Multi-hazard　coupling　is　a　vital　issue　for　the　performance　evaluating　of　offshore　wind　turbine　(OWTs),　whose　servicing　period　may　encounter　wind,　wave,　earthquake,　and　thrust　force　caused　by　the　operating　scenarios.　However,　due　to　the　uncertainty　of　earthquake　in　occurrence,　it　is　a　challenging　topic　to　determine　the　multi-hazard　coupling　of　OWT　as　the　initialized　time　of　earthquake　(ITOE)　is　fully　stochastic.　This　paper　proposed　a　comprehensive　multi-hazard　combination　method　for　the　coupling　action　of　wind-wave-earthquake　excitations,　emphasizing　the　randomness　of　the　initialized　time　of　earthquake　loads　in　operating　loads.　Subsequently,　an　accurate　three-dimensional　finite　element　model　of　5-MW　OWT　is　established.　Then,　cloud-based　fragility　analysis　of　OWTs　in　parked　and　operating　conditions　is　conducted　through　extensive　nonlinear　time-history　analysis　of　the　combining　loads　of　winds,　waves,　and　earthquakes.　The　distinction　between　pulse-like　and　non-pulse-like　earthquakes　is　made　using　a　pulse　identification　and　extraction　technique.　The　results　indicate　that　the　thrust　force　during　the　operation　increases　the　vulnerability　of　OWTs　compared　to　the　parked　state.　Additionally,　the　thrust　force　predominantly　acts　in　the　fore-aft　direction,　making　this　orientation　more　susceptible　to　failure　than　the　side-to-side　direction　at　the　ultimate　limit　state.　Furthermore,　the　analysis　confirms　that　the　pulse-type　earthquakes　result　in　a　higher　probability　of　damage　compared　to　the　non-pulse　records,　for　both　parked　and　operating　scenarios.　©　2024　Elsevier　Ltd