Motion-based optimum design of a slender steel footbridge and assessment of its dynamic behaviour

The improvement of construction materials together with the current aesthetic requirements has led the modern footbridges to a continuous increase in their slenderness. For this reason, the design of their structural systems is mainly conditioned by its dynamic response under pedestrian action. For long-span footbridges, control devices are needed to prevent unacceptable dynamic responses while providing economical designs. However, for medium-span footbridges, it is still possible to control their dynamic response via the modification of their natural frequencies. In this paper, an alternative motion-based design method is first proposed and further implemented for the design of a real footbridge. The main idea of this approach is to optimally determine the structural stiffness distribution to verify an adequate comfort class, while minimizing the self-weight. Furthermore, the uncertainties of its modal parameters are considered during its design. After the construction of the footbridge, its dynamic behaviour was experimentally assessed, with satisfactory results.     

A method for predicting the lateral girder response of footbridges induced by pedestrians

A numerical method is proposed to predict the lateral girder response induced by pedestrians on footbridges. The method is based on the motion of equations including the coefficients of the rate of a pedestrian’s lateral force, pedestrian density, rate of synchronized pedestrians, and pedestrians’ attitude to large vibration amplitude. These coefficients were determined by the field measured data of two slender footbridges and the experimental data of pedestrian induced forces. The lateral girder responses were then predicted for these bridges with different pedestrian densities by the proposed numerical method. They agreed reasonably well with the field measured girder responses of these bridges, which verified the proposed prediction method.     

Bemessungskonzept für fußgängerinduzierte Brückenschwingungen

Design concept for the analysis of pedestrian‐induced bridge vibration. Unexpected vibrations of footbridges, e.g. during inauguration of Millennium Bridge in London and Passerelle Solferino in Paris, have drawn engineers' attention to more accurate forecast models to determine pedestrian‐induced vibrations and especially pedestrian‐structure‐interaction of light and slightly damped footbridges in the design phase. This contribution presents a programme to simulate bridge vibrations with realistic ‘numerical pedestrians’, which is calibrated against measured response under real pedestrian loading. By means of this simulation tool observed vibrations and pedestrian‐structure‐interaction phenomena can be analysed. In a second step an engineering model based on a spectral approach is derived, which enables to determine characteristic pedestrian‐induced structural response. Hence, if necessary the design of the footbridge can be adjusted or damping measures can be planned to fulfill serviceability requirements. A design concept for the dynamic analysis of the reversible serviceability limit state, which fulfills the Eurocode requirements, is described and an innovative consideration and definition of comfort criteria are proposed.     

Serviceability assessment of footbridges in unrestricted pedestrian traffic conditions

A critical analysis of the procedures available in the literature for the serviceability assessment of footbridges in unrestricted pedestrian traffic conditions is presented. Based on a full probabilistic model of the loading, Monte Carlo simulations are carried out and a critical discussion concerning the role of the statistical distribution of the random walking parameters on the footbridge dynamic response is provided. Furthermore, numerical results are compared with the ones obtained by simplified procedures. Finally, a graphical procedure is proposed which permits a simple evaluation of footbridge maximum acceleration as a function of the modal mass, damping ratio and expected average pedestrian flow.     

Einsatz von multiplen Schwingungstilger‐Systemen an schlanken Fußgängerbrücken

The Application of Multiple Tuned Mass Damper Systems at slender footbridges. While for standard footbridge only a few vibration modes are within the critical footfall frequency range and hove to be considered for the dynamic design, lightweight structures dis‐play multiple modes in that frequency range. Furthermore the modal masses are very little so also the smaller load components for the excitation of higher harmonic vibration modes can become significant to assess the vibration susceptibility. Various observations have been made during experimental tests of these structures and will be introduced in this contribution using the example of a canopy walk structure and a stress ribbon bridge. To understand the observed effects at such continuous dynamic systems for pedestrian loading, numerical calculations have been performed for which a similar lightweight structure has been modelled and pedestrian loading was simulated with several footfall frequencies. Similar to the experimentally investigated structures it was found that the multimodal dynamic response of the bridges strongly depends on the pedestrian loading (footfall frequency). Experimental tests have shown, that the application of a Tuned Mass Damper System to dampen only the critical mode that is within the footfall frequency range is not sufficient to reduce the multi‐modal dynamic response of the lightweight bridge structures under pedestrian so the occurring accelerations remain below certain comfort levels. Therefore the concept of Multiple Tuned Mass Dampers was introduced to the bridge structure and its practicability was investigated.     

Uncertainty quantification of structural flexibility identified from input–output measurement data for reliability analysis

In contrast to the traditional uncertainty quantification of the modal parameters identified from the output-only measurement data, this study develops an uncertainty propagation and quantification method for structural flexibility identified from input–output measurement data and then uses the derived flexibility matrix for structural reliability analysis. First, a novel procedure for variance estimations of the complete system matrix of the state-space model is derived based on first-order perturbation theory. Then, the mode scaling factors and integrated modal flexibility are subsequently derived and quantified. Finally, the predicted displacements and their uncertainty intervals are used to implement the reliability analysis in terms of the structural displacement serviceability limit state (SLS). The accuracies of the derived expressions are verified by a numerical example through the comparison of variance values estimated from Monte Carlo simulations. The simulation example also indicates that we can expect to identify structural parameters with higher reliability if the input force to the structure is measured, and the identified modal scaling and corresponding flexibility matrix undergo more uncertainty than those of the modal parameters. Finally, we apply the proposed uncertainty quantification method to a scaled three-story frame structure to demonstrate its practicability. The proposed method bridges a gap between the identified structural flexibility and structural reliability analysis directly by the probability category.     

步行荷载的功率谱模型及其应用研究

基于傅里叶级数的步行荷载确定性模型，由于忽略了荷载的随机性，会高估人行桥、大跨度楼板在共振作用下的动力响应。为此，应考虑行人步行荷载的随机性，在1007条连续步行荷载记录的基础上，提出了前4阶主谐波和次谐波局部区域的功率谱建模方式。各阶谱线经行人体重、各阶能量、步行频率和阶数归一化后可统一表达为两项高斯函数之和的形式，模型中参数由试验数据统计分析得到。结合随机振动理论，给出了由步行功率谱计算楼板加速度响应的方法。通过理论计算值与10m×6m楼板模型的试验值以及火车站楼板实测对比，可知，所建议的功率谱模型的预测结果合理。     

Noncontact Operational Modal Analysis of Structural Members by Laser Doppler Vibrometer

Abstract:   A system that uses ambient vibration and two laser Doppler vibrometer (LDV) is developed for noncontact operational modal analysis of structural members. The system employs natural excitation technique (NExT) to generate the cross-correlation functions from laser signals, and the eigensystem realization algorithm (ERA) to identify modal parameters of structural members. To facilitate simultaneous modal identification, time-synchronization technique and construction of cross-correlation functions from ambient response of laser signals are proposed. Performance of the proposed system is verified experimentally by evaluating the consistency and accuracy of identification results in different measurement conditions. The work presented here is an extension of the previous study, where a modal-based damage detection method using LDV was formulated. In the present study, application of LDV for structural parameters identification of a combined dynamical system is proposed. A model that represents the connection properties in terms of additional stiffness and damping is developed, and its importance for structural damage detection is discussed. The study shows that the presence of simulated damage in a steel connection can be detected by tracking the modal phase difference and by quantifying the additional stiffness and damping .     

Operational Modal Parameter Identification from Power Spectrum Density Transmissibility

Abstract: Operational modal analysis subjected to ambient or natural excitation under operational conditions has recently drawn great attention. In this article, the power spectrum density transmissibility (PSDT) is proposed to extract the operational modal parameters of a structure. It is proven that the PSDT is independent of the applied excitations and transferring outputs at the system poles. As a result, the modal frequencies and mode shapes can be extracted by combing the PSDTs with different transferring outputs instead of different load conditions where the outputs from only one load condition are needed. A five‐story shear building subjected to a set of uncorrelated forces at different floors is adopted to verify the property of PSDTs and illustrate the accuracy of the proposed method. Furthermore, a concrete‐filled steel tubular half‐through arch bridge tested in the field under operational conditions is used as a real case study. The identification results obtained from currently developed method have been compared with those extracted from peak‐picking method, stochastic subspace identification, and finite element analysis. It is demonstrated that the operational modal parameters identified by the current technique agree well with other independent methods. The real application to the field operational vibration measurements of a full‐sized bridge has shown that the proposed PSDTs are capable of identifying the operational modal parameters (natural frequencies and mode shapes) of a structure.     

Influence of hanger system on structural behaviour of suspension footbridges under pedestrian dynamic loads

For structural safety of footbridges and for the comfort of their users, it is essential to consider the effect of human induced vibrations. In suspension footbridges, hanger systems can affect dynamic performances. In order to improve the aerodynamic stability of the footbridges, inclined hangers can be used instead of vertical ones, but inclined hangers are more liable to undergo fatigue and slackness. In this paper, a suspension footbridge with inclined hangers has been examined as a case study. To reduce internal forces, fatigue and slackness in hangers, horizontal cables have been attached to inclined hangers. These added cables may also increase the stiffness and dynamic performance of the footbridge. In this study, the dynamic characteristics of footbridges with inclined and modified hangers such as natural modes (vertical, lateral, and torsional) and frequencies, as well as the vertical and lateral accelerations of the deck have been investigated. Also, hanger parameters such as the force, slackness, overstress, and the fatigue of inclined and modified hangers have been compared. Results showed that the modified bridge demonstrates superior performance when compared with conventional ones.     

Enhanced Hilbert–Huang transform and its application to modal identification

The well‐known Hilbert–Huang transform (HHT) consists of empirical mode decomposition to extract intrinsic mode functions (IMFs) and Hilbert spectral analysis to obtain time–frequency characteristics of IMFs through the Hilbert transform. There are two mathematical requirements that limit application of the Hilbert transform. Moreover, noise effects caused by the empirical mode decomposition procedure add a scatter to derivative‐based instantaneous frequency determined by the Hilbert transform. In this paper, a new enhanced HHT is proposed in which by avoiding mathematical limitations of the Hilbert spectral analysis, an additional parameter is employed to reduce the noise effects on the instantaneous frequencies of IMFs. To demonstrate the efficacy of the proposed method, two case studies associated with structural modal identification are selected. In the first case, through identification of a typical 3‐DOF structural model subjected to a random excitation, accuracy of the enhanced method is verified. In the second case, ambient response data recorded from a real 15‐story building are analyzed, and nine modal frequencies of the building are identified. The case studies indicate that the enhanced HHT provides more accurate and physically meaningful results than HHT and is capable to be an efficient tool in structural engineering applications. Copyright © 2012 John Wiley & Sons, Ltd.     

Wind‐induced inter‐story drift analysis and equivalent static wind load for multiple targets of tall buildings

In super high‐rise buildings with varying story heights, the wind‐induced inter‐story drifts might violate the specified limit. However, these effects have seldom been concerned in wind‐induced response analysis. The theory and application of equivalent static wind load (ESWL) for wind‐induced inter‐story drifts of super high‐rise buildings were studied in this paper. A spectral decomposition method suitable for multi‐point excitation problems was firstly proposed. The formula of ESWL targeting for largest inter‐story drift was derived. For more reasonable structural design, the ESWL for multiple targets including displacement atop of building and inter‐story drifts at all story levels is put forward, in which the dominant modal inertial forces are adopted as the based load vectors. The presented methods were finally verified by its application for the wind‐induced response analysis for a tallest super tall building in Guangzhou. The researched results showed that the proposed spectral decomposition method not only has the same precision as the complete quadratic combination method but also possesses higher computation efficiency. The ESWL for multiple targets produces the same static responses for all the specified wind‐induced response, so it is much more rational for wind‐resistant structural design. Meanwhile, it is more reasonable to select the wind‐induced responses in the same direction simultaneously as the targeted values for obtaining the required ESWLs; however, the ESWL targeting for the wind‐induced responses in all degrees of freedom would generate more queer and unrealistic ESWLs distribution. Copyright © 2015 John Wiley & Sons, Ltd.     

Identification of Instantaneous Modal Parameter of Time‐Varying Systems via a Wavelet‐Based Approach and Its Application

This work presents an efficient approach using time‐varying autoregressive with exogenous input (TVARX) model and a substructure technique to identify the instantaneous modal parameters of a linear time‐varying structure and its substructures. The identified instantaneous natural frequencies can be used to identify earthquake damage to a building, including the specific floors that are damaged. An appropriate TVARX model of the dynamic responses of a structure or substructure is established using a basis function expansion and regression approach combined with continuous wavelet transform. The effectiveness of the proposed approach is validated using numerically simulated earthquake responses of a five‐storey shear building with time‐varying stiffness and damping coefficients. In terms of accuracy in determining the instantaneous modal parameters of a structure from noisy responses, the proposed approach is superior to typical basis function expansion and regression approach. The proposed method is further applied to process the dynamic responses of an eight‐storey steel frame in shaking table tests to identify its instantaneous modal parameters and to locate the storeys whose columns yielded under a strong base excitation.     

Noncontact cable force estimation with unmanned aerial vehicle and computer vision

Cables and hangers are critical components of long‐span bridges, tension forces of them are needed to be accurately measured for ensuring the safety of bridges. Traditionally, cable tension forces are measured by attached accelerometers or elastomagnetic (EM) sensors, however, applying these sensors into engineering practice are time‐consuming, labor‐intensive, and highly dangerous. To address these problems, an unmanned aerial vehicle (UAV)‐based noncontact cable force estimation method with computer vision technologies was proposed in this article. Basic concept of the proposed method is to use the UAV‐installed camera for capturing vibration images of cables from a certain distance and cable dynamic properties are extracted by analyzing captured images. It includes two aspects: (a) a line segments detector (LSD) was employed for detecting cable edges from captured video and a line matching algorithm was further proposed for extracting dynamic displacements; (b) the frequency difference of adjacent higher modal frequencies identified from relative displacements of the cable was employed for cable force calculation to avoid the difficulty of extracting fundamental frequency from UAV‐captured video. It should be noted that relative displacement herein refers to the difference between displacements of two points on the same cable. Advantages of the proposed method lie in that the proposed LSD and matching algorithm are more robust than traditional correlation‐based algorithm for calculating dynamic displacements of bridge cables and it does not need to adjust predefined parameters (i.e., subset size in correlation‐based algorithms). In addition, the combination of relative displacement and frequency difference‐based cable force estimation has the capability of enhancing the Fourier spectrum magnitude of bridge cables and reducing the effect of UAV motion on extraction of cable vibration frequencies. The effectiveness and robustness of the proposed method was verified by using an experimental inclined cable and field‐testing data of a long‐span suspension bridge. Results show that calculated cable forces with UAV technology have a good agreement with reference values measured by attached accelerometers and fixed camera, demonstrating correctness and robustness of the proposed method for cable force estimation.     

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.     

A Quantum‐Inspired Genetic Algorithm‐Based Optimization Method for Mobile Impact Test Data Integration

The traditional impact test method needs a large number of sensors deployed on the entire structure, which cannot meet the requirements of rapid bridge testing. A new mobile impact test method is proposed by sequentially testing the substructures then integrating the test data of all substructures for flexibility identification of the entire structure. The novelty of the proposed method is that the quantum‐inspired genetic algorithm (QIGA) is proposed to improve computational efficiency by transforming the scaling factor sign determination problem to an optimization problem. Experimental example of a steel–concrete composite slab and numerical example of a three‐span continuous rigid‐frame bridge are studied which successfully verify the effectiveness of the proposed method.     

复合粘结节点强度—断裂预测模型

减聚力单元在有限元模型中被用以预测粘结节点的破坏，为明确表达减聚力单元，提出了一个新的强度一断裂模型。所提出的模型统一了预测初始破坏的强度标准以及预测破坏进程的断裂标准。通过在黏合剂—黏合剂界面以及粘结元素之间配置减聚力单元，模拟初始和界面破坏过程以及内聚裂缝。有限元表达中包含了黏合剂的几何非线性。通过节点配置的静态平衡预测同期裂缝和路径，结点包括双臂梁、单搭接接头、裂缝剪切搭接等。对这些节点的准静态有限元分析预测和试验结果的定性和定量分析显示，两者比较吻合。     

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.     

Mode shape linearization and correction in coupled dynamic analysis of wind‐excited tall buildings

The three‐dimensional mode shapes found in modern tall buildings complicate the use of the high‐frequency base balance (HFBB) technique in wind tunnel testing for predicting their wind‐induced loads and effects. The linearized‐mode‐shape (LMS) method was recently proposed to address some of the complications in the calculation of the generalized wind forces, which serve as the input to modal analysis for predicting wind‐induced dynamic responses of tall buildings. An improved LMS method, called the advanced linearized‐mode‐shape (ALMS) method, is developed in this paper by introducing torsional mode shape corrections to account for the partial correlation of torques over building height. The ALMS method has been incorporated into the accurate complete quadratic combination method in the coupled dynamic analysis to form a comprehensive procedure for the determination of equivalent static wind loads (ESWLs) for structural design of complex tall buildings. The improved accuracy in the prediction of generalized forces by the ALMS method has been validated by a 60‐storey benchmark building with multiple‐point simultaneous pressure measurements. A practical 40‐storey residential building with significant swaying and torsional effects is presented to demonstrate the effectiveness of the proposed wind load and response analysis procedure based on the HFBB data. Copyright © 2010 John Wiley & Sons, Ltd.     

行人-结构竖向动力耦合效应试验研究

对于轻质大跨度钢桥结构,行人-结构之间的相互作用会使结构动力特性和行人荷载特性发生改变。为此,针对行人-结构竖向动力耦合效应对结构动力参数和行人荷载动载因子的影响进行试验研究。通过测试行人在8种不同步行频率下行走时结构的动力响应,得到60人次554组有效加速度响应时程,进行运行模态分析;利用无线六轴蓝牙加速度传感器,分别在刚性地面和柔性桥面上开展了3种不同步行频率下行走激励的动力特性试验,得到了60人次1200条有效加速度时程,并对其进行傅里叶变换。结果表明：考虑行人-结构竖向动力耦合效应,人行桥自振频率略有减小,阻尼比显著增加,且随着同步行走人数的增加,结构频率及阻尼比变化率逐渐减小。由于桥梁自振力的存在,行人荷载作用于刚性地面上的动载因子(dynamic load factor,DLF)大于柔性地面上的,试验结果表明,相较于刚性地面,行人在柔性桥面上行走时的第一阶动载因子减小14.7%。给出了刚性地面和柔性桥面前四阶行人荷载动载因子拟合公式,其可为柔性结构下考虑行人 结构相互作用的生物力模型的建立提供参考。