Statistical significance of modal parameters of bridge systems identified from strong motion data

Modal parameters of structural systems have commonly been determined using system identification (SI) methods for damage detection and health monitoring. For determining the deterioration of the integrity of structural systems correctly, modal parameters of a healthy structure have to be obtained with adequate certainty so that these parameters can be used as reliable references for the healthy system to compare with those of the damaged system. In this study, the statistical significance of modal parameters identified using strong motion time histories recorded on two bridge structures is assessed. The confidence intervals of identified modal frequencies and damping ratios are obtained using Monte Carlo simulations and sensitivity analyses in conjunction with eigenrealization algorithm. The dependence of the statistical bounds on model parameters is examined. The effect of using different number of sensors on the statistical significance is evaluated using simulated time history data from a validated finite element model of a bridge. Copyright © 2005 John Wiley & Sons, Ltd.     

基于响应面的预应力混凝土桥动力有限元模型研究

建立了基于正交实验的响应面模型和精细有限元模型,并将其用于中华大桥的有限元模型修正,通过实测动力数据对修正后的有限元模型计算结果进行了验证。基于修正后的有限元模型,分析了预应力对预应力钢筋混凝土桥梁模态信息（频率和振型）的影响,以及单元类型对桥梁模态频率的影响。结果表明,修正后的有限元模型能够比较准确地反映桥梁实际结构的动力特性,基于响应面模型和遗传算法的修正方法可有效地用于大桥的健康监测和状态评估;预应力对预应力钢筋混凝土桥梁模态信息的影响较小,建模时可不予精确考虑;对于由多根预应力混凝土梁组成的桥梁体系,采用实体单元分析较好。     

Analysis of the observed seismic response of a highway bridge

Strong-motion accelerograms obtained on the San Juan Bautista 156/101 Separation Bridge during the 6 August 1979 Coyote Lake, California, earthquake are used to examine the response of this multiple-span bridge to moderate levels of earthquake loading. Although the bridge was not damaged, the records are of significant engineering interest as they are the first to be recorded on a highway bridge structure in North America. A technique of system identification is used to determine optimal modal parameters for linear models which can closely replicate the observed time-domain seismic response of the bridge. Time variations in frequency and damping in the horizontal response are identified using a moving-window analysis. A three-dimensional finite element model is developed to study the bridge response in detail. The first two horizontal modal frequencies computed from this model are in excellent agreement with information obtained during the system identification analysis provided the finite element model's expansion joints are locked, preventing relative translational motions from occurring across the joints. Locking is confirmed by the observed seismic deformations of the structure in the fundamental mode. Fundamental vertical frequencies of the individual spans, predicted by the finite element model, are in very good agreement with ambient vibration test data.     

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.     

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.     

基于双层深度置信网络的梁桥结构损伤识别方法研究

为高效准确识别桥梁结构损伤,将深度学习与结构动力特性相结合,提出基于双层深度置信网络的桥梁结构损伤识别方法。首先取结构前3阶竖向振动频率和跨中节点前3阶竖向振动模态位移为参数,将其共同作为首层深度置信网络(DBN)的输入数据对结构的损伤位置进行识别;然后以1阶竖向振动的模态位移差作为参数,基于二层DBN对结构损伤程度进行预测;最后以郑许市域铁路桥梁为例进行验证。计算结果显示,当不考虑误差时,基于双层深度置信网络的结构损伤方法进行识别且结果精确;当噪声程度不超过10%时,定位识别结果准确率达100%;当噪声程度不超过15%时,定量识别结果最大绝对误差限不超过1.15%,识别结果准确;与传统的BP神经网络方法相比,本方法识别精度更高,抗噪性更强。     

大跨度预应力混凝土连续刚构桥的动力特性分析

介绍了福建泉州后渚大桥——大跨度预应力混凝土连续刚构桥的现场环境振动实验．并利用频域中的单模态识别法(SDOFI)、峰值法(PP)和时域中的随机子空间识别法(SSI)分别进行桥梁动力特性识别。利用ANSYS建立了全桥三维有限元模型并进行了理论模态分析,基于参数分析和环境振动测试结果对有限元模型进行了标定,建立了该桥的基准有限元模型,该模型可服务于桥梁长期健康监测与状态评估。     

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。     

Damage identification of a 3D full scale steel–concrete composite structure with partial‐strength joints at different pseudo‐dynamic load levels

Partial‐strength composite steel–concrete moment‐resisting (MR) frame structures represent an open research field in seismic design from both a theoretical and an experimental standpoint. Among experimental techniques, vibration testing is a well‐known and powerful technique for damage detection, localization and quantification, where actual modal parameters of a structure at different states can be determined from test data by using system identification methods. However, the identification of semi‐rigid connections in framed structures is limited, and hence this paper focuses on a series of vibration experiments that were carried out on a realistic MR frame structure, following the application of pseudo‐dynamic and quasi‐static cyclic loadings at the European laboratory for structural assessment of the Joint Research Centre at Ispra, Italy, with the scope of understanding the structural behaviour and identifying changes in the dynamic response. From the forced vibration response, natural frequencies, damping ratios, modal displacements and rotations were extracted using the circle fitting technique. These modal parameters were used for local and global damage identification by updating a 3D finite element model of the intact structure. The identified results were then correlated with observations performed on the structure to understand further the underlying damage mechanisms. Finally, the latin hypercube sampling technique, a variant of the Monte Carlo method, was employed in order to study the sensitivity of the updated parameters of the 3D model to noise on the modal inputs. Copyright © 2009 John Wiley & Sons, Ltd.     

润扬斜拉桥有限元模拟及模态分析

本文主要研究润扬长江大桥北汊斜拉桥以结构健康监测和状态评估为目标的空间有限元模型建立过程中的一些基础性问题。在建模过程中,尽可能多地考虑了一些影响全桥有限元模型精度的因素:如斜拉索的几何非线性(重力垂度和初始应力),将构造正交各向异性钢箱梁桥面板用复合材料力学的方法等效为物理正交各向异性板等。然后应用所建立的有限元模型进行模态分析,最后将有限元模态计算结果与环境振动试验结果进行比较,验证了润扬斜拉桥有限元模型的有效性。由此建立的有限元模型可以为该桥的结构健康监测和状态评估提供分析的基础。     

Two‐stage damage detection algorithms of structure using modal parameters identified from recursive subspace identification

Structural damage assessment under external loading, such as earthquake excitation, is an important issue in structural safety evaluation. In this regard, appropriate data analysis and feature extraction techniques are required to interpret the measured data and to identify the state of the structure and, if possible, to detect the damage. In this study, the recursive subspace identification with Bona‐fide LQ renewing algorithm (RSI‐BonaFide‐Oblique) incorporated with moving window technique is utilized to identify modal parameters such as natural frequencies, damping ratios, and mode shapes at each instant of time during the strong earthquake excitation. From which the least square stiffness method (LSSM) combined with the model updating technique, called efficient model correction method (EMCM), is used to estimate the first‐stage system stiffness matrix using the simplified model from the previously identified modal parameters (nominal model). In the second stage, 2 different damage assessment algorithms related to the nominal system stiffness matrix were derived. First, the model updating technique, called EMCM, is applied to correct the nominal model by the newly identified modal parameters during the strong motion. Second, the element damage index can be calculated using element damage index method (EDIM) to quantify the damage extent in each element. Verification of the proposed methods through the shaking table test data of 2 different types of structures and a building earthquake response data is demonstrated to specify its corresponding damage location, the time of occurrence during the excitation, and the percentage of stiffness reduction.     

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.     

苏通大桥结构健康状态评估技术研究与应用（3）：主梁损伤定位

为提高基于模态参数的损伤识别方法的损伤敏感性和噪声鲁棒性,将多源数据融合技术引入到苏通大桥主梁损伤定位方法中。基于D-S证据理论对模态柔度和模态应变能指标进行数据融合,并以苏通大桥扁平钢箱梁为分析对象,对融合后损伤定位指标的应用效果进行了讨论。结果表明：基于数据融合的损伤定位方法具有较强的损伤敏感性,只需要较少的低阶模态信息就能识别主梁的早期损伤;数据融合后,损伤定位指标可以在较强的噪声环境下准确地识别斜拉桥钢箱梁的损伤,具有较好的工程实用性。     

Vibration‐based damage assessment of steel structure using global and local response measurements

Damage assessment of a structure involves acquiring and identifying dynamic characteristics of the structure and using these characteristics to evaluate behavior and performance. In this study, an unsymmetrical three‐story steel structure (fabricated with one weak column in the first floor) was tested on shaking table and subjected to a series of earthquake excitations with increasing level of excitation back to back. Besides, white noise excitation was also applied in between the earthquake excitation to serve as the reference state. Both the traditional sensing system (accelerometer and linear variable differential transformer) and the local optical tracker system were implemented in the structure to collect the vibration‐based responses. For operational modal analysis, structural response from white noise excitation will be used in this study. First, the traditional system identification using global response data is used (multivariate autoregressive (AR)‐model) to extract system natural frequencies and mode shapes from all different set of white noise responses after earthquake excitation. The migration of AR‐coefficient ellipse error from each sensor response was used to identify the damage location. Second, blind source separation technique was used to identify the modal contribution of the structure from each test, which provide information to detect the damage severity. Finally, from the local optical tracker array data, the principal component analysis was applied to quantify the earthquake‐induce local stress of the structural member. Combine the result from damage detection using global measurement and the identified local element stress, one can locate and quantify the damage. Copyright © 2015 John Wiley & Sons, Ltd.     

基于高斯曲率模态相关系数的梁桥支座损伤识别研究

为方便地检测梁桥支座损伤,提出了利用运营桥梁实测模态位移结合其无损状态的模态位移判断支座损伤的高斯曲率模态相关系数法。通过简支梁桥的室内试验,验证了利用高斯曲率模态相关系数判定支座损伤的合理性以及该方法中无损状态下的模态位移可以通过模态试验和有限元模拟两种方法获得。利用该方法对实际简支梁桥和连续梁桥进行的支座损伤识别结果表明:高斯曲率模态相关系数法可准确识别出单支座和多支座损伤的支座损伤位置,具有较强的鲁棒性,可将此方法应用于实际工程中的支座损伤识别。     

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.     

Rapid evaluation and damage assessment of instrumented highway bridges

This study focuses on the use of strong motion data recorded during earthquakes and aftershocks to provide a preliminary assessment of the structural integrity and possible damage in bridges. A system identification technique is used to determine dynamical characteristics and high‐fidelity first‐order linear models of a bridge from low level earthquake excitations. A finite element model is developed and updated using a genetic algorithm optimization scheme to match the frequencies identified and to simulate data from a damaging earthquake for the bridge. Here, two criteria are used to determine the state of the structure. The first criteria uses the error between the data recorded or simulated by the calibrated nonlinear finite element model and the data predicted by the linear model. The second criteria compares relative displacements of the structure with displacement thresholds identified using a pushover analysis. The use of this technique can provide an almost immediate, yet reliable, assessment of the structural health of an instrumented bridge after a seismic event. Copyright © 2011 John Wiley & Sons, Ltd.     

Damage identification of structures with uncertain frequency and mode shape data

A statistical method with combined uncertain frequency and mode shape data for structural damage identification is proposed. By comparing the measured vibration data before damage or analytical finite element model of the intact structure with those measured after damage, the finite element model is updated so that its vibration characteristic changes are equal to the changes in the measured data as closely as possible. The effects of uncertainties in both the measured vibration data and finite element model are considered as random variables in model updating. The statistical variations of the updated finite element model are derived with perturbation method and Monte Carlo technique. The probabilities of damage existence in the structural members are then defined. The proposed method is applied to a laboratory tested steel cantilever beam and frame structure. The results show that all the damages are identified correctly with high probabilities of damage existence. Discussions are also made on the applicability of the method when no measurement data of intact structure are available. Copyright © 2002 John Wiley & Sons, Ltd.     

佛开高速九江大桥模态测试与分析

对主跨为160m的预应力砼变截面连续梁桥佛开高速九江大桥进行了理论与实验模态分析．首先介绍了环境激励条件下现场模态测试布置及过程,利用随机子空间法（SSI）进行了桥梁模态参数识别．建立了桥梁有限元模型．并对理论和实验模态分析结果进行了比较和讨论。实验与有限元计算结果在竖向模态频率及振型上总体吻合较好。测试结果可以为有限元模型修正提供依据：模态测试与有限元分析相结合．可以为桥梁长期健康监测和损伤评估提供较可靠的基准模型。