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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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Damage assessment is one of the crucial topics in the operation of structures. Multiplicities of structural elements and joints are the main challenges about damage assessment of space structure. Vibration-based damage evaluation seems to be effective and useful for application in industrial conditions and the low-cost. A method is presented to detect and assess structural damages from changes in mode shapes. First, the mechanism of using two-dimensional continuous wavelet transform is applied for damage localization. Second, finite element model updating technique is utilized as an inverse optimization problem by applying the charged system search algorithm to assess the damage in each element sited in the first stage. The study indicates the potentiality of the developed code to assess the damages of space structures without concerning about the size and shape of structure. A series of numerical examples with different damage scenarios have been carried out in the double layer space structures and the results confirm the reliability and applicability of introduced method.

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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.