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.     

Dynamic characteristics and seismic behavior of prefabricated steel stairs in a full‐scale five‐story building shake table test program

This paper investigates the dynamic characteristics and seismic behavior of prefabricated steel stairs in a full‐scale five‐story building shake table test program. The test building was subjected to a suite of earthquake input motions and low‐amplitude white noise base excitations first, while the building was isolated at its base, and subsequently while it was fixed to the shake table platen. This paper presents the modal characteristics of the stairs identified using the data recorded from white noise base excitation tests as well as the physical and measured responses of the stairs from the earthquake tests. The observed damage to the stairs is categorized into three distinct damage states and is correlated with the interstory drift demands of the building. These shake table tests highlight the seismic vulnerability of modern designed stair systems and in particular identifies as a key research need the importance of improving the deformability of flight‐to‐building connections. Copyright © 2015 John Wiley & Sons, Ltd.     

Damage assessment through structural identification of a three‐story large‐scale precast concrete structure

This paper investigates the damage assessment of a three‐story half‐scale precast concrete building resembling a parking garage through structural identification. The structure was tested under earthquake‐type loading on the NEES large high‐performance outdoor shake table at the University of California San Diego in 2008. The tests provide a unique opportunity to capture the dynamic performance of precast concrete structures built under realistic boundary conditions. The effective modal parameters of the structure at different damage states have been identified from white‐noise and scaled earthquake test data with the assumption that the structure responded in a quasi‐linear manner. Modal identification has been performed using the deterministic‐stochastic subspace identification method based on the measured input–output data. The changes in the identified modal parameters are correlated to the observed damage. In general, the natural frequencies decrease, and the damping ratios increase as the structure is exposed to larger base excitations, indicating loss of stiffness, development/propagation of cracks, and failure in joint connections. The analysis of the modal rotations and curvatures allowed the localization of shear and flexural damages respectively and the checking of the effectiveness of repair actions. Copyright © 2013 John Wiley & Sons, Ltd.     

A method for stochastic seismic response analysis of non-classically damped structures

A method to calculate the stationary random response of a non-classically damped structure is proposed that features clearly-defined physical meaning and simple expression. The method is developed in the frequency domain, The expression of the proposed method consists of three terms, i.e., modal velocity response, modal displacement response, and coupled (between modal velocity and modal displacement response), Numerical results from the parametric study and three example structures reveal that the modal velocity response term and the coupled term are important to structural response estimates only for a dynamic system with a tuned mass damper. In typical cases, the modal displacement term can provide response estimates with satisfactory accuracy by itself, so that the modal velocity term and coupled term may be ignored without loss of accuracy, This is used to simplify the response computation of non-classically damped structures. For the white noise excitation, three modal correlation coefficients in closed form are derived. To consider the modal velocity response term and the coupled term, a simplified approximation based on white noise excitation is developed for the case when the modal velocity response is important to the structural responses. Numerical results show that the approximate expression based on white noise excitation can provide structural responses with satisfactory accuracy~     

The non‐stationary cross‐correlation coefficients in the seismic analysis of MDOF structural systems

A method concerning the evaluation, in a very compact form, of the non‐stationary modal cross‐correlation coefficients of MDOF structural systems subjected to seismic excitations is presented. It is available both in the case when the excitation is considered as a white‐noise process and when it is considered as a filtered process. The evaluation of these coefficients is required when a transient seismic analysis is performed by the use of the modal response spectrum approach. This is necessary when the strong‐motion phase of the earthquake is significantly short with respect to the fundamental period of the structure. Copyright © 2003 John Wiley & Sons, Ltd.     

A response‐based decoupling criterion for multiply‐supported secondary systems

It is often infeasible to carry out coupled analyses of multiply‐supported secondary systems for earthquake excitations. ‘Approximate’ decoupled analyses are then resorted to, unless the response errors due to those are significantly high. This study proposes a decoupling criterion to identify such cases where these errors are likely to be larger than an acceptable level. The proposed criterion is based on the errors in the primary system response due to decoupling and has been obtained by assuming (i) the input excitation to be an ideal white noise process, (ii) cross‐modal correlation to be negligible, and (iii) the combined system to be classically damped. It uses the modal properties of the undamped combined system, and therefore, a perturbation approach has been formulated to determine the combined system properties in case of light to moderately heavy secondary systems. A numerical study has been carried out to illustrate the accuracy achieved with the proposed perturbation formulation. The proposed decoupling criterion has been validated with the help of two example primary‐secondary systems and four example excitation processes. Copyright © 2002 John Wiley & Sons, Ltd.     

基于振动台实验的结构损伤识别研究

选择美国加州大学圣地亚哥分校7层钢筋混凝土剪力墙足尺结构振动台实验,开展结构损伤识别研究,实验采用白噪声、环境振动和不同强度的地震动交替激发,记录地震动激发实验前后的结构反应。基于该记录计算和对比自振频率和振型曲率的变化、剪切波走时及其变化和结构层间位移角,分析发现一层和二层振型曲率较大,走时较长,走时变化也较大,现场检查发现一层和二层的破坏也较为严重,这些参数可用于识别结构损伤程度和定位损伤位置,而自振频率和层间位移角变化仅可反映出结构损伤程度,难以揭示结构损伤位置。     

Damage identification of a 3D full scale steel–concrete composite structure with partial‐strength joints at different pseudo‐dynamic load levels

Partial‐strength composite steel–concrete moment‐resisting (MR) frame structures represent an open research field in seismic design from both a theoretical and an experimental standpoint. Among experimental techniques, vibration testing is a well‐known and powerful technique for damage detection, localization and quantification, where actual modal parameters of a structure at different states can be determined from test data by using system identification methods. However, the identification of semi‐rigid connections in framed structures is limited, and hence this paper focuses on a series of vibration experiments that were carried out on a realistic MR frame structure, following the application of pseudo‐dynamic and quasi‐static cyclic loadings at the European laboratory for structural assessment of the Joint Research Centre at Ispra, Italy, with the scope of understanding the structural behaviour and identifying changes in the dynamic response. From the forced vibration response, natural frequencies, damping ratios, modal displacements and rotations were extracted using the circle fitting technique. These modal parameters were used for local and global damage identification by updating a 3D finite element model of the intact structure. The identified results were then correlated with observations performed on the structure to understand further the underlying damage mechanisms. Finally, the latin hypercube sampling technique, a variant of the Monte Carlo method, was employed in order to study the sensitivity of the updated parameters of the 3D model to noise on the modal inputs. Copyright © 2009 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.     

Multi‐angle,multi‐damage fragility curves for seismic assessment of bridges

The scope of this study is to investigate the effect of the direction of seismic excitation on the fragility of an already constructed, 99‐m‐long, three‐span highway overpass. First, the investigation is performed at a component level, quantifying the sensitivity of local damage modes of individual bridge components (namely, piers, bearings, abutments, and footings) to the direction of earthquake excitation. The global vulnerability at the system level is then assessed for a given angle of incidence of the earthquake ground motion to provide a single‐angle, multi‐damage probabilistic estimate of the bridge overall performance. A multi‐angle, multi‐damage, vulnerability assessment methodology is then followed, assuming uniform distribution for the angle of incidence of seismic waves with respect to the bridge axis. The above three levels of investigation highlight that the directivity of ground motion excitation may have a significant impact on the fragility of the individual bridge components, which shall not be a priori neglected. Most importantly, depending on the assumptions made for the component to the system level transition, this local sensitivity is often suppressed. It may be therefore necessary, based on the ultimate purpose of the vulnerability or the life cycle analysis, to obtain a comprehensive insight on the multiple damage potential of all individual structural and foundation components under multi‐angle excitation, to quantify the statistical correlation among the distinct damage modes and to identify the components that are both most critical and sensitive to the direction of ground motion and carefully define their limit states which control the predicted bridge fragility. Copyright © 2015 John Wiley & Sons, Ltd.     

Shake table testing of an elevator system in a full‐scale five‐story building

This paper investigates the seismic performance of a functional traction elevator as part of a full‐scale five‐story building shake table test program. The test building was subjected to a suite of earthquake input motions of increasing intensity, first while the building was isolated at its base and subsequently while it was fixed to the shake table platen. In addition, low‐amplitude white noise base excitation tests were conducted while the elevator system was placed in three different configurations, namely, by varying the vertical location of its cabin and counterweight, to study the acceleration amplifications of the elevator components due to dynamic excitations. During the earthquake tests, detailed observation of the physical damage and operability of the elevator as well as its measured response are reported. Although the cabin and counterweight sustained large accelerations because of impact during these tests, the use of well‐restrained guide shoes demonstrated its effectiveness in preventing the cabin and counterweight from derailment during high‐intensity earthquake shaking. However, differential displacements induced by the building imposed undesirable distortion of the elevator components and their surrounding support structure, which caused damage and inoperability of the elevator doors. It is recommended that these aspects be explicitly considered in elevator seismic design. Copyright © 2016 John Wiley & Sons, Ltd.     

Evolution of modal characteristics of a mid-rise cold-formed steel building during construction and earthquake testing

Vibration-based structural identification is an essential technique for assessing structural conditions by inferring information from the dynamic characteristics of structures. However, the robustness of such techniques in monitoring the progressive damage of real structures has been validated with only a handful of research efforts, largely due to the paucity of monitoring data recorded from damaged structures. In a recent experimental program, a mid-rise cold-formed steel building was constructed at full scale atop a large shake table and subsequently subjected to a unique multi-hazard scenario including earthquake, post-earthquake fire, and finally post-fire earthquake loading. Complementing the simulated hazard events, low-amplitude vibration tests, including ambient vibrations and white noise base excitation tests, were conducted throughout the construction and the test phases. Using the vibration data collected during the multi-hazard test program, this paper focuses on understanding the modal characteristics of the cold-formed steel building in correlation with the construction and the structural damage progressively induced by the simulated hazard events. The modal parameters of the building (i.e., natural frequencies, damping ratios, and mode shapes) are estimated using two input–output and two output-only time-domain system identification techniques. Agreement between the evolution of modal parameters and the observations of the progression of physical damage demonstrates the effectiveness of the vibration-based system identification techniques for structural condition monitoring and damage assessment.     

Stochastic analysis of structures and piping systems subjected to stationary multiple support excitations

A stochastic method has been developed for seismic analysis of structures and piping systems subjected to multiple support excitations. In either the time or the frequency domain, mean and extreme values of structural and piping system response can be found, including the effects of cross-correlations of modal response and cross-correlations of multiple support excitations. Stationary white noise and stationary filtered white noise ground excitations are used. A computer program has been developed to carry out the stochastic seismic analysis. Results for a realistic nuclear power plant structure and piping system with and without modal cross-correlations and support excitation cross-correlations are compared. From these results, it is concluded that neglecting cross-correlations can lead to large errors. The stochastic method reported is shown to be more accurate than the response spectrum method and more economical than the time-history method; therefore, it is recommended for seismic analysis of nuclear power plants.     

Influence of the construction process and nonstructural components on the modal properties of a five‐story building

A full‐scale five‐story reinforced concrete building was built and tested on the NEES‐UCSD shake table during the period from May 2011 to May 2012. The purpose of this test program was to study the response of the structure and nonstructural components and systems (NCSs) and their dynamic interaction during seismic base excitation of different intensities. The building specimen was tested first under a base‐isolated condition and then under a fixed‐based condition. As the building was being erected, an accelerometer array was deployed on the specimen to study the evolution of its modal parameters during the construction process and placement of major NCSs. A sequence of dynamic tests, including daily ambient vibration, shock (free vibration) and forced vibration tests (low‐amplitude white noise and seismic base excitations), were performed on the building at different stages of construction. Different state‐of‐the‐art system identification methods, including three output‐only and two input‐output methods, were used to estimate the modal properties of the building. The obtained results allow to investigate in detail the effects of the construction process and NCSs on the dynamic parameters of this building system and to compare the modal properties obtained from different methods, as well as the performance of these methods. Copyright © 2015 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.     

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.     

The complete SRSS modal combination rule

The complete Square‐Root‐of‐Sum‐of‐Squares (c‐SRSS) modal combination rule is presented. It expresses the structural response in terms of uncoupled SDOF modal responses, yet accounting fully for modal response variances and cross‐covariances. Thus, it is an improvement over the classical SRSS rule which neglects contributions from modal cross‐covariances. In the c‐SRSS rule the spectral moments of the structural response are expressed rigorously in terms of the spectral moments of uncoupled modal responses and of some coefficients that can be computed straightforwardly as a function of modal frequencies and damping, without involving the computation of cross‐correlation coefficients between modal responses. An example shows an application of the c‐SRSS rule for structural systems with well separated and closely spaced modal frequencies, subjected to wide‐band and narrow‐band excitations. Comparisons with response calculations using the SRSS and the Complete Quadratic Combination rules are given and discussed in detail. Based on the c‐SRSS rule a response spectrum formulation is introduced to estimate the maximum structural response. An example considering a narrow‐band excitation from the great Mexico earthquake of September 19, 1985, is given and the accuracy of the response spectrum formulation is examined. Copyright © 2010 John Wiley & Sons, Ltd.     

Fragility curves for reinforced concrete structures in Skopje (Macedonia) region

A method for the development of earthquake intensity–damage relations, given as fragility curves and damage probability matrices is proposed in this paper. The proposed method is applied on reinforced-concrete frame-wall structures. Two sets of fragility curves and damage probability matrices are developed. The first one is for reinforced-concrete frame structures lower than 10 stories. For this purpose, a six-story frame structure is used. The other set is defined for reinforced-concrete frame-wall structures higher than 10 stories. A 16-story frame-wall structure was chosen as a sample. The sample structures were designed according to Macedonian design code. The conditions of the local seismic hazard were the subject of special concern for the development of earthquake intensity–damage relations. Because of the limited number of real time histories from the Skopje region, a set of 240 synthetic time histories were generated. Geological dates from the Skopje region were used. Response of the sample structures under earthquake excitation was defined performing nonlinear dynamic analysis. Modeling of the nonlinear behavior of the structural elements was completed according to state-of-the-art methods in this field. A modified Park and Ang damage model was chosen as a measure of the structure's response to earthquake excitation. Five damage states were defined to express the condition of damage. As a result of the analytical research, the values of the global damage index corresponding to each damage state were determined. Using the dates from the nonlinear dynamic analysis of the sample structures under all 240 synthetic time histories, the two sets of fragility curves and damage probability matrices were defined.     

Algorithms for time synchronization of wireless structural monitoring sensors

Dense networks of wireless structural health monitoring systems can effectively remove the disadvantages associated with current wire‐based sparse sensing systems. However, recorded data sets may have relative time‐delays due to interference in radio transmission or inherent internal sensor clock errors. For structural system identification and damage detection purposes, sensor data require that they are time synchronized. The need for time synchronization of sensor data is illustrated through a series of tests on asynchronous data sets. Results from the identification of structural modal parameters show that frequencies and damping ratios are not influenced by the asynchronous data; however, the error in identifying structural mode shapes can be significant. The results from these tests are summarized in Appendix A. The objective of this paper is to present algorithms for measurement data synchronization. Two algorithms are proposed for this purpose. The first algorithm is applicable when the input signal to a structure can be measured. The time‐delay between an output measurement and the input is identified based on an ARX (auto‐regressive model with exogenous input) model for the input–output pair recordings. The second algorithm can be used for a structure subject to ambient excitation, where the excitation cannot be measured. An ARMAV (auto‐regressive moving average vector) model is constructed from two output signals and the time‐delay between them is evaluated. The proposed algorithms are verified with simulation data and recorded seismic response data from multi‐story buildings. The influence of noise on the time‐delay estimates is also assessed. Copyright © 2004 John Wiley & Sons, Ltd.     

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.