Non-stationary frequency domain system identification using time-frequency representations

System properties of buildings and bridges may vary with time due to temperature changes, aging or extreme loadings. To identify these time-varying system properties, this study proposes a new output-only non-stationary system identification (SI) framework based on instantaneous or marginal spectra derived from the time-frequency representation, e.g., short time Fourier or wavelet transform. Spectra derived from these time-frequency representations are very popular in tracking time-varying frequencies; however, they have seldom been used to identify the time-varying damping ratio because a short window needed to capture the time-varying information amplifies the bandwidth significantly, which may lead to considerably overestimating the damping ratio. To overcome this shortcoming, this study modifies the theoretical frequency response function (FRF) to explicitly account for the windowing effect, and therefore enables SI directly using instantaneous or marginal spectra derived from the wavelet or short time Fourier transform. The response spectrum estimated using the short time window and the modified FRF are both influenced by the same time window, thus the instantaneous or time-localized marginal spectrum of response can be fitted to the modified FRF to identify frequency and damping ratio at each time instant. This spectral-based SI framework can reliably identify damping in time-varying systems under non-stationary excitations. The efficacy of the proposed framework is demonstrated by both numerical and full-scale examples, and also compared to the time-domain SI method, stochastic subspace identification (SSI), since the time-domain SI approaches and their extensions are popular in identifying time-varying systems utilizing recursive algorithms or moving windows.