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Non-destructive damage detection methods analyze the output data collected from sensors to track the changes in the dynamic characteristics of the structure and detect the occurrence of damages. continuous recording and analysis of data to be aware of its safety and serviceability requires a network of sensors that are selected optimally and intelligently. Saving the cost of equipping the structure with this optimal sensor network, along with reducing damage detection error, has turned the issue of selecting the number and location of sensors into an optimization problem from an economic and functional point of view. Model order reduction methods along with optimization tools can play an effective role in selecting the master degrees of freedom. These methods divide the degrees of freedom of the structure into two groups of master and slave degrees of freedom. The master degrees of freedom appear in the process of calculating the mode shapes and natural frequencies, and the slave degrees of freedom are excluded from the equations. Finally, using the transfer matrix, the complete mode shapes are calculated using the mode shapes of the master degrees of freedom. In this paper, considering the key role of modal parameter recognition in structural damage detection, the performance and accuracy of different methods of dynamical model order reduction in the optimal sensor placement problem was studied. The 2d truss stucture and two-dimensional shear frame are modeled and analyzed. The sensor placement should be considered in such a way that the mode shape identification is done with sufficient accuracy and proper recognition. One of the effective tools in order to achieve this goal is to use the capabilities of metaheuristic optimization algorithms along with the capability of dynamic model reduction methods in the stage of identifying the mode shapes and before identifying the damages of structure. Combining model order reduction methods with metaheuristic optimization algorithms so that the selection of appropriate degrees of freedom for sensor installation (master degrees of freedom) leads to the most accurate identification of structural modes shapes is one of the main objectives of this study. The objective functions selected based on modal assurance criteria (MAC) and Fisher information matrix (FIM) and the capabilities of multi objective particle swarm optimization algorithm (MOPSO) to achieve the optimal number and proper arrangement of sensors are used to better identify the structural mode shapes and proper arrangement of sensors and obtained for system identification purposes. The results report better performance of SEREP and IDC methods in selection of master degrees of freedom and identifying the mode shapes of 2d truss and shear frame structures. According to the modeling and analysis performed for optimal placement of sensors using different model reduction methods, it can be concluded that the improved dynamic condensation (IDC) method is more accurate than other methods in identifying shear frame mode shapes and gives a smaller maximum non-diagonal MAC matrix element. Also, as the number of sensors increases due to the addition of information to the Fisher matrix, the Fisher matrix determinant increases and second objective function decreases. On the other hand, by reducing the number of available sensors, a limited number of modes can be detected. In this case, the best way to receive the structural modal information would be to place more available sensors on the lower and upper floors of the shear frame. Eventually, it can be concluded that the use of IDC and SEREP methods to select master degrees of freedom for sensor installation leads to better identification of modal parameters of the structure. Therefore, the capabilities of these methods can be used to identify damage in structures with a limited number of sensors.

Keywords: System Identification, Multiobjective Optimization, Model Reduction, Optimal Sensor Placement, MAC

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