桥梁损伤识别的实用模型修正方法研究

对面向损伤识别的桥梁结构模型修正实用方法进行了研究。提出了基于振动特性测量的三步模型修正策略和综合利用通用有限元程序ANSYS的优化功能进行模型修正的方法。为了缩减待修正的参数,根据计算目标函数对每个单元参数的敏感性,进行子结构划分,通过对子结构参数的修正进行结构损伤的大致定位,然后对确定为损伤的子结构的每个单元进行参数修正,进行结构的损伤定量识别和状态评估。修正算法的优化方法采用ANSYS一阶优化方法和随机搜索方法,敏感性分析和模型修正完全基于ANSYS软件进行,较适合于实际工程的应用。为了说明方法的可行性,以某一实际三跨预应力钢筋混凝土连续箱梁桥为仿真算例,以结构模型的单元刚度衰减来模拟损伤,进行损伤识别,达到了较好的效果。     

Uncertainty and Sensitivity Analysis of Damage Identification Results Obtained Using Finite Element Model Updating

Abstract: A full‐scale seven‐story reinforced concrete shear wall building structure was tested on the UCSD‐NEES shake table in the period October 2005–January 2006. The shake table tests were designed so as to damage the building progressively through several historical seismic motions reproduced on the shake table. A sensitivity‐based finite element (FE) model updating method was used to identify damage in the building. The estimation uncertainty in the damage identification results was observed to be significant, which motivated the authors to perform, through numerical simulation, an uncertainty analysis on a set of damage identification results. This study investigates systematically the performance of FE model updating for damage identification. The damaged structure is simulated numerically through a change in stiffness in selected regions of a FE model of the shear wall test structure. The uncertainty of the identified damage (location and extent) due to variability of five input factors is quantified through analysis‐of‐variance (ANOVA) and meta‐modeling. These five input factors are: (1–3) level of uncertainty in the (identified) modal parameters of each of the first three longitudinal modes, (4) spatial density of measurements (number of sensors), and (5) mesh size in the FE model used in the FE model updating procedure (a type of modeling error). A full factorial design of experiments is considered for these five input factors. In addition to ANOVA and meta‐modeling, this study investigates the one‐at‐a‐time sensitivity analysis of the identified damage to the level of uncertainty in the identified modal parameters of the first three longitudinal modes. The results of this investigation demonstrate that the level of confidence in the damage identification results obtained through FE model updating, is a function of not only the level of uncertainty in the identified modal parameters, but also choices made in the design of experiments (e.g., spatial density of measurements) and modeling errors (e.g., mesh size). Therefore, the experiments can be designed so that the more influential input factors (to the total uncertainty/variability of the damage identification results) are set at optimum levels so as to yield more accurate damage identification results.     

Structural parameter identification and damage detection for a steel structure using a two-stage finite element model updating method

A two-stage eigensensitivity-based finite element (FE) model updating procedure is developed for structural parameter identification and damage detection for the IASC-ASCE structural health monitoring benchmark steel structure on the basis of ambient vibration measurements. In the first stage, both the weighted least squares and Bayesian estimation methods are adopted for the identification of the connection stiffness of beam-column joints and Young’s modulus of the structure; then the damage detection is conducted via the FE model updating procedure for detecting damaged braces with different damage patterns of the structure. Comparisons between the FE model updated results and the experimental data show that the eigensensitivity-based FE model updating procedure is an effective tool for structural parameter identification and damage detection for steel frame structures.     

基于响应面的桥梁有限元模型修正

采用试验设计和回归分析方法,以显式的响应面模型逼近特征量与设计参数间复杂的隐式函数关系,得到简化的结构模型(Meta-model),给出有限元模型修正过程。针对复杂的土木工程结构,讨论样本选择、修正参数选取以及如何从众多因素中较合理地建立结构的响应面模型。用数值模拟算例和六跨连续梁桥环境振动试验结果,实现基于响应面模型的土木工程结构有限元模型修正,并与传统的基于灵敏度方法直接对结构有限元模型修正结果进行比较。结果表明,基于响应面方法的有限元模型修正和验证,能显著提高修正的效率,修正过程计算简洁、迭代收敛快,避开每次迭代都需要进行有限元计算,易于工程实际应用。     

Numerical Evaluation of Vibration‐Based Methods for Damage Assessment of Cable‐Stayed Bridges

Abstract: This study investigated a number of different damage detection algorithms for structural health monitoring of a typical cable‐stayed bridge. The Bayview Bridge, a cable‐stayed bridge in Quincy, Illinois, was selected for the study. The focus was in comparing the viability of simplified techniques for practical applications. Accordingly, the numerical analysis involved development of a precise linear elastic finite element model (FEM) to simulate various structural health monitoring test scenarios with accelerometers. The Effective Independence Method was employed to locate the best distribution of the accelerometers along the length of the bridge. The simulated accelerometer data based on the FEM analysis was employed for the evaluation of the four damage identification methods investigated here. These methods included the Enhanced Coordinate Modal Assurance Criterion, Damage Index Method, Mode Shape Curvature Method, and Modal Flexibility Index Method. Some of these methods had been previously applied only to a number of specific bridges. However, the investigation here provides the relative merits and shortcomings of the damage detection methods in long‐span cable‐stayed bridges.     

Cyber‐physical approach to the optimization of semiactive structural control under multiple earthquake ground motions

This paper presents a cyber‐physical approach to optimize the semiactive control of a base‐isolated structure under a suite of earthquakes. The approach uses numerical search algorithms to guide the exploration of the design space and real‐time hybrid simulation (RTHS) to evaluate candidate designs, creating a framework for real‐time hybrid optimization (RHTO). By supplanting traditional numerical analysis (i.e., finite element methods) with RTHS, structural components that are difficult to model can be represented accurately while still capturing global structural performance. The efficiency of RTHO is improved for multiple design excitations with the creation of a multiinterval particle swarm optimization (MI‐PSO) algorithm. As a proof‐of‐concept, RTHO is applied to improve the seismic performance of a base‐isolated structure with supplemental control. The proposed RTHO framework with MI‐PSO is a versatile technique for multivariate optimization under multiple excitations. It is well suited for the accurate and rapid evaluation of structures with nonlinear experimental substructures, in particular, those that do not undergo permanent damage such as structural control devices. The RTHO framework integrates popular optimization algorithms with advanced experimental methods, creating an exciting new cyber‐physical approach to design.     

基于桥梁优化理论的有限元模型修正技术

针对桥梁的试验模态和有限元分析模型存在的误差,提出一套可靠的基准有限元模型,并利用基于优化理论的有限元模型修正技术,对一个短跨桥模型进行损伤识别,通过损伤刚度来定量的描述该短跨桥的损伤程度,并得出了一些有益的结论。     

Dynamic test and finite element model updating of bridge structures based on ambient vibration

The dynamic characteristics of bridge structures are the basis of structural dynamic response and seismic analysis, and are also an important target of health condition monitoring. In this paper, a three-dimensional finite-element model is first established for a highway bridge over a railroad on No.312 National Highway. Based on design drawings, the dynamic characteristics of the bridge are studied using finite element analysis and ambient vibration measurements. Thus, a set of data is selected based on sensitivity analysis and optimization theory; the finite element model of the bridge is updated. The numerical and experimental results show that the updated method is more simple and effective, the updated finite element model can reflect the dynamic characteristics of the bridge better, and it can be used to predict the dynamic response under complex external forces. It is also helpful for further damage identification and health condition monitoring.     

Vibration-based operational modal analysis of the Mikron historic arch bridge after restoration

This research presents finite element modelling, vibration-based operational modal analysis, and finite element model updating of a restored historic arch bridge. Mikron historic bridge, constructed on F?rt?na River in Rize, Turkey, is the subject of this case study. The General Directorate for Highways of Turkey repaired the bridge's main structural elements, arches, sidewalls, and filler material in 1998. To construct a 3D finite element model of the bridge, ANSYS finite element software estimated the analytical dynamic characteristics. Induced ambient vibrations such as human walking and wind excited the model bridge to allow measurement of the bridge's responses. Enhanced frequency domain decomposition in frequency domain and stochastic subspace identification in time domain methodologies extracted experimental dynamic characteristics. A comparison of the analytical and experimental results showed significant agreement between mode shapes, but some differences in natural frequencies appeared. Consequently, updating the finite element model of the bridge by changing boundary conditions minimised the differences between analytical and experimental natural frequencies. After the finite element model updating process, the differences between natural frequencies declined from 7% to 2%.     

Earthquake analysis of reinorced concrete minarets using ambient vibration test results

This paper describes a Turkish style reinforced concrete minaret, its finite element model, modal testing, finite element model updating and earthquake behaviour, before and after model updating. The minaret of a mosque located in Trabzon, Turkey is selected as an application. A three‐dimensional (3D) model of the minaret and its modal analysis is performed to obtain analytical frequencies and mode shapes using ANSYS finite element program. The ambient vibration tests are conducted on the minaret under natural excitations such as wind effects and human movement. The output‐only modal parameter identification is carried out by Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification methods in Operational Modal Analysis software and in doing so, dynamic characteristics (natural frequencies, mode shapes and damping ratios) are determined. A 3D finite element model of the minaret is updated to minimize the differences between analytical and experimental modal properties by changing some uncertain modelling parameters such as material properties and boundary conditions. The earthquake behaviour of the minaret is investigated using 1992 Erzincan earthquake before and after finite element model updating. Maximum differences in the natural frequencies are reduced from 21% to 8%, and good agreement is found between analytical and experimental natural frequencies. In addition to this, it is realized that finite element model updating is effective on the earthquake behaviour of the minaret. Copyright © 2008 John Wiley & Sons, Ltd.     

Wavelet‐based approach of time series model for modal identification of a bridge with incomplete input

Identification of modal parameters of a bridge from its earthquake responses is crucial for performing damage assessment of the structure. However, all the input base excitations of the bridge may not be measured because of economic concerns and sensor malfunctions. Consequently, evaluating the modal parameters of a bridge under the consideration of incomplete input measurements is a challenging and important task. An approach that combines the continuous Cauchy wavelet transform with an autoregressive time‐varying moving average with exogenous input (AR‐TVMA‐X) model is proposed in this study to identify the modal parameters of a multispan bridge under multiple support earthquake excitations with incomplete measurements. The efficiency and efficacy of the proposed approach are first validated using numerically simulated responses of a three‐span continuous beam subjected to multiple support nonstationary excitations. A standard procedure of using the proposed approach to identify the modal parameters is established according to comprehensive studies on the effects of noise in the data, the number of supports whose excitations are used in the AR‐TVMA‐X model, and the orders of the AR‐TVMA‐X model on the accuracy of identifying the modal parameters. This procedure is further applied to process the earthquake responses of a two‐span cable‐stayed 510‐m‐long bridge to demonstrate the engineering applicability of the proposed approach.     

Dynamic test and finite element model updating of bridge structures based on ambient vibration

The dynamic characteristics of bridge structures are the basis of structural dynamic response and seismic analysis, and are also an important target of health condition monitoring. In this paper, a three-dimensional finite-element model is first established for a highway bridge over a railroad on No.312 National Highway. Based on design drawings, the dynamic characteristics of the bridge are studied using finite element analysis and ambient vibration measurements. Thus, a set of data is selected based on sensitivity analysis and optimization theory; the finite element model of the bridge is updated. The numerical and experimental results show that the updated method is more simple and effective, the updated finite element model can reflect the dynamic characteristics of the bridge better, and it can be used to predict the dynamic response under complex external forces. It is also helpful for further damage identification and health condition monitoring. __________ Translated from Chinese Journal of Huazhong University of Science and Technology (Urban Science Edition), 2006, 23(4): 57–60 [译自: 华 中科技大学学报(城市科学版)]     

Ambient vibration testing and updating of the finite element model of a simply supported beam bridge

An ambient vibration test on a concrete bridge constructed in 1971 and calibration of its finite element model are presented. The bridge is characterized by a system of post-tensioned and simply supported beams. The dynamic characteristics of the bridge, i.e. natural frequencies, mode shapes and damping ratios were computed from the ambient vibration tests by using the Eigensystem Realization Algorithm (ERA). Then, these characteristics were used to update the finite element model of the bridge by formulating an optimization problem and then using Genetic Algorithms (GA) to solve it. From the results of the ambient vibration test of this type of bridge, it is concluded that two-dimensional mode shapes exist: in the longitudinal and transverse; and these experimentally obtained dynamic characteristics were also achieved in the analytical model through updating. The application of GAs as optimization techniques showed great versatility to optimize any number and type of variables in the model.     

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.     

应用曲率模态理论识别实桥模型损伤的研究

在曲率模态理论基础上,针对目前损伤研究一般采用的简单等直梁或杆件等简化模型与实际桥梁差别较大的情况,参照实际城市道路桥梁建立有限元损伤模型,通过计算研究了大型桥梁损伤的结构响应特点,验证了曲率模态对大型结构整体损伤、局部损伤都有较好的敏感性,可为实际公路桥梁损伤的测量和识别提供参考。     

基于二阶泰勒级数展开和风驱动优化算法的结构有限元模型修正

为得到结构响应与修正参数之间的函数关系、简化参数迭代过程，通过推导结构响应关于修正参数的一阶与二阶泰勒级数展开，并选用具有寻优效率高、全局搜索能力强的风驱动优化算法，建立了基于二阶泰勒级数展开和风驱动优化算法的结构有限元模型修正方法。同时，为求解响应关于修正参数的二阶泰勒级数展开，采用差分法近似求得响应关于修正参数的一阶和二阶偏导数。利用该方法对算例模型进行了修正，并对比了一阶和二阶泰勒级数展开的修正效果。结果表明：二阶泰勒级数展开的修正效果明显优于一阶泰勒级数展开，增加二阶偏导数项可以更好地反映响应与修正参数之间的函数关系。基于该方法，采用实桥的静动力测试数据对青林湾大桥的有限元模型进行了修正，修正后的有限元模型能够较好地反映大桥的实际状况。     

基于DSCM-FEMU的岩石力学参数反演研究

将数字散斑相关方法(DSCM)与有限元模型修正方法(FEMU)相结合,建立了岩石力学参数反演流程。首先,通过数字散斑相关方法,获取实验中岩石试件受载条件下的应变场;其次,利用有限元模拟方法,获取数值模型中的应力场;最后,构建最小二乘目标函数,并且通过不断更新有限元模型中给定的力学参数进行优化计算。当目标函数收敛时,得到与实验结果最匹配的力学参数。研究结果表明:(1)数字散斑相关方法与有限元模型修正法相结合,可以实现材料的力学参数反演;(2)得到以实验应变场、有限元应力场、材料弹性模量和泊松比组成的参数优化目标函数;(3)以三点弯曲实验为例,反演得到花岗岩的弹性模量和泊松比。     

基于有限元模型和不完备模态测试信息的结构损伤识别方法研究

本文在有限元模型的基础上,建立了一种基于不完备模态测试信息的损伤识别方法。采用Levenberg-Marquardt非线性最小二乘算法对建立的杆系结构损伤识别方程进行求解,并通过一拱桥的数值计算结果表明,该方法可以同时进行结构的损伤定位和定量研究,在测试数据不完备及一定数据噪声水平条件下,本文的方法仍有较好的损伤识别能力。     

Development of a baseline for structural health monitoring for a curved post-tensioned concrete box–girder bridge

The establishment of a baseline is essential for long-term structural health monitoring and performance evaluation. Usually, field testing data and finite element (FE) model are two critical tools used to develop the baseline. In this paper, the establishment of the baseline field database for a curved post-tensioned concrete bridge with expansion bearings is first introduced to include the effect of varying temperature conditions on the field testing data. This database uses data collected from a full year and is based on an undamaged status. The development of a baseline FE model for the bridge is then discussed. Model updating for the FE model are detailed in this paper which includes calibration of material properties, utilization of spring bearing elements, and replacement of Mindlin plate elements (MP4) on box–girder by recently developed cracked Mindlin plate elements (MP4C) to represent the bridge service conditions. A good agreement in modal results has been observed between the baseline FE model and the baseline field data. The proposed structural health baseline can be used for near real-time damage detection, development of monitoring techniques, and condition assessment. Finally, as an application of the baseline, this FE model is used for an earthquake simulation with a selected ground motion on the bridge. The seismic analysis demonstrates the beneficial effect of the guided expansion bearings on the bridge deck in the longitudinal direction.     

基于环境激励的连续刚构桥模态参数识别及有限元模型修正

一个合理准确的有限元模型是大型桥梁健康监测系统中损伤识别及安全评估、预警的前提。以一座三跨预应力混凝土连续刚构桥为例,根据设计资料,利用ANSYS建立其初始三维有限元模型,利用其健康监测系统采集得到的加速度时程数据,采用随机子空间法对实际结构的模态频率进行识别,依据识别结果,在参数灵敏度分析的基础上,根据最优化理论对该桥的有限元模型进行修正。研究结果表明,经修正后的有限元模型能真实准确地反映该桥梁结构的真实动力特性,可以作为健康监测中损伤识别、安全评估等研究工作的基准模型。