Time–frequency analysis and applications in time-varying/nonlinear structural systems: A state-of-the-art review:

Nonlinear dynamic behaviors of civil engineering structures have been observed not only under extreme loads but also during normal operations. Characterization of the time-varying property or nonlinearity of the structures must account for temporal evolution of the frequency and amplitude contents of nonstationary vibration responses. Neither time analysis nor frequency analysis method alone can fully describe the nonstationary characteristics. In this article, an attempt is made to review the milestone developments of time–frequency analysis in the past few decades and summarize the fundamental principles and structural engineering applications of wavelet analysis and Hilbert transform analysis in system identification, damage detection, and nonlinear modeling. This article is concluded with a brief discussion on challenges and future research directions with the application of time–frequency analysis in structural engineering.