong excitations, which arguably are more pertinent to seismic design. In this study, we present a new identification method through which a structure's dynamic characteristics can be extracted using only seismic response (output) signals. In this method, first, the response signals’ spatial time‐frequency distributions are used for blindly identifying the classical mode shapes and the modal coordinate signals. Second, cross‐relations among the modal coordinates are employed to determine the system's natural frequencies and damping ratios on the premise of linear behavior for the system. We use simulated (but realistic) data to verify the method, and also apply it to a real‐life data set to demonstrate its utility. Copyright © 2012 John Wiley & Sons, Ltd.     

Damage detection on framed structures: modal curvature evaluation using Stockwell Transform under seismic excitation

The key parameters for damage detection and localization are eigenfrequencies, related equivalent viscous damping factors and mode shapes. The classical approach is based on the evaluation of these structural parameters before and after a seismic event, but by using a modern approach based on time-frequency transformations it is possible to quantify these parameters throughout the ground shaking phase. In particular with the use of the S-Transform, it is possible to follow the temporal evolution of the structural dynamics parameters before, during and after an earthquake. In this paper, a methodology for damage localization on framed structures subjected to strong motion earthquakes is proposed based on monitoring the modal curvature variation in the natural frequency of a structure. Two examples of application are described to illustrate the technique: Computer simulation of the nonlinear response of a model, and several laboratory(shaking table) tests performed at the University of Basilicata(Italy). Damage detected using the proposed approach and damage revealed via visual inspections in the tests are compared.     

Improved dynamic correction method in seismic analysis of both classically and non‐classically damped structures

A step‐by‐step approximate procedure taking into consideration high‐frequency modes, usually neglected in the modal analysis of both classically and non‐classically damped structures, is presented. This procedure can be considered as an extension of traditional modal correction methods, like the mode‐acceleration method and the dynamic correction method, which are very effective for structural systems subjected to forcing functions described by analytical laws. The proposed procedure, herein called improved dynamic correction method, requires two steps. In the first step, the number of differential equations of motion are reduced and consequently solved by using the first few undamped mode‐shapes. In the second step, the errors due to modal truncation are reduced by correcting the dynamic response and solving a new set of differential equations, formally similar to the original differential equations of motion. The difference between the two groups of differential equations lies in the forcing vector, which is evaluated in such a way as to correct the effects of modal truncation on applied loads. Copyright © 2001 John Wiley & Sons, Ltd.     

Monitoring of structural systems by using frequency data

The present work evaluates the possibility of using dynamic data to assess structural integrity. It addresses the problem of understanding when it is sufficient to measure and use only natural frequencies, thus avoiding the need to measure modal shapes. The classic problem of detecting damage in beams, or beam assemblies, due to concentrated cracks, or damage spread over a structural member is dealt with. Damage is represented as a decrease in stiffness and linear behaviour before and after the event assumed to have caused damage is considered. Damage is restricted to a few unknown sections or elements, so that only the modification of few parameters of the system need to be determined. This study thus rejects assumptions unrelated to the physical aspects of the problem, in contrast to many papers on the subject. The amount of data to locate and quantify damage correctly is discussed; general considerations lead to the conclusion that a unique and reliable estimate of the damage can be obtained using only few additional frequency data with respect to the number of damaged zones. Continuous and discrete (finite element) models are examined. Finally the paper considers the applications to both analytical and experimental data of the procedure developed, which takes account of the peculiar characteristics of damage detection problem. Copyright © 1999 John Wiley & Sons, Ltd.     

Modal identification of a centrifuge soil model using subspace state space method

In this paper, modal parameters of a layered soil system comprising of a soft clay layer overlying a dense sand layer are identified from accelerometer recordings in a centrifuge test. For the first time, the subspace state space system identification (4SID) method was employed to identify the natural frequencies, damping ratios, and complex valued mode shapes while considering the non-proportional damping in a soil system. A brief review of system identification concepts needed for application of the 4SID techniques to structural modal identification is provided in the paper. The identified natural frequencies were validated against those estimated by transfer function spectra. The computed normal mode shapes were compared with closed-form solutions obtained from the one-dimensional shear wave propagation equation. The identified modal parameters were then employed to synthesize state space prediction models which were subsequently used to simulate the soil response to three successive base motions. The identified models captured acceleration time-histories and corresponding Fourier spectra reasonably well in the small and moderate shaking events. In the stronger third shaking event, the model performed well at greater soil depths, but was less accurate near the surface where nonlinearities dominated.     

Modeling of environmental influence in structural health assessment for reinforced concrete buildings

One branch of structural health monitoring (SHM) utilizes dynamic response measurements to assess the structural integrity of civil infrastructures. In particular,modal frequency is a widely adopted indicator for structural damage since its square is proportional to structural stiffness. However,it has been demonstrated in various SHM projects that this indicator is substantially affected by fluctuating environmental conditions. In order to provide reliable and consistent information on the health status of the monitored structures,it is necessary to develop a method to filter this interference. This study attempts to model and quantify the environmental influence on the modal frequencies of reinforced concrete buildings. Daily structural response measurements of a twenty-two story reinforced concrete building were collected and analyzed over a one-year period. The Bayesian spectral density approach was utilized to identify the modal frequencies of this building and it was clearly seen that the temperature and humidity fluctuation induced notable variations. A mathematical model was developed to quantify the environmental effects and model complexity was taken into consideration. Based on a Timoshenko beam model,the full model class was constructed and other reduced-order model class candidates were obtained. Then,the Bayesian modal class selection approach was employed to select the one with the most suitable complexity. The proposed model successfully characterizes the environmental influence on the modal frequencies. Furthermore,the estimated uncertainty of the model parameters allows for assessment of the reliability of the prediction. This study not only improves the understanding about the monitored structure,but also establishes a systematic approach for reliable health assessment of reinforced concrete buildings.