The dynamic behavior of inelastic structures during an earthquake is a complicated non-stationary process that is affected by the random characteristics of seismic ground motions.The conventional Fourier analysis describes the feature of a dynamic process by decomposing the signal into infinitely long sine and cosine series,which loses all time-located information.However,both time and frequency localizations are necessary for the analysis of an evolutionary spectrum of non-stationary processes.In this paper,an analytical approach for seismic ground motions is developed by applying the wavelet transform,which focuses on the energy input to the structure.The procedure of identification of the instantaneous modal parameters based on the continuous wavelet transform (CWT) is given in detail.And then,a novel method using the auto-regressive moving average (ARMA),called "prediction extension",is presented to remedy the edge effect during the numerical computation of the CWT.The effectiveness of the method is verified by the use of the benchmark model developed by the American Society of Civil Engineers (ASCE).Finally,a scale modal with three-storey reinforced concrete frame-share wall structure is made and tested on a shaking table to investigate the relation between the dynamic properties of structures and energy accumulation and its change rates during the earthquake.The results have shown that the wavelet transform is able to provide a deep insight into the identity of transient signals through time-frequency maps of the time variant spectral decomposition.