This paper proposes a novel output-only damage identification method based on the unsupervised blind source separation (BSS) technique termed independent component analysis (ICA). It is discovered that ICA biases to extract sparse component, which typically indicates damage, from the observed mixture signals. The measured structural responses are first preprocessed by wavelet transform (WT). The wavelet-domain signals are then fed as mixtures into the BSS model, which is solved by ICA. The obtained “interesting” source with sharp spike and its associated spatial signature in the recovered mixing matrix reveal damage instant and location respectively. Following which, identification of the time-varying modes is carried out by ICA using the structural responses before and after the identified damage instant. For illustration, numerical simulations are conducted, where damage is modeled by abrupt stiffness variation in the time-varying system. Experimental and real-world seismic-excited structure examples with time-varying stiffness are also presented to illustrate the capability of the developed WT–ICA method. Results show that the WT–ICA algorithm realizes accurate and robust blind identification of damage instant and location in single or multiple damage events.