To　balance　the　convergence　rate　and　steady-state　error　of　blind　source　separation　(BSS)　algorithms,　an　efficient　equivariant　adaptive　separation　via　independence　(Efficient　EASI)　algorithm　is　proposed　based　on　separating　indicator,　which　was　derived　from　the　convergence　condition　of　EASI,　and　can　be　used　to　evaluate　the　separation　degree　of　separated　signals.　Furthermore,　a　nonlinear　monotone　increasing　function　between　suitable　step　sizes　and　separating　indicator　is　constructed　to　adaptively　adjust　step　sizes,　and　forgetting　factor　is　employed　to　weaken　effects　of　data　at　the　initial　stage.　Numerical　case　studies　and　experimental　studies　on　a　test　bed　with　shell　structures　are　provided　to　validate　the　efficiency　improvement　of　the　proposed　method.　This　study　can　benefit　for　vibration　&　acoustic　monitoring　and　control,　and　machinery　condition　monitoring　and　fault　diagnosis.