Fault　diagnosis　of　critical　rotating　machinery　components　is　necessary　to　ensure　safe　operation.　However,　the　commonly　used　rotating　machinery　fault　diagnosis　methods　are　generally　based　on　the　single-channel　signal　processing　method,　which　is　not　suitable　for　processing　multi-channel　signals.　Thus,　to　extract　features　and　carry　out　the　intelligent　diagnosis　of　multi-channel　signals,　a　novel　method　for　rotating　machinery　fault　diagnosis　is　proposed.　Firstly,　a　novel　nonlinear　dynamics　technique　named　the　multivariate　generalized　refined　composite　multi-scale　sample　entropy　was　presented　and　applied　to　extract　fusion　entropy　features　of　multi-channel　signals.　Secondly,　a　practical　manifold　learning　known　as　supervised　isometric　mapping　was　introduced　to　map　the　high-dimensional　fusion　entropy　features　in　a　low-dimensional　space.　In　a　third　step,　the　Harris　hawks　optimization-based　support　vector　machine　was　applied　to　carry　out　the　intelligent　fault　recognition.　Finally,　aiming　to　verify　the　effectiveness　of　the　proposed　method　and　present　its　advantages,　it　was　applied　to　analyze　the　rotating　machinery　system　bearing　and　gear　data.　The　experimental　results　have　shown　that　the　method　at　hand　can　accurately　identify　various　faults　in　both　the　bearings　and　gears.　Furthermore,　in　addition　to　being　suitable　for　multi-channel　signal　fault　diagnosis,　it　had　higher　recognition　accuracy　compared　to　other　multi-channel　or　single-channel　methods.　©　2021,　The　Author(s),　under　exclusive　licence　to　Springer　Nature　B.V.