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.     

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.     

Analysis of the observed seismic response of a highway bridge

Strong-motion accelerograms obtained on the San Juan Bautista 156/101 Separation Bridge during the 6 August 1979 Coyote Lake, California, earthquake are used to examine the response of this multiple-span bridge to moderate levels of earthquake loading. Although the bridge was not damaged, the records are of significant engineering interest as they are the first to be recorded on a highway bridge structure in North America. A technique of system identification is used to determine optimal modal parameters for linear models which can closely replicate the observed time-domain seismic response of the bridge. Time variations in frequency and damping in the horizontal response are identified using a moving-window analysis. A three-dimensional finite element model is developed to study the bridge response in detail. The first two horizontal modal frequencies computed from this model are in excellent agreement with information obtained during the system identification analysis provided the finite element model's expansion joints are locked, preventing relative translational motions from occurring across the joints. Locking is confirmed by the observed seismic deformations of the structure in the fundamental mode. Fundamental vertical frequencies of the individual spans, predicted by the finite element model, are in very good agreement with ambient vibration test data.     

A reassessment of dynamic characteristics of the Quincy Bayview Bridge using output‐only identification techniques

A reassessment of the dynamic characteristics of the 542 m cable‐stayed Bayview Bridge in Quincy, Illinois, is presented using a newly developed output‐only system identification technique. The technique is applied to an extensive set of ambient vibration response data acquired from the bridge in 1987. Vertical, torsional and transverse modal frequencies of the deck are identified, and uncertainty in damping values are estimated using an automated procedure on several redundant measurements at four locations. Important practical implementation issues associated with the implementation of the procedure and selection of algorithm design parameters for stochastic subspace identification techniques are discussed. An overall mean and standard deviation of damping of 1.0±0.8% is estimated considering all identified vertical, torsional and transverse modes in the 0–2 Hz band. The mean damping for the fundamental vertical mode (0.37 Hz) is identified as 1.4±0.5%, and for the first coupled torsion–transverse mode (0.56 Hz) is identified as 1.1±0.8%. Variability in the damping estimates is shown to decrease as estimated modal RMS acceleration levels increase. Standard deviations on estimated damping range from 0.05% to 2%. The results are shown to be a substantial improvement in the evaluation of damping compared to earlier spectral analysis conducted on the same data set. Copyright © 2005 John Wiley & Sons, Ltd.     

System identification of a building from multiple seismic records

This paper describes the identification of finite dimensional, linear, time‐invariant models of a 4‐story building in the state space representation using multiple data sets of earthquake response. The building, instrumented with 31 accelerometers, is located on the University of California, Irvine campus. Multiple data sets, recorded during the 2005 Yucaipa, 2005 San Clemente, 2008 Chino Hills and 2009 Inglewood earthquakes, are used for identification and validation. Considering the response of the building as the output and the ground motion as the input, the state space models that represent the underlying dynamics of the building in the discrete‐time domain corresponding to each data set are identified. The time‐domain Eigensystem Realization Algorithm with the Observer/Kalman filter identification procedure are adopted in this paper, and the modal parameters of the identified models are consistently determined by constructing stabilization diagrams. The four state space models identified demonstrate that the response of the building is amplitude dependent with the response frequency and damping, being dependent on the magnitude of ground excitation. The practical application of this finding is that the consistency of this building response to future earthquakes can be quickly assessed, within the range of ground excitations considered (0.005g–0.074g), for consistency with prior response—this assessment of consistent response is discussed and demonstrated with reference to the four earthquake events considered in this study. Inclusion of data sets relating to future earthquakes will enable the findings to be extended to a wider range of ground excitation magnitudes. Copyright © 2010 John Wiley & Sons, Ltd.     

Tracking modal parameters from building seismic response data using recursive subspace identification algorithm

Tracking modal parameters and estimating the current structural state of a building from seismic response measurements, particularly during strong earthquake excitations, can provide useful information for building safety assessment and the adaptive control of a structure. Therefore, online or recursive identification techniques need to be developed and implemented for building seismic response monitoring. This paper develops and examines different methods to track modal parameters from building seismic response data. The methods include recursive data‐driven subspace identification (RSI‐DATA) using Givens rotation algorithm, and RSI‐DATA using Bona fide algorithm. The question on how well the results of RSI‐DATA reflect the real condition is investigated and verified with a bilinear SDOF simulation study. Time‐varying modal parameters of a four‐story reinforced concrete school building are identified based on a series of earthquake excitations, including several seismic events, large and small. Discussions on the different methods' ability to track the time‐varying modal parameters are presented. The variation of the identified building modal frequencies and damping ratios from a series of event‐by‐event seismic responses, particularly before and after retrofitting of the building is also discussed. Copyright © 2017 John Wiley & Sons, Ltd.     

Traffic‐induced variability in dynamic properties of cable‐stayed bridge

The traffic‐induced variability in the dynamic properties of a cable‐stayed bridge is investigated using ambient vibration measurements. Under a relatively steady wind and temperature environment, the ambient vibration test was conducted on the bridge with normal traffic conditions and totally 24 h acceleration response time histories were recorded. These data are divided into 12 sections with each data section containing 2 h measurements. Thereby the modal variability due to changing traffic loading is investigated through post‐processing of the data in each section in both amplitude and frequency domains. The result indicates that the natural frequencies of the global modes can exhibit as much as 1% variation within a day. The modal amplitudes of each mode as well as the modal deflection at each measurement position vary insignificantly. The damping ratios however are sensitive to the vibration intensity, especially when the deck vibration exceeds a certain level. Copyright © 2002 John Wiley & Sons, Ltd.     

System identification of the Vincent Thomas suspension bridge using earthquake records

The Vincent Thomas Bridge in the Los Angeles metropolitan area, is a critical artery for commercial traffic flow in and out of the Los Angeles Harbor, and is at risk in the seismically active Southern California region, particularly because it straddles the Palos Verdes fault zone. A combination of linear and non‐linear system identification techniques is employed to obtain a complete reduced‐order, multi‐input–multi‐output (MIMO) dynamic model of the Vincent Thomas Bridge based on the dynamic response of the structure to the 1987 Whittier and 1994 Northridge earthquakes. Starting with the available acceleration measurements (which consists of 15 accelerometers on the bridge structure and 10 accelerometers at various locations on its base), an efficient least‐squares‐based time‐domain identification procedure is applied to the data set to develop a reduced‐order, equivalent linear, multi‐degree‐of‐freedom model. Although not the main focus of this study, the linear system identification method is also combined with a non‐parametric identification technique, to generate a reduced‐order non‐linear mathematical model suitable for use in subsequent studies to predict, with good fidelity, the total response of the bridge under arbitrary dynamic environments. Results of this study yield measurements of the equivalent linear modal properties (frequencies, mode shapes and non‐proportional damping) as well as quantitative measures of the extent and nature of non‐linear interaction forces arising from strong ground shaking. It is shown that, for the particular subset of observations used in the identification procedure, the apparent non‐linearities in the system restoring forces are quite significant, and they contribute substantially to the improved fidelity of the model. Also shown is the potential of the identification technique under discussion to detect slight changes in the structure's influence coefficients, which may be indicators of damage and degradation in the structure being monitored. Difficulties associated with accurately estimating damping for lightly damped long‐span structures from their earthquake response are discussed. The technical issues raised in this paper indicate the need for added spatial resolution in sensor instrumentation to obtain identified mathematical models of structural systems with the broadest range of validity. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Identification of modal parameters of non‐classically damped linear structures under multi‐component earthquake loading

A method for parametric system identification of classically damped linear system in frequency domain is adopted and extended for non‐classically damped linear systems subjected up to six components of earthquake ground motions. This method is able to work in multi‐input/multi‐output (MIMO) case. The response of a two‐degree‐of‐freedom model with non‐classical damping, excited by one‐component earthquake ground motion, is simulated and used to verify the proposed system identification method in the single‐input/multi‐output case. Also, the records of a 10 storey real building during the Northridge earthquake is used to verify the proposed system identification method in the MIMO case. In this case, at first, a single‐input/multi‐output assumption is considered for the system and modal parameters are identified, then other components of earthquake ground motions are added, respectively, and the modal parameters are identified again. This procedure is repeated until all four components of earthquake ground motions which are measured at the base level of the building are included in the identification process. The results of identification of real building show that consideration of non‐classical damping and inclusion of the multi‐components effect of earthquake ground motions can improve the least‐squares match between the finite Fourier transforms of recorded and calculated acceleration responses. Copyright © 2006 John Wiley & Sons, Ltd.     

Application of subspace identification technique to long‐term seismic response monitoring of structures

This paper addresses the issue of structural system identification using earthquake‐induced structural response. The proposed methodology is based on the subspace identification algorithm to perform identification of structural dynamic characteristics using input–output seismic response data. Incorporated with subspace identification algorithm, a scheme to remove spurious modes is also used to identify real system poles. The efficiency of the proposed method is shown by the analysis of all measurement data from all measurement directly. The recorded seismic response data of three structures (one 7‐story RC building, one midisolation building, and one isolated bridge), under Taiwan Strong Motion Instrumentation Program, are analyzed during the past 15 years. The results present the variation of the identified fundamental modal frequencies and damping ratios from all the recorded seismic events that these three structures had encountered during their service life. Seismic assessment of the structures from the identified system dynamic characteristics during the period of their service is discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

An active mass damper designed using ARX models of a building structure

This study proposes a new design method for an active mass damper (AMD) that is based on auto‐regressive exogenous models of a building structure. The proposed method uses the results of system identification in the field of active structural control. The uncontrolled structure is identified as auto‐regressive exogenous models via measurements under earthquake excitation and forced vibration. These models are linked with an equation of motion for the AMD to introduce a state equation and output equation for the AMD–structure interaction system in the discrete‐time space; the equations apply modern control theories to the AMD design. In the numerical applications of a 10‐degree‐of‐freedom building structure, linear quadratic regulator control is used to understand the fundamental characteristics of the proposed design procedure. The feedback control law requires the AMD's acceleration, velocity and stroke; the structure's acceleration; and the ground acceleration as vibration measurements. The numerical examples confirm the high applicability and control effectiveness of the proposed method. One remarkable advantage of the proposed method is that an equation of motion for the structure becomes unnecessary for designing controllers. Copyright © 2016 John Wiley & Sons, Ltd.     

Parameter identification of torsionally coupled shear buildings from earthquake response records

This paper presents an efficient procedure to determine the natural frequencies, modal damping ratios and mode shapes for torsionally coupled shear buildings using earthquake response records. It is shown that the responses recorded at the top and first floor levels are sufficient to identify the dominant modal properties of a multistoried torsionally coupled shear building with uniform mass and constant eccentricity even when the input excitation is not known. The procedure applies eigenrealization algorithm to generate the state‐space model of the structure using the cross‐correlations among the measured responses. The dynamic characteristics of the structure are determined from the state‐space realization matrices. Since the mode shapes are obtained only at the instrumented floor (top and first floors) levels, a new mode shape interpolation technique has been proposed to estimate the mode shape coefficients at the remaining floor levels. The application of the procedure has been demonstrated through a numerical experiment on an eight‐storied torsionally coupled shear building subjected to earthquake base excitation. The results show that the proposed parameter identification technique is capable of identifying dominant modal parameters and responses even with significant noise contamination of the response records. Copyright © 2008 John Wiley & Sons, Ltd.     

System identification applied to long‐span cable‐supported bridges using seismic records

This paper presents the application of system identification (SI) to long‐span cable‐supported bridges using seismic records. The SI method is based on the System Realization using Information Matrix (SRIM) that utilizes correlations between base motions and bridge accelerations to identify coefficient matrices of a state‐space model. Numerical simulations using a benchmark cable‐stayed bridge demonstrate the advantages of this method in dealing with multiple‐input multiple‐output (MIMO) data from relatively short seismic records. Important issues related to the effects of sensor arrangement, measurement noise, input inclusion, and the types of input with respect to identification results are also investigated. The method is applied to identify modal parameters of the Yokohama Bay Bridge, Rainbow Bridge, and Tsurumi Fairway Bridge using the records from the 2004 Chuetsu‐Niigata earthquake. Comparison of modal parameters with the results of ambient vibration tests, forced vibration tests, and analytical models are presented together with discussions regarding the effects of earthquake excitation amplitude on global and local structural modes. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluation of the measured seismic response of the Mexico City Cathedral

The seismic response of the Mexico City Cathedral built of very soft soil deposits is evaluated by using motions recorded in various parts of the structure during several moderate earthquakes. This unique set of records provides significant insight into the seismic response of this and other similar historic stone masonry structures. Free‐field ground motions are carefully compared in time and frequency domains with motions recorded at building basement. The dynamic characteristics of the structure are inferred from the earthquake records by using system identification techniques. Variation of seismic response for different seismic intensities is discussed. It is shown that, due to the soil–structure interaction, due to large differences between dominant frequencies of earthquake ground motions at the site and modal frequencies of vibration of the structure, and due to a particularly high viscous damping, seismic amplifications of ground motion in this and similar historic buildings erected on soft soil deposits are much smaller than that induced in most modern constructions. Nevertheless, earthquake records and analytical results show that several components of the structure such as its central dome and the bell towers may be subjected to local vibrations that significantly amplify ground motions. Overall, results indicate that in its present state the structure has an acceptable level of seismic safety. Copyright © 2008 John Wiley & Sons, Ltd.     

System identification of linear structures based on Hilbert–Huang spectral analysis. Part 1: normal modes

Based on the Hilbert–Huang spectral analysis, a method is proposed to identify multi‐degree‐of‐freedom (MDOF) linear systems using measured free vibration time histories. For MDOF systems, the normal modes have been assumed to exist. In this method, the measured response data, which are polluted by noises, are first decomposed into modal responses using the empirical mode decomposition (EMD) approach with intermittency criteria. Then, the Hilbert transform is applied to each modal response to obtain the instantaneous amplitude and phase angle time histories. A linear least‐square fit procedure is proposed to identify the natural frequency and damping ratio from the instantaneous amplitude and phase angle for each modal response. Based on a single measurement of the free vibration time history at one appropriate location, natural frequencies and damping ratios can be identified. When the responses at all degrees of freedom are measured, the mode shapes and the physical mass, damping and stiffness matrices of the structure can be determined. The applications of the proposed method are illustrated using three linear systems with different dynamic characteristics. Numerical simulation results demonstrate that the proposed system identification method yields quite accurate results, and it offers a new and effective tool for the system identification of linear structures in which normal modes exist. Copyright © 2003 John Wiley & Sons, Ltd.     

Two‐stage damage detection algorithms of structure using modal parameters identified from recursive subspace identification

Structural damage assessment under external loading, such as earthquake excitation, is an important issue in structural safety evaluation. In this regard, appropriate data analysis and feature extraction techniques are required to interpret the measured data and to identify the state of the structure and, if possible, to detect the damage. In this study, the recursive subspace identification with Bona‐fide LQ renewing algorithm (RSI‐BonaFide‐Oblique) incorporated with moving window technique is utilized to identify modal parameters such as natural frequencies, damping ratios, and mode shapes at each instant of time during the strong earthquake excitation. From which the least square stiffness method (LSSM) combined with the model updating technique, called efficient model correction method (EMCM), is used to estimate the first‐stage system stiffness matrix using the simplified model from the previously identified modal parameters (nominal model). In the second stage, 2 different damage assessment algorithms related to the nominal system stiffness matrix were derived. First, the model updating technique, called EMCM, is applied to correct the nominal model by the newly identified modal parameters during the strong motion. Second, the element damage index can be calculated using element damage index method (EDIM) to quantify the damage extent in each element. Verification of the proposed methods through the shaking table test data of 2 different types of structures and a building earthquake response data is demonstrated to specify its corresponding damage location, the time of occurrence during the excitation, and the percentage of stiffness reduction.     

Full-scale dynamic testing of the Alamillo cable-stayed bridge in Sevilla (Spain)

Accelerations and displacements due to dynamic excitation by simulated traffic consisting of two trucks, were measured on the deck and tower of the Alamillo cable-stayed bridge. Also the dynamic testing program included the measurement with accelerometers of the free-damped vibration of the 26 cables achieved by means of quick-releasing force. From these measurements it was possible to obtain the dynamic parameters of the bridge (natural frequencies and damping ratios) and the real forces in the cables. In the paper, only the tests, results and conclusions related to dynamic parameters of the bridge are presented. The objective of the dynamic tests herein described was to validate the mathematical modelling and the wind-tunnel models used in the dynamic analysis of the bridge in front of traffic and wind-forces. As the agreement between dynamic parameters of the real bridge and theoretical and scaled models was very satisfactory, the correct dynamic behaviour of the bridge in response to traffic and wind (vortex shedding, flutter, etc.) can be deduced jointly with the correct alignment and expected internal forces in the permanent state in tower and deck.     

高耸塔结构动力特性的监测与分析

使用适合于高柔结构的测试系统和测试技术,监测了塔,陕西塔和天津塔在环境振动激励下不同高程的加速度反应,使用在ＭＡＴＬＡＢ语言环境下编制的数据处理,分析,模态识别程序在微机上对各测点输出信号进行了处理,分析,识别得出３座塔结构平动前１０阶模态频率和前３阶模态阻尼比。