In　this　paper,　relying　on　the　Volterra　series　nonlinear　system　model　and　the　high-order　kernel　Hilbert＇s　reconstructed　kernel　fast　solved　algorithm,　a　fault　feature　frequency　domain　identification　method　based　on　Volterra　high-order　kernel　generalized　frequency　response　graph　analysis　is　proposed.　Firstly,　the　method　uses　the　system　input　and　output　vibration　signals　to　determine　the　Volterra　model.　Then,　the　Volterra　high-order　kernel　function　is　solved　quickly　by　reproducing　kernel　Hilbert　space　method,　and　the　generalized　frequency　response　function　is　used　to　identify　the　model.　Finally,　multidimensional　high-order　spectral　pattern　analysis　is　used　to　separate　and　extract　the　fault　and　degree　characteristic　information　implied　by　frequency　and　phase　coupling　in　the　third-order　kernel　function.　Following　the　theoretical　approach,　in　the　experimental　part,　this　paper　uses　the　planetary　gearbox　fault　loading　test　rig　to　complete　the　data　collection　and　establishes　the　Volterra　experimental　model　through　the　measured　data.　The　generalized　frequency　responses　of　each　order　kernel　function　are　compared　and　analyzed　and　the　capability　of　distinguishing　and　the　adaptability　of　different　order　kernel　functions　for　the　degree　of　crack　failure　are　discussed.　The　effects　of　changing　the　memory　length　of　the　Volterra　model　and　the　order　of　the　kernel　function　on　the　recognition　result　are　verified.　The　final　experimental　results　show　that　the　use　of　reproducing　kernel　Hilbert　space　can　effectively　avoid　the　dimension　disaster　problem　that　occurs　in　the　high-order　kernel　solution　process.　Moreover,　the　third-order　kernel　can　describe　more　intuitively　the　nonlinear　system　model　under　multifactor　coupling　than　the　second-order　kernel.　Finally,　Volterra　series　model　the　third-order　kernel＇s　generalized　frequency　response　can　effectively　distinguish　between　nondefective　and　faulty　gears,　and　its　resolution　is　enough　to　distinguish　the　degree　of　failure　of　gear　cracks.