Hilbert-Huang Based Approach for Structural Damage Detection

When measured data contain damage events of the structure, it is important to extract the information of damage as much as possible from the data. In this paper, two methods are proposed for such a purpose. The first method, based on the empirical mode decomposition (EMD), is intended to extract damage spikes due to a sudden change of structural stiffness from the measured data thereby detecting the damage time instants and damage locations. The second method, based on EMD and Hilbert transform is capable of (1) detecting the damage time instants, and (2) determining the natural frequencies and damping ratios of the structure before and after damage. The two proposed methods are applied to a benchmark problem established by the ASCE Task Group on Structural Health Monitoring. Simulation results demonstrate that the proposed methods provide new and useful tools for the damage detection and evaluation of structures.     

Nonlinear Identification of Lumped-Mass Buildings Using Empirical Mode Decomposition and Incomplete Measurement

Most structures exhibit some degrees of nonlinearity such as hysteretic behavior especially under damage. It is necessary to develop applicable methods that can be used to characterize these nonlinear behaviors in structures. In this paper, one such method based on the empirical mode decomposition (EMD) technique is proposed for identifying and quantifying nonlinearity in damaged structures using incomplete measurement. The method expresses nonlinear restoring forces in semireduced-order models in which a modal coordinate approach is used for the linear part while a physical coordinate representation is retained for the nonlinear part. The method allows the identification of parameters from nonlinear models through linear least-squares. It has been shown that the intrinsic mode functions (IMFs) obtained from the EMD of a response measured from a nonlinear structure are numerically close to its nonlinear modal responses. Hence, these IMFs can be used as modal coordinates as well as provide estimates for responses at unmeasured locations if the mode shapes of the structure are known. Two procedures are developed for identifying nonlinear damage in the form of nonhysteresis and hysteresis in a structure. A numerical study on a seven-story shear-beam building model with cubic stiffness and hysteretic nonlinearity and an experimental study on a three-story building model with frictional magnetoreological dampers are performed to illustrate the proposed method. Results show that the method can quite accurately identify the presence as well as the severity of different types of nonlinearity in the structure.     

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.     

Multivariate Statistical Approach to Structural Damage Detection

The issue of structural damage detection is addressed through an innovative multivariate statistical approach in this paper. By invoking principal component analysis, the vibration responses acquired from the structure being monitored are represented by the multivariate data of the sample principal component coefficients (PCCs). A damage indicator is then defined based on a multivariate exponentially weighted moving average control chart analysis formulation, involving special procedures to allow for the effects of the estimated parameters and to determine the upper control limits in the control chart analysis for structural damage detection applications. Also, a data shuffling procedure is proposed to remove the autocorrelation probably present in the obtained sample PCCs. This multivariate statistical structural damage detection scheme can be applied to either the time domain responses or the frequency domain responses. The efficacy and advantages of the scheme are demonstrated by the numerical examples of a five-story shear frame and a shear wall as well as the experimental example of the I-40 Bridge benchmark.     

Phase I IASC-ASCE Structural Health Monitoring Benchmark Problem Using Simulated Data

Structural health monitoring (SHM) is a promising field with widespread application in civil engineering. Structural health monitoring has the potential to make structures safer by observing both long-term structural changes and immediate postdisaster damage. However, the many SHM studies in the literature apply different monitoring methods to different structures, making side-by-side comparison of the methods difficult. This paper details the first phase in a benchmark SHM problem organized under the auspices of the IASC–ASCE Structural Health Monitoring Task Group. The scale-model structure adopted for use in this benchmark problem is described. Then, two analytical models based on the structure—one a 12 degree of freedom (DOF) shear-building model, the other a 120-DOF model, both finite element based—are given. The damage patterns to be identified are listed as well as the types and number of sensors, magnitude of sensor noise, and so forth. MATLAB computer codes to generate the response data for the various cases are explained. The codes, as well as details of the ongoing Task Group activities, are available on the Task Group web site at 〈http://wusceel.cive.wustl.edu/asce.shm/〉.     

Structural Damage Diagnosis and Assessment under Seismic Excitations

This study proposes a method of detecting, locating, and quantifying structural damage by directly using structural vibration measurements in the time domain. In this method, the coupling effect of the damage at different locations in the structure on the structural vibratory responses is eliminated by projecting these measured quantities onto some specific subspaces. As a result, the structural system, generally modeled with multiple degree of freedom, is decomposed into several independent single-degree-of-freedom (SDOF) systems, every one of which is only associated with the damage at one certain location or region. A monitor is designed as an observer to detect the structural damage related to each SDOF system. A decision-making scheme is developed to correlate the monitor’s output to the occurrence of the damage. The severity of the damage is estimated with a traditional system identification method in an iterative way. The analysis of the effects of measurement noise is also included. Numerical examples are presented to demonstrate the effectiveness of the proposed method.     

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.     

Multimetric Sensing for Structural Damage Detection

Vibration-based damage detection methods have been widely studied for structural health monitoring of civil infrastructure. Acceleration measurements are frequently employed to extract the dynamic characteristics of the structure and locate damage because they can be obtained conveniently and possess relatively little noise. However, considering the fact that damage is a local phenomenon, the sole use of acceleration measurements that are intrinsically global structural responses limits damage detection capabilities. This paper investigates the possibility of using both global and local measurements to improve the accuracy and robustness of damage detection methods. A multimetric approach based on the damage locating vector method is proposed. Numerical simulations are conducted to verify the efficacy of the proposed approach.     

Structural Health Monitoring and Damage Assessment Using Frequency Response Correlation Criteria

Two frequency response correlation criteria, namely the global shape correlation (GSC) function and the global amplitude correlation (GAC) function, are established tools to quantify the correlation between predictions from a finite-element (FE) model and measured data for the purposes of FE model validation and updating. This paper extends the application of these two correlation criteria to structural health monitoring and damage detection. In addition, window-averaged versions of the GSC and GAC, namely WAIGSC and WAIGAC, are defined as effective damage indicators to quantify the change in structural response. An integrated method of structural health monitoring and damage assessment, based on the correlation functions and radial basis function neural networks, is proposed and the technique is applied to a bookshelf structure with 24 measured responses. The undamaged and damaged states, single and multiple damage locations, as well as damage levels, were successfully identified in all cases studied. The ability of the proposed method to cope with incomplete measurements is also discussed.     

Bayesian Probabilistic Inference for Nonparametric Damage Detection of Structures

This paper presents a Bayesian hypothesis testing-based probabilistic assessment method for nonparametric damage detection of building structures, considering the uncertainties in both experimental results and model prediction. A dynamic fuzzy wavelet neural network method is employed as a nonparametric system identification model to predict the structural responses for damage evaluation. A Bayes factor evaluation metric is derived based on Bayes’ theorem and Gaussian distribution assumption of the difference between the experimental data and model prediction. The metric provides quantitative measure for assessing the accuracy of system identification and the state of global health of structures. The probability density function of the Bayes factor is constructed using the statistics of the difference of response quantities and Monte Carlo simulation technique to address the uncertainties in both experimental data and model prediction. The methodology is investigated with five damage scenarios of a four-story benchmark building. Numerical results demonstrate that the proposed methodology provides an effective approach for quantifying the damage confidence in the structural condition assessment.     

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.     

Damage Detection Utilizing the Damage Index Method to a Benchmark Structure

This paper addresses the first generation benchmark problem on structural health monitoring developed by the ASCE Task Group on Structural Health Monitoring. The focus of the problem is a four-story model of an existing physical model at the University of British Columbia where simulated data are used for the system identification. Modal parameters were extracted using the frequency domain decomposition method. Rather than relying on data from the undamaged structure, a new proposed methodology based on ratios between stiffness and mass values from the eigenvalue problem is presented to identify the undamaged state of the structure. Once the structural identification is complete, the damage index method is used to detect the location and severity of damage. By not relying on undamaged structure information, this approach may be applicable to existing structures that may already incorporate some amount of damage.     

Vibration-based Damage Detection of Structures by Genetic Algorithm

Vibration-based methods are being rapidly applied to detect structural damage. The usual approaches incorporate sensitivity analysis and the optimization algorithm to minimize the discrepancies between the measured vibration data and the analytical data. However, conventional optimization methods are gradient based and usually lead to a local minimum only. Genetic algorithms explore the region of the whole solution space and can obtain the global optimum. In this paper, a genetic algorithm with real number encoding is applied to identify the structural damage by minimizing the objective function, which directly compares the changes in the measurements before and after damage. Three different criteria are considered, namely, the frequency changes, the mode shape changes, and a combination of the two. A laboratory tested cantilever beam and a frame are used to demonstrate the proposed technique. Numerical results show that the damaged elements can be detected by genetic algorithm, even when the analytical model is not accurate.     

Wind Response Control of Building with Variable Stiffness Tuned Mass Damper Using Empirical Mode Decomposition/Hilbert Transform

The effectiveness of a novel semiactive variable stiffness-tuned mass damper (SAIVS-TMD) for the response control of a wind-excited tall benchmark building is investigated in this study. The benchmark building considered is a proposed 76-story concrete office tower in Melbourne, Australia. It is a slender building 306 m tall with a height to width ratio of 7.3; hence, it is wind sensitive. Across wind load data from wind tunnel tests are used in the present study. The objective of this study is to evaluate the new SAIVS-TMD system, that has the distinct advantage of continuously retuning its frequency due to real time control and is robust to changes in building stiffness and damping. In comparison, the passive tuned mass damper (TMD) can only be tuned to a fixed frequency. A time varying analytical model of the tall building with the SAIVS-TMD is developed. The frequency tuning of the SAIVS-TMD is achieved based on empirical mode decomposition and Hilbert transform instantaneous frequency algorithm developed by the writers. It is shown that the SAIVS-TMD can reduce the structural response substantially, when compared to the uncontrolled case, and it can reduce the response further when compared to the case with TMD. Additionally, it is shown the SAIVS-TMD reduces response even when the building stiffness changes by ±15% and is robust; whereas, the TMD loses its effectiveness under such building stiffness variations. It is also shown that SAIVS-TMD can reduce the response similar to an active TMD; however, with an order of magnitude less power consumption.     

Detection of Changes in Global Structural Stiffness Coefficients Using Acceleration Feedback

This technical note presents an extension of a previous study where two methods for detecting structural damage have been developed by using displacement and velocity measurements. In this study, acceleration feedback is used in detecting changes in global structural stiffness coefficients of lumped-mass-shear-beam models. The previously developed method relies on the decoupling of effects of changes in stiffness at different locations and the use of displacement or velocity feedback has proven to be effective. Extension to the use of acceleration feedback using existing formulation is not trivial in that the desired decoupling effect cannot be achieved by simple coordinate transformation because the acceleration itself is directly related to the stiffness coefficients. An approach to circumvent this difficulty is presented and it involves increasing the order of time derivatives of the linear system so that the acceleration becomes the “velocity” of the new system. The performance of the proposed method is demonstrated using an illustrative example of a three-story model with stiffness changes at different floors. Numerical studies are also conducted to evaluate the time horizons required to normalize monitor outputs for the effective and efficient detection of stiffness changes.     

Two-Stage Structural Health Monitoring Approach for Phase I Benchmark Studies

This paper presents a two-stage structural health monitoring methodology and applies it to the Phase I benchmark study sponsored by the IASC-ASCE Task Group on Structural Health Monitoring. In the first stage, modal parameters are identified using measured structural response from the undamaged system and then from the (possibly) damaged system. In the second stage, these data are used to update a parametrized structural model of the system using Bayesian system identification. The approach allows one to obtain not only estimates of the stiffness parameters but also the probability that damage in any substructure exceeds any specified threshold expressed in terms of a fractional stiffness loss. It successfully identifies the location and severity of damage in all cases of the benchmark problem.     

Description of Structural Damage Caused by the Terrorist Attack on the Pentagon

On September 11, 2001, an airliner was intentionally crashed into the Pentagon. It struck at the first elevated slab on the west wall, and slid approximately 310?ft (94.5?m) diagonally into the building. The force of the collision demolished numerous columns and the fa?ade of the exterior wall, and induced damage to first-floor columns and the first elevated slab over an area approximately 90?ft (27.4?m) wide and 310?ft (94.5?m) long. None of the building collapsed immediately. The portion that remained standing, even after an intense fire, sustained substantial damage at the first-floor level.     

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.     

Identification of Structural Systems Using an Evolutionary Strategy

The problem of system identification is an inverse problem of difficult solution. Currently, difficulties lie in the development of algorithms that use measured data from the system to characterize it without significant a priori knowledge of the system. In this paper, a parameter estimation technique based on an evolution strategy (an optimization algorithm inspired by natural evolution) is presented to overcome some of the difficulties encountered in the field. Using this method, a set of direct problems is solved instead of directly tackling the inverse problem. If the uniqueness of the identification solution is guaranteed for the assumed model and the available data, this heuristic method is able to find a solution without incurring restrictions of other classical optimization methods, like the need for reliable initial estimates and convergence to local optima. Some results obtained with this algorithm are presented for the identification of 3 degrees of freedom (DOF) and a 10?DOF structural system under conditions including limited input/output data, noise polluted signals, and no prior knowledge of mass, damping, or stiffness of the system.