Abstarct: Structural health monitoring aims to extract characteristics of structures by using structural response and performing reverse analysis, and detect damages by tracking changes occurred in the characteristics. Structural damage identification is of fundamental importance because if it is detected in time, it is possible to prevent the occurrence of catastrophic failures. The occurrence of damage causes change in physical characteristics of a structure such as stiffness, mass and damping, which affects the vibration responses. Therefore, in recent decades, non-destructive methods of damage identification using the vibration responses have been considered. In this research, problem of damage detection in two-dimensional continuous structures under plane stress assumption is studied. Damage is assumed in the form of reduction of material density in elements of finite element model of the structure. A method is proposed to extract damage-sensitive features by considering time domain responses as time series and performing analysis on them. The time domain responses utilized here are the nodal accelerations measured at limited points of the structure under ambient loads, which are obtained by the Newmark method and contaminated with uniformly random noise in order to simulate real conditions. Singular spectrum analysis (SSA) is the method used here to analyze time series to present singular values as damage-sensitive features. The problem of damage detection is presented as a topology optimization problem and the objective function is formed baxsed on the difference of singular values in the main structure and its analytical model. densities of elements are considered as design variables and for proper damage modeling, the solid isotropic materials with penalization method (SIMP) are used. Also, the steepest descent method is used to solve the problem of optimization. The sensitivity analysis or in other words the derivation of the objective function with respect to the design variables is done with the finite difference and analytical methods. In this way, the location and severity of the damage is finally identified. In order to evaluate the correctness of the proposed method, some numerical examples are examined. The obtained results show the accuracy and efficiency of the method in damage identification.