Fault feature analysis of cracked gear based on LOD and analytical-FE method

•A new signal decomposition method named LOD is proposed.•An new analytical-FE method for the gear tooth crack mesh stiffness is proposed.•The assist-SIF method integrates the advantages of AM and FEM.•A dynamic model of gear system is estabolished, which combines the LOD method with the assist-SIF method, is used to realize the diagnosis of gear crack.•Simulated and experimental signals verify the validity and superiority of LOD method.