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In recent years, the damage identification of structures becomes more attractive for researchers in order to assess ‎the quantify condition of structural system during service life. Moreover, identifying the damage location and ‎severity is very important after disaster such as earthquake and terrorist attak. Structures can be also damaged by ‎normal activity such as corrosion, aging, fatique, wind, waveload etc. Therefore the structural health monitoring is ‎an emerging field to ensure the continues and periodic performance of structures. In this paper, identification of the ‎extent and location of damages in structures are studied by analytical method using artificial bee colony ‎optimization (ABC). In the analytical method, the mass and stiffness matrices of structure could be determine by ‎the finite element procedure. Considering the stiffness matrix of healthy structure and that of the damage structure, ‎the location and severity of the damage could be determined. It is assumed that the global mass matrix remains ‎unchanged after the damage occures in the structure. The natural frequencies and mode shapes of damaged ‎structure can be obtained by measurement. In the study, the damage characteristics are known. Then by applying ‎the eigenvalue equation, the stiffness matrix is determined for damaged structure. Finding the extent and location ‎of damage is introduced as an inverse problem. Using the conventional methods are very expensive and time ‎consuming, while metaheuristic evolutionary computing method is capable to solve complex combinational ‎optimization problems. Swarm intelligence algorithm introduces the collactive behavior of social insects colonies ‎to solve optimization problems. Artificial bee colony algoritm is an evolutionary computing method, which is ‎developed, based on the intelligent foraging behavior of honeybee swarm. Each food source is considered as a ‎possible solution. The location and quality of the nectar from the flower is related to the damage properties and ‎fitness function, respectively. The dimension of every artificial employed bee is equal to the number of member of ‎the structure. Then quality value of the food source is evaluated by the fitness function. The best fitness value is ‎memorized in each search. When the fitness value denote improved after a predefined iterative, the new possible ‎solution will be considered. In the ABC process, the number of food source, the limit and the maximum cycle ‎number are three control parameters. In the optimization problem, applying a proper objective function is one of ‎the indispesable part of the process. Since the structural damage detection is a highly nonlinear problem, a proper ‎objective function can detect the damage accurately and quackly. There are various methods for damage detection, ‎which generaly can be classified into two categories, static and dynamic method. Because of the efficiency of the ‎dynamic method, the objective function is selected based on the dynamic technique, which utilize the eigenvalue ‎problem. In the mathematical equation of the objective function, the mass and stiffness matrix of healthy structure ‎is defined by finite element method. The natural frequencies and mode shapes obtained by the measurement. The ‎stiffness matrix of damaged structure is determined with the optimization algorithm to minimize the objective ‎function. In a measurement test, the used sensors cannot detect all of the degrees freedom of a structure, therefore ‎the obtained information in measurement include a limited number of frequencies or mode shapes. In addition, to ‎avoid a time consuming process, it may be decided to utilize only a limit number of frequencies obtained by the ‎measurement. The system equivalent reduction expansion process (SEREP), which is an accurate and efficient ‎technique of model reduction, is utilized in the paper. Moreover, the damage detection is examined through three ‎numerical examples, plane and space truss and palne frame, each one has two damage scenarios, which include ‎noisy measurement data. The results indicate that the proposed method is a powerfull procedure to detect damages ‎in structures.‎

Keywords: Damage detection, Artificial bee colony algorithm, SEREP codensatation.

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