Civil　engineering　structures　in　operation　are　likely　to　suffer　damage.　During　the　service　life,　structural　damage　evolves　gradually　from　minor　to　severe.　However,　most　current　studies　focus　on　damage　localization　and　quantification　of　damage　severity,　and　hence　little　attention　has　been　paid　to　the　detection　of　time-varying　damage.　This　paper　aims　to　propose　a　new　approach　for　tracking　the　damage　evolution　of　beam　structures.　In　this　approach,　the　wavelet　threshold　method　is　used　at　first　to　denoise　the　response　signal.　After　that,　the　variational　mode　decomposition　(VMD)　is　introduced　to　decompose　the　denoised　response　signal　into　several　mono-components　adaptively.　A　proposed　index　of　wavelet　total　energy　change　(WTEC)　is　then　applied　to　the　new　decomposed　signals　to　localize　damages　of　beam　structures.　On　a　basis　of　this,　a　time-varying　damage　index　called　wavelet　energy　change　ratio　(WECR)　is　established　via　the　continuous　wavelet　transform　and　time　window　techniques　and　then　applied　to　the　response　at　the　damaged　position　for　tracking　damage　evolution.　The　proposed　method　is　verified　via　a　numerical　example　of　a　simply　supported　beam　(its　length　and　area　of　cross　section　are　5　m　and　0.04　m2,　respectively)　with　a　sudden　and　a　linear　stiffness　reduction　under　1940　El　Centro　ground　acceleration　record.　In　addition,　an　experiment　on　a　10-meters-long　steel　bridge　with　abrupt　stiffness　reduction　under　a　moving　load　is　investigated　to　demonstrate　the　effectiveness　and　accuracy　of　the　proposed　time-varying　damage　detection　method.　The　results　show　that　the　index　of　WTEC　is　able　to　localize　damages　of　beam　structures　effectively　whatever　they　are　a　single　damage　position　or　multiple　damage　positions.　Moreover,　the　damage　evolution　can　be　tracked　by　the　proposed　index　of　WECR　accurately　even　though　random　noises　and　end　effects　pose　a　great　impact　on　the　time-varying　damage　detection　results.　©　2023　Elsevier　Ltd