Application of 3D Time-frequency Analysis in Monitoring Full-scale Structural Response

Structural responses to severe loads such as due to typhoons and earthquakes are very complicated, with nonlinear and non-stationary characteristics. When external forces are applied to the structure, vibrations of different frequencies and magnitudes are excited. If any of the vibrations cannot be damped within a reasonable period of time, damage to the structure is inevitable. The damage would cause a shift of the natural frequency of the structure. Therefore it is possible to assess the integrity of the structure through monitoring this frequency shift. This has been increasingly done using integrated GPS and accelerometer systems that exploit their complementary features. Data collected using such systems are usually analysed using the Fast Fourier Transform (FFT). The shortcoming of the FFT is that the spectrum represents the relative strength of vibrations of different frequencies over the whole data set. Recent research undertaken by the authors using Short Time Fast Fourier Transform (STFT) does give information on the temporal evolution of the dominant frequency in time series by a twodimensional plot. However in the two-dimensional plot only the frequencies with highest amplitude are considered, other frequencies that might be of interest to the civil engineers are ignored. The significantly extended 3D spectral analysis reported in this paper can track the temporal evolution of all the frequency components within the detectable discrete spectrum and effectively represents the result in the three dimensions of frequency, time and magnitude. The dominant frequency can also be highlighted and tracked on the 3D mesh. The frequency domain coherent analysis based on this 3D analysis framework can further enhance common signals detected using different sensors. The 3D spectrogram analysis methodology has been applied to analyse data collected during a typhoon as well as an earthquake event with an integrated GPS and accelerometer system deployed on a 108m steel tower in Japan.