• Structural Monitoring and Maintenance
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• v.4 no.1
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• pp.53-68
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• 2017

The response sensitivity method in time domain has been applied extensively for damage identification. In this paper, the relationship between the error of damage identification and the sensitivity matrix is investigated through perturbation analysis. An index is defined according to the perturbation amplify effect and an optimal sensor placement method is proposed based on the minimization of that index. A sequential sub-optimal algorithm is presented which results in consistently good location selection. Numerical simulations with a two-dimensional high truss structure are conducted to validate the proposed method. Results reveal that the damage identification using the optimal sensor placement determined by the proposed method can identify multiple damages of the structure more accurately.

• Structural Engineering and Mechanics
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• v.63 no.6
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• pp.779-788
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• 2017

System identification and damage detection for structural health monitoring have received considerable attention. Various time domain analysis methodologies based on measured vibration data of structures have been proposed. Among them, recursive least-squares estimation of structural parameters which is also known as parametric Kalman filter (PKF) approach has been studied. However, the conventional PKF requires that all the external excitations (inputs) be available. On the other hand, structural uncertainties are inevitable for civil infrastructures, it is necessary to develop approaches for probabilistic damage detection of structures. In this paper, a parametric Kalman filter with unknown inputs (PKF-UI) is proposed for the simultaneous identification of structural parameters and the unmeasured external inputs. Analytical recursive formulations of the proposed PKF-UI are derived based on the conventional PKF. Two scenarios of linear observation equations and nonlinear observation equations are discussed, respectively. Such a straightforward derivation of PKF-UI is not available in the literature. Then, the proposed PKF-UI is utilized for probabilistic damage detection of structures by considering the uncertainties of structural parameters. Structural damage index and the damage probability are derived from the statistical values of the identified structural parameters of intact and damaged structure. Some numerical examples are used to validate the proposed method.

• Smart Structures and Systems
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• v.12 no.6
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• pp.619-640
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• 2013

It is highly desirable to explore efficient algorithms for detecting structural damage of large size structural systems with limited input and output measurements. In this paper, a new structural damage detection algorithm based on substructure approach is proposed for large size structural systems with limited input and output measurements. Inter-connection effect between adjacent substructures is treated as 'additional unknown inputs' to substructures. Extended state vector of each substructure and its unknown excitations are estimated by sequential extended Kalman estimator and least-squares estimation, respectively. It is shown that the 'additional unknown inputs' can be estimated by the algorithm without the measurements on the substructure interface DOFs, which is superior to previous substructural identification approaches. Also, structural parameters and unknown excitation are estimated in a sequential manner, which simplifies the identification problem compared with other existing work. Structural damage can be detected from the degradation of the identified substructural element stiffness values. The performances of the proposed algorithm are demonstrated by several numerical examples and a lab experiment. Measurement noise effect is considered. Both the simulation results and experimental data validate that the proposed algorithm is viable for structural damage detection of large size structural systems with limited input and output measurements.

• Structural Engineering and Mechanics
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• v.82 no.6
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• pp.771-783
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• 2022

Structural damage identification (SDI) methods have been proposed to monitor the safety of structures. However, the traditional SDI methods using modal parameters, such as natural frequencies and mode shapes, are not sensitive enough to structural damage. To tackle this problem, this paper proposes a new SDI method based on transmissibility assurance criterion (TAC) and weighted Schatten-p norm regularization. Firstly, the transmissibility function (TF) has been proved a useful damage index, which can effectively detect structural damage under unknown excitations. Inspired by the modal assurance criterion (MAC), TF and MAC are combined to construct a new damage index, so called as TAC, which is introduced into the objective function together with modal parameters. In addition, the weighted Schatten-p norm regularization method is adopted to improve the ill-posedness of the SDI inverse problem. To evaluate the effectiveness of the proposed method, some numerical simulations and experimental studies in laboratory are carried out. The results show that the proposed method has a high SDI accuracy, especially for weak damages of structures, it can precisely achieve damage locations and quantifications with a good robustness.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2574-2580
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• 2002

In this paper, an experimental verification has been conducted for the frequency response function (FRF)-based structural damage identification method (SDIM) proposed for beam structures. The FRF-based SDIM requires the natural frequencies and mode shapes measured in the intact state and the FRF-data measured in the damaged state. Experiments are conducted for the cantilevered beam specimens with one slot and with three slots. It is shown that the proposed FRF-based SDIM provides damage identification results that agree quite well with true damage state.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.12 s.243
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• pp.1586-1596
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• 2005

In this paper, a structural damage identification method (SDIM) is developed to identify the line crack-like directional damages generated within a cylindrical shell. First, the equations of motion for a damaged cylindrical shell are derived. Based on a theory of continuum damage mechanics, a small material volume containing a directional damage is represented by the effective orthotropic elastic stiffness, which is dependent of the size and the orientation of the damage with respect to the global coordinates. The present SDIM is then derived from the frequency response function (FRF) directly solved from the equations of motion of a damaged shell. In contrast with most existing SDIMs which require the modal parameters measured in both intact and damaged states, the present SDIM may require only the FRF-data measured at damaged state. By virtue of utilizing FRF-data, one may choose as many sets of excitation frequency and FRF measurement point as needed to acquire a sufficient number of equations for damage identification analysis. The numerically simulated damage identification tests are conducted to study the feasibility of the present SDIM.

• Structural Engineering and Mechanics
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• v.53 no.2
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• pp.261-276
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• 2015

Structural damage and moving load identification are the two aspects of structural system identification. However, they universally coexist in the damaged structures subject to unknown moving load. This paper proposed a dynamic response sensitivity-based model updating method to simultaneously identify the structural damage and moving force. The moving force which is equivalent as the nodal force of the structure can be expressed as a series of orthogonal polynomial. Based on the system Markov parameters by the state space method, the dynamic response and the dynamic response derivatives with respect to the force parameters and elemental variations are analytically derived. Afterwards, the damage and force parameters are obtained by minimizing the difference between measured and analytical response in the sensitivity-based updating procedure. A numerical example for a simply supported beam under the moving load is employed to verify the accuracy of the proposed method.

• Structural Monitoring and Maintenance
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• v.2 no.1
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• pp.77-93
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• 2015

The idea of using measured dynamic characteristics for damage detection is attractive because it allows for a global evaluation of the structural health and condition. However, vibration-based damage detection for complex structures such as long-span cable-supported bridges still remains a challenge. As a suspension or cable-stayed bridge involves in general thousands of structural components, the conventional damage detection methods based on model updating and/or parameter identification might result in ill-conditioning and non-uniqueness in the solution of inverse problems. Alternatively, methods that utilize, to the utmost extent, information from forward problems and avoid direct solution to inverse problems would be more suitable for vibration-based damage detection of long-span cable-supported bridges. The auto-associative neural network (ANN) technique and the probabilistic neural network (PNN) technique, that both eschew inverse problems, have been proposed for identifying and locating damage in suspension and cable-stayed bridges. Without the help of a structural model, ANNs with appropriate configuration can be trained using only the measured modal frequencies from healthy structure under varying environmental conditions, and a new set of modal frequency data acquired from an unknown state of the structure is then fed into the trained ANNs for damage presence identification. With the help of a structural model, PNNs can be configured using the relative changes of modal frequencies before and after damage by assuming damage at different locations, and then the measured modal frequencies from the structure can be presented to locate the damage. However, such formulated ANNs and PNNs may still be incompetent to identify damage occurring at the deck members of a cable-supported bridge because of very low modal sensitivity to the damage. The present study endeavors to enhance the damage identification capability of ANNs and PNNs when being applied for identification of damage incurred at deck members. Effort is first made to construct combined modal parameters which are synthesized from measured modal frequencies and modal shape components to train ANNs for damage alarming. With the purpose of improving identification accuracy, effort is then made to configure PNNs for damage localization by adapting the smoothing parameter in the Bayesian classifier to different values for different pattern classes. The performance of the ANNs with their input being modal frequencies and the combined modal parameters respectively and the PNNs with constant and adaptive smoothing parameters respectively is evaluated through simulation studies of identifying damage inflicted on different deck members of the double-deck suspension Tsing Ma Bridge.

• Smart Structures and Systems
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• v.15 no.1
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• pp.15-40
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• 2015

This paper proposes a structural damage identification approach based on the power spectral density transmissibility (PSDT), which is developed to formulate the relationship between two sets of auto-spectral density functions of output responses. The accuracy of response reconstruction with PSDT is investigated and the damage identification in structures is conducted with measured acceleration responses from the damaged state. Numerical studies on a seven-storey plane frame structure are conducted to investigate the performance of the proposed damage identification approach. The initial finite element model of the structure and measured acceleration measurements from the damaged structure are used for the identification with a dynamic response sensitivity-based model updating method. The simulated damages can be identified accurately without and with a 5% noise effect included in the simulated responses. Experimental studies on a steel plane frame structure in the laboratory are performed to further verify the accuracy of response reconstruction with PSDT and validate the proposed damage identification approach. The locations of the introduced damage are detected accurately and the stiffness reductions in the damaged elements are identified close to the true values. The identification results demonstrated the accuracy of response reconstruction as well as the correctness and efficiency of the proposed damage identification approach.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.2 s.107
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• pp.115-123
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• 2006

A feasibility of using the topology optimization method for structural damage identification is investigated for the first time. The frequency response functions (FRFs) are assumed to be constructed by the finite element models of damaged and undamaged structures. In addition to commonly used resonances, antiresonances are employed as the damage identifying modal parameters. For the topology optimization formulation, the modal parameters of the undamaged structure are made to approach those of the damaged structure by means of the constraint equations, while the objective function is an explicit penalty function requiring clear black-and-white images. The developed formulation is especially suitable for damage identification problems dealing with many modal parameters. Although relatively simple numerical problems were considered in this investigation, the possibility of using the topology optimization method for structural damage identification is suggested through this research.