The　physical　meaning　of　phase　difference　controls　the　occurrence　time　of　peak　values　of　triangular　series,　which　can　be　abbreviated　as　peak　arrival　time.　This　article　describes　a　method　for　deducing　the　correspondence　between　the　energy　distribution　characteristics　in　the　time　domain　and　the　peak　arrival　time.　The　variation　laws　of　acceleration　time-history　curve　of　natural　seismic　wave　can　be　transformed　into　its　energy　distribution　characteristics　in　time　domain.　Based　on　the　needs　of　seismic　engineering,　this　article　proposes　a　conversion　formula　to　describe　the　relationship　between　the　peak　arrival　time　and　the　energy　distribution　characteristics　in　the　time　domain.　To　ensure　that　the　variation　laws　of　acceleration　time-history　curve　of　artificial　seismic　waves　are　more　consistent　with　those　of　natural　seismic　waves,　a　normal-fitting　annealing　algorithm　is　proposed　based　on　the　normal-fitting　method.　The　proposed　method　not　only　considers　the　frequency　distribution　characteristics　of　the　peak　arrival　time　comprehensively　but　also　optimizes　the　fitting　parameters　according　to　the　actual　situation.　The　results　of　all　the　experimental　cases　verify　the　rationality　and　reliability　of　the　proposed　method.