monitoring and retrofitting of large-scale infrastructure is of paramount importance specifically when they are subjected to natural hazards like strong wind, severe earthquakes or man-made excitation. once the rich vibration data is collected from the structures, a robust system identification method is required to extract the hidden structural information, and undertake necessary condition assessment and rehabilitation. most of the traditional modal identification methods are reliant on stationarity assumption of the vibration re- sponse and posed difficulty while analyzing nonstationary vibration occurred due to natural hazards. apart from the excitation-induced nonstationarity, the inherent damages in the structure also cause frequency-dependent nonstationarity in the response. with such combination of both amplitude and frequency-dependent nonstationary response, the modal identification becomes a signifcantly challenging task. recently tensor decomposition based methods are emerged as powerful and yet generic blind (i.e. without requiring a knowledge of input characteristics) signal decomposition tool for structural modal identification. in this thesis, a tensor decomposition based system identification method is further explored to estimate modal parameters using amplitude- dependent nonstationary vibration generated due to either earthquake or pedestrian in- duced excitation in a structure. the effects of lag parameters and sensor densities on tensor decomposition are studied with respect to the extent of nonstationarity of the responses characterized by the stationary duration and peak ground acceleration of the earthquake. a suite of more than 1400 earthquakes is used to investigate the performance of the pro- posed method under a wide variety of ground motions utilizing both complete and partial measurements of a high-rise building model. apart from the earthquake, human-induced nonstationary vibration of a real-life pedestrian bridge is also used to verify the accuracy of the proposed method. once the method is verified using amplitude-based nonstationary response, cauchy continuous wavelet transform is integrated with the tensor decomposition to track time- varying characteristics of each modal responses and detect the progressive damage. with such an integrated framework, the proposed method is able to identify both amplitude and frequency-dependent nonstationary responses. the proposed technique is validated using a suite of numerical studies as well as a laboratory experiment where the progressive damage is simulated in the structural component with a heating torch.