Abstarct: Structural health monitoring (SHM) is a branch of engineering science that focuses on the continuous monitoring of the performance of structures during their service life. This approach calculates key parameters such as stiffness, mass, and energy absorption by collecting dynamic data from the structure’s responses to external forces, and uses advanced analytical methods to detect any anomalies. Rapid damage detection is crucial in this field, as it can prevent structural disasters. Damage is any disturbance that disrupts the desired function of a structure, and this affects the vibration responses of the structure by changing its mechanical properties. In recent years, vibration-baxsed techniques have been widely accepted by researchers due to their high accuracy and reliability. In this study, the problem of damage detection in shell structures is investigated. Damage is defined as a decrease in material density in the elements of the finite element model of the structure. A method is proposed that extracts damage-sensitive features by using time-domain responses in the form of time series and their analysis. These responses include nodal accelerations measured at limited points of the structure under environmental loads, which are calculated and extracted using Abaqus software. To extract damage-sensitive features, the singular spectrum analysis (SSA) method is used to obtain singular values from the time series. The damage detection problem is designed as a topology optimization problem and the objective function is defined baxsed on the difference in singular values between the reference model and the analytical model of the structure. In order to accurately model the damage, the solid isotropic material method with penalty (SIMP) is used and the design variable is assigned to the density of each element. To solve the optimization and minimization problem of the objective function, the steepest descent method is used. Sensitivity analysis is also performed using the finite difference method to examine the changes in the objective function with respect to the design variables. Upon completion of the optimization process and convergence of the results, the location and severity of the damage are identified. To evaluate the accuracy and efficiency of the proposed method, several numerical examples have been studied. The results show that topology optimization using singular values is an effective method for detecting damage in structures. Effective factors such as the extent and severity of the damage, the number of sensors, and their location have a significant impact on the accuracy and performance improvement of the proposed method.