In　damage　identification　of　civil　structures,　training　deep　neural　networks　(DNNs)　often　requires　a　large　volume　of　annotated　training　data.　However,　artificial　damage　to　real-world　structures　is　always　forbidden,　resulting　in　insufficient　data　for　training.　Transfer　learning　provides　a　solution　that　allows　structural　damage　information　in　a　data-rich　domain　to　be　transferred　and　shared　as　the　prior　knowledge　to　a　data-scarce　domain,　thereby　indirectly　augmenting　available　training　data　in　the　latter　domain.　To　this　end,　a　multi-task　transfer　learning　strategy　has　been　adopted　for　the　purpose　of　achieving　cross-domain　damage　identification　between　a　plane　frame　in　the　source　domain　and　a　three-dimensional　frame　in　the　target　domain.　The　strategy　can　share　the　learning　knowledge　from　the　domain　with　sufficient　training　data　to　the　target　domain　with　insufficient　data.　Thereby,　the　DNN　(named　DNN#2)　in　the　target　domain　can　be　trained　on　a　small　amount　of　training　data.　Owing　to　their　ability　in　data　feature　extraction,　stacked　auto-encoders　(SAEs)　are　used　to　construct　the　desirable　DNN#1　and　DNN#2　corresponding　to　different　damage　identification　tasks,　named　Task#1　and　Task#2,　in　the　two　domains.　The　two　DNNs　share　the　hidden　layers　in　order　to　share　damage　feature　information　between　the　source　and　target　domains.　The　training　datasets　of　the　two　domains　are　first　used　to　jointly　pre-train　the　auto-encoders’　parameters　in　an　unsupervised　learning　way.　Afterwards,　a　supervised　fine-tuning　step　is　carried　out　to　retraining　the　entire　SAEs　for　better　performance.　By　these　means,　Task#2　receives　some　prior　knowledge　from　Task#1,　and　thus,　it　is　accomplished　on　limited　training　data　when　Task#1　is　synchronously　achieved.　The　analysis　results　demonstrate　that　the　proposed　multi-task　learning　strategy　requires　only　a　single　training　session　to　simultaneously　realize　the　cross-domain　damage　identification　of　two　different　steel　frames.　©　2024　Elsevier　Ltd