The　frequent　occurrence　of　rotating　machinery　faults　seriously　affects　the　operation　of　the　equipment　and　the　production　of　the　enterprise.　And　it　is　worth　mentioning　that　there　are　few　single　faults　in　the　rotating　equipment　failure　while　the　multiple　faults　are　the　norm,　which　undoubtedly　increases　the　difficulty　for　fault　diagnosis.　Therefore,　it　is　of　great　essentiality　to　address　compound　faults　of　rotating　machinery.　A　novel　compound　faults　separation　method　based　on　intrinsic　characteristic-scale　decomposition　(ICD)　was　suggested　to　detect　multi-faults　in　the　case　of　underdetermined　blind　source　separation　(UBSS)　when　traditional　diagnosis　techniques　fail.　To　achieve　UBSS,　ICD　is　utilized　to　decompose　a　single　observation　signal　into　multiple　product　components　(PCs).　Then,　sparse　representation　is　used　to　improve　the　signal　sparsity,　guaranteeing　the　normal　operation　of　the　sparse　component　analysis　(SCA)　algorithm.　In　addition,　because　the　compound　fault　features　cannot　only　be　extracted　by　ICD,　the　spares-promoted　PCs　are　arranged　in　the　SCA　processing　to　separate　the　multiple　signal.　Simulations　and　experiments　based　on　the　proposed　method　was　successfully　verified.　Meanwhile,　the　Empirical　mode　decomposition　(EMD)-based　independent　component　analysis　(ICA)　is　utilized　as　a　contrast　to　verify　the　effectiveness　of　suggested　method.　The　results　suggest　that　the　proposed　method　can　deal　with　the　multiple　signal　separation　of　roller　bearing.　©　2020,　Springer　Nature　Switzerland　AG.