Singular　value　decomposition　(SVD)　is　an　effective　tool　for　analyzing　the　signals　from　mechanical　systems　and　for　fault　diagnosis,　which　is　a　non-parametric　signal　analysis　method　free　from　phase　shift　and　waveform　distortion.　In　SVD,　the　embedding　dimension　of　the　Hankel　matrix　is　an　important　parameter　that　directly　influences　the　effectiveness　of　the　SVD.　However,　the　embedding　dimension　is　usually　determined　by　experience,　which　is　quite　subjective　and　limits　the　applicability　of　SVD.　As　such,　a　novel　SVD　method,　named　adaptive　SVD　(ASVD),　is　proposed　in　this　paper.　In　ASVD,　novel　criteria　are　defined　to　obtain　the　specific　embedding　dimensions　for　different　mechanical　signals　by　means　of　numerical　simulation.　A　novel　phenomenon,　that　the　singular　value　pairs　change　periodically　with　the　step　size　of　half-cycle　sampling　points,　is　found　and　it　can　be　used　to　calculate　specific　embedding　dimension　instead　of　selecting　it　from　a　range　using　experience.　Meanwhile,　the　envelope　spectral　amplitude　ratio　index　is　developed　for　addressing　the　issue　of　excessive　decomposition　in　classic　SVD.　Lastly,　an　ASVD-based　bearing　fault　diagnosis　method　is　proposed　to　adaptively　select　useful　sub-signals　and　to　detect　faults.　Both　simulated　signal　and　experiment　signals,　collected　from　different　bearing　test　rigs　are　used　to　verify　the　effectiveness　of　the　proposed　method.　The　results　show　that　the　proposed　method　has　a　satisfactory　ability　to　eliminate　interference　noise　and　detect　bearing　fault.