Dynamic Field Test, System Identification, and Modal Validation of an RC Minaret: Preprocessing and Postprocessing the Wind-Induced Ambient Vibration Data

The investigation of dynamic response for civil engineering structures largely depends on a detailed understanding of their dynamic characteristics, such as the natural frequencies, mode shapes, and modal damping ratios. Dynamic characteristics of structures may be obtained numerically and experimentally. The finite-element method is widely used to model structural systems numerically. However, there are some uncertainties in numerical models. Material properties and boundary conditions may not be modeled correctly. There may be some microcracks in the structures, and these cracks may directly affect the modeling parameters. Modal testing gives correct uncertain modeling parameters that lead to better predictions of the dynamic behavior of a target structure. Therefore, dynamic behavior of special structures, such as minarets, should be determined with ambient vibration tests. The vibration test results may be used to update numerical models and to detect microcracks distributed along the structure. The operational modal analysis procedure consists of several phases. First, vibration tests are carried out, spectral functions are produced from raw measured acceleration records, dynamic characteristics are determined by analyzing processed spectral functions, and finally analytical models are calibrated or updated depending on experimental analysis results. In this study, an ambient vibration test is conducted on the minaret under natural excitations, such as wind effects and human movement. The dynamic response of the minaret is measured through an array of four trixial force-balanced accelerometers deployed along the whole length of the minaret. The raw measured data obtained from ambient vibration testing are analyzed with the SignalCAD program, which was developed in MATLAB. The employed system identification procedures are based on output-only measurements because the forcing functions are not available during ambient vibration tests. The ModalCAD program developed in MATLAB is used for dynamic characteristic identification. A three-dimensional model of the minaret is constructed, and its modal analysis is performed to obtain analytical frequencies and mode shapes by using the ANSYS finite-element program. The obtained system identification results have very good agreement, thus providing a reliable set of identified modal properties (natural frequencies, damping ratios, and mode shapes) of the structure, which can be used to calibrate finite-element models and as a baseline in health monitoring studies.     

Application of Structural Health Monitoring Techniques to Track Structural Changes in a Retrofitted Building Based on Ambient Vibration

One of the issues complicating the reliability assessment of structural health monitoring (SHM) methodologies slated for implementation under field conditions for damage detection in conjunction with typical infrastructure systems, is the paucity of experimental measurements from such structures. Particularly lacking is the availability of experimental data from physical structures, where quantifiable changes are made in the structure while SHM studies are being performed. That is precisely the focus of this paper. As a result of the 1994 Northridge Earthquake, a critical six-story building in the metropolitan Los Angeles region was found to need significant seismic mitigation measures. The building was instrumented with 14 state-of-the-art strong-motion accelerometers that were placed at various locations and in different orientations throughout the building. The instrumentation network was used to acquire extensive ambient vibration data sets at regular intervals that covered the whole construction phase, during which the building evolved from its original condition to the retrofitted status. This paper evaluates the usefulness of the natural excitation technique (NExT) in conjunction with the eigensystem realization algorithm (ERA) to determine the evolution of the modal properties of the subject building during the various phases of its retrofit process. Further, an assessment is made of the influence on the system identification results of significant user-selectable parameters such as: data window size and overlap; reference degree-of-freedom; and the dimensions of the associated Hankel matrix. In spite of the very low levels of ambient excitation, and the low spatial resolution of the sensors, use of the NExT/ERA algorithm yielded excellent identification results of the dominant modes of the building. Changes in the identified structural frequencies are correlated with the time that specific structural changes were made. It is shown that this unique collection of data can be extremely useful in calibrating the accuracy and sensitivity of various SHM schemes, as well as in providing useful identification parameter guidelines that can assist in the planning and deployment of sensor networks and associated data collection schemes for SHM applications.     

Structural Health Monitoring by Recursive Bayesian Filtering

A new vision of structural health monitoring (SHM) is presented, in which the ultimate goal of SHM is not limited to damage identification, but to describe the structure by a probabilistic model, whose parameters and uncertainty are periodically updated using measured data in a recursive Bayesian filtering (RBF) approach. Such a model of a structure is essential in evaluating its current condition and predicting its future performance in a probabilistic context. RBF is conventionally implemented by the extended Kalman filter, which suffers from its intrinsic drawbacks. Recent progress on high-fidelity propagation of a probability distribution through nonlinear functions has revived RBF as a promising tool for SHM. The central difference filter, as an example of the new versions of RBF, is implemented in this study, with the adaptation of a convergence and consistency improvement technique. Two numerical examples are presented to demonstrate the superior capacity of RBF for a SHM purpose. The proposed method is also validated by large-scale shake table tests on a reinforced concrete two-span three-bent bridge specimen.     

Bridge Safety Evaluation Based on Monitored Live Load Effects

A novel approach to evaluating safety of existing bridges based on monitored structural responses and component conditions is presented in this paper. A limit state equation is developed for the measured strain data from structural health monitoring (SHM). The new concepts of the condition function, α(s,t), and prediction function, ζ(s,t), are introduced. The condition function is utilized to estimate the strains at locations other than the strain gauge locations. This function is related to the structural condition assessment results, strain gauge locations, and failure modes under consideration. The prediction function is used to predict the extreme values of the SHM data in the future. An illustration of the proposed approach is provided on an existing highway bridge in Pennsylvania, which had been monitored from 2001 to 2005 by the Advanced Technology for Large Structural Systems Center, a National Engineering Research Center at Lehigh University, Bethlehem, Pa. This study provides the basis for integrating achievable SHM data into structural safety evaluation, and establishes a valid platform for life-cycle, cost-oriented, and reliability-based infrastructure management systems using structural health monitoring.     

Stiffness Assessment through Modal Analysis of an RC Slab Bridge before and after Strengthening

As part of Main Roads Western Australia’s (MRWA) bridge management and bridge upgrading program, MRWA bridge no. 3014 was assessed to evaluate its condition before and after strengthening works with carbon-fiber-reinforced-polymers (CFRP). The assessment process coupled analytical results with field observations and dynamic testing of the structure. Vibration-based structural assessment of the bridge was conducted before and after the completion of the upgrading works. This paper presents the results of the vibration tests and modal analysis performed before and after the structure upgrading. In particular, the change in the structural properties and stiffness, before and after the strengthening, based on the analyses of the updated models of the bridge, is presented and discussed. The results demonstrate the effectiveness of using the dynamic assessment method to determine the elastic flexural stiffness of bridge structures retrofitted with CFRP.     

Modal Testing, Finite-Element Model Updating, and Dynamic Analysis of an Arch Type Steel Footbridge

This paper describes an arch type steel footbridge, its analytical modeling, modal testing, finite-element model updating, and dynamic analysis. A modern steel footbridge which has an arch type structural system and is located on the Karadeniz coast road in Trabzon, Turkey is selected as an application. An analytical modal analysis is performed on the developed three-dimensional finite-element model of footbridge to provide analytical frequencies and mode shapes. Field ambient vibration tests on the footbridge deck under natural excitation such as human walking and traffic loads are conducted. The output-only modal parameter identification is carried out by using peak picking of the average normalized power spectral densities in the frequency domain and stochastic subspace identification in the time domain, and dynamic characteristics such as natural frequencies, mode shapes, and damping ratios are determined. The finite-element model of the footbridge is updated to minimize the differences between analytically and experimentally estimated modal properties by changing some uncertain modeling parameters such as material properties. Dynamic analyses of the footbridge before and after finite-element model updating are performed using the 1992 Erzincan earthquake record. At the end of the study, maximum differences in the natural frequencies are reduced from 22 to only 5% and good agreement is found between analytical and experimental dynamic characteristics such as natural frequencies and mode shapes by model updating. Also, maximum displacements and principal stresses before and after model updating are compared with each other.     

Vibration Performance of a Large Cantilever Grandstand during an International Football Match

Vibration problems in stadia are becoming more common due to increased structural slenderness and more lively dynamic crowd excitation. Unfortunately, there is very little guidance available to design engineers dealing with the assessment and design of stadia structures. This paper presents unique data from a program of modal testing and in-service monitoring of a large contemporary cantilever grandstand in the United Kingdom. The in-service monitoring was carried out during an international football match, during which the stadium was full to capacity. Modal properties obtained from the testing on the empty structure are presented and the results from in-service monitoring are described. It is found that crowd occupation can significantly alter the modal properties of a stadium, and that the changes can vary according to the crowd configuration. Additionally, previously proposed methods for assessment of vibration serviceability have been applied and it has been shown that they can lead to inconsistent results, which is a result of their sensitivity to the data acquisition and analysis techniques used. It is concluded that it is very important that consistent methods of data acquisition, analysis, and vibration serviceability assessment are utilized by future researchers and practitioners. Also, further research is required to define vibration serviceability limits using the state-of-the-art vibration dose approach.     

Inclusion of Crawl Tests and Long-Term Health Monitoring in Bridge Serviceability Analysis

Due to limited resources, structural health monitoring (SHM) of highway bridges has to be integrated in structural performance assessment in a cost-effective manner. The instrumentation and the long-term SHM procedures are generally chosen with emphasis on most critical bridge components for a particular failure mode. However, global structural analysis is necessary to obtain useful structural performance information. It is then a major challenge to use monitoring data at some locations to perform a structural reliability analysis at other locations. In this paper, a methodology for lifetime serviceability analysis of existing steel girder bridges including crawl tests and long-term monitoring information is presented. The case where the initial goal of monitoring is to provide data for a fatigue analysis of some bridge components is considered. The monitoring results are used to perform a structural reliability analysis of different sections that are critical considering serviceability of the bridge. Limit state equations are used firstly by adhering to the load and strength formulas and requirements set forth in AASHTO specifications, and secondly by integrating monitoring information. Serviceability with respect to permanent deformation under overload is estimated for the girders with these two different methods and a time-dependent performance analysis is conducted by considering corrosion penetration. The proposed approach is applied to the I-39 Northbound Bridge over the Wisconsin River in Wisconsin. A monitoring program of that bridge was performed by the Advanced Technology for Large Structural Systems Center at Lehigh University.     

Bridge Structural Condition Assessment Based on Vibration and Traffic Monitoring

A stochastic model of traffic excitation on bridges is developed assuming that the arrival of vehicles traversing a bridge (modeled as an elastic beam) follows a Poisson process, and that the contact force of a vehicle on the bridge deck can be converted to equivalent dynamic loads at the nodes of the beam elements. The parameters in this model, such as the Poisson arrival rate and the stochastic distribution of vehicle speeds, are obtained by image processing of traffic video data. The model reveals that traffic excitations on bridges are spatially correlated. This important characteristic is usually incorrectly ignored in most output-only methods for the identification of bridge structural properties using traffic-induced vibration measurement data. In this study, the stochastic traffic excitation model with partial traffic information is incorporated in a Bayesian framework, to evaluate the structural properties and update their uncertainty for condition assessment of the bridge superstructure. The vehicle weights are also estimated simultaneously in this procedure. The proposed structural assessment methodology is validated on an instrumented highway bridge.     

Finite-Element Analysis and Vibration Testing of a Two-Span Masonry Arch Bridge

This paper presents the analytical modeling, modal testing, and finite-element model updating for a two-span masonry arch bridge. An Ottoman masonry arch bridge built in the 19th century and located at Camlihemsin, Rize, Turkey is selected as an example. Analytical modal analysis is performed on the developed 3D finite-element model of the bridge to obtain dynamic characteristics. The ambient vibration tests are conducted under natural excitation such as human walking. The operational modal analysis is carried out using peak picking method in the frequency domain and stochastic subspace identification method in the time domain, and dynamic characteristics (natural frequencies, mode shapes, and damping ratios) are determined experimentally. Finite-element model of the bridge is updated to minimize the differences between analytically and experimentally estimated dynamic characteristics by changing boundary conditions. At the end of the study, maximum differences in the natural frequencies are reduced on average from 18 to 7% and a good agreement is found between analytical and experimental dynamic characteristics after finite-element model updating.     

Structural Identification and Damage Detection from Noisy Modal Data

In this paper we present a simple, yet powerful, method for the identification of stiffness matrices of structural and mechanical systems from information about some of their measured natural frequencies and corresponding mode shapes of vibration. The method is computationally efficient and is shown to perform remarkably well in the presence of measurement errors in the mode shapes of vibration. It is applied to the identification of the stiffness distribution along the height of a simple vibrating structure. An example illustrating the method’s ability to detect structural damage that could be highly localized in a building structure is also given. The efficiency and accuracy with which the method yields estimates of the system’s stiffness from noisy modal measurement data makes it useful for rapid, on-line damage detection of structures.     

Application of a Statistical Model Updating Approach on Phase I of the IASC-ASCE Structural Health Monitoring Benchmark Study

This paper addresses the problem of structural health monitoring (SHM) and damage detection based on a statistical model updating methodology which utilizes the measured vibration responses of the structure without any knowledge of the input excitation. The emphasis in this paper is on the application of the proposed methodology in Phase I of the benchmark study set up by the IASC–ASCE Task Group on structural health monitoring. Details of this SHM benchmark study are available on the Task Group web site at 〈http://wusceel.cive.wustl.edu/asce.shm〉. The benchmark study focuses on important issues, such as: (1) measurement noise; (2) modeling error; (3) lack of input measurements; and (4) limited number of sensors. A statistical methodology for model updating is adopted in this paper to establish stiffness reductions due to damage. This methodology allows for an explicit treatment of the measurement noise, modeling error, and possible nonuniqueness issues characterizing this inverse problem. The paper briefly describes the methodology and reports on the results obtained in detecting damage in all six cases of Phase I of the benchmark study assuming unknown (ambient) data. The performance, limitations, and difficulties encountered by the proposed statistical methodology are discussed.     

Combined Experimental-Operational Modal Testing of Footbridges

In combined vibration testing, an artificial, measured force is used in operational conditions. This requires the identification of a system model that takes both the measured and the operational excitation into account. Advantages with respect to the classical operational modal analysis approach are the possibility of obtaining mass-normalized mode shapes and the increase of the excitation level and its frequency content. An advantage with respect to the classical experimental modal analysis approach, where the ambient excitation is not modeled, but considered as disturbing noise, is the possibility of using excitation levels that are of the same amplitude, or even smaller, than the ambient excitation levels. In this paper, combined modal testing of footbridges is explored using two case studies: a steel arch footbridge with spans of 75.2 m and 30.3 m and a concrete stress-ribbon footbridge with spans of 30 m and 28 m. The comparison of the modal parameters (eigenfrequencies, damping ratios, mode shapes, and modal scaling factors) obtained from a combined vibration test with the ones obtained from other modal tests and from a finite-element model, demonstrates the feasibility of using small and practical excitation devices for the modal testing of footbridges.     

Condition Assessment of Shear Connectors in Slab-Girder Bridges via Vibration Measurements

The paper presents a field study on condition assessment of the shear connectors in a full slab-girder bridge via vibration measurements. First, a model updating technique is employed to assess the condition of the whole structure, including boundary conditions, bearings, girders, slab, and shear connectors, from the accelerations on the slab measured in vibration testing. Then, a new damage index based on the difference of frequency response functions on the slab and the corresponding points on the girder is developed to evaluate the condition of shear connectors. The advantage of the new method lies in the fact that it does not need any reference data (undamaged data) for the structure. Compared with the results obtained using the model updating technique, the method is more reliable and accurate in assessing the condition of the shear connectors between the slab and girders. The effects of measurement noise on the damage identification results and the damage quantification are also studied through numerical simulation.     

Finite-Element Analysis of Lamb Wave Propagation in a Thin Aluminum Plate

Structural health monitoring (SHM) is an emerging technology that can be used to identify, locate, and quantify structural damages before failure. Among SHM techniques, Lamb waves are widely used since they can cover large areas from a single location. The development of various structural simulation programs has lead to increasing interest in whether SHM data obtained from the simulation can be verified by experimentation. The objective of this research is to determine the Lamb wave responses of SHM models using the finite-element software package ABAQUS CAE as a computational tool for an isotropic plate. These results are compared to experimental results and theoretical predictions under isothermal and thermal gradient conditions to assess the sensitivity of piezoelectric generated Lamb wave propagation. Simulations of isothermal tests are conducted over a temperature range of 0–190°F using 100 and 300?kHz as excitation frequencies. The changes in temperature-dependent material properties are used to measure the differences in the response signal’s waveform and propagation speed. An analysis of the simulated signal response data demonstrated that elevated temperatures delay the Lamb wave propagation, although the delays are found to be minimal at the temperatures tested.     

Dynamic and Static Behavior of a Curved-Girder Bridge with Varying Boundary Conditions

A curved, three-span continuous, steel I-girder bridge in Salt Lake City was tested in order to determine its dynamic and static load carrying properties for three boundary condition states. For each of the three boundary condition states, two dynamic forced vibration methods were applied to the bridge as well as a static live-load test. The first forced vibration method used an eccentric mass shaker. The second method involved striking the side of the bridge with an impact hammer. The live-load test was performed by slowly driving a truck at a crawl speed across the bridge. Velocity transducers, accelerometers, and strain gauges were utilized to record the response of the bridge. The analysis and compilation of recorded dynamic response of the bridge enabled the preparation of mode shapes and natural frequencies for each boundary condition. This paper discusses the resulting changes in relevant dynamic properties and compares them with the changes in the static properties that were determined from the bridge response recorded from the live-load tests.     

Analytical Approach for Detection of Multiple Cracks in a Beam

An analytical approach for the detection of a beam with multiple cracks is presented in this article. The method is based on the bending vibration theory of Euler-Bernoulli beam and the cracks are treated as massless rotational springs, by which the cracked beam is separated into a number of segments of perfect beams. By using the nontrivial solution condition of the vibration mode of the beam elements, specially using the transfer matrix method for the multiple cracks detection, the crack identification equation of the cracked beam is obtained explicitly, which is a function of natural frequencies, the locations, and depths of the cracks. Since the natural frequencies of a cracked beam can be measured through many of the structural testing methods, then the relations of the locations and the depths of the cracks can be determined explicitly from the identification equation of a cracked beam which geometrical and physical parameters as well as the boundary conditions are given. The results of some examples are shown and the present method is validated with the existing and measured experimental data. The detection for other types of beams with different number of cracks and various boundary conditions can also be obtained by a similar procedure.     

Baseline Models for Bridge Performance Monitoring

A baseline model is essential for long-term structural performance monitoring and evaluation. This study represents the first effort in applying a neural network-based system identification technique to establish and update a baseline finite element model of an instrumented highway bridge based on the measurement of its traffic-induced vibrations. The neural network approach is particularly effective in dealing with measurement of a large-scale structure by a limited number of sensors. In this study, sensor systems were installed on two highway bridges and extensive vibration data were collected, based on which modal parameters including natural frequencies and mode shapes of the bridges were extracted using the frequency domain decomposition method as well as the conventional peak picking method. Then an innovative neural network is designed with the input being the modal parameters and the output being the structural parameters of a three-dimensional finite element model of the bridge such as the mass and stiffness elements. After extensively training and testing through finite element analysis, the neural network became capable to identify, with a high level of accuracy, the structural parameter values based on the measured modal parameters, and thus the finite element model of the bridge was successfully updated to a baseline. The neural network developed in this study can be used for future baseline updates as the bridge being monitored periodically over its lifetime.     

Enhanced Realization∕Identification of Physical Modes

Physical structures are often sufficiently complicated to preclude constructing an accurate mathematical model of the system dynamics from simple analysis using the laws of physics. Consequently, determination of an accurate model requires utilization of (generally noisy) output measurements from dynamic tests. In this paper, we present a robust method for constructing accurate, structural‐dynamic models from discrete time‐domain measurements. The method processes the measurements in order to determine the number of modes present, the damping and frequency of each mode, and the mode shape. The structure may be highly damped. Although the mode‐shape identification is more sensitive to measurement noise than the order, frequency, and damping identification, the method is considerably less sensitive to noise than other leading methods. Accurate detection of the modal parameters and mode shapes is demonstrated for modes with damping ratios exceeding 15%.     

Vibration Characteristics of K?mürhan Highway Bridge Constructed with Balanced Cantilever Method

K?mürhan Highway Bridge is a reinforced concrete box girder bridge located on the 51st km of Elaz??–Malatya Highway over the F?rat River. Because of the fact that the K?mürhan Bridge is the only bridge in this part of F?rat, it has major logistical importance. So, this paper aims to determine dynamic characteristics such as natural frequencies, mode shapes, and damping ratios of the bridge using experimental measurements and finite-element analyses to evaluate current behavior. The experimental measurements are carried out by ambient vibration tests under traffic loads. Due to the expansion joint in the middle of the bridge, special measurement points are selected and experimental test setups are constituted. Vibration data are gathered from the both box girder and bridge deck. Measurement time, frequency span, and effective mode number are determined by considering similar studies and literature. The peak picking method in the frequency domain is used for the output-only modal identification. An analytical modal analysis is performed on the developed two- and three-dimensional finite-element model of the bridge using SAP2000 software to provide the analytical frequencies and mode shapes. At the end of the study, dynamic characteristics of the Elaz?? and Malatya parts of the bridge obtained from the experimental measurements are compared with each other and transverse effects on the bridge are determined. Also, experimental and analytical dynamic characteristics are compared. Good agreement is found between dynamic characteristics in the all measurement test setups performed on the box girder and bridge deck and analytical modal analyses.