Finite element model updating for structures with parametric constraints

This paper presents a finite element (FE) model updating procedure applied to complex structures using an eigenvalue sensitivity‐based updating approach. The objective of the model updating is to reduce the difference between the calculated and the measured frequencies. The method is based on the first‐order Taylor‐series expansion of the eigenvalues with respect to some structural parameters selected to be adjusted. These parameters are assumed to be bounded by some prescribed regions which are determined according to the degrees of uncertainty that exist in the parameters. The changes of these parameters are found iteratively by solving a constrained optimization problem. The improvement of the current study is in the use of an objective function that is the sum of a weighted frequency error norm and a weighted perturbation norm of the parameters. Two weighting matrices are introduced to provide flexibility for individual tuning of frequency errors and parameters' perturbations. The proposed method is applied to a 1/150 scaled suspension bridge model. Using 11 measured frequencies as reference, the FE model is updated by adjusting ten selected structural parameters. The final updated FE model for the suspension bridge model is able to produce natural frequencies in close agreement with the measured ones. Copyright © 2000 John Wiley & Sons, Ltd.     

Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method

This paper presents a novel nonlinear finite element (FE) model updating framework, in which advanced nonlinear structural FE modeling and analysis techniques are used jointly with the extended Kalman filter (EKF) to estimate time‐invariant parameters associated to the nonlinear material constitutive models used in the FE model of the structural system of interest. The EKF as a parameter estimation tool requires the computation of structural FE response sensitivities (total partial derivatives) with respect to the material parameters to be estimated. Employing the direct differentiation method, which is a well‐established procedure for FE response sensitivity analysis, facilitates the application of the EKF in the parameter estimation problem. To verify the proposed nonlinear FE model updating framework, two proof‐of‐concept examples are presented. For each example, the FE‐simulated response of a realistic prototype structure to a set of earthquake ground motions of varying intensity is polluted with artificial measurement noise and used as structural response measurement to estimate the assumed unknown material parameters using the proposed nonlinear FE model updating framework. The first example consists of a cantilever steel bridge column with three unknown material parameters, while a three‐story three‐bay moment resisting steel frame with six unknown material parameters is used as second example. Both examples demonstrate the excellent performance of the proposed parameter estimation framework even in the presence of high measurement noise. Copyright © 2015 John Wiley & Sons, Ltd.     

大跨桥梁结构损伤诊断与安全评估的多尺度有限元模拟研究

探讨了以结构损伤诊断与安全评估为目标的大跨桥梁结构多尺度有限元模拟的策略与方案。在有限元模型误差来源分析的基础上,提出了大跨桥梁结构模型误差的分层次修正方法。通过对润扬长江大桥斜拉桥的有限元建模和模型修正过程,提出了大跨斜拉桥结构以损伤诊断与安全评估为目标的多尺度有限元模拟方法。研究表明,大跨桥梁结构的多尺度有限元模拟必须建立在模型误差分析的基础上,并采用模型误差的分层次修正方法才能较好的满足多尺度有限元模拟的技术要求。     

大跨斜拉桥的近断层地震响应及减震控制

近断层地震长周期成分丰富,存在速度大脉冲效应;而大跨度斜拉桥一般采用半漂浮体系或漂浮体系,所以固有频率较低。为了研究大跨度斜拉桥在近断层地震作用下的反应规律及减震措施,利用ANSYS软件分析了某半漂浮体系的大跨斜拉桥在近断层地震作用下的时程响应,并对其减震控制方法进行了探讨。研究表明,大跨度斜拉桥的近断层地震响应随着PGV/PGA值的增大而增大,且增大幅度较大,近场脉冲效应较为显著;对于近断层地震作用,不建议采用塔梁弹性连接装置作为主梁纵漂的减震措施,而采用参数适宜的铅挤压阻尼器和粘滞阻尼器则均能获得很好的减震效果;由于大跨度斜拉桥的近断层地震反应较大,应提高其支座的设计允许位移。     

Shake table experimental study of cable-stayed bridges with two different design strategies of H-shaped towers

As one of the main load-carrying components of cable-stayed bridges,bridge towers are typically required to remain elastic even when subjected to severe ground motions with a 2%-3%probability of exceedance in 50 years.To fulfill this special requirement imposed by current seismic design codes,reinforcement ratios in the bridge towers have to be kept significantly higher than if limited ductility behavior of the tower is allowed.In addition,since the foundation capacity is closely related to the moment and shear capacities of the bridge tower,a large increase in bridge construction cost for elastically designed cable-stayed bridge is inevitable.To further investigate the possibility of limited ductility bridge tower design strategies,a new 1/20-scale cable-stayed bridge model with H-shaped bridge towers designed according to strong strut-weak tower column design was tested.The shake table experimental results are compared with a previous strong tower column-weak strut designed full bridge model.A comparison of the results show that ductility design with plastic hinges located on tower columns,i.e.,strong strut-weak tower column design,is another effective seismic design strategy that results in only small residual displacement at the top of the tower column,even under very severe earthquake excitations.     

斜拉桥结构减震设计优化研究

位于中强以上地震烈度区的大跨斜拉桥结构,如果采用传统的抗震设计方法,通常很难满足结构的抗震设计要求,因此采取一定的减震措施显得非常必要。本文以某一总长为2 088m的大跨双塔双索面斜拉桥为分析算例,对斜拉桥结构的减震设计进行了研究。合理的减震结构体系是取得良好减震效果的前提,通过分析对比,该大跨斜拉桥横向采用局部减震体系最为合理,即只在近塔辅助墩处设置横向粘滞阻尼器,其它塔、墩处采用常规的横向约束方案。为使减震结构得到更好的减震效果,还应对减震装置参数进行优化设计。由于采取了合理的减震结构体系、较优的减震装置参数,使该大跨斜拉桥取得了很好的减震设计效果。     

多点激励下大跨度斜拉桥地震反应分析

大跨斜拉桥是交通运输的枢纽工程,一旦在地震中遭到破坏,将会造成巨大的直接和间接经济损失.由于大跨斜拉桥的跨度大,在地震中地震波到达不同桥墩的时间存在差异,这会对大跨斜拉桥的地震反应产生很大影响.因此,对大跨斜拉桥在多点输入下的反应开展研究,对进行正确有效的抗震设计,确保其抗震安全性具有非常重要的意义.本文分析了多点激励下大跨度斜拉桥的地震反应,并与一致激励下大跨度斜拉桥的地震反应进行了对比,研究了多点激励对大跨度斜拉桥地震反应的影响.     

地震作用下大跨度悬索桥几何非线性影响分析

大跨度悬索桥几何非线性主要来自3个方面：缆索垂度效应、梁柱效应、大位移引起的几何形状变化。鉴于地震波高频成分振幅大,低频成分振幅小的特点,很难对地震作用下大跨度悬索桥几何非线性的影响做出定性判断。目前大跨度桥梁的几何非线性研究主要集中在斜拉桥,且不同的学者得出了不同的结论。本文以逐级加大振幅的Ⅳ类场地多条地震波为激励,通过对称与非对称的2座典型大跨度悬索桥的几何非线性影响对比分析,探讨了几何非线性对大跨度悬索桥重要地震响应量的影响程度及其原因,并提出了相应的抗震设计参考建议。     

Model‐based multi‐metric control of uniaxial shake tables

Shake tables provide a direct means by which to evaluate structural performance under earthquake excitation. Because the entire structure is mounted on the base plate and subjected to the ground motion in real time, dynamic effects and rate‐dependent behavior can be accurately represented. Shake table control is not straightforward as the desired signal is an acceleration record, while most actuators operate in displacement feedback for stability. At the same time, the payload is typically large relative to the capacity of the actuator, leading to pronounced control‐structure interaction. Through this interaction, the dynamics of the specimen influence the dynamics of the shake table, which can be problematic when specimens change behavior because of damage or other nonlinearities. Moreover, shake tables are themselves inherently nonlinear, making it difficult to accurately recreate a desired acceleration record over a broad range of amplitudes and frequencies. A model‐based multi‐metric shake table control strategy is proposed to improve tracking of the desired acceleration of a uniaxial shake table, remaining robust to nonlinearities including changes in specimen condition. The proposed strategy is verified for the shake table testing of both linear and nonlinear structures. Copyright © 2013 John Wiley & Sons, Ltd.     

System versus component response of a two-span reinforced concrete bridge system

A large-scale 20.5 m long asymmetric two-span reinforced concrete bridge was tested to failure using the shake table system at the University of Nevada Reno. Upon completion of testing, in depth analytical modeling was conducted to evaluate the accuracy of conventional methods in reproducing the bridge model response and to develop a model for further study. Utilizing the experimentally verified computer model, the system effect was investigated, comparing the system and response of individual bents as well as the response of several other bridge models. In comparing computational model of the shake table specimen and models of the individual bents with tributary mass, it was shown that for all of the columns in this study, there was generally not an increase in hysteretic energy or large displacement cycles from system response at given displacement demand. The response of the bents for each high amplitude test motion was also compared. It was shown that there were significant differences in the bent demands for a given excitation due to system effects. In addition to the shake table model, four bridge systems with a constant total lateral stiffness were used in a parametric study to determine the system effect. The symmetric and uniform versions of the bridge specimen were shown to be comparable in nonlinear performance to the bridge specimen for the same high amplitude demand. The failure progression of the bridge model and the analytical comparisons suggested that the reserve capacity from varied column heights could provide a beneficial substructure redundancy.     

基于分布式应变监测的大跨度斜拉桥结构损伤探测

结构损伤具有典型的局部性质,通常表现为局部应变的异常。结构应变的分布式监测与损伤敏感特征分析,是实现大跨桥梁损伤探测与定位的理想途径之一。但是,由于环境噪声的影响,对分布式应变信号的监测往往不能准确反映结构出现的损伤状况。因此,提出了通过小波变换对分布式光纤测试的斜拉桥桥面应变分布进行多尺度分析的方法。这种方法可以克服分布式光纤应变监测信号受观测噪声和空间分辨率平均效应的不利影响,准确地确定空间域信号奇异点在桥面的位置。同时,在实验室建立了比尺为1∶150的模型斜拉桥。通过对斜拉桥数值模型与物理模型试验结果的分析和比较,验证了所提出方法的有效性。     

基于粘滞阻尼器的元江大桥减震设计方案

为了提高大跨度桥梁的抗震性能水平,基于粘滞阻尼器的结构减震控制技术成为专家学者研究的重点和工程设计人员首先考虑的抗震设防措施。现有成果主要集中在大跨度公路斜拉桥的研究和应用,在山区的非规则高墩钢桁连续梁桥研究的较少。以云南省元江大桥为例,采用Midas/civil建立弹性分析的有限元模型,对元江大桥进行了动力特性分析。采用快速非线性时程分析方法对粘滞阻尼器参数进行了优化分析,并且总结了粘滞阻尼器参数对高墩连续梁桥的减震作用规律。最后,通过有控和无控结构的地震动响应对比分析,评价了安装阻尼器后的结构主控部位的减震效果。结果表明:减震控制提高了结构的安全性。     

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。     

Implementation of online model updating in hybrid simulation

Hybrid simulation combines numerical and experimental methods for cost‐effective, large‐scale testing of structures under simulated earthquake loading. Structural system level response can be obtained by expressing the equation of motion for the combined experimental and numerical substructures, and solved using time‐stepping integration similar to pure numerical simulations. It is often assumed that a reliable model exists for the numerical substructures while the experimental substructures correspond to parts of the structure that are difficult to model. A wealth of data becomes available during the simulation from the measured experiment response that can be used to improve upon the numerical models, particularly if a component with similar structural configuration and material properties is being tested and subjected to a comparable load pattern. To take advantage of experimental measurements, a new hybrid test framework is proposed with an updating scheme to update the initial modeling parameters of the numerical model based on the instantaneously‐measured response of the experimental substructures as the test progresses. Numerical simulations are first conducted to evaluate key algorithms for the selection and calibration of modeling parameters that can be updated. The framework is then expanded to conduct actual hybrid simulations of a structural frame model including a physical substructure in the laboratory and a numerical substructure that is updated during the tests. The effectiveness of the proposed framework is demonstrated for a simple frame structure but is extendable to more complex structural behavior and models. Copyright © 2013 John Wiley & Sons, Ltd.     

Non-linear earthquake-response analysis of long-span cable-stayed bridges: Applications

The dynamic non-linear behaviour of three-dimensional long-span cable-stayed bridges under seismic loadings is studied. The cases of multiple-support as well as uniform seismic excitations of these long and flexible structures are considered. Different sources of non-linearity for such bridges are included in the analysis, as outlined in the companion paper. In this accompanying analysis a tangent stiffness iterative procedure is utilized to estimate the non-linear seismic response. Numerical examples are presented in which a comparison between a linear earthquake-response analysis (based on the utilization of the tangent stiffness matrix of the bridge at the dead-load deformed state which is obtained from the geometry of the bridge under gravity load conditions) and a non-linear earthquake response analysis using the step-by-integration procedure is made. In these examples two three-dimensional bridge models representing recent and future trends in cable-stayed bridge design are utilized. The study sheds some light on the salient features of the seismic analysis and design of these long contemporary bridges. In addition, parameters affecting the seismic response of these bridges are discussed: other factors considered are non-linearity, uniformity and spatial variation of ground motion inputs and structural configuration.     

大跨度斜拉桥地震响应非线性时程分析

以有限元分析理论为基础,结合某大跨度斜拉桥工程实例,利用ANSYS软件建立有限元模型,通过修正后的El Centro波分别考虑横向、竖向及纵向输入,采用时程分析方法对其进行地震反应分析.计算分析表明:考虑几何非线性后,结构的内力和位移响应明显增大,且对主梁和索塔内力与位移的影响程度及规律也不尽相同,须区别对待分析.同时表明该桥抗震性能良好,地震荷载不控制设计.由此得出结论,对于斜拉桥这类柔性体系, 不可忽视结构几何非线性的影响.     

Influence of structural parameters on dynamic characteristics and wind-induced buffeting responses of a super-long-span cable-stayed bridge

A 3D finite element (FE) model for the Sutong cable-stayed bridge (SCB) is established based on ANSYS. The dynamic characteristics of the bridge are analyzed using a subspace iteration method. Based on recorded wind data, the measured spectra expression is presented using the nonlinear least-squares regression method. Turbulent winds at the bridge site are simulated based on the spectral representation method and the FFT technique. The influence of some key structural parameters and measures on the dynamic characteristics of the bridge are investigated. These parameters include dead load intensity, as well as vertical, lateral and torsional stiffness of the steel box girder. In addition, the influence of elastic stiffness of the connection device employed between the towers and the girder on the vibration mode of the steel box girder is investigated. The analysis shows that all of the vertical, lateral and torsional buffeting displacement responses reduce gradually as the dead load intensity increases. The dynamic characteristics and the structural buffeting displacement response of the SCB are only slightly affected by the vertical and torsional stiffness of the steel box girder, and the lateral and torsional buffeting displacement responses reduce gradually as the lateral stiffness increases. These results provide a reference for dynamic analysis and design of super-long-span cable-stayed bridges.     

Simulation of floor response spectra in shake table experiments

Among several different experimental techniques, used to test the response of structures and to verify their seismic performance, the shake table testing allows to reproduce the conditions of true effects of earthquake ground motions in order to challenge complex model structures and systems. However, the reproduction of dynamic signals, due to the dynamics of the shake table and of the specimen, is usually imperfect even though closed‐loop control in a shake table system is used to reduce these errors and obtain the best fidelity reproduction. Furthermore, because of the dynamic amplifications in the specimen, the signal recorded at desired locations could be completely different from the expected effect of shake table motion. This paper focuses on the development of practical shake table simulations using additional ‘open loop’ feedforward compensation in form of inverse transfer functions (i.e. the ratio of the output structural response to an input base motion in the frequency domain) in order to obtain an acceptable reproduction of desired acceleration histories at specific locations in the specimen. As the first step, a well‐known global feedforward procedure is reformulated for the compensation of the table motion distortions due to the servo‐hydraulic system. Subsequently, the same concept is extended to the table‐structure system to adjust the shake table input in order to achieve a desired response spectrum at any floor of the specimen. Implementations show how such a method can be used in any experimental facility. Copyright © 2010 John Wiley & Sons, Ltd.     

Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage. This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform (WPT). The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum (WPES) has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.