Cross-Modal Strain Energy Method for Estimating Damage Severity

A newly developed damage severity estimation method, termed as cross-modal strain energy (CMSE) method, which is capable of accurately estimating the damage magnitude of multiple damaged members, is presented. While all existing damage severity estimation methods that utilize modal strain energy are either employing an iterative solution procedure or involving significant approximations, the CMSE method is an exact, noniterative solution method. Furthermore, the development of the CMSE method is under the assumption that the mass distributions of the baseline and damaged structures are unknown, but identical. Implementing this method requires only the information of a few modes measured from the damaged structure. Numerical studies are demonstrated for a three-dimensional five-story frame structure based on synthetic data generated from finite element models.     

Improved Damage Quantification from Elemental Modal Strain Energy Change

An improved structural damage quantification algorithm is presented based on the elemental modal strain energy change before and after the occurrence of damage in a structure. The algorithm includes the analytical stiffness and mass matrices of the system in the damage quantification. It reduces significantly the modal truncation error and the finite-element modeling error from higher analytical modes in the computation, and it improves the convergence properties of the existing algorithm by Shi et al. (2000). “Structural damage detection from elemental modal strain energy change.” J. Eng. Mech., 126(12), 1216–1223]. The effectiveness of the proposed algorithm is demonstrated via a numerical example and experimental results from a two-storey steel portal frame, and it is demonstrated to be an efficient and robust method for damage quantification.     

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.     

Modeling the Impact of Failed Members for Progressive Collapse Analysis of Frame Structures

During the past decade, increasing attention has been focused on the design of buildings to resist progressive collapse. Previously, the authors presented a nonlinear solution procedure for progressive collapse analysis of planar frame structures. In the current study, a modeling strategy to account for the impact of failed members against other structural components is developed to extend the capabilities of the initial models. Assumptions made in approximating the effects of impact on the overall behavior of frame structures are discussed. An example illustrating the importance of accounting for the effects of impact on predicting progressive collapse is also given. Results indicate that the impact velocity plays the most significant role in causing failure of intact beam elements.     

Energy Damage Detection Strategy Based on Strain Responses for Long-Span Bridge Structures

An energy damage detection strategy through disposing strain responses has been developed. First, the strain-based energy dynamic indexes for a system with multiple degrees of freedom were derived from the frequency response function (FRF) of strain responses and energy spectra density. Then, the traditional mode-shape curvature strategy and the proposed strain-based energy damage detection strategy were both used to analyze a long-span cable-stayed bridge, and it was found through comparison that the proposed strain-based energy damage detection strategy solved the shortcomings of the traditional mode-shape curvature strategy. Finally, damage location, damage quantification, and noise pollution resistance analysis for a long-span cable-stayed bridge with different degrees of damage were carried out to verify the effectiveness of the proposed strain-based energy damage detection strategy. The numerical analysis showed that the proposed strain-based energy damage detection strategy can locate damage positions accurately, and it also has good damage quantification and noise pollution resistance abilities.     

Damage Assessment for 2D Multicracked Materials/Structures by Using Mc-Integral

An efficient method is presented to characterize the damage state for two-dimensional multicracked elastic solids. This method is based on the concept of a path-independent Mc-integral, through which the surface energy associated with creation of all the cracks is evaluated. On one hand, when the cracked media are homogeneously stressed, the correspondence relation between the effective material moduli and Mc is established. On the other hand, when the cracked solids are nonhomogeneously stressed, the effective structural stiffness is determined by using the result of Mc. Through proper use of Mc, the damage state of the cracked structure can be assessed both qualitatively and quantitatively.     

Uncoupling of Potential Energy in Nonlinear Seismic Analysis of Framed Structures

A computational analysis method is presented to investigate the potential energy of fully nonlinear framed structures and other energy characteristics due to earthquake ground motions. The overall potential energy is directly related to the stiffness of the structure, and it consists of three components in a fully nonlinear system: (1) strain energy representing the storing energy that is associated with the linear elastic portion of the structural response; (2) higher-order energy representing the energy associated with the geometric nonlinear effect of the overall structural response, which is derived from finite element method; and (3) plastic energy representing the energy dissipated by material inelasticity of the structure, and it is being derived analytically. The merit of proposed analysis method lies in the uncoupling of geometric nonlinearity and material inelasticity effects before solving for the equation of motion, and this leads directly to the analytical representations of each energy form. Both plastic energy and higher-order energy based on single-degree-of-freedom system are studied in detail to demonstrate the beauty of the proposed analysis method. In addition, a method of generating energy density spectra is also proposed, which is useful to enhance the understanding energy characteristics in seismic analysis. Finally, a five-story frame is used as a numerical example to illustrate the effectiveness and robustness of the proposed method.     

Experimental Verification of the Flexibility-Based Damage Locating Vector Method

In recent years, numerous approaches have been proposed for detecting damage in structures, in which the flexibility-based damage locating vector (DLV) method is one of the promising techniques. By computing a set of load vectors from the change of the flexibility matrix before and after damage and then applying them as static forces to the undamaged analytical model for static computation, the DLV method is able to locate damage in structures. The main purpose of this paper is to experimentally verify this method. Following a brief introduction and discussion of the motivation for the flexibility-based method, an overview of the DLV method and construction of the flexibility matrix from limited sensor information is presented. The DLV method is then experimentally verified employing a 5.6 m (18 ft)-long three-dimensional truss structure. To simulate damage in the structure, the original truss member is replaced by one with reduced stiffness. Experimental results show that the DLV method can successfully detect the damage using a limited number of sensors and modes.     

Modeling Steel Frame Buildings in Three Dimensions. II: Elastofiber Beam Element and Examples

This is the second of two papers describing a procedure for the three-dimensional nonlinear time-history analysis of steel-framed buildings. An overview of the procedure and the theory for the panel zone element and the plastic hinge beam element are presented in part I. In this paper, the theory for an efficient new element for modeling beams and columns in steel frames called the elastofiber element is presented, along with four illustrative examples. The elastofiber beam element is divided into three segments—two end nonlinear segments and an interior elastic segment. The cross sections of the end segments are subdivided into fibers. Associated with each fiber is a nonlinear hysteretic stress-strain law for axial stress and strain. This accounts for coupling of nonlinear material behavior between bending about the major and minor axes of the cross section and axial deformation. Examples presented include large deflection of an elastic cantilever beam, cyclic loading of a cantilever beam, pushover analysis of a 20-story steel moment-frame building to collapse, and strong ground motion analysis of a two-story unsymmetric steel moment-frame building.     

Damage Detection of FRP-Strengthened Concrete Structures Using Capacitance Measurements

In this study, a new concept for detecting air voids, water intrusion, and glue infiltration damages in fiber-reinforced polymers (FRPs)-strengthened concrete structures was developed. The concept, based on detecting the local dielectric permittivity variations, was employed to design coplanar capacitance sensors (CCSs) to detect such defects. An analytical model was used to introduce the sensor operation theory and analyze the influence of different sensor parameters on the output signals and to optimize sensor design. Two dimensional finite element (FE) simulations were performed to assess the validity of the analytical results and to evaluate other sensor design-related parameters. To experimentally verify the FE model, dielectric properties of various materials involved in FRP-strengthened concrete systems were measured. In addition, two concrete specimens strengthened with FRP laminates and containing preinduced defects were constructed and inspected in a laboratory setting. Good agreement was found between experimental capacitance measurements and those predicated by the FE simulations. The proposed CCS design, coupled with commercially available portable capacitance meters, would facilitate field implementation of the proposed technique for rapid inspection of FRP-strengthened concrete structures without the need for sophisticated data analyses usually required by other more expensive and time consuming methods.     

Parameter Estimation for Multiple-Input Multiple-Output Modal Analysis of Large Structures

Experimental modal analysis (EMA) has been explored as a technology for condition assessment and damage identification of constructed structures. However, successful EMA applications such as damage detection to constructed systems pose certain difficulties. The properties of constructed systems are influenced by temperature changes as well as other natural influences such as movements in addition to any deterioration and damage. Writers were challenged in their attempts to measure the dynamic properties of an aged bridge by EMA due to inconsistencies within the data set due to short-term variations in ambient conditions. A complex interaction was observed between the dynamic properties of the bridge, hour-to-hour changes in temperature, and controlled damages applied to the bridge. Inconsistencies in the data set made curve fitting difficult for some common parameter estimation algorithms that have been designed to handle consistent data sets. Although the quality of measurements within the entire data set was affected by time variance and nonlinearity, increasing the number of reference measurements significantly improved the reliability of the information which could be extracted. In conjunction with the multiple-input multiple-output technique, a parameter estimation method using complex mode indicator function (CMIF) was developed and implemented in this study to determine the modal properties with proper scaling to obtain modal flexibility. This method proved to be very successful among many others with the data acquired from the aged and deteriorated highway bridge. In this paper, challenges in reliable identification of modal parameters from large structures are reviewed and the new CMIF based algorithm is documented. The method is evaluated on actual bridge data sets from a damage detection research study.     

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.     

Modeling Steel Frame Buildings in Three Dimensions. I: Panel Zone and Plastic Hinge Beam Elements

A procedure for efficient three-dimensional nonlinear time-history analysis of steel framed buildings is derived. It incorporates two types of nonlinear beam elements—the plastic hinge type and the elastofiber type—and nonlinear panel zone elements to model yielding and strain-hardening in moment-frames. Floors and roofs of buildings are modeled using 4-node elastic diaphragm elements. The procedure utilizes an iteration strategy applied to an implicit time-integration scheme to solve the nonlinear equations of motion at each time step. Geometric nonlinearity is included. An overview of the procedure and the theories for the panel zone and the plastic hinge elements are presented in this paper. The theory for the elastofiber element along with illustrative examples are presented in a companion paper. The plastic hinge beam element consists of two nodes at which biaxial flexural yielding is permitted, leading to the formation of plastic hinges. Elastic rotational springs are connected across the plastic hinge locations to model strain-hardening. Axial yielding is also permitted. The panel zone element consists of two orthogonal panels forming a cruciform section. Each panel may yield and strain-harden in shear.     

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.     

Seismic Energy Dissipation of Inelastic Structures with Tuned Mass Dampers

The energy transfer process of using a tuned mass damper (TMD) in improving the ability of inelastic structures to dissipate earthquake input energy is investigated. Inelastic structural behavior is modeled by using the force analogy method, which is the backbone of analytically characterizing the plastic energy dissipation in the structure. Numerical simulations are performed to study the energy responses of structures with and without TMD installed. The effectiveness of TMD in reducing energy responses is also studied by using plastic energy spectra for various structural yielding levels. Results show that the use of TMD enhances the ability of the structures to store larger amounts of energy inside the TMD that will be released at a later time in the form of damping energy when the response is not at a critical state, thereby increasing the damping energy dissipation while reducing the plastic energy dissipation. This reduction of plastic energy dissipation relates directly to the reduction of damage in the structure, and TMD is therefore concluded to be quite effective in protecting structures from suffering major damage during an earthquake. However, storing energy in the TMD is restricted if the structure becomes plastic at a small displacement level. In this case, the effectiveness of TMD diminishes, and the structural response becomes practically the same as those without TMD installed.     

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.     

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.     

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.