Most damage detection methods have difficulty in detecting damage using only measurement data due to the existence of external noise. It is necessary to reduce the noise effect to obtain accurate information and to detect damage by the output-only measurement without baseline data at intact state and input data. This work imported the power spectral density estimation (PSE) of a signal to reduce the noise effect. By estimating the PSE to characterize the frequency content of the signal, this study proposes a damage detection method to trace the damage by the curvature of the PSE. Two numerical applications examine the applicability of the proposed method depending on a window function, frequency resolution, and the number of overlapping data in the PSE method. The knowledge obtained from the numerical applications leads to a series of experiments that substantiate the potential of the proposed method.