消能减震建筑结构的附加有效阻尼比估计

为估计一栋实际消能减震建筑结构在地震作用下的附加有效阻尼比,提出了一种基于有限元模型修正技术的阻尼比估计和验证方法。考虑到结构初始有限元模型存在较大模型误差,采用基于结构振动模态参数的直接模型更新方法修正初始有限元模型,其中,对于实测振型不完整问题,利用振型扩阶方法补充完整振型。基于模态应变能概念,利用整体结构模态参数识别值,推导了油阻尼器支撑系统附加给结构的有效阻尼比和有效频率的计算公式,并估计了主体结构的频率和阻尼比。以一组实际地震动监测数据为例,采用建议方法估计有效阻尼比和有效频率,通过对比修正模型的预测响应与实际监测数据,验证了建议方法的有效性。     

Response surface‐based finite‐element model updating of a historic masonry minaret for operational modal analysis

This study aimed to use the response surface (RS) method for finite element (FE) model updating, using operational modal analysis (OMA). The RS method was utilized to achieve better agreement between the numerical and field‐measured structure response. The OMA technique for the field study was utilized to obtain modal parameters of the selected historic masonry minaret. The natural frequencies and mode shapes were experimentally determined by the enhanced frequency domain decomposition (EFDD) method. The optimum results between the experimental and numerical analyses were found by using the optimization method. The central composite design was used to construct the design of experiments, and the genetic aggregation approach was performed to generate the RS models. After obtaining the RS models, an attempt was made to converge the natural frequency values corresponding to the five‐mode shapes with the frequency values identified by the experimental analysis. ANSYS software was used to perform 3D finite element (FE) modeling of the historic masonry minaret and to numerically identify the natural frequencies and mode shapes of the minaret. The results of the experimental, initial, and updated FE model were compared with each other. Significant differences can be seen when comparing the experimental and analytical results with the initial conditions.     

Candidate model construction of a cable-stayed bridge using parameterised sensitivity-based finite element model updating

An efficient method for constructing multiple candidate finite element (FE) models which are consistent with the measured dynamic properties of a civil structure is presented. A parameterised sensitivity-based FE model updating method was developed to permit a feasible FE model set for the target structure to be produced. In this method, an aggregated multi-objective function, which is defined by the weighted sum of the error functions, is parameterised by its relative weighting factors. By introducing multiple parameter sets for the weighting factors, a number of optimal updated FE models are produced that permit both the natural frequency errors and mode shape errors to be simultaneously minimised. The effectiveness of the proposed method is illustrated by an example using an existing cable-stayed bridge. The findings show that error-minimised, well-distributed FE models can be obtained in terms of modal frequency errors and mode shape errors. The high quality of the candidate model sets is also verified by observations showing that the distributions of the structural parameters are consistent through each updated FE models, and the characteristic features of the target structure such as non-symmetric mode shapes are relatively well captured.     

结构动力模型的改进直接修正方法及工程应用

直接模型修正方法是一类经典的解析动力模型修正技术,该方法具有计算高效和精确匹配目标模态参数等优点,但仅考虑与频率和振型相关的约束,导致修正模型预测的模态参与因子与实际识别值存在差异。针对该模态参数匹配不完备问题,提出了一种改进的直接模型修正方法。改进方法考虑模态参与因子在质量矩阵中的修正,采用约束最小化技术,推导了质量矩阵的最优解,并结合已有的刚度矩阵修正技术实现结构模型修正。以一栋实际消能减震建筑结构为应用对象,利用结构地震监测数据估计的模态参数,采用改进方法修正结构初始有限元模型,验证了改进修正方法的准确性。     

Modal Response‐Based Visual System Identification and Model Updating Methods for Building Structures

This article proposes a new system identification (SI) method using the modal responses obtained from the dynamic responses of a structure for estimating modal parameters. Since the proposed SI method visually extracts the mode shape of a structure through the plotting of modal responses based on measured data points, the complex calculation process for the correlation and the decomposition for vibration measurements required in SI methods can be avoided. Also, without dependence on configurations of SI methods inducing variations of modal parameters, mode shapes and modal damping ratios can be stably extracted through direct implementation of modal response. To verify the feasibility of the proposed method, the modal parameters of a shear frame were extracted from modal displacement data obtained from a vibration test, and the results were compared with those obtained from the existing frequency domain SI method. The proposed method introduces the maximum modal response ratio of each mode computed by modal displacement data, and from this, the contribution of each mode and each measured location to the overall structural response is indirectly evaluated. Moreover, this article proposes a model updating method establishing the error functions based on the differences between the analytical model and measurement for the natural frequencies and the modal responses reflecting both mode shape and modal contribution. The validity of the proposed method is verified through the response prediction and modal contributions of the models obtained from model updating based on dynamic displacement from a shaking table test for a shear‐type test frame.     

铁路简支梁桥下部结构健康状态动力评估方法研究

提出一种以实测横桥向整体振动、横桥向局部振动和顺桥向局部振动模态的不同组合为输入,采用模型修正技术和优化算法识别铁路简支梁桥下部结构的物理参数,从而实现对墩身、基础和支座病害进行定位和定量分析的动力学方法。进一步,建立了针对下部结构系统中各构件的评估准则和评估流程。对两座铁路桥梁进行现场试验,并依据所提评估方法和评估准则对其健康状态进行评估,理论分析结果现场评估结果一致,从而证明所提方法的准确性和有效性。     

采用静态和动态法改进有限元模型进行桥梁评估

通过有限元模型升级,将有限元分析与现场测量相结合,其潜力毋庸置疑。然而,简单化的初始模型和缺少测量可能导致升级的模型参数隐藏了不准确的模型假设,而不是提高实际结构参数的评估。因此,所提出方法的目标主要是在采用非线性优化对参数进行评估之前,借助手工模型的精度消除不精确的模型简化。此外,引进多级响应目标函数,结合不同类型的测量获得参数评估的坚实基础。所提方法被用于世界上最大的Svinesund单孔桥,研究表明采用非线性模型可对模型参数进行精确评估。     

Real-time structural health monitoring of a supertall building under construction based on visual modal identification strategy

This paper presents a real-time structural health monitoring technique for a supertall building under construction, Lotte World Tower (LWT), the tallest building in Korea. To evaluate the state and safety of the supertall building under construction, this study presents a visual modal identification method to identify mode shape and damping ratio based on modal responses from the monitoring system. In the method, mode shape and damping are visually identified from the time history plotting of well-filtered modal responses in real time. Since the presented method does not include a kind of complex calculation for measured data required in the previous SI methods, it can avoid time consuming in system identification (SI) as well as variation in value of modal parameter extracted from measurement. An ambient vibration test on the LWT under construction was performed in 2015. Using the test data, the presented method identified the mode shapes and damping of the LWT visually with small variations without any complicated computations. Further, this study presents a model updating method with a simplified pseudo frame model to construct a baseline model for the LWT under construction using measured modal responses. The validity of the updated model for the LWT was verified through estimations of mode shape and structural responses.     

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.     

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.     

Finite element model updating on small-scale bridge model using the hybrid genetic algorithm

Finite element (FE) model-based dynamic analysis has been widely used to predict the dynamic characteristics of civil structures. FE model updating method based on the hybrid genetic algorithm, by combining genetic algorithm and the modified Nelder–Mead's simplex method, is presented to improve bridge structures' FE model. An objective function is formulated as a linear combination of fitness functions on natural frequencies, mode shapes and static deflections using measurements and analytical results to update both stiffness and mass simultaneously. A commercial FE analysis tool, which can utilise previously developed element library and solution algorithms, is adopted for applications on diversified and complex structures. The validity of the proposed method is verified by using a simply supported bridge model with three I-shaped girders. FE models such as grid, beam-shell and shell model are considered to modify initial FE models on the experimental structure. Experimental results suggest that the proposed method can be applied efficiently to various FE models and is feasible and effective when this method is applied to identify FE modelling errors.     

Free vibration of non-uniformly ring stiffened cylindrical shells using analytical, experimental and numerical methods

In this research, the free vibration analysis of cylindrical shells with circumferential stiffeners, i.e. rings with non-uniform stiffeners eccentricity and unequal stiffeners spacing is investigated using analytical, experimental and finite elements (FE) methods. Ritz method is applied in analytical solution while stiffeners treated as discrete elements. The polynomial functions are used for Ritz functions and natural frequency results for simply supported stiffened cylindrical shell with equal rings spacing and constant eccentricity is compared with other's analytical and experimental results, which showed good agreement. Also, a stiffened shell with unequal rings spacing and non-uniform eccentricity with free–free boundary condition is considered using analytical, experimental and FE methods. In experimental method, modal testing is performed to obtain modal parameters, including natural frequencies, mode shapes and damping in each mode. In FE method, two types of modeling, including shell and beam elements and solid element are used, applying ANSYS software. The analytical and the FE results are compared with the experimental one, showing good agreements. Because of insufficient experimental modal data for non-uniformly stiffeners distribution, the results of modal testing obtained in this study could be as useful reference for validating the accuracy of other analytical and numerical methods for free vibration analysis.     

基于灵敏度分析和优化方法的异形钢结构烟囱模型修正

为了给异形钢结构烟囱的抗风、抗震计算及健康监测提供可靠的有限元计算模型,采用钢结构烟囱风洞试验模型的模态参数作为基准,将灵敏度分析和优化方法与大型有限元分析软件相结合修正烟囱结构模型的有限元模型。首先对烟囱结构参数化建模,然后通过灵敏度分析选择合适的优化变量,最后应用一阶优化方法修正烟囱结构的有限元模型。结构构件间连接的过分简化常会带来较大误差,因此烟囱结构的部分连接节点采用半刚性计算模型。结果表明,经过修正后的有限元模型动力计算结果与试验结果非常接近。     

Improved bridge evaluation through finite element model updating using static and dynamic measurements

The potential of combining finite element (FE) analysis with on-site measurement through finite element model updating is indisputable. However, simplified initial models and too few measurements can lead to updated model parameters which conceal inaccurate modelling assumptions rather than improve estimates of the actual structural parameters. Therefore, the methodology proposed aims primarily to eliminate inaccurate modelling simplification by means of manual model refinements before parameters are estimated by non-linear optimization. In addition, multi-response objective functions are introduced, which allow combing different types of measurements to obtain a solid basis for parameter estimation. The proposed methodology was applied to one of the world’s largest single-arch bridges, the new Svinesund Bridge, and disclosed a need to use a non-linear model in order to estimate the structural parameters more accurately. The resultant model could reproduce the measurements with significantly improved accuracy without assigning unrealistic values to model parameters.     

Three-dimensional finite element modelling of long-span cable-stayed bridges

Finite element (FE) modelling is a prominent way to simulate both static and dynamic characteristics of cable-stayed bridges to understand their structural complexities. Many initial FE models have not been successful in the analysis of the structural behaviour of cable-stayed bridges. This paper presents the details of an updated FE modelling procedure for long-span cable-stayed bridges. The design information of Tatara Bridge with an 850-m main span is considered for numerical studies. The dynamic properties of the FE model, including mode shapes and natural frequencies, are compared with field vibration test results to validate the presented modelling process. Sensitivity analysis of structural parameters is also applied to update effective parameters and understand the structural behaviour of the bridge. The new and beneficial aspects presented in this paper regarding FE modelling procedure and finding effective material and structural parameters will be useful for future design and analysis of cable-stayed bridges.     

在役T构桥梁的有限元模型修正

有限元模型修正是建立精确的基准有限元模型的基础。以在役T构桥梁——324国道乌龙江大桥为工程背景,利用ANSYS软件建立了全桥结构的三维有限元模型,进行了结构静、动力数值模拟分析,并与实测结果进行了比较;结果表明,未修正的有限元模型计算结果与实测结果存在较大误差。通过参数灵敏度分析,确定了对桥梁结构静、动力特性影响均较大的参数;采用零阶和一阶算法,基于自振频率与静力挠度组合的目标函数,对乌龙江大桥有限元模型进行了修正。修正后的有限元模型能较真实地反映结构的实际状态,可作为该桥梁长期健康监测与状态评估的基准有限元模型。     

悬索桥主塔结构的有限元模拟方法研究：2.模型修正与验证

本文在文献[1]建立的润扬悬索桥主塔的初始有限元模型基础上,采用基于灵敏度分析的模型参数修正方法,结合主塔动力特性的测试结果对主塔的初始有限元模型进行了动力修正。通过三种修正方案的比较,可以看出考虑梁柱节点刚域的影响以及修正参数的上、下限值约束的修正方案最可行。修正后的润扬悬索桥主塔模型能全面、正确地反映主塔结构的动力特性,可作为主塔结构健康监测与安全评估的基准有限元模型。     

悬索桥主塔结构的有限元模拟方法研究：1．初始模型

在有限元模型误差来源分析的基础之上,以润扬悬索桥主塔结构环境振动测试结果为基准,提出了分层次分阶段的修正主塔结构有限元模型的方法。首先依据设计图纸建立最初的有限元模型,经过模型阶次误差分析和结构误差分析之后,确定了主塔各构件单元划分的数目和梁柱节点刚性区域的模拟方法。在此基础之上,文献[1]将进一步对本文所建立的初始有限元模型进行参数误差的修正,从而最终建立润扬悬索桥主塔结构的基准有限元模型。     

A modal-based Kalman filtering framework for mode extraction and decomposition of damped structures

The mode shape is one of the important modal parameters that enables to visualize the intrinsic behavior of a structure as well as the quantity of interest by extracting or separating modal response from measurements. In this study, a new output-only framework is proposed to extract modes using a modal-based Kalman filter defined in the modal space and identify the mode shape by manipulating the correlation between the separated modes and the measured responses. It is also shown that the proposed framework can be extended to estimate the mode shapes of a non-classically damped structure in state space when the state variable is constructed from the measured responses and applied to the modal-based Kalman filter. The mode shape estimation framework proposed in this study was verified by numerical simulations and full-scale measurements. From the verification examples and their results, it was noted that the proposed modal identification framework is not influenced by the presence of noise, and it can be applied to identify the state-space mode shapes of non-classically damped systems as well as systems with very closely distributed modes such as buildings equipped with tuned mass dampers.     

Use of Ritz method for damage detection of reinforced and post-tensioned concrete beams

Damage-induced changes in modal characteristics can be detected using experimental modal analysis. In this article, based on changes in natural frequency, mode shapes, and damping ratios, a methodology for detecting damage location and severity is presented. The damage was induced by application of point load at half span location on the reinforced and post-tensioned concrete beams. The load was gradually increased to obtain different crack patterns to be used in simulation of damage scenarios. Experimental modal analysis was performed on the undamaged and damaged beams. The natural frequency and mode shapes were used to determine the location of damage. The approach is developed at an element level with a conventional finite element (FE) model by Ritz method, which is called Ritz damage detection method (RDDM). The mathematical model for both damped and undamped damaged structures have been established through the eigenvalue equations. The singular value decomposition (SVD) technique is used for determination of damage or sound index. These indexes are sensitive to the change of dynamic characteristics due to damages. This approach is applied to five simply supported post-tensioned concrete beams. The numerical results show that the exact location and severity of damage for different simulated damage scenarios could be efficiency found by the present methodology.