A new gear weak feature extraction method based on modified symplectic geometry mode decomposition

The symplectic geometry mode decomposition (SGMD) is an effective analysis method applying to nonlinear and non-stationary signal. However, applying SGMD to gear signal, the weak fault feature is hard to be extracted, leading to the fault diagnosis failure. The reason lies in that the embedding dimension selection method of trajectory matrix lacks selection criteria, the construction type of trajectory matrix will result in spectral leakage, and it uses QR factorization tending to error diffusion when decomposing singular matrix. This paper proposes modified symplectic geometry mode decomposition (MSGMD) and concentrates on weak feature abstraction for gear fault diagnosis. First, a new embedding dimension choice strategy is proposed to select the ideal parameter, solving the problem of parameter solidification in SGMD. Then, the trajectory matrix is modified with “wraps around” method, which enhances the oscillation component and reduces the residual energy, and weak state features can be fully explored. Finally, singular value decomposition (SVD) takes the place of QR factorization to enhance the decomposition process, making the original signal feature information more completely. Simulated and experimental analysis demonstrate that MSGMD has excellent feature extractive ability in diagnosing gear fault with weak feature. The proposed method provides an effective way to diagnose gear fault of practical signal.