A review of time-frequency methods for structural vibration analysis

This paper presents a review of time-frequency distribution tools for the analysis of non-linear vibrations of structures. The theoretical basis of the moving window discrete Fourier transform (DFT), the moving window auto-regressive (AR) model, the harmonic wavelet transform, the Wigner–Ville (WV) and the Windowed Wigner–Ville (WWV) bilinear distributions are presented. The strengths and weaknesses of each technique are demonstrated by applying them to a variety of synthetic signals. Then the methods are applied to real vibration data taken from experiments on a damaged reinforced concrete beam. It is shown that, for this simple structure, the DFT and AR moving window, wavelet and WWV methods give similar estimates of the time-frequency relationship for the fundamental mode, though the AR model estimate is much noisier than the others.