Structural Damage Detection from Modal Strain Energy Change

A structural damage detection method based on modal strain energy (MSE) change before and after damage is presented in this paper. The localization of damage based on MSE of each structural element is briefly presented, and the sensitivity of the MSE with respect to a damage is derived. The sensitivity is not based on any series expansion and is a function of the analytical mode shape changes and the stiffness matrix. Only incomplete measured mode shapes and analytical system matrices are required in this damage localization and quantification approach. Results from a numerical example and an experiment on a single-bay, two-story portal steel frame structure are investigated. The effects of measurement noise and truncated analytical mode shapes are discussed. Results indicate that the proposed approach is noise sensitive, but it can localize single and multiple damages. Damage quantification of two damages is successful with a maximum of 14% error under a 5% measurement noise.     

Model-Based Damage Identification in a Continuous Bridge Using Vibration Data

Damage often causes changes in the dynamic characteristics of a structure such as frequencies and mode shapes. Vibration-based damage identification techniques utilize the changes in the dynamic characteristics of a structure to determine the location and extent of damage in the structure. Such techniques are applied in this study to the Crowchild Bridge, a steel-free deck continuous bridge located in western Canada. While the numerical models of the bridge are correlated with the measured dynamic characteristics, computer simulation is used to study the identification of a number of different damage patterns, and the effects of measurement errors and incomplete mode shapes on the quality of results are evaluated. The effectiveness of some selected damage identification techniques is examined; the potential difficulties in identifying the damage are outlined; and areas of further research are suggested. A three-dimensional finite-element model and a simple two-dimensional girder model of the bridge have been constructed to study the usefulness of the selected damage identification methods. Another promising damage detection method proposed here is based on the application of neural networks that combines a vibration-based method.     

Structural Damage Detection Using Empirical Mode Decomposition: Experimental Investigation

This paper presents an experimental investigation on the applicability of the empirical mode decomposition (EMD) for identifying structural damage caused by a sudden change of structural stiffness. A three-story shear building model was constructed and installed on a shaking table with two springs horizontally connected to the first floor of the building to provide additional structural stiffness. Structural damage was simulated by suddenly releasing two pretensioned springs either simultaneously or successively. Various damage severities were produced using springs of different stiffness. A series of free vibration, random vibration, and earthquake simulation tests were performed on the building with sudden stiffness changes. Dynamic responses including floor accelerations and displacements, column strains, and spring releasing time instants were measured. The EMD was then applied to measured time histories to identify damage time instant and damage location for various test cases. The comparison of identified results with measured ones showed that damage time instants could be accurately detected in terms of damage spikes extracted directly from the measurement data by EMD. The damage location could be determined by the spatial distribution of the spikes along the building. The influence of damage severity, sampling frequency, and measured quantities on the performance of EMD for damage detection was also discussed.     

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.     

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%.     

Stiffness Evaluation and Damage Detection of Ceramic Candle Filters

This paper presents a nondestructive evaluation method to identify the structural stiffness of ceramic candle filters. A ceramic candle filter is a hollow cylindrical structure made of a porous ceramic material used in advanced, coal-fired power generation systems. The candle filters need to sustain an extreme thermal and chemical environment over a great period of time to protect the gas turbine components from exposure to particulate matter. A total of 92 new candle filters and 29 used candle filters have been tested nondestructively using a dynamic characterization technique. All filters were subjected to an excitation force, and the response was picked up by an accelerometer in a free-free boundary condition. The frequency response function and vibration mode shapes of each filter were evaluated. Beam vibration equations and finite-element models were built to calculate the filter's dynamic response. Results indicate that the vibration signatures can be used as an index to quantify the structural properties of ceramic candle filters. The results also show estimations of the overall bending stiffness values for four different types of candle filters. The used filters show a trend of stiffness degradation, which was related to the filter's exposure time. Damage detection procedures using modal strain energy and finite-element simulation were studied for detection of a localized damage in the candle filter. The location and the size of the damaged section can be identified using the measured model strain energy.     

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.     

Assessment of Soil Stiffness Properties by Dynamic Tests on Bridges

This paper presents a method to determine soil stiffness properties using measured structural modes of bridges. Normally, the identified mode shapes have to be smoothed. The mode shapes are approximated using functions describing the transverse vibration of distributed–parameter systems. Artificial coefficients are introduced into this solution in order to sum up the error contributions of displacements and its derivatives up to second order. Then, a pier-soil model based on normalized mechanical impedance functions is used. Applying this method along with more than one vertical mode shape leads to acceptable and more accurate results. The amplitudes of pier bottom vibrations are chosen as the suitable weights for the averaging procedure. For the Warth Bridge situated near Vienna, shear wave velocities and shear moduli at the pier foundations have been estimated. The results correspond quite well to the geological investigation.     

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.     

Improved Damage Localization and Quantification Using Subset Selection

Because a structure’s modal parameters (natural frequencies and mode shapes) are affected by structural damage, finite- element model updating techniques are often applied to locate and quantify structural damage. However, the dynamic behavior of a structure can only be observed in a narrow knowledge space, which usually causes nonuniqueness and ill-posedness in the damage detection problem formulation. Thus, advanced optimization techniques are a necessary tool for solving such a complex inverse problem. Furthermore, a preselection process of the most significant damage parameters is helpful to improve the efficiency of the damage detection procedure. A new approach, which combines a parameter subset selection process with the application of damage functions is proposed herein to accomplish this task. Starting with a simple 1D beam, this paper first demonstrates several essential concepts related to the proposed model updating approach. A more advanced example considering a 2D model is then considered. To determine the capabilities of this approach for more complex structures, a trust region-based optimization method is adopted to solve the corresponding nonlinear minimization problem. The objective is to provide an improved robust solution to this challenging problem.     

Selection of Physical and Geometrical Properties for the Confinement of Vibrations in Nonhomogeneous Beams

Confinement of flexural vibrations in nonhomogeneous beams is formulated as one of two types of an inverse eigenvalue problem. In the first problem, the beam’s geometrical and physical parameters and natural frequencies are determined for a prescribed set of confined mode shapes. In the second problem, the beam’s parameters are approximated for a given set of confined mode shapes and frequencies. In both problems, a set of mode shapes, which satisfy all of the boundary conditions and yield vibration confinement in prespecified spatial subdomains of the beam, are selected. Because closed-form solutions are not available, we discretize the spatial domain using the differential quadrature method. As a result, the eigenvalue problem is replaced by a system of algebraic equations, which incorporates the values of the beam’s parameters at all grid points. These equations constitute a well-posed eigenvalue problem, which can be readily solved to determine an equal number of unknowns characterizing the beam properties. In both confinement problems, the unknown physical and geometrical properties must be positive and are approximated using functions constructed from polynomials. These functions are specified at the beam’s left end, right end, or both. Numerical simulations are conducted to confirm convergence of the solution of the inverse eigenvalue problem. It is shown that the physical and geometrical properties can be reconstructed from a few mode shapes. The approximate parameters are finally substituted in the eigenvalue problem to confirm the confined mode shapes of the beam.     

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.     

Efficient Model Correction Method with Modal Measurement

An efficient model correction method is proposed by using the modal measurement from a structural system. The method corrects/updates the mass and stiffness matrix without imposing any parameterization. It considers the information from both the nominal finite-element model and the measurement of modal frequencies and mode shapes. The method is computationally very efficient and it does not require computation of the complete set of eigenvalues and eigenvectors of the nominal model. Instead, only the nominal eigenvalues and eigenvectors of the modes to be corrected are needed. The Gram-Schmidt orthogonalization process is used to construct a basis that satisfies the mass orthogonality condition. This basis is used to transform the eigenvectors of the nominal model so that the corrected model is compatible with the measurement. A thousand-degree-of-freedom chainlike system and a 1,440-degree-of-freedom structural frame are used to illustrate the proposed method.     

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.     

Overview of Vibrational Structural Health Monitoring with Representative Case Studies

In the field of nondestructive evaluation and damage detection, there is continued interest in the utilization of vibrational techniques. Structural damage will result in permanent changes in the distribution of structural stiffness. These changes may be detected through structural monitoring. Because of the direct relationship of stiffness, mass, and damping of a multi-degree-of-freedom system to the natural frequencies, mode shapes, and modal damping values, many studies have been directed at using these dynamic properties for the purpose of structural health monitoring. The use of vibrational monitoring is a developing field of structural analysis and is capable of assisting in both detecting and locating structural damage. Vibrational data have been shown to be most useful when used in conjunction with other monitoring systems if a remote and robust damage detection scheme is desired. This paper includes a literature review that summarizes the basic approaches to vibrational monitoring, suggested guidelines for sensor selection and monitoring, and concludes with three example case studies.     

Structural Damage Detection from Wavelet Coefficient Sensitivity with Model Errors

The sensitivity of the wavelet coefficient from structural responses with respect to the system parameters is analytically derived. It is then used in a sensitivity-based inverse problem for structural damage detection with sinusoidal or impulsive excitation and acceleration and strain measurements. The sensitivity of the wavelet coefficient is shown more sensitive than the response sensitivity with an example of a single story plane frame. It is further found not sensitive to different types of model errors in the initial model including the support stiffness, mass density and flexural rigidity of members, damping ratio, and the excitation force. Simulation results show that the damage information is carried mostly in the higher vibration modes of the structure as diagnosed with the corresponding wavelet coefficients from its dynamic responses. A wavelet combination encompasses all the frequency bandwidth is used in the successful identification of a reinforced concrete beam in the laboratory.     

Vibrational Tension Measurement of External Tendons in Segmental Posttensioned Bridges

A rapid and economical vibrational tension measurement method is presented to detect distress in external tendons used in segmental posttensioned bridges. This method provides a complementary technique to traditional inspection methods currently employed in the field. The natural frequency and overtones produced by an impact excitation are measured and used to determine the tendon segment’s tension and flexural stiffness using a differential equation describing a stiff string with clamped-clamped boundary conditions. The flexural stiffness is not negligible in tendons of this type causing the vibration modes to be inharmonically related. This method provides consistent (typically within 1%) and reasonably accurate (typically within 10%) estimates of tendon tension. Accuracy can be improved by lessening uncertainty in input constants such as the tendon mass and tendon length. Application examples from several in-service bridges have shown that detection of corrosion damage, improper tensioning, and force distribution effects from friction at deviation blocks can be detected.     

Damage Localization by Directly Using Incomplete Mode Shapes

A sensitivity- and statistical-based method to localize structural damage by direct use of incomplete mode shapes is presented. The method is an extension of the multiple damage location assurance criterion (MDLAC), developed by Messina et al. by using incomplete mode shape instead of modal frequency. This approach makes use of the good sensitivity of mode shape to local damage. The damage detection strategy is to localize the damage sites first by using incomplete measured mode shapes, and then to detect the damage site and extent again by using measured natural frequencies, which have a better accuracy than mode shapes. A plane truss structure is analyzed as a numerical example to compare the performance of the proposed method with the multiple damage location assurance criterion. Results indicate that the new method is more accurate and robust in damage localization with or without noise effect.     

Identification and Monitoring of Modal Parameters in Aircraft Structures Using the Natural Excitation Technique (NExT) Combined with the Eigensystem Realization Algorithm (ERA)

The early detection of cracks, fatigue, corrosion, and structural failure in aging aircraft is one of the major challenges in the aircraft industry. Common inspection techniques are time consuming and hence can have strong economic implications due to aircraft downtime. As a result, during the past decade a number of methodologies have been proposed for detecting structural damage based on variations in the structure’s dynamic characteristics. This paper describes the implementation of the natural excitation technique (NExT) combined with the eigensystem realization algorithm (ERA) to determine the dynamic characteristics of a T-34A Mentor acrobatic category aircraft and a modified DC-3 cargo/transport category aircraft. In-flight acceleration data were processed using NExT-ERA to monitor the predominant natural frequencies and associated mode shapes of the aircraft for varying flight conditions. The results show the effectiveness of this modal identification methodology and the possibility of implementing it in a real-time structural health monitoring system for aircraft.     

Modal Strain Energy Decomposition Method for Damage Localization in 3D Frame Structures

This article presents a newly developed modal strain energy decomposition method for damage localization that is capable of identifying damage to individual members of three-dimensional (3D) frame structures. This method is based on decomposing the modal strain energy of each structural member (or element) into two parts, one associated with the element’s axial coordinates and the other with its transverse coordinates. In turn, two damage indicators are calculated for each member to perform the damage localization analysis. Implementing this method requires only a small number of mode shapes identified from both the damaged and baseline structures. Numerical studies are conducted of a 3D five-story frame structure and also a complicated offshore template platform, based on synthetic data generated from finite-element models. In addition to providing theoretical insights to illustrate the advantages of using this newly developed method, this article also demonstrates numerically that the new method is capable of localizing various kinds of damaged elements (a vertical pile, horizontal beam, or slanted brace) at a template offshore structure.