System identification applied to long‐span cable‐supported bridges using seismic records

This paper presents the application of system identification (SI) to long‐span cable‐supported bridges using seismic records. The SI method is based on the System Realization using Information Matrix (SRIM) that utilizes correlations between base motions and bridge accelerations to identify coefficient matrices of a state‐space model. Numerical simulations using a benchmark cable‐stayed bridge demonstrate the advantages of this method in dealing with multiple‐input multiple‐output (MIMO) data from relatively short seismic records. Important issues related to the effects of sensor arrangement, measurement noise, input inclusion, and the types of input with respect to identification results are also investigated. The method is applied to identify modal parameters of the Yokohama Bay Bridge, Rainbow Bridge, and Tsurumi Fairway Bridge using the records from the 2004 Chuetsu‐Niigata earthquake. Comparison of modal parameters with the results of ambient vibration tests, forced vibration tests, and analytical models are presented together with discussions regarding the effects of earthquake excitation amplitude on global and local structural modes. Copyright © 2007 John Wiley & Sons, Ltd.     

Dynamic performance of twin curved cable‐stayed bridges

The dynamic behaviour of two curved cable‐stayed bridges, recently constructed in northern Italy, has been investigated by full‐scale testing and theoretical models. Two different excitation techniques were employed in the dynamic tests: traffic‐induced ambient vibrations and free vibrations. Since the modal behaviour identified from the two types of test are very well correlated and a greater number of normal modes was detected during ambient vibration tests, the validity of the ambient vibration survey is assessed in view of future monitoring. For both bridges, 11 vibration modes were identified in the frequency range of 0ndash;10Hz, being a one‐to‐one correspondence between the observed modes of the two bridges. Successively, the information obtained from the field tests was used to validate and improve 3D finite elements so that the dynamic performance of the two systems were assessed and compared based on both the experimental results and the updated theoretical models. Copyright © 2003 John Wiley & Sons, Ltd.     

Vibration characteristics of a suspension bridge under traffic and no traffic conditions

This paper presents the variations of vibration under different traffic conditions on the Fatih Sultan Mehmet suspension bridge in Istanbul, Turkey.The main intention is to determine the vibration amplifications under heavy-traffic as opposed to no-traffic conditions. This is the first study in this particular area that has been performed on this bridge, over which an average of 200,000 cars pass daily. Two full-scale ambient vibration surveys were carried out on two different days to determine the response of the bridge to diverse traffic conditions. Initial measurements were taken as the bridge experienced heavy stress conditions caused by rush-hour traffic. Secondary measurements were recorded after closing the bridge to traffic. The data were analyzed to gauge the vibration effects of heavy-traffic conditions on the bridge and to determine the effects of different traffic conditions on the free vibration characteristics of the bridge. The analyses were performed utilizing different amplification methods. Results show that there are important differences in the amplifications of the vibration amplitudes. Especially heavy-traffic on the bridge causes the vibration response of the bridge to be intensified in comparison to no-traffic conditions. Additionally, predominant frequencies are shifted as a direct result of traffic load acting on the bridge. Even more importantly and is probably analogous for all long-span bridges, is the fact that any movement causing vibration on the bridge is carried and amplified along its length. These significant amplifications indicate the important effect of varying traffic loads and how the bridge responds to the diverse movements it experiences. Copyright © 2011 John Wiley & Sons, Ltd.     

A reassessment of dynamic characteristics of the Quincy Bayview Bridge using output‐only identification techniques

A reassessment of the dynamic characteristics of the 542 m cable‐stayed Bayview Bridge in Quincy, Illinois, is presented using a newly developed output‐only system identification technique. The technique is applied to an extensive set of ambient vibration response data acquired from the bridge in 1987. Vertical, torsional and transverse modal frequencies of the deck are identified, and uncertainty in damping values are estimated using an automated procedure on several redundant measurements at four locations. Important practical implementation issues associated with the implementation of the procedure and selection of algorithm design parameters for stochastic subspace identification techniques are discussed. An overall mean and standard deviation of damping of 1.0±0.8% is estimated considering all identified vertical, torsional and transverse modes in the 0–2 Hz band. The mean damping for the fundamental vertical mode (0.37 Hz) is identified as 1.4±0.5%, and for the first coupled torsion–transverse mode (0.56 Hz) is identified as 1.1±0.8%. Variability in the damping estimates is shown to decrease as estimated modal RMS acceleration levels increase. Standard deviations on estimated damping range from 0.05% to 2%. The results are shown to be a substantial improvement in the evaluation of damping compared to earlier spectral analysis conducted on the same data set. Copyright © 2005 John Wiley & Sons, Ltd.     

Modal identification of structures from ambient vibration,free vibration,and seismic response data via a subspace approach

This work presents a unified procedure for determining the natural frequencies, modal damping ratios and modal shapes of a structure from its ambient vibration, free vibration and earthquake response data. To evaluate the coefficient matrices of a state‐space model, the proposed procedure applies a subspace approach cooperating with an instrumental variable concept. The dynamic characteristics of a structure are determined from the coefficient matrices. The feasibility of the procedure is demonstrated through processing an in situ ambient vibration measurement of a five‐storey steel frame, an impulse response measurement of a three‐span continuous bridge, and simulated earthquake responses of five‐storey steel frames from shaking table tests. The excellent agreement of the results obtained herein with those published previously confirms the feasibility of the present procedure. Copyright © 2001 John Wiley & Sons, Ltd.     

Ambient vibration measurements on a cable-stayed bridge

An extensive programme of full-scale ambient vibration tests has been conducted to measure the dynamic response of a 542 m (centre span of 274 m) cable-stayed bridge—the Quincy Bayview Bridge in Illinois. A microcomputer-based system was used to collect and analyse the ambient vibration data. A total of 25 modal frequencies and associated mode shapes were identified for the deck structure within the frequency range of 0–2 Hz. Also, estimations were made for damping ratios. The experimental data clearly indicated the occurrence of many closely spaced modal frequencies and spatially complicated mode shapes. Most tower modes were found to be associated with the deck modes, implying a considerable interaction between the deck and tower structure. No detectable levels of motion were evident at the foundation support of the pier. The results of the ambient vibration survey were compared to modal frequencies and mode shapes computed using a three-dimensional finite element model of the bridge. For most modes, the analytic and experimental modal frequencies and mode shapes compare quite well, especially for the vertical modes. Based on the findings of this study, a linear elastic finite element model appears to be capable of capturing much of the complex dynamic behaviour of the bridge with very good accuracy, when compared to the low-level dynamic responses induced by ambient wind and traffic excitations.     

Application of non‐linear multiple tuned mass dampers to suppress man‐induced vibrations of a pedestrian bridge

This paper presents an application of multiple tuned mass dampers (MTMDs) with non‐linear damping devices to suppress man‐induced vibrations of a 34m long pedestrian bridge. The damping force generated by each of these damping devices is simply a drag force from liquid acting on an immersed section. The quadratic non‐linear property of these devices was directly determined from free vibration tests of a simple laboratory set‐up. Dynamic models of the bridge and pedestrian loads were constructed for numerical investigation based on field measurement data. The control effectiveness of non‐linear MTMDs was examined along with its sensitivity against estimation errors in the bridge's natural frequency and magnitude of pedestrian load. The numerical results indicated that the optimum non‐linear MTMD system was as effective and robust as its linear counterpart. Then, a six‐unit non‐linear MTMD system was designed, constructed, and installed on the bridge. Field measurements after the installation confirmed the effectiveness of non‐linear MTMDs, and the measurement results were in good agreement with numerical predictions. After the installation, the average damping ratio of the bridge was raised from 0.005 to 0.036 and the maximum bridge accelerations measured during walking tests were reduced from about 0.80–1.30 ms^?2 to 0.27–0.40 ms^?2, which were within an acceptable range. Copyright © 2003 John Wiley & Sons, Ltd.     

基于局部测点模态测试的简支梁桥承载刚度评定试验研究

快速可靠地检测服役桥梁的承载刚度对保障道路交通线路的安全运营具有重要意义。文章提出一种基于局部测点模态测试的简支梁桥承载刚度评定方法,并以某实际工程中一座简支梁桥为试验对象,对所提方法的可行性和准确性进行验证。设计传统桥梁荷载试验的中载和偏载加载方案,测得各工况下简支梁桥跨中截面的实测静挠度,基于环境激励进行联合测点模态试验和局部测点模态试验,预测简支梁桥跨中截面的模态挠度,并结合桥梁理论挠度计算结构挠度校验系数。结果表明：中载、偏载工况下联合测点模态试验预测的跨中截面模态挠度与静载试验跨中截面实测静挠度的相对误差最大不超过5.7%,基本满足工程精度的要求;联合跨中截面测点和桥面加载点测点的联合测点模态试验能够准确评估桥梁的承载刚度;仅在跨中截面布置传感器的局部测点模态试验预测的模态挠度基本等价于联合测点模态试验预测的模态挠度,两者的相对误差小于2%,局部测点模态测试预测的跨中截面挠度校验系数与静载试验的实测挠度校验系数相比具有很好的一致性。     

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.     

Dynamic investigation of a hybrid suspension and cable‐stayed bridge

Ambient and forced vibration tests were carried out on the Beauharnois bridge, a unique, 177‐m combined suspension and cable‐stayed structure near Montreal, Canada. A rehabilitation program was completed on the bridge during which the deck was completely rebuilt with an orthotropic slab on two steel trusses. The rehabilitation program also included the addition of two pairs of stay cables on both towers, creating a hybrid suspension system. The paper presents a series of dynamic tests performed to evaluate the dynamic properties and the dynamic amplification factor (DAF) for the rehabilitated bridge. The experimental program involved the measurement of vertical, transverse, and longitudinal acceleration responses of the deck and tower under ambient and controlled traffic loads. Displacement, strain, and integrated acceleration DAFs were computed under different loading conditions. Modal properties were evaluated and used to correlate a three‐dimensional finite element model for the bridge, including non‐linear cable behaviour. The paper discusses the experimental setup as well as the techniques used to evaluate vibration frequencies, mode shapes, and the DAF. Correlation of numerical dynamic properties and experimental results is also presented. Copyright © 2000 John Wiley & Sons, Ltd.     

基于经验模式分解的随机子空间识别方法

提出了基于经验模式分解（EMD）的环境激励结构模态参数随机子空间识别（SSI）方法。该方法用设置间断频率的EMD将结构环境振动响应原始信号分解成若干个基本模式分量（IMF）,使每一个基本模式分量仅为结构的某一阶固有模态,进而用随机子空间方法进行模态参数识别。实桥环境振动实验分析结果表明,该方法能有效地避免结构各阶模态之间的相互影响,能够更清晰方便地得到结构的模态参数。     

Full‐scale dynamic response of an RC building under weak seismic motions using earthquake recordings,ambient vibrations and modelling

In countries with a moderate seismic hazard, the classical methods developed for strong motion prone countries to estimate the seismic behaviour and subsequent vulnerability of existing buildings are often inadequate and not financially realistic. The main goals of this paper are to show how the modal analysis can contribute to the understanding of the seismic building response and the good relevancy of a modal model based on ambient vibrations for estimating the structural deformation under weak earthquakes. We describe the application of an enhanced modal analysis technique (frequency domain decomposition) to process ambient vibration recordings taken at the Grenoble City Hall building (France). The frequencies of ambient vibrations are compared with those of weak earthquakes recorded by the French permanent accelerometric network (RAP) that was installed to monitor the building. The frequency variations of the building under weak earthquakes are shown to be less (∼2%) and therefore ambient vibration frequencies are relevant over the elastic domain of the building. The modal parameters extracted from ambient vibrations are then used to determine the 1D lumped‐mass model in order to reproduce the inter‐storey drift under weak earthquakes and to fix a 3D numerical model that could be used for strong earthquakes. The correlation coefficients between data and synthetic motion are close to 80 and 90% in horizontal directions, for the 1D and 3D modelling, respectively. Copyright © 2009 John Wiley & Sons, Ltd.     

Structural identification with incomplete output‐only data and independence of measured information for shear‐type systems

Structural identification is the inverse problem of estimating physical parameters of a structural system from its vibration response measurements. Incomplete instrumentation and ambient vibration testing generally result in incomplete and arbitrarily normalized measured modal information, often leading to an ill‐conditioned inverse problem and non‐unique identification results. The identifiability of any parameter set of interest depends on the amount of independent available information. In this paper, we consider the identifiability of the mass and stiffness parameters of shear‐type systems in output‐only situations with incomplete instrumentation. A mode shape expansion‐cum‐mass normalization approach is presented to obtain the complete mass normalized mode shape matrix, starting from the incomplete non‐normalized modes identified using any operational modal analysis technique. An analysis is presented to determine the minimum independent information carried by any given sensor set‐up. This is used to determine the minimum necessary number and location of sensors from the point of view of minimum necessary information for identification. The different theoretical discussions are illustrated using numerical simulations and shake table experiments. It is shown that the proposed identification algorithm is able to obtain reliably accurate physical parameter estimates under the constraints of minimal instrumentation, minimal a priori information, and unmeasured input. The sensor placement rules can be used in experiment design to determine the necessary number and location of sensors on the monitored system. John Wiley & Sons, Ltd.     

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.     

基于环境振动的斜拉桥拉索基频识别

斜拉索是现代斜拉桥最重要的结构构件，索力在斜拉桥的施工控制和长期监测中起着重要作用。振动测试法是斜拉桥索力测定、监测和状态评估中应用最广泛的一种方法。振动法测索力的关键在于准确地识别出索的基频。本文使用自功率谱和倒频谱方法，基于MATLAB平台，开发出了斜拉桥拉索环境振动模态分析图形用户交互(GUI)工具箱，实现了斜拉索基频的快速自动识别。应用本文的方法，对福州青洲闽江主跨605m斜拉桥拉索的环境振动实测加速度数据进行了分析处理，斜拉索基频识别方便直观，结果可靠。     

预应力混凝土连续梁桥振动特性变异及舒适度评价

由于预应力损失、混凝土收缩徐变、超载等原因,预应力混凝土桥梁出现了较强的振动。本文通过对福建省福州市闽江三桥全桥环境振动试验和正常运营条件下24小时的监测,研究预应力混凝土连续梁桥的动力特性及其变异和振动舒适度,结果表明:在较为稳定的风和温湿度环境下,固有频率在一天内的最大变化为3.06%,模态阻尼比的最大变化为37.93%,舒适度的狄克曼指标降到“能忍受短时间振动”的区域。     

Ambient vibration based seismic evaluation of isolated Gülburnu highway bridge

This paper describes ambient vibration based seismic evaluation procedure of an isolated highway bridge. The procedure includes finite element modeling, ambient vibration testing, finite element model updating and time history analysis. Gülburnu Highway Bridge located on the Giresun–Espiye state highway is selected as a case study. Three dimensional finite element model of the bridge is created by SAP2000 software to determine the dynamic characteristics analytically. Since input force is not measured, Operational Modal Analysis is applied to identify dynamic characteristics. Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods are used to obtain experimental dynamic characteristics. Analytical and experimental dynamic characteristic are compared with each other and finite element model of the bridge is updated by changing of material properties to reduce the differences between the results. Analytical model of the bridge after model updating is analyzed using 1992 Erzincan earthquake record to determine the seismic behavior. EW, NS and UP components of the ground motion are applied to the bridge at the longitudinal, transverse and vertical directions, respectively. It is demonstrated that the ambient vibration measurements are enough to identify the most significant modes of highway bridges. Maximum differences between the natural frequencies are reduced averagely from 9% to 2% by model updating. It is seen from the earthquake analyses that friction pendulum isolators are very effective in reducing the displacements and internal forces.     

System identification and modeling of a dynamically tested and gradually damaged 10‐story reinforced concrete building

This paper discusses the dynamic tests, system identification, and modeling of a 10‐story reinforced concrete building. Six infill walls were demolished in 3 stages during the tests to introduce damage. In each damage stage, dynamic tests were conducted by using an eccentric‐mass shaker. Accelerometers were installed to record the torsional and translational responses of the building to the induced excitation, as well as its ambient vibration. The modal properties in all damage states are identified using 2 operational modal analysis methods that can capture the effect of the wall demolition. The modal identification is facilitated by a finite element model of the building. In turn, the model is validated through the comparison of the numerically and experimentally obtained modal parameters. The validated model is used in a parametric study to estimate the influence of structural and nonstructural elements on the dynamic properties of the building and to assess the validity of commonly used empirical formulas found in building codes. Issues related to the applicability and feasibility of system identification on complex structures, as well as considerations for the development of accurate, yet efficient, finite element models are also discussed.     

Verification of system identification utilizing shaking table tests of a full‐scale 4‐story steel building

This paper verifies the feasibility of the proposed system identification methods by utilizing shaking table tests of a full‐scale four‐story steel building at E‐Defense in Japan. The natural frequencies, damping ratios and modal shapes are evaluated by single‐input‐four‐output ARX models. These modal parameters are prepared to identify the mass, damping and stiffness matrices when the objective structure is modelled as a four degrees of freedom (4DOF) linear shear building in each horizontal direction. The nonlinearity in stiffness is expressed as a Bouc–Wen hysteretic system when it is modelled as a 4DOF nonlinear shear building. The identified hysteretic curves of all stories are compared to the corresponding experimental results. The simple damage detection is implemented using single‐input‐single‐output ARX models, which require only two measurements in each horizontal direction. The modal parameters are equivalent‐linearly evaluated by the recursive Least Squares Method with a forgetting factor. When the structure is damaged, its natural frequencies decrease, and the corresponding damping ratios increase. The fluctuation of the identified modal properties is the indirect information for damage detection of the structure. Copyright © 2015 John Wiley & Sons, Ltd.     

One‐year monitoring of the Z24‐Bridge: environmental effects versus damage events

When using the analysis of vibration measurements as a tool for health monitoring of bridges, the problem arises of separating abnormal changes from normal changes in the dynamic behaviour. Normal changes are caused by varying environmental conditions such as humidity, wind and most important, temperature. The temperature may have an impact on the boundary conditions and the material properties. Abnormal changes on the other hand are caused by a loss of stiffness somewhere along the bridge. It is clear that the normal changes should not raise an alarm in the monitoring system (i.e. a false positive), whereas the abnormal changes may be critical for the structure's safety. In the frame of the European SIMCES‐project, the Z24‐Bridge in Switzerland was monitored during almost one year before it was artificially damaged. Black‐box models are determined from the healthy‐bridge data. These models describe the variations of eigenfrequencies as a function of temperature. New data are compared with the models. If an eigenfrequency exceeds certain confidence intervals of the model, there is probably another cause than the temperature that drives the eigenfrequency variations, for instance damage. Copyright © 2001 John Wiley & Sons, Ltd.