Abstract: Aiming at the insufficiency of the traditional intensity envelope function of time-domain does not fully represent the statistical characteristics of ground motions，a method of establishing statistical model of intensity envelope based on energy duration is proposed. The statistical model of intensity envelope of typical earthquake waves considering different site types is obtained. In view of the fact that the single peak power spectrum based on filtering white noise cannot precisely represent actual multi-peak phenomena and strong non-stationarity of power spectrum，a more accurate multi-peak power spectrum model is adopted. On this basis，a statistical model and an equivalent function model of time-varying power spectrum（evolutionary spectrum）are proposed based on wavelet packet transform. Both of them satisfy marginal condition and non-negativity in time-frequency domain，and characterize the non-stationarity in time-frequency domain accurately and intricately. The analysis examples show that the accuracy of the statistical model and its equivalent function model of time-varying power spectra are higher than the traditional power spectral function model for structural random vibration analysis.