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It is well known that damaged structural members may alter the behavior of the structures considerably. Careful observation of these changes has often been viewed as a means to identify and assess the location and severity of damages in structures. Among the responses of a structure, natural frequencies are both relatively easy to obtain and independent from external excitation, and therefore, could be used as a measure of the structure's behavior before and after an extreme event which might have lead to damage in the structure. Inverse problem of detection and assessment of structural damage using the changes in natural frequencies is addressed in this paper. This can be considered as an optimization problem with the location and severity of the damages being its variables. The objective is to set these variables such that the natural frequencies of the finite element model correspond to the experimentally measured frequencies of the actual damaged structure. In practice, although the exact number of damaged elements is unknown, it is usually believed to be small compared to the total number of elements of the structure. In beams and frames particularly, the necessity to divide the structural members into smaller ones in order to detect the location of the cracks more accurately, deepens this difference. This can significantly improve the performance of the optimization algorithms in solving the inverse problem of damage detection. In this paper, the Charged System Search algorithm developed by Kaveh and Talatahari [1] is improved to comprise the above mentioned point. The performance of the improved algorithm is then compared to the standard one in order to emphasize the efficiency of the proposed algorithm in damage detection inverse problems.

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This paper presents an efficient method for updating the structural finite element model. Model updating is performed through minimizing the difference of recorded acceleration of real damaged structure and hypothetical damaged structure, by updating physical parameters in each phase using iterative process of Levenberg-Marquardt algorithm. This algorithm is based on sensitivity analysis and provides a linear solution for nonlinear damage detection problem. The presented method is capable of detecting the exact location and ratio of structural damage in the presence of noise or incomplete data.

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An effective method utilizing the differential evolution algorithm (DEA) as an optimisation solver is suggested here to detect the location and extent of single and multiple damages in structural systems using time domain response method. Changes in acceleration response of structure are considered as a criterion for damage occurrence. The acceleration of structures is obtained using Newmark method. Damage is simulated by reducing the elasticity modulus of structural members. Three illustrative examples are numerically investigated, considering also measurement noise effect. All the numerical results indicate the high accuracy of the proposed method for determining the location and severity of damage.

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In this paper, topology optimization is utilized for damage detection in three dimensional elasticity problems. In addition, two mode expansion techniques are used to derive unknown modal data from measured data identified by installed sensors. Damages in the model are assumed as reduction of mass and stiffness in the discretized finite elements. The Solid Isotropic Material with Penalization (SIMP) method is used for parameterizing topology of the structure. Difference between mode shapes of the model and real structure is minimized via a mathematical based algorithm. Analytical sensitivity analysis is performed to obtain derivatives of objective function with respect to the design variables. In order to illustrate the accuracy of the proposed method, four numerical examples are presented.

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In this study, the finite element model updating was simulated by reducing the stiffness of the members. Due to lack of access to the experimental results, the data obtained from an analytical model were used in the proposed structural damage scenarios. The updating parameters for the studied structures were defined as a reduction coefficient applied to the stiffness of the members. Parameter variations were calculated by solving an unconstrained nonlinear optimization problem. The objective function in the optimization problem was proposed based on the Multi-Degree-of-Freedom (MDOF) equations of motion as well as the dynamic characteristics of the studied structure. Only the first natural frequency of the damaged structure was used in the proposed updating process, and only one vibration mode was used in the updating problem and damage identification procedure. In addition, as elimination of high-order terms in the proposed formula introduced errors in the final response, the variations of natural frequency and vibration mode for higher-order terms were included in the free vibration equation of the proposed objective function. The Colliding Bodies Optimization (CBO) algorithm was used to solve the optimization problem. The performance of the proposed method was evaluated using the numerical examples, where different conditions were applied to the studied structures. The results of the present study showed that, the proposed method and formulation were capable of efficiently updating the dynamic parameters of the structure as well as identifying the location and severity of the damage using only the first natural frequency of the structure.