Parameter identification of framed structures using an improved finite element model‐updating method—Part II: application to experimental data

In this study, we determine an updated finite element model of a reinforced concrete building—which was damaged from shaking during 1994 Northridge earthquake—using forced‐vibration test data and a novel model‐updating technique. Developed and verified in the companion paper (viz. BVLSrc, Earthquake Eng. Struct. Dyn. 2006; this issue), this iterative technique incorporates novel sensitivity‐based relative constraints to avoid ill conditioning that results from spatial incompleteness of measured data. We used frequency response functions and natural frequencies as input for the model‐updating problem. These data were extracted from measurements obtained during a white‐noise excitation applied at the roof of the building using a linear inertial shaker. Flexural stiffness values of properly grouped structural members, modal damping ratios, and translational and rotational mass values were chosen as the updating parameters, so that the converged results had direct physical interpretations, and thus, comparisons with common parameters used in seismic design and evaluation of buildings could be made. We investigated the veracity of the updated finite element model by comparing the predicted and measured dynamic responses under a second, and different type of forced (sine‐sweep) vibration, test. These results indicate that the updated model replicates the dynamic behaviour of the building reasonably well. Furthermore, the updated stiffness factors appear to be well correlated with the observed building damage patterns (i.e. their location and severity). Copyright © 2006 John Wiley & Sons, Ltd.     

Parameter identification for on‐line model updating in hybrid simulations using a gradient‐based method

To improve the efficiency of model fitting, parameter identification techniques have been actively investigated. Recently, the applications of parameter identification migrated from off‐line model fitting to on‐line model updating. The objective of this study is to develop a gradient‐based method for model updating to advance hybrid simulation also called hybrid test. A novel modification of the proposed method, which can reduce the number of design variables to improve the identification efficiency, is illustrated in detail. To investigate the model updating, simulated hybrid tests were conducted with a 5‐story steel frame equipped with buckling‐restrained braces (BRBs) utilized in the shaking table tests conducted in E‐Defense in Japan in 2009. The calibrated analytical model that was verified with the test results can serve as the reference model. In the simulated hybrid tests, the physical BRB substructure is numerically simulated by utilizing a truss element with the 2‐surface model identical to the part of the reference model. Such numerical verification allows simulation of measurement errors for investigation on the performance of the proposed method. Moreover, the feasibility of sharing the identified parameter values, which were obtained from the physical substructure responses, with the relevant numerical models is also verified with the artificial component responses derived from the physical experiments.     

Subspace system identification of support‐excited structures—part I: theory and black‐box system identification

This paper reviews the theoretical principles of subspace system identification as applied to the problem of estimating black‐box state‐space models of support‐excited structures (e.g., structures exposed to earthquakes). The work distinguishes itself from past studies by providing readers with a powerful geometric interpretation of subspace operations that relates directly to theoretical structural dynamics. To validate the performance of subspace system identification, a series of experiments are conducted on a multistory steel frame structure exposed to moderate seismic ground motions; structural response data is used off‐line to estimate black‐box state‐space models. Ground motions and structural response measurements are used by the subspace system identification method to derive a complete input–output state‐space model of the steel frame system. The modal parameters of the structure are extracted from the estimated input–output state‐space model. With the use of only structural response data, output‐only state‐space models of the system are also estimated by subspace system identification. The paper concludes with a comparison study of the modal parameters extracted from the input–output and output‐only state‐space models in order to quantify the uncertainties present in modal parameters extracted from output‐only models. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic finite element model updating of prestressed concrete continuous box-girder bridge

The dynamic finite element model(FEM) of a prestressed concrete continuous box-girder bridge,called the Tongyang Canal Bridge,is built and updated based on the results of ambient vibration testing(AVT)using a real-coded accelerating genetic algorithm(RAGA).The objective functions are defined based on natural frequency and modal assurance criterion(MAC) metrics to evaluate the updated FEM.Two objective functions are defined to fully account for the relative errors and standard deviations of the natural fr...     

System identification of a concrete arch dam and calibration of its finite element model

A magnitude 4.3 earthquake occurred near Pacoima Dam on 13 January 2001. An accelerometer array that had been upgraded after the Northridge earthquake recorded the motion with 17 channels on the dam and the dam–foundation interface. Using this data, properties of the first two modes are found from a system identification study. Modal properties are also determined from a forced vibration experiment performed in 2002 and indicate a significantly stiffer system than is estimated from the 2001 earthquake records. The 2001 earthquake, although small, must have induced temporary nonlinearity. This has implications for structural health monitoring. The source of the nonlinear behaviour is believed to be loss of stiffness in the foundation rock. A finite element model of Pacoima Dam is constructed and calibrated to match modal properties determined from the system identification study. A dynamic simulation of the 2001 earthquake response produces computed motions that agree fairly well with the recorded ones. Copyright © 2006 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.     

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.     

Probabilistic approach for modal identification using non‐stationary noisy response measurements only

This paper addresses the problem of identification of the modal parameters for a structural system using measured non‐stationary response time histories only. A Bayesian time‐domain approach is presented which is based on an approximation of the probability distribution of the response to a non‐stationary stochastic excitation. It allows one to obtain not only the most probable values of the updated modal parameters and stochastic excitation parameters but also their associated uncertainties using only one set of response data. It is found that the updated probability distribution can be well approximated by a Gaussian distribution centred at the most probable values of the parameters. Examples using simulated data are presented to illustrate the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

Subspace system identification of support excited structures—part II: gray‐box interpretations and damage detection

A theoretical framework is presented for the estimation of the physical parameters of a structure (i.e., mass, stiffness, and damping) from measured experimental data (i.e., input–output or output‐only data). The framework considers two state‐space models: a physics‐based model derived from first principles (i.e., white‐box model) and a data‐driven mathematical model derived by subspace system identification (i.e., black‐box model). Observability canonical form conversion is introduced as a powerful means to convert the data‐driven mathematical model into a physically interpretable model that is termed a gray‐box model. Through an explicit linking of the white‐box and gray‐box model forms, the physical parameters of the structural system can be extracted from the gray‐box model in the form of a finite element discretization. Prior to experimental verification, the framework is numerically verified for a multi‐DOF shear building structure. Without a priori knowledge of the structure, mass, stiffness, and damping properties are accurately estimated. Then, experimental verification of the framework is conducted using a six‐story steel frame structure under support excitation. With a priori knowledge of the lumped mass matrix, the spatial distribution of structural stiffness and damping is estimated. With an accurate estimation of the physical parameters of the structure, the gray‐box model is shown to be capable of providing the basis for damage detection. With the use of the experimental structure, the gray‐box model is used to reliably estimate changes in structural stiffness attributed to intentional damage introduced. Copyright © 2012 John Wiley & Sons, Ltd.     

Efficient Bayesian sensor placement algorithm for structural identification: a general approach for multi‐type sensory systems

In this paper, a Bayesian sequential sensor placement algorithm, based on the robust information entropy, is proposed for multi‐type of sensors. The presented methodology has two salient features. It is a holistic approach such that the overall performance of various types of sensors at different locations is assessed. Therefore, it provides a rational and effective strategy to design the sensor configuration, which optimizes the use of various available resources. This sequential algorithm is very efficient due to its Bayesian nature, in which prior distribution can be incorporated. Therefore, it avoids the possible unidentifiability problem encountered in a sequential process, which starts with small number of sensors. The proposed algorithm is demonstrated using a shear building and a lattice tower with consideration of up to four types of sensors. Copyright © 2014 John Wiley & Sons, Ltd.     

Multi‐scale modelling approach for the pushover analysis of existing RC shear walls—Part I: Model formulation

This work focuses on the modelling issues related to the adoption of the pushover analysis for the seismic assessment of existing reinforced concrete (RC) structures. To this purpose a prototype reference structure, one of the RC shear walls designed according to the multi‐fuse concept and tested on shaking table for the CAMUS project, is modelled at different levels of refinement. The meso‐scale of a stiffness‐based fibre element and the micro‐scale of the finite element (FE) method are herein adopted; in the latter separate elements are adopted for the concrete, the steel and the steel–concrete interface. This first of the two companion papers presents in detail the wall under study, illustrating the design philosophy, the geometry of the wall, the instrumentation set‐up and the test programme. The two modelling approaches are then described; the most important points in terms of element formulation and constitutive relations for materials are presented and discussed for each approach, in the light of the particular design of the wall and of its experimental behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

Dynamic performance of twin curved cable‐stayed bridges

The dynamic behaviour of two curved cable‐stayed bridges, recently constructed in northern Italy, has been investigated by full‐scale testing and theoretical models. Two different excitation techniques were employed in the dynamic tests: traffic‐induced ambient vibrations and free vibrations. Since the modal behaviour identified from the two types of test are very well correlated and a greater number of normal modes was detected during ambient vibration tests, the validity of the ambient vibration survey is assessed in view of future monitoring. For both bridges, 11 vibration modes were identified in the frequency range of 0ndash;10Hz, being a one‐to‐one correspondence between the observed modes of the two bridges. Successively, the information obtained from the field tests was used to validate and improve 3D finite elements so that the dynamic performance of the two systems were assessed and compared based on both the experimental results and the updated theoretical models. Copyright © 2003 John Wiley & Sons, Ltd.     

Damage detection of base‐isolated buildings using multi‐input multi‐output subspace identification

A damage detection algorithm of structural health monitoring systems for base‐isolated buildings is proposed. The algorithm consists of the multiple‐input multiple‐output subspace identification method and the complex modal analysis. The algorithm is applicable to linear and non‐linear systems. The story stiffness and damping as damage indices of a shear structure are identified by the algorithm. The algorithm is further tuned for base‐isolated buildings considering their unique dynamic characteristics by simplifying the systems to single‐degree‐of‐freedom systems. The isolation layer and the superstructure of a base‐isolated building are treated as separate substructures as they are distinctly different in their dynamic properties. The effectiveness of the algorithm is evaluated through the numerical analysis and experiment. Finally, the algorithm is applied to the existing 7‐story base‐isolated building that is equipped with an Internet‐based monitoring system. Copyright © 2004 John Wiley & Sons, Ltd.     

Non‐linear system identification of the versatile‐typed structures by a novel signal processing technique

Non‐linear structural identification problems have raised considerable research efforts since decades, in which the Bouc–Wen model is generally utilized to simulate non‐linear structural constitutive characteristic. Support vector regression (SVR), a promising data processing method, is studied for versatile‐typed structural identification. First, a model selection strategy is utilized to determine the unknown power parameter of the Bouc–Wen model. Meanwhile, optimum SVR parameters are selected automatically, instead of tuning manually. Consequently, the non‐linear structural equation is rewritten in linear form, and is solved by the SVR technique. A five‐floor versatile‐type structure is studied to show the effectiveness of the proposed method, in which both power parameter known and unknown cases are investigated. Copyright © 2007 John Wiley & Sons, Ltd.     

基于随机子空间的结构参数识别及振动台试验验证

本文依照实际工程的背景,提出一种改进的随机子空间参数识别方法;考虑了实际的结构振动测试,提出一种基于参考点的随机子空间系统识别方法。本文最后对此方法在五层钢框架结构模型上进行了振动台试验验证,试验结果表明,该方法具有良好的识别效果。     

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.     

Blind modal identification of output‐only structures in time‐domain based on complexity pursuit

Output‐only modal identification is needed when only structural responses are available. As a powerful unsupervised learning algorithm, blind source separation (BSS) technique is able to recover the hidden sources and the unknown mixing process using only the observed mixtures. This paper proposes a new time‐domain output‐only modal identification method based on a novel BSS learning algorithm, complexity pursuit (CP). The proposed concept—independent ‘physical systems’ living on the modal coordinates—connects the targeted constituent sources (and their mixing process) targeted by the CP learning rule and the modal responses (and the mode matrix), which can then be directly extracted by the CP algorithm from the measured free or ambient system responses. Numerical simulation results show that the CP method realizes accurate and robust modal identification even in the closely spaced mode and the highly damped mode cases subject to non‐stationary ambient excitation and provides excellent approximation to the non‐diagonalizable highly damped (complex) modes. Experimental and real‐world seismic‐excited structure examples are also presented to demonstrate its capability of blindly extracting modal information from system responses. The proposed CP is shown to yield clear physical interpretation in modal identification; it is computational efficient, user‐friendly, and automatic, requiring little expertise interactions for implementations. Copyright © 2013 John Wiley & Sons, Ltd.     

Two‐dimensional physically based finite element runoff model for small agricultural watersheds: II. Model testing and field application

Mathematical models are useful analysis tools to understand problems in watersheds associated with runoff, and to find solutions through land use changes and best management practices. However, before a model is applied in the field, it must be tested and checked to ensure that the model represents the real world adequately. In this paper, a two‐dimensional physically based finite element runoff model ROMO2D has been verified and validated by comparing the model output with analytic solution under simplified conditions, published data, and field measurements. Calibration of the model was done manually through a multi‐objective calibration procedure, using observed field data. Before going for field validation/application of ROMO2D, analysis was carried out to determine the optimum number of finite elements into which the watershed should be discretized and the size of the time step. A sensitivity analysis of the model was performed using the observed values of watershed parameters. The model was applied to a 1·45 ha agricultural watershed located in the Shiwalik foothills (India) to simulate runoff. The results demonstrated the potential of the model to simulate runoff from small agricultural watersheds for individual storm events with reasonable accuracy. Copyright © 2008 John Wiley & Sons, Ltd.