Abstarct: Considering the important and fundamental role of structures in providing security and welfare of the society, if the structure is not properly designed, its implementation and maintenance can cause irreparable problems. Therefore, in addition to the proper design and implementation of the structure, the continuous control of the structure's health in order to prevent the damage and unfortunate consequences resulting from it are very serious and vital. By monitoring the health of civil engineering structures, it is possible to detect early failure, structural damage and functional problems. Structural health monitoring can check the performance of civil structures by using measured data and data interpretation algorithms, correctly evaluate the current condition and predict the remaining life of the structure and in addition to increasing the reliability of the structure, it can reduce its maintenance costs. In this research, damage detection in bending plates is done by using the topology optimization method. Damage is taken into account in the form of density reduction in the elements of the finite element model, and by considering the responses of the time domain in the form of time series and with the help of singular spectrum analysis, the features sensitive to damage are extracted. The responses of the time domain are the nodal accelerations measured under the environmental load, which are calculated by the Newmark method. In order to simulate the real environmental load conditions, it is combined with uniform random noise. The issue of damage detection is presented as a topology optimization problem, and with the formation of the objective function baxsed on the difference of singular values in the main structure and the analytical model, the design variables are assigned to the density of each element. In order to properly model the damage, the method of solid isotropic materials with penalty (SIMP) is used, and to solve the problem of optimization and minimization of the objective function, the steepest descent method is used. Sensitivity analysis (that is, derivation of the objective function with respect to the design variables) is performed with two methods, finite difference and analytical derivation, and finally the location and severity of the damage in the structure are determined.