The role of signal-based nonlinear system identification methods for the rapid post-earthquake damage assessment of reinforced concrete (RC) bridge piers is explored. Experimental data from the shaking table tests of six RC columns with and without corrosion damage are used as benchmark data. The specimens are excited under three different ground motions with different time-series characteristics, structural detailing, and corrosion levels. The proposed system identification methods make use of accelerations alone (but not displacements as these are costly in-situ) to estimate the instantaneous frequency. The Wigner-Ville distribution and Hilbert transform are utilised due to their high resolution in both time and frequency domains.A combination of modal filtering and thresholding, using instantaneous amplitudes, are employed to attenuate the unreliable spikes in the Hilbert transform's instantaneous frequency estimates. Their performance is benchmarked against a moving linear regression and standard white-noise tests. The comparison of the experimental results and time-frequency analysis indicates that the Wigner-Ville distribution and the Hilbert transform can produce reliable rapid damage detection when the response amplitude is large. The Wigner-Ville distribution has better robustness and higher resolution. The robustness of the more computationally efficient Hilbert transform can be significantly improved by the introduction of modal filtering and thresholding.