Story-by-story estimation of the stiffness parameters of laterally-torsionally coupled buildings using forced or ambient vibration data: I. Formulation and verification

A new parameter estimation algorithm is described for identifying the stiffness properties of torsionally coupled shear buildings from their linear response due to ambient excitations or during low-amplitude forced-vibration tests. The algorithm is based on the time-domain equations of motion, and yields estimates of the stiffness properties using a measure of the equilibrium of forces acting on each floor over a time interval. The banded structure of the stiffness matrix — a property intrinsic to torsion-shear buildings — is exploited to decompose the initial inverse problem into several problems of reduced size. This decomposition allows the identification of lateral and torsional stiffnesses of individual stories, independent of the others. The algorithm utilizes vibration data where input excitation is known/measured, which is typical for forced-vibration tests and earthquakes. If the ambient vibrations of the structure are adequately uncorrelated to the (unknown) external forces that induce such vibrations, then the algorithm can also be modified for output-only system identification. The proposed algorithm is verified — and its various attributes are investigated — using simulation data from the ‘Analytical Phase I’ of the IASC (International Association for Structural Control)-ASCE (American Society of Civil Engineers) benchmark studies. The companion article is devoted to the algorithm's application to experimental data, using data from the ‘Experimental Phase’ of the same benchmark studies. Copyright © 2011 John Wiley & Sons, Ltd.     

基于大地脉动的新型损伤识别指数

阐述了一种新型损伤识别指数,进行该指数稳定性验算和计算绘制损伤指数变化率与损伤程度的关系曲线。数值模拟结果显示,该指数对小损伤敏感,可以进行损伤判定与标定,具有一定潜力。     

Damage localization under ambient vibration using changes in flexibility

In recent years, Structural Health Monitoring (SHM) has emerged as a new research area in civil engineering. Most existing health monitoring methodologies require direct measurement of input excitation for implementation. However, in many cases, there is no easy way to measure these inputs - or alternatively to externally excite the structure. Therefore, SHM methods based on ambient vibration have become important in civil engineering. In this paper, an approach is proposed based on the Damage Location Vector (DLV) method to handle the ambient vibration case. Here, this flexibility-matrix-based damage localization method is combined with a modal expansion technique to eliminate the need to measure the input excitation. As a by-product of this approach, in addition to determining the location of the damage, an estimate of the damage extent also can be determined. Finally, a numerical example analyzing a truss structure with limited sensors and noisy measurement is provided to verify the efficacy of the proposed approach. Sponsored by: Notional Science Foundation Grant CMS 99-00234     

On the repeatability and consistency of three-component ambient vibration array measurements

Ambient vibration measurements with small, temporary arrays that produce estimates of surface wave dispersion have become increasingly popular as a low-cost, non-invasive tool for site characterisation. An important requirement for these measurements to be meaningful, however, is the temporal consistency and repeatability of the resulting dispersion and spatial autocorrelation curve estimates. Data acquired within several European research projects (NERIES task JRA4, SESAME, and other multinational experiments) offer the chance to investigate the variability of the derived data products. The dataset analysed here consists of repeated array measurements, with several years of time elapsed between them. The measurements were conducted by different groups in different seasons, using different instrumentations and array layouts, at six sites in Greece and Italy. Ambient vibration amplitude spectra and locations of dominant sources vary between the two measurements at each location. Still, analysis indicates that this does not influence the derived dispersion information, which is stable in time and neither influenced by the instrumentation nor the analyst. The frequency range over which the dispersion curves and spatial autocorrelation curves can be reliably estimated depends on the array dimensions (minimum and maximum aperture) used in the specific deployment, though, and may accordingly vary between the repeated experiments. The relative contribution of Rayleigh and Love waves to the wavefield can likewise change between repeated measurements. The observed relative contribution of Rayleigh waves is generally at or below 50%, with especially low values for the rural sites. Besides, the visibility of higher modes depends on the noise wavefield conditions. The similarity of the dispersion and autocorrelation curves measured at each site indicates that the curves are stable, mainly determined by the sub-surface structure, and can thus be used to derive velocity information with depth. Differences between velocity models for the same site derived from independently determined dispersion and autocorrelation curves—as observed in other studies—are consequently not adequately explained by uncertainties in the measurement part.     

Isolation of soil-structure interaction effects by full-scale forced vibration tests

Forced vibration tests designed to isolate the effects of soil-structure interaction are described and the results obtained for the nine-storey reinforced concrete Millikan Library Building are analysed. It is shown that it is possible to determine experimentally the fixed-base natural frequencies and modal damping ratios of the superstructure. These values may be significantly different from the resonant frequencies and damping ratios of the complete structure-foundation-soil system. It is also shown that forced vibration tests can be used to obtain estimates of the foundation impedance functions. In the case of the Millikan Library it is found that during forced vibration tests the rigid-body motion associated with translation and rocking of the base accounts for more than 30 per cent of the total response on the roof and that the deformation of the superstructure at the fundamental frequencies of the system is almost entirely due to the inertial forces generated by translation and rocking of the base.     

Hybrid vibration experiments with a bridge foundation system model

In order to improve seismic design technology of bridges, it is necessary to evaluate the vibration characteristics of a bridge–soil system that consists of soil, foundation structure, pier and superstructure. However, there have been few experimental studies on seismic behavior of bridge–soil system. In this paper, we conducted the hybrid vibration experiment on seismic behavior of bridge–soil system, and examined the applicability of hybrid vibration experiment to study seismic response of bridge–soil system. Based on the experiment results, seismic response of bridge was quantitatively studied.     

Effective ambient vibration testing for validating numerical models of concrete dams

Ambient vibration tests were conducted on a 56 metre high concrete gravity dam to measure its modal properties for validating a finite element model of the dam–reservoir–foundation system. Excitation was provided by wind, by reservoir water cascading down the spillweir, and by the force of water released through outlet-pipes. Vibrations of the dam were measured using accelerometers, and 3-hour data records were acquired from each location. Data were processed by testing for stationarity and rejecting non-stationary portions before Fourier analysis. Power spectra with low variance were generated from which natural frequencies of the dam were identified clearly and modal damping factors estimated. Modal analysis of the frequency response spectra yielded mode shapes for the six lowest lateral modes of vibration of the dam. The finite element model for the dam was analysed using EACD-3D, and the computed mode shapes and natural frequencies compared well with the measured results. The study demonstrates that ambient vibration testing can offer a viable alternative to forced vibration testing when only the modal properties of a dam are required. Copyright © 1999 John Wiley & Sons, Ltd.     

Modal identification of structures from ambient vibration,free vibration,and seismic response data via a subspace approach

This work presents a unified procedure for determining the natural frequencies, modal damping ratios and modal shapes of a structure from its ambient vibration, free vibration and earthquake response data. To evaluate the coefficient matrices of a state‐space model, the proposed procedure applies a subspace approach cooperating with an instrumental variable concept. The dynamic characteristics of a structure are determined from the coefficient matrices. The feasibility of the procedure is demonstrated through processing an in situ ambient vibration measurement of a five‐storey steel frame, an impulse response measurement of a three‐span continuous bridge, and simulated earthquake responses of five‐storey steel frames from shaking table tests. The excellent agreement of the results obtained herein with those published previously confirms the feasibility of the present procedure. Copyright © 2001 John Wiley & Sons, Ltd.     

Experimental and finite element studies of the forced vibration response of morrow point dam

Measured accelerations and water pressures obtained during a recent forced vibration test on a large thin arch dam at high water are compared to predictions from a finite element model for which water compressibility is both included and neglected. The numerical model is calibrated using the antisymmetric response data because they are only slightly affected by water compressibility; good agreement is obtained. In the effort to reproduce the symmetric response data, for which water compressibility plays a strong role, the calibrated model shows better correlation when water compressibility is included, but the agreement is still inadequate. A successful isolation of the fundamental water resonance from the experimental data shows significantly different features from those of the numerical water model, indicating possible inaccuracy in the assumed geometry and/or boundary conditions for the reservoir. Some other results at low water level are also included.     

Dynamic characteristics of soil-foundation interaction system detected from forced vibration test and earthquake observation

This paper presents some results on the following subjects obtained from in-situ forced vibration tests and earthquake observations. (1) The characteristics of the radiation damping of soil-foundation interaction systems vs. non-dimensional frequency a₀ (=ωr/V_s) were experimentally estimated by the equivalent damping ratios h_H ( = K′_H/2K_H) and h_R ( = K′_R/2K_R), which were defined by complex stiffnesses 1K_H (= K_H + iK_H) and 1K_R (= K_R + iK′_R) of soil. The results for h_H and h_R of base rock were compared with those of soft soil. (2) A comparative study of experimental and theoretical results was made. The theoretical results were obtained from elastic half-space theory. (3) A semi-empirical equation to estimate the equivalent S-wave velocity for the elastic half-space model is proposed here, considering the effects of layered media. (4) Various comparisons of the results of 1 K_H, 1 K_R, h_H and h_R of forced vibration tests and earthquake observations were made.     

Field experiments on wave propagation and vibration isolation by using wave barriers

In this paper, the obtained results from the experimental studies describe the basic characteristics of wave propagation and ability of possible measures to reduce the impact of soil vibrations on structural response for both active and passive isolation cases. A series of field tests on the foundation vibrations generated by electrodynamic shaker are performed to examine the screening efficiency of open and in-filled trench barriers which are constructed for full-scale measurement. From field measurements of amplitude with and without the barrier, the amplitude reduction ratio is estimated at different points of interest. Wave propagating characteristics and frequency-dependent screening effects of the wave barriers are investigated according to various isolation material stiffnesses. The remarkable outcomes from these experimental studies can be briefly generalized as follows: backfilled trench with softer material than soil is more effective for the passive isolation than the active one. The reduction effects of wave barriers depend on the frequency of vibration source for both passive and active isolation cases. In-situ measurements confirm that vibration screening systems using open or in-filled trench barriers can be applied as a reduction measure for soil vibrations due to a moving load which is considered as stationary wave source in this problem.     

The importance of ambient and forced vibration measurements for the results of seismic performance assessment of buildings obtained by using a simplified non-linear procedure: case study of an old masonry building

The seismic performance assessment of existing masonry buildings involves many uncertainties, whose impact can be reduced to some extent by using non-destructive in-situ tests of such buildings, at least when destructive in-situ tests, which can provide more reliable results, cannot be performed. In this paper the extent of the potential beneficial effects achievable by calibration of a structural model of a building to its experimentally estimated vibration periods has been investigated. This was done by performing measurements of ambient and forced vibrations on an old two-storey masonry building, and by then assessing its seismic performance using a simplified nonlinear method. The results of numerical investigations revealed that the natural vibration periods of such buildings can be reproduced with sufficient accuracy, although it is possible that they will be overestimated or underestimated by analysts by up to around 40 %. This means that the accuracy of the prediction of the intermediate results of the seismic performance assessment of any particular building can be significantly increased by calibration of the structural model. Additionally, the beneficial effects of such calibration were observed even in the case of the final outcome of the nonlinear analysis, which is expressed through the near-collapse limit state capacity in terms of the peak ground acceleration.     

钢结构房屋动力特性脉动法测试研究

对上海地区的10幢钢结构建筑进行脉动法测试并采集数据,得到广义钢结构房屋的动力特性。选取其中1栋典型建筑通过多次测试和数值模拟分别验证测试的稳定性和准确性。通过分析处理测试数据建立钢结构建筑一阶周期与结构层数或高度的线性关系式,并归纳总结了等效阻尼比的测试结果,为验证结构动力特性理论计算结果、钢结构建筑减震隔震设计以及鉴定、加固改造、损伤识别提供依据。     

Natural frequencies measured from ambient vibration response of the arch dam of Mauvoisin

The resonance frequencies of the 250‐m‐high arch dam of Mauvoisin are obtained by way of ambient vibration tests. It is observed that the resonance frequencies initially increase with rising water level and then decrease with a further rise. This is linked to the two competing features of increasing entrained mass of water (reduction of the resonance frequencies) and of dam stiffening due to closing of the vertical construction joints (augmentation of the resonance frequencies). The ambient vibration test results are complemented by those obtained during earthquakes at an array of 12 accelerographs. Copyright © 2000 John Wiley & Sons, Ltd.     

Changes in dynamic characteristics of Lorca RC buildings from pre- and post-earthquake ambient vibration data

This paper estimates fundamental translational period and damping ratio parameters and examines the changes in dynamic characteristics of a set of low-to-medium rise buildings in Lorca town (SE of Spain) affected by the May 11th, 2011 earthquake. These building parameters have been calculated analysing structural dynamic response from ambient vibration measurements recorded at top RC buildings pre- and post earthquake, using the Fast Fourier Transform and the Randomdec technique. The empirical expression relating period \((T)\) and number of floor \((N)\) here obtained analysing ambient noise recorded on 59 healthy buildings before the earthquake is \(T= (0.054\pm 0.002)\, N\) , very similar to others empirical period–height relationships obtained for RC structures in the European built environment but quite different from code provisions. Measurements performed in 34 damaged buildings show a period elongation after the quake according to \(T^{*} =(0.075\pm 0.002)\,N\) expression. Moreover, we found a rise of the fundamental period with the EMS’s grade of damage of buildings. In contrast to natural frequency, damping ratio \((\xi )\) do not shows a significant variation with earthquake damage degree and the product \(\xi \, T\) remains near constant.     

土-箱形基石础-框架结构相互作用的顶部小幅激振试验研究

设计并完成了野外大比例(1:2)土-箱形基础-框架结构相互作用系统顶部小幅激振试验.通过改变上部结构质量和基础侧限埋深,激振试验得到了同一基础不同上部结构质量与同一上部结构不同基础侧限埋深等5种工况下相互作用对系统自振频率及箱形基础阻抗函数的影响.由试验结果分析可知,当上部结构质量增加时,上部结构与土体间的相对刚度降低,相互作用对系统自振频率的影响减弱;同时由于上部结构和基础间惯性相互作用的影响,基础阻抗函数随上部结构质量的增加而增加.随着基础侧限埋深的减小,基础刚度降低,相互作用体现得更加明显.与理论结果相比,无侧限埋深基础的平动和转动基础阻抗值和理论值吻合较好.由于基础侧边回填土剪切模量小于基础底部土体剪切模量,所以同理论值相比试验得到的基础侧限埋深对基础阻抗影响系数相对较小.     

土-箱形基础-框架结构相互作用的顶部小幅激振试验研究

设计并完成了野外大比例(1∶2)土-箱形基础-框架结构相互作用系统顶部小幅激振试验。通过改变上部结构质量和基础侧限埋深,激振试验得到了同一基础不同上部结构质量与同一上部结构不同基础侧限埋深等5种工况下相互作用对系统自振频率及箱形基础阻抗函数的影响。由试验结果分析可知,当上部结构质量增加时,上部结构与土体间的相对刚度降低,相互作用对系统自振频率的影响减弱;同时由于上部结构和基础间惯性相互作用的影响,基础阻抗函数随上部结构质量的增加而增加。随着基础侧限埋深的减小,基础刚度降低,相互作用体现得更加明显。与理论结果相比,无侧限埋深基础的平动和转动基础阻抗值和理论值吻合较好。由于基础侧边回填土剪切模量小于基础底部土体剪切模量,所以同理论值相比试验得到的基础侧限埋深对基础阻抗影响系数相对较小。     

Buoyancy forced interaction between estuary and inner shelf: observation

In May and June of 1990 we explored the hydrographic variability of the Delaware Estuary and the adjacent inner shelf with shipboard instruments. We found significant three-dimensional density variability both within the estuary and on the shelf. We found weak vertical stratification but strong transverse variability within the estuary, with denser water concentrating in the center of the estuary and two branches of lighter water near both shores. On the shelf, the buoyant estuarine water forms a southward flowing coastal current in the direction of Kelvin wave phase propagation (downstream). ADCP observations and thermal wind calculations indicate a flow of 10–20 cm s⁻¹ downstream. Both the width of the coastal current and the magnitude of horizontal density gradients undergo substantial variations along the shelf.