Damage Localization and Finite-Element Model Updating Using Multiresponse NDT Data

New techniques for both finite-element model updating and damage localization are presented using multiresponse nondestructive test (NDT) data. A new protocol for combining multiple parameter estimation algorithms for model updating is presented along with an illustrative example. This approach allows for the simultaneous use of both static and modal NDT data to perform model updating at the element level. A new damage index based on multiresponse NDT data is presented for damage localization of structures. This index is based on static and modal strain energy changes in a structure as a result of damage. This method depicts changes in physical properties of each structural element compared to its initial state using NDT data. Deficient or potentially damaged structural elements are then selected as the unknown parameters to be updated by parameter estimation. Error function normalization, error function stacking, and multiresponse parameter estimation methods are proposed for using multiple data types for simultaneous stiffness and mass parameter estimation. Also, multiple sets of measurements with various sizes and missing data points can be utilized. This paper uses a laboratory grid model of a bridge deck built at the University of Cincinnati Infrastructure Institute and the corresponding NDT data for validation of the above damage localization and model updating methods. Multiresponse parameter estimation has been utilized to update the stiffness of bearing pads, and both the stiffness and mass of the connections, using static and dynamic NDT data. The static and modal responses of the updated grid model presented a closer match with the NDT data than the responses from the initial model.     

Ambient Vibration Data Analysis for Structural Identification and Global Condition Assessment

System identification is an area which deals with developing mathematical models to characterize the input-output behavior of an unknown system by means of experimental data. Structural health monitoring (SHM) provides the tools and technologies to collect and analyze input and output data to track the structural behavior. One of the most commonly used SHM technologies is dynamic testing. Ambient vibration testing is a practical dynamic testing method especially for large civil structures where input excitation cannot be directly measured. This paper presents a conceptual and reliable methodology for system identification and structural condition assessment using ambient vibration data where input data are not available. The system identification methodology presented in this study is based on the use of complex mode indicator functions (CMIFs) coupled with the random decrement (RD) method to identify the modal parameters from the output only data sets. CMIF is employed for parameter identification from the unscaled multiple-input multiple-output data sets generated using the RD method. For condition assessment, unscaled flexibility and the deflection profiles obtained from the dynamic tests are presented as a conceptual indicator. Laboratory tests on a steel grid and field tests on a long-span bridge were conducted and the dynamic properties identified from these tests are presented. For demonstrating condition assessment, deflected shapes obtained from unscaled flexibility are compared for undamaged and damaged laboratory grid structures. It is shown that structural changes on the steel grid structure are identified by using the unscaled deflected shapes.     

Structural Reliability Estimation with Vibration-Based Identified Parameters

This paper presents a unique structural reliability estimation method incorporating structural parameter identification results based on the seismic response measurement. In the shaking table test, a three-bent concrete bridge model was shaken to different damage levels by a sequence of earthquake motions with increasing intensities. Structural parameters, stiffness and damping values of the bridge were identified under damaging seismic events based on the seismic response measurement. A methodology was developed to understand the importance of structural parameter identification in the reliability estimation. Along this line, a set of structural parameters were generated based on the Monte Carlo simulation. Each of them was assigned to the base bridge model. Then, every bridge model was analyzed using nonlinear time history analyses to obtain damage level at the specific locations. Last, reliability estimation was performed for bridges modeled with two sets of structural parameters. The first one was obtained by the nonlinear time history analysis with the Monte Carlo simulated parameters which is called nonupdated structural parameters. The second one was obtained by updating the first set in Bayesian sense based on the vibration-based identification results which is called updated structural parameters. In the scope of this paper, it was shown that residual reliability of the system estimated using the updated structural parameters is lower than the one estimated using the nonupdated structural parameters.     

Structural Damage Detection and Assessment from Modal Response

This paper presents a global damage detection and assessment algorithm based on a parameter estimation method using a finite-element model and the measured modal response of a structure. Damage is characterized as a reduction of the member constitutive parameter from a known baseline value. An optimization scheme is proposed to localize damaged parts of the structure. The algorithm accounts for the possibility of multiple solutions to the parameter estimation problem that arises from using spatially sparse measurements. Errors in parameter estimates caused by sensitivity to measurement noise are reduced by selecting a near-optimal measurement set from the data at each stage of the localization algorithm. Damage probability functions are computed upon completion of the localization process for candidate elements. Monte Carlo methods are used to compute the required probabilities based on the statistical distributions of the parameters for the damaged and the associated baseline structure. The algorithm is tested in a numerical simulation environment using a planar bridge truss as a model problem.     

Structural Damage Detection Using Dynamic Properties Determined from Laboratory and Field Testing

Studies have shown that experimentally determined dynamic properties can be used to identify the characteristics of a structure. In this paper, a damage detection technique is developed and demonstrated using system identification, finite-element modeling, and a modal update process. The proposed approach, SFM, provides a rapid estimate of damage locations and magnitudes. The proposed methodology is applied to three case studies. The first is a numerical simulation using computer generated data. The second is an ASCE benchmark problem for structural health monitoring, where the results can be compared to other researchers. The third is a full-scale highway bridge that was field tested using a forced vibration shaking machine. In this case study, the bridge was shaken in several states of damage and the proposed methodology was utilized to detect and determine the location and extent of the damage. It was found that, using the collected data, the SFM approach was able to consistently predict the location of damage as well as estimate the magnitude of the damage.     

Damage Identification on the Tilff Bridge by Vibration Monitoring Using Optical Fiber Strain Sensors

Vibration testing is a well-known practice for damage identification of civil engineering structures. The real modal parameters of a structure can be determined from the data obtained by tests using system identification methods. By comparing these measured modal parameters with the modal parameters of a numerical model of the same structure in undamaged condition, damage detection, localization, and quantification is possible. This paper presents a real-life application of this technique to assess the structural health of the 50-year old bridge of Tilff, a prestressed three-cell box-girder concrete bridge with variable height. A complete ambient vibration survey comprising both vertical accelerations and axial strains has been carried out. The in situ use of optical fiber strain sensors for the direct measurement of modal strains is an original contribution of this work. It is a big step forward in the exploration of modal curvatures for damage identification because the accuracy in calculating the modal curvatures is substantially improved by directly measuring modal strains rather than deriving the modal curvatures from acceleration measurements. From the ambient vibrations, natural frequencies, damping factors, modal displacements and modal curvatures are extracted by the stochastic subspace identification method. These modal parameters are used for damage identification which is performed by the updating of a finite element model of the intact structure. The obtained results are then compared to the inspections performed on the bridge.     

Vibration Testing at Meazza Stadium: Reliability of Operational Modal Analysis to Health Monitoring Purposes

In the last years an increasing interest has been devoted to all the topics related to the security and safety of people. Particular attention has been paid to health monitoring of large civil structures hosting many people, such as high-rise buildings and stadiums. Some extraordinary events, such as the Millennium Bridge oscillations in London, excited by pedestrians, or the Bruce Springsteen concert at the Ullevi Stadium in which coordinated jumps from the crowd caused serious damage to the structure, and drew attention toward a deeper and more careful study of all those problems related to the dynamic behavior of civil structures and their interaction with crowds. Research on these topics is also aimed, among others, at developing techniques allowing for a continuous monitoring of the structure, starting from a set of measurements that can be performed continuously, 24?h a day, without the need to stop the structure's functionality. The vast scientific literature confirms the possibility of relating structural health to the evolution of modal parameters, often reaching the aim of localizing any eventual damage, a task otherwise impossible with different techniques. This paper shows part of a long lasting project involving Politecnico di Milano in the setting up of a permanent health monitoring system at the G. Meazza Stadium in Milan. The aim of this project was the evaluation of the actual health state of the structures constituting the stands of the stadium and the deployment of a permanent monitoring system to record the vibration levels reached in all substructures during each event. Evaluation of the actual structure condition was performed by the use of ambient vibration, which was also checked against traditional experimental modal analysis, performed by using an inertial force given by a hydraulic actuator and a detailed measurement mesh. This offered the chance to exploit all possible information concerning natural frequencies, modal shapes, and damping factors. This task is extremely time consuming and expensive, therefore, it cannot be repeated very often. The possibility of using the data coming from the permanent monitoring system, which is about to be installed, is then an attractive perspective to improve structural diagnosis. It is expected that using operational modal analysis techniques will mean knowledge of the excitation applied to the structure will not be required. The parameter estimation obtained by this technique is usually affected by a spread, given both by the uncertainty of the adopted identification techniques and the influence of external parameters, such as crowd loading or temperature. As damage identification is related to changes of the modal parameters, the evaluation of their normal spread is fundamental to fix a threshold in order to identify possible worrysome situations. This paper deals with the identification of the spread in the modal parameter estimation of one of the grandstands of the so-called 3° ring of the G. Meazza Stadium in Milan, performed analyzing data collected over more than one year. Vibration data have been recorded during different events, such as soccer matches and concerts. The considered data came from a set of sensors similar to that which is to be installed for the permanent monitoring system, to check about the possibility to use the monitoring system as a diagnostic tool for the structure. A study was also carried out to identify critical aspects in the sensors’ choice and their placement, in order to provide useful information about the design of the permanent monitoring system. The presented results can be used to determine confidence intervals out of which changes in the modal properties can be considered anomalous, and so, worthy of being deeply investigated to assess structural integrity.     

Fast Bayesian FFT Method for Ambient Modal Identification with Separated Modes

Previously a Bayesian theory for modal identification using the fast Fourier transform (FFT) of ambient data was formulated. That method provides a rigorous way for obtaining modal properties as well as their uncertainties by operating in the frequency domain. This allows a natural partition of information according to frequencies so that well-separated modes can be identified independently. Determining the posterior most probable modal parameters and their covariance matrix, however, requires solving a numerical optimization problem. The dimension of this problem grows with the number of measured channels; and its objective function involves the inverse of an ill-conditioned matrix, which makes the approach impractical for realistic applications. This paper analyzes the mathematical structure of the problem and develops efficient methods for computations, focusing on well-separated modes. A method is developed that allows fast computation of the posterior most probable values and covariance matrix. The analysis reveals a scientific definition of signal-to-noise ratio that governs the behavior of the solution in a characteristic manner. Asymptotic behavior of the modal identification problem is investigated for high signal-to-noise ratios. The proposed method is applied to modal identification of two field buildings. Using the proposed algorithm, Bayesian modal identification can now be performed in a few seconds even for a moderate to large number of measurement channels.     

Bayesian Probabilistic Approach to Structural Health Monitoring

A Bayesian probabilistic methodology for structural health monitoring is presented. The method uses a sequence of identified modal parameter data sets to compute the probability that continually updated model stiffness parameters are less than a specified fraction of the corresponding initial model stiffness parameters. In this approach, a high likelihood of reduction in model stiffness at a location is taken as a proxy for damage at the corresponding structural location. The concept extends the idea of using as indicators of damage the changes in structural model parameters that are identified from modal parameter data sets when the structure is initially in an undamaged state and then later in a possibly damaged state. The extension is needed, since effects such as variation in the identified modal parameters in the absence of damage, as well as unavoidable model error, lead to uncertainties in the updated model parameters that in practice obscure health assessment. The method is illustrated by simulating on-line monitoring, wherein specified modal parameters are identified on a regular basis and the probability of damage for each substructure is continually updated.     

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.     

Modal Identification Algorithm with Unmeasured Input

This paper investigates the possibility of generating a time‐domain modal identification algorithm that does not need measurements of the input signals. Such a technique is useful when complete input data acquisition cannot be performed. The approach is based on the Yule‐Walker equations, extended to the case where the input signal is not white noise. The algorithm is written recursively both to minimize data acquisition and to be flexible enough when time‐varying modal parameters are tracked. Natural frequencies and damping ratios are extracted with an error magnitude inferior to impulse response techniques but superior to methods using the input time history. From a computational aspect, the algorithm only introduces scalar inversions, which presents an important gain of time and stability. Examples and comparisons with other techniques are presented. The case where a change in the modal parameter values occur is also highlighted. A normalized error, taking into account the quality and the swiftness of the new estimation, is introduced.     

Impedance-Based Method for Nondestructive Damage Identification

A structural damage identification technique based on the impedance method is presented in this paper using smart piezoelectric transducer (PZT) patches. A modeling framework is developed to determine the structural impedance response and the dynamic output forces of PZT patches from the electric admittance measurements. A damage identification scheme for solving the nonlinear optimization problem is proposed to locate and quantify the structural damage through the minimization of the discrepancy between the structural impedance response and the numerically computed frequency response. The proposed technique does not use modal analysis or model reduction, and only the electric admittance measurements of PZT patches and the analytical system matrices are required. A beam example has been employed to illustrate the effectiveness of the proposed algorithm numerically. Furthermore, the influence of the measurement noise on the results has been investigated.     

Dynamic Testing for Structural Identification of a Bridge

Structural identification via modal analysis in structural mechanics is gaining popularity in recent years, despite conceptual difficulties connected with its use. This paper is devoted to illustrating the advantages and also the indeterminacy characterizing structural identification problems for bridge structures, even in rather simple instances. In particular, an identification procedure based on modal analysis and finite-element model updating is presented for the characterization of a concrete bridge whose constructive typology is quite diffuse in the area of Friuli Venezia Giulia, Italy. Experience has suggested (so as to restrict the indeterminacy frequently affecting identification issues) resorting to all the a priori information on the system and mindfully selecting the parameters to be identified. The analysis pointed out some particularities in the modeling of bridge typology under study, otherwise not a priori detectable from an analytical point of view.     

Vibration Serviceability of a Building Floor Structure. I: Dynamic Testing and Computer Modeling

Buildings with large column-free floors or long-cantilevered structures can be susceptible to annoying vibrations due to everyday occupants’ activities such as walking. Computer modeling and analytical representation of building structural properties to predict the floor response subjected to excitations due to human activities are important issues that require further studies. Vibration testing and analysis of built structures can assist in more accurate estimation of structure dynamic properties. This paper presents the results of the modal testing conducted on an office building floor and analysis of the collected vibration measurements. It compares these results with the structural response using computer analyses. It also presents a sensitivity study to assess the importance of various structural parameters on the floor dynamic response. From the results presented, it is concluded that for the structure used in this study the raised flooring and nonstructural elements acted mainly as added mass and did not contribute to the floor damping. Conclusions are also made on the importance of various structural parameters on floor response and the analysis of the modal test results.     

Determination of Physical Parameters of Stiffened Plates using Genetic Algorithm

An investigation on stiffened isotropic and composite plates has been conducted to determine the geometric and material parameters for the plate, as well as the stiffener from experimental modal data and finite element predictions using a genetic algorithm (GA). The problem is formulated as a global minimization of the error function defined by the difference in undamped eigenvalues and eigenvectors, as predicted from the finite-element modeling to that obtained experimentally. The parameter estimation problem is solved using a GA implementing selection, crossover, and mutation operators to obtain the global minimum solution. Because stiffeners contribute substantially to the overall rigidity of the plate assembly, their position, physical properties, and orientation create considerable variation of the modal properties, as compared to the bare plate with similar construction. This makes each of the stiffened plate identification problems rather unique. GAs have been the subject of considerable interest in providing a robust search procedure for a global optimum solution for such difficult minimization problems. The method is demonstrated on a few simulated examples on stiffened plates to investigate the uniqueness and convergence of results. The methodology, although slow in execution, is found to be very robust, even in the presence of noise, for isolating interesting zones of the search space. Unlike many traditional optimization techniques, it does not get stuck at a particular local minimum due to its parallelism.     

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.     

Assessment of Highway Bridge Upgrading by Dynamic Testing and Finite-Element Model Updating

The Land Transport Authority of Singapore has a continuing program of highway bridge upgrading for refurbishing and strengthening bridges to allow for increasing vehicle traffic and increasing axle loads. One subject of this program has been a short-span bridge taking a busy main road across a coastal inlet near a major port facility. Experiment-based structural assessments of the bridge were conducted before and after upgrading works including strengthening. Each assessment exercise comprised three separate components: (1) a strain and acceleration monitoring exercise lasting approximately one month; (2) a full-scale dynamic test carried out in a single day without closing the bridge; and (3) a finite-element model updating exercise to identify structural parameters and mechanisms. This paper presents the dynamic testing and the modal analysis used to identify the vibration properties and the quantification of the effectiveness of the upgrading through the subsequent model updating. Before and after upgrade, similar sets of vibration modes were identified, resembling those of an orthotropic plate with relatively weak transverse bending stiffness. Conversion of bearings from nominal simple supports to nominal full fixity was shown via model updating to be the principal cause of natural frequency increases of up to 50%. The utility of the combined experimental and analytical process in direct identification of structural properties has been proven, and the procedure can be applied to other structures and their capacity assessments.     

Bayesian Analysis of the Phase II IASC–ASCE Structural Health Monitoring Experimental Benchmark Data

A two-step probabilistic structural health monitoring approach is used to analyze the Phase II experimental benchmark studies sponsored by the IASC–ASCE Task Group on Structural Health Monitoring. This study involves damage detection and assessment of the test structure using experimental data generated by hammer impact and ambient vibrations. The two-step approach involves modal identification followed by damage assessment using the pre- and postdamage modal parameters based on the Bayesian updating methodology. An Expectation–Maximization algorithm is proposed to find the most probable values of the parameters. It is shown that the brace damage can be successfully detected and assessed from either the hammer or ambient vibration data. The connection damage is much more difficult to reliably detect and assess because the identified modal parameters are less sensitive to connection damage, allowing the modeling errors to have more influence on the results.     

Study of Time-Domain Techniques for Modal Parameter Identification of a Long Suspension Bridge with Dense Sensor Arrays

While numerous studies have been published concerning the application of a variety of system identification techniques in conjunction with vibration measurements from civil infrastructure systems, there is a paucity of publications addressing the influence of algorithm-specific control parameters that impact the correct and efficient application of the selected identification scheme. Furthermore, as dense sensor arrays become widely accessible in civil infrastructure applications, voluminous amounts of multichannel data streams are becoming available for processing, thus imposing new demands on identification procedures regarding high-dimensionality (in both the spatial as well as the temporal domains) requirements that may render some methods inapplicable if careful attention is not paid to practical implementation issues. This paper provides a comprehensive study of three time-domain identification algorithms applied in conjunction with the Natural Excitation Technique in order to extract the modal parameters of a newly constructed long-span bridge that was monitored, in its virgin state, over a relatively long period of time with a state-of-the-art dense sensor array. The three methods used are: the eigensystem realization algorithm (ERA), the ERA with data correlations, and the least squares algorithm. One of the critical issues in the mentioned algorithms, is selection of the reference degree-of-freedom (DOF). Previous experiences have shown that one cannot rely on a single reference DOF for identification of all modes. Consequently, the aforementioned identification formulations were modified to include multiple reference DOF, simultaneously, or one at a time. An autonomous algorithm was presented to distinguish the genuine structural modes from spurious noise or computational modes. Based on some parameter studies, some useful guidelines for the selection of critical user-selectable parameters are presented.     

Overview of a Modal-Based Condition Assessment Procedure

Condition assessment is a term that is used to describe the process of characterizing the physical condition of constructed systems. This paper summarizes a condition assessment (CA) procedure based on a complete system of field-testing, finite element (FE) modeling, and load rating. Experimental techniques, including both modal testing and truckload testing, are used to collect measurements of the constructed systems. The basic mechanism and procedure of the FE modeling and calibration are presented. Different physical parameters of FE models are adjusted during the calibration process using both static and dynamic responses as criteria to achieve convergence between experimental measurements and analytical results using carefully developed objective functions. Finally, a bridge load rating is completed on the basis of the calibrated model. These developments are described and illustrated using a representative bridge as an example.