Based　on　the　sample　entropy　algorithm　in　nonlinear　dynamics,　an　improved　sample　entropy　method　is　proposed　in　the　aerodynamic　system　instability　identification　for　the　stall　precursor　detection　based　on　the　nonlinear　feature　extraction　algorithm　in　an　axial　compressor.　The　sample　entropy　algorithm　is　an　improved　algorithm　based　on　the　approximate　entropy　al-gorithm,　which　quantifies　the　regularity　and　the　predictability　of　data　in　time　series.　Combined　with　the　spatial　modes　representing　for　the　rotating　stall　in　the　circumferential　direction,　the　recognition　capacity　of　the　sample　entropy　is　displayed　well　on　the　detection　of　stall　inception.　The　indications　of　rotating　waves　are　extracted　by　the　circumferential　analysis　from　modal　wave　energy.　The　significant　ascendant　in　the　amplitude　of　the　spatial　mode　is　a　pronounced　feature　well　before　the　imminence　of　stall.　Data　processing　with　the　spatial　mode　effectively　avoids　the　problems　of　inaccurate　identification　of　a　single　measuring　point　only　depending　on　pressure.　Due　to　the　different　selections　of　similarity　tolerance,　two　kinds　of　sample　entropy　are　obtained.　The　properties　of　the　development　process　of　the　identification　model　show　obvious　mutation　phenomena　at　the　boundary　of　instability,　which　reveal　the　inherent　charac-teristic　in　aerodynamic　system.　Then　the　dynamic　difference　quotient　is　computed　according　to　the　difference　quotient　criterion,　after　the　smooth　management　by　discrete　wavelet.　The　rapid　increase　of　difference　quotient　can　be　regarded　as　a　significant　feature　of　the　system　approach-ing　the　flow　instability.　It　is　proven　that　based　on　the　principle　of　sample　entropy　algorithm,　the　nonlinear　characteristic　of　rotating　stall　can　be　well　described.　The　inception　can　be　suggested　by　about　12-68　revolutions　before　the　stall　arrival.　This　prediction　method　presenting　is　ac-counted　for　the　nonlinearity　of　the　complex　flow　in　stall,　which　is　in　a　view　of　data　fusion　sys-tem　of　pressure　for　the　spatial　mode　tracking.　(c)　2023　The　Authors.　Publishing　services　by　Elsevier　B.V.　on　behalf　of　KeAi　Communications　Co.　Ltd.　This　is　an　open　access　article　under　the　CC　BY-NC-ND　license　(http://creativecommons.org/licenses/by-nc-nd/4.0/).