On a modal damping identification model for non-classically damped linear building structures subjected to earthquakes

A simple modal damping identification model developed by the present authors for classically damped linear building frames is extended here to the non-classically damped case. The modal damping values are obtained with the aid of the frequency domain modulus of the roof-to-basement transfer function and the resonant frequencies of the structure (peaks of the transfer function) as well as the modal participation factors and mode shapes of the undamped structure. The assumption is made that the modulus of the transfer function of the non-classically damped structure matches the one of the classically damped structure in a discrete manner, i.e., at the resonant frequencies of that function modulus. This proposed approximate identification method is applied to a number of plane building frames with and without pronounced non-classical damping under different with respect to their frequency content earthquakes and its limitations and range of applicability are assessed with respect to the accuracy of both the identified damping ratios and that of the seismic structural response obtained by classical mode superposition and use of those identified modal damping ratios.     

基于BP神经网络的网格结构损伤识别与试验研究

针对网格结构中杆件数量众多,但节点数总是远远小于杆件数的特点,损伤识别中采用了基于BP神经网络技术和面向节点的损伤初步定位方法的网格结构损伤识别的三步法。对双层柱面网壳结构模型在不同杆件去掉时的四种损伤情况下的振动特性进行了实测,并以实测低阶模态的频率变化率和少数测点的振型分量作为神经网络输入参数,对模型的各种损伤情况进行了识别。结果表明,所用的方法可以精简神经网络的结构,并提高其模式识别的能力。该方法可用于对大型复杂结构的损伤识别。     

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.     

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。     

A refined Frequency Domain Decomposition tool for structural modal monitoring in earthquake engineering

Output-only structural identification is developed by a refined Frequency Domain Decomposition(rFDD) approach, towards assessing current modal properties of heavy-damped buildings(in terms of identification challenge), under strong ground motions. Structural responses from earthquake excitations are taken as input signals for the identification algorithm. A new dedicated computational procedure, based on coupled Chebyshev Type Ⅱ bandpass filters, is outlined for the effective estimation of natural frequencies, mode shapes and modal damping ratios. The identification technique is also coupled with a Gabor Wavelet Transform, resulting in an effective and self-contained time-frequency analysis framework. Simulated response signals generated by shear-type frames(with variable structural features) are used as a necessary validation condition. In this context use is made of a complete set of seismic records taken from the FEMA P695 database, i.e. all 44 "Far-Field"(22 NS, 22 WE) earthquake signals. The modal estimates are statistically compared to their target values, proving the accuracy of the developed algorithm in providing prompt and accurate estimates of all current strong ground motion modal parameters. At this stage, such analysis tool may be employed for convenient application in the realm of Earthquake Engineering, towards potential Structural Health Monitoring and damage detection purposes.     

Modal identification of a centrifuge soil model using subspace state space method

In this paper, modal parameters of a layered soil system comprising of a soft clay layer overlying a dense sand layer are identified from accelerometer recordings in a centrifuge test. For the first time, the subspace state space system identification (4SID) method was employed to identify the natural frequencies, damping ratios, and complex valued mode shapes while considering the non-proportional damping in a soil system. A brief review of system identification concepts needed for application of the 4SID techniques to structural modal identification is provided in the paper. The identified natural frequencies were validated against those estimated by transfer function spectra. The computed normal mode shapes were compared with closed-form solutions obtained from the one-dimensional shear wave propagation equation. The identified modal parameters were then employed to synthesize state space prediction models which were subsequently used to simulate the soil response to three successive base motions. The identified models captured acceleration time-histories and corresponding Fourier spectra reasonably well in the small and moderate shaking events. In the stronger third shaking event, the model performed well at greater soil depths, but was less accurate near the surface where nonlinearities dominated.     

On the natural frequencies of infilled frames

Three approximate models are considered for the evaluation of the first few natural frequencies and associated mode shapes of infilled frames, a commonly occurring composite structural system formed by the combination of plane frames and filler walls. The reasonableness of the models is checked with the available experimental results and with the corresponding finite element solutions. The multiple strut model, wherein the infills are replaced by a set of equivalent multiple struts, can account for the frame–infill separation and infill openings and this model is seen to be an improvement over the single equivalent diagonal strut models proposed by earlier investigators. The shear—flexure cantilever analogy, by rationally evaluating the fundamental frequency, aids the equivalent lateral load procedures of the earthquake analysis. For dealing with the frames with central infill openings an equivalent plane frame model is discussed. Besides presenting the approximate models, the effect of frame—infill separation in reducing the fundamental frequency is investigated and an empirical relation is presented in this regard. Also some of the factors influencing the frame—infill contact lengths are studied and this indicates that the contact lengths are highly sensitive and indeterminate. Some constructional methods for avoiding separation and ensuring effective composite action between the frame and infill are also suggested.     

Earthquake‐induced structural response output‐only identification by two different Operational Modal Analysis techniques

Output‐only system identification is developed here towards assessing current modal dynamic properties of buildings under seismic excitation. Earthquake‐induced structural response signals are adopted as input channels for two different Operational Modal Analysis (OMA) techniques, namely, a refined Frequency Domain Decomposition (rFDD) algorithm and an improved Data‐Driven Stochastic Subspace Identification (SSI‐DATA) procedure. Despite that short‐duration, non‐stationary, earthquake‐induced structural response signals shall not fulfil traditional OMA assumptions, these implementations are specifically formulated to operate with seismic responses and simultaneous heavy damping (in terms of identification challenge), for a consistent estimation of natural frequencies, mode shapes, and modal damping ratios. A linear ten‐storey frame structure under a set of ten selected earthquake base‐excitation instances is numerically simulated, by comparing the results from the two identification methods. According to this study, best up‐to‐date, reinterpreted OMA techniques may effectively be used to characterize the current dynamic behaviour of buildings, thus allowing for potential Structural Health Monitoring approaches in the Earthquake Engineering range.     

Effect of random material variability on seismic design parameters of steel frames

Whereas an increase in material yield stress beyond the code specified characteristic value enhances plastic capacity, it may cause a reduction in overall ductility and energy absorption capability of steel frames. Since quality control of various shapes of sections used on site is difficult to impose, the effect of this random variability on design response parameters should be accounted for in earthquake-resistant regulations. Moreover, the required weak-beam/strong-column design principle in particular, and failure mode control in general, could be undermined if the yield stresses in beam and column assume two opposite extremes in a random sample. This paper addresses the problem of defining the expected range of response parameters in a steel frame with randomly varying yield stress. A simple portal frame is designed using code specified characteristic values and verified by non-linear transient dynamic analysis. The influence of yield stress variability, including the degree of correlation between beam and column material properties, on several response parameters is assessed through a Monte Carlo simulation study. Results are presented from both univariate and bivariate statistical analyses that quantify the relationship between input (material) and output (response) parameters. Assessment of the interdependence of output parameters given a particular model for yield stress variability is also undertaken. It is shown that certain response parameters exhibit more favourable statistical properties than others. Thus, the implications for seismic code design are discussed in the light of these results.     

在线监测环境下土木结构的模态识别研究

建立在线监测环境下结构考虑时效的模态识别计算方案。采用基于各测点加速度响应互功率谱的频域多参考点模态识别法来实现结构模态参数的抽取,从而绕过了监测环境下激励监测的技术难题;并用频域的平均法使识别参数的拟合曲线平滑和发现参数的变化趋势。通过对美国结构健康监测研究小组公布的Benchmark问题的第一阶段解析模型模拟加速度响应数据的识别,表明本文采用的算法有较好的识别精度和识别速度,是一个可行的在线监测环境下的模态识别计算方案。     

A three-stage identification approach for hysteretic systems

This paper deals with the identification of the parameters of a smoothed hysteretic model which was proposed by Bouc and Wen with emphasis on restoring force hysteresis. The problem of estimating the parameters of this system on the basis of input-output data, possibly noise corrupted, is considered. Through the application of various simulated time histories from the hysteretic model, a three-stage systematic method of system identification was proposed. Four different methods of identification are arranged and conducted in this three-stage system identification. The first stage, a sequential regressional analysis is used to identify the equivalent linear system from which elastic or inelastic response can be identified. The identified parameters can be used in the stage when the system is in elastic response. In the second stage, both time domain least-squares method and Gauss-Newton method are applied. The convergence of the Gauss-Newton method can be guaranteed if the identified results from least-squares method are adopted as the initial values for Gauss-Newton method. In the third stage, the extended Kalman filtering technique is needed to identify the noise-corrupt data. Application of this algorithm to a SDOF non-deteriorating system is verified.     

Response‐only modal identification of structures using strong motion data

Dynamic characteristics of structures — viz. natural frequencies, damping ratios, and mode shapes — are central to earthquake‐resistant design. These values identified from field measurements are useful for model validation and health‐monitoring. Most system identification methods require input excitations motions to be measured and the structural response; however, the true input motions are seldom recordable. For example, when soil–structure interaction effects are non‐negligible, neither the free‐field motions nor the recorded responses of the foundations may be assumed as ‘input’. Even in the absence of soil–structure interaction, in many instances, the foundation responses are not recorded (or are recorded with a low signal‐to‐noise ratio). Unfortunately, existing output‐only methods are limited to free vibration data, or weak stationary ambient excitations. However, it is well‐known that the dynamic characteristics of most civil structures are amplitude‐dependent; thus, parameters identified from low‐amplitude responses do not match well with those from strong excitations, which arguably are more pertinent to seismic design. In this study, we present a new identification method through which a structure's dynamic characteristics can be extracted using only seismic response (output) signals. In this method, first, the response signals’ spatial time‐frequency distributions are used for blindly identifying the classical mode shapes and the modal coordinate signals. Second, cross‐relations among the modal coordinates are employed to determine the system's natural frequencies and damping ratios on the premise of linear behavior for the system. We use simulated (but realistic) data to verify the method, and also apply it to a real‐life data set to demonstrate its utility. Copyright © 2012 John Wiley & Sons, Ltd.     

A system identification approach to the detection of changes in both linear and non-linear structural parameters

This paper explores the potential of a new time domain identification procedure to detect changes in structural dynamic characteristics on the basis of measurements. This procedure is verified using mathematical models simulated on the computer. The experiments involve two eight-storey steel structures with and without energy devices, and a 47-storey building at San Francisco during the Loma Prieta earthquake. The recursive instrumental variable method and extended Kalman filter algorithm are used as identification algorithms. An exploratory investigation is made of the usefulness of various indices, such as mode shape and storey drift, that can be extracted accurately from identification to quantify changes in the characteristics of the physical system. It is concluded that the change of storey drift is the key information to the detection of changes in structural parameters, from which the proposed system identification algorithm can be applied with an appropriate inelastic model to simulate the dynamic behaviour of real structures undergoing strong ground motion excitations.     

Substructural first‐ and second‐order model identification for structural damage assessment

This paper presents two methods to perform system identification at the substructural level, taking advantage of reduction in the number of unknowns and degrees of freedom (DOFs) involved, for damage assessment of fairly large structures. The first method is based on first‐order state space formulation of the substructure where the eigensystem realization algorithm (ERA) and the observer/Kalman filter identification (OKID) are used. Identification at the global level is then performed to obtain the second‐order model parameters. In the second method, identification is performed at the substructural level in both the first‐ and second‐order model identification. Both methods are illustrated using numerical simulation studies where results indicate their significantly better performance than identification using the global structure, in terms of efficiency and accuracy. A 12‐DOF system and a fairly large structural system with 50 DOFs are used where the effects of noisy data are considered. In addition to numerical simulation studies, laboratory experiments involving an eight‐storey frame model are carried out to illustrate the performance of the proposed method. The identification results presented in terms of the stiffness integrity index show that the proposed methodology is able to locate and quantify damage fairly accurately. Copyright © 2005 John Wiley & Sons, Ltd.     

Dynamic response of a staggered wall-beam structure

A method for the dynamic analysis of staggered wall-beam frames is developed using consistent mass terms which are derived and given in simple terms. The method uses effective stiffnesses for wall-beam elements developed in an earlier paper. Experiments using a nine storey 1 : 15 scale perspex model are described. The first three natural frequencies of the model were obtained using two methods: sinusoidal external excitation of the structure with the base fixed and white noise excitation employing a single degree-of-freedom shake table, in the latter method with and without the addition of mass throughout the model. Agreement between analytical predictions of the first three natural frequencies and mode shapes and experimentally determined values is considered satisfactory, particularly for the first two modes. The lumped mass assumption gave reasonable results for these two cases, whereas the consistent mass theory gave reasonable results for the first three natural frequencies.     

Vector fragility surfaces for reinforced concrete frames in Europe

Traditional approaches to damage estimation in earthquake loss modelling make use of relationships between scalar intensity measures and scalar engineering demand parameters. In this study we present a series of vector-valued fragility surfaces computed for low- and mid-rise reinforced concrete frames typical of those found in Europe. The use of vectors of intensity measures can result in conditional standard deviations of logarithmic engineering demand parameters that are up to 50 % smaller than those from traditional scalar methods. These reductions have significant implications for the shapes of loss curves, particularly for long return periods. The most efficient vector corresponds to a combination of spectral acceleration and a spectral shape parameter, \(\langle \ln S_a, \ln N_p\rangle \) , when used to predict maximum interstorey drifts. The study also demonstrates that engineering demand parameters have significant heteroskedasticity with respect to various intensity measures and that this feature must be modelled correctly when constructing fragility curves. This feature of the models presented herein has not previously been accounted for during the development of fragility curves or surfaces.     

A model to simulate special concentrically braced frames beyond brace fracture

Special concentrically braced frames (SCBFs) are commonly used as the lateral‐load resisting system in buildings. SCBFs primarily sustain large deformation demands through inelastic action in the brace, including compression buckling and tension yielding; secondary yielding may occur in the gusset plate and framing elements. The preferred failure mode is brace fracture. Yielding, buckling, and fracture behavior results in highly nonlinear behavior and accurate analytical modeling of these frames is required. Prior research has shown that continuum models are capable of this level of simulation. However, those models are not suitable for structural engineering practice. To enable the use of accurate yet practical nonlinear models, a research study was undertaken to investigate modeling parameters for line‐element models, which is a more practical modeling approach. This portion of the study focused on methods to predict brace fracture. A fracture modeling approach simulated the nonlinear, cyclic response of SCBFs by correlating onset of fracture to the maximum strain range in the brace. The model accounts for important brace design parameters including slenderness, compactness, and yield strength. Fracture data from over 40 tests was used to calibrate the model and included single‐brace component, single story frame, and full‐scale multistory frame specimens. The proposed fracture model is more accurate and simpler than other, previously proposed models. As a result, the proposed model is an ideal candidate for practical performance simulation of SCBFs. Copyright © 2012 John Wiley & Sons, Ltd.     

Automatic modal parameter identification of high arch dams: feasibility verification

Modal parameters, including fundamental frequencies, damping ratios, and mode shapes, could be used to evaluate the health condition of structures. Automatic modal parameter identification, which plays an essential role in realtime structural health monitoring, has become a popular topic in recent years. In this study, an automatic modal parameter identification procedure for high arch dams is proposed. The proposed procedure is implemented by combining the density-based spatial clustering of applications with noise (DBSCAN) algorithm and the stochastic subspace identification (SSI). The 210-m-high Dagangshan Dam is investigated as an example to verify the feasibility of the procedure. The results show that the DBSCAN algorithm is robust enough to interpret the stabilization diagram from SSI and may avoid outline modes. This leads to the proposed procedure obtaining a better performance than the partitioned clustering and hierarchical clustering algorithms. In addition, the errors of the identified frequencies of the arch dam are within 4%, and the identified mode shapes are in agreement with those obtained from the finite element model, which implies that the proposed procedure is accurate enough to use in modal parameter identification. The procedure is feasible for online modal parameter identification and modal tracking of arch dams.

     

Dynamic characteristics of coupled wall-frame systems

The paper presents the first three natural frequencies and the corresponding mode shapes for fixed-base multistorey buildings which can be idealized as an equivalent planar coupled shear wall connected in series to an equivalent frame. The coupled wall is modelled as a continuum of uniform properties and the frame as a uniform shear beam, the connection between the two elements being taken as continuous. Solutions are obtained by treating the structure as a lumped parameter system with twenty equidistant discrete masses having only translational inertia. The relevant flexibility matrix is, however, generated from the exact solution of the governing differential equation for the continuum subjected to point loading. The results are presented for various combinations of the three non-dimensional parameters which are sufficient to describe all the geometric and material properties of the system. The mode shapes are presented in terms of the first three normal modes of a uniform slender cantilever. The non-dimensional base shears required for the response spectrum analysis of buildings of the type under consideration are also given for the three modes and for the various combinations of the three non-dimensional parameters mentioned above. The use of the results is illustrated by an example.     

Dual state–parameter estimation of hydrological models using ensemble Kalman filter

Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state–parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously; (2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model.