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.　©　2021,　Editorial　Board　of　Journal　of　Vibration　Engineering.　All　right　reserved.