Engineering　structures　in　operation　are　time-varying　or　nonlinear　systems　and　the　resultant　response　signals　are　usually　non-stationary,　closely-spaced　and　even　mode-overlapped　in　frequency　domain.　For　such　structures,　it　is　vital　to　identify　time-varying　modal　parameters　by　a　way　of　signal　processing,　which　therefore　provides　basis　for　health　monitoring,　safety　assessment　and　vibration　control　of　engineering　structures.　However,　two　critical　challenges　arise　in　the　time-dependent　modal　parameter　identification:　(1)　the　effective　decomposition　of　closely-spaced　and　overlapped　modes　from　non-stationary　response　signals　of　time-varying　structures;　(2)　the　precise　extraction　of　time-varying　modal　parameters,　e.g.　instantaneous　frequency　(IF),　from　the　decomposed　components.　To　address　these　issues　mentioned　above,　a　new　IF　identification　method　consisting　of　generally　demodulated　and　adaptive　variational　mode　decomposition　(GDAVMD)　and　multi-synchrosqueezing　transform　(MSST)　is　proposed　for　non-stationary　signals　of　time-varying　structures.　In　this　method,　an　index　of　mean　frequency　is　established　at　first　as　the　fitness　function　of　the　particle　swarm　optimization　algorithm　to　adaptively　select　the　parameter　combination　including　the　number　of　modal　components　and　penalty　factor.　Then,　a　generalized　demodulation　algorithm　is　performed　to　yield　a　generally　demodulated　variational　mode　decomposition　tool　that　can　be　used　for　separating　closely-spaced　or　mode-overlapped　components.　Following　the　successful　non-stationary　signal　decomposition　via　the　proposed　GDAVMD　method,　MSST　is　introduced　to　identify　IFs　of　the　decomposed　component　signals　due　to　its　superiority　on　time-frequency　energy　concentration　and　computational　efficiency.　The　effectiveness　and　accuracy　of　the　proposed　IF　identification　method　are　verified　via　two　numerical　examples　and　a　steel　cable　with　time-varying　tension　forces.　The　results　demonstrate　that　the　proposed　GDAVMD　algorithm　behaves　better　than　the　standard　variational　mode　decomposition　(VMD)　on　the　decomposition　of　multi-component　signals　with　several　overlapped　modes　on　condition　that　the　optimum　parameter　combination　is　predetermined.　Moreover,　its　combination　with　MSST　(GDAVMD+MSST)　enables　a　more　accurate　IF　estimation　result　than　VMD+MSST.　©　2025　Institution　of　Structural　Engineers