Early fault detection for spiral bevel gears is crucial to ensure normal operation and prevent accidents. The harmonic components, excited by the time-varying mesh stiffness, always appear in measured vibration signal. How to extract the periodical impulses that indicate gear localized fault buried in the intensive noise and interfered by harmonics is a challenging task. In this paper, a novel Periodical Sparse-Assisted Decoupling (PSAD) method is proposed as an optimization problem to extract fault feature from noisy vibration signal. The PSAD method decouples the impulsive fault feature and harmonic components based on the sparse representation method. The sparsity within and across groups property and the periodicity of the fault feature are incorporated into the regularizer as the prior information. The nonconvex penalty is employed to highlight the sparsity of fault features. Meanwhile, the weight factor based on ${\ell }_2$ norm of each group is constructed to strengthen the amplitude of fault feature. An iterative algorithm with Majorization–Minimization (MM) is derived to solve the optimization problem. Simulation study and experimental analysis confirm the performance of the proposed PSAD method in extracting and enhancing defect impulses from noisy signal. The suggested method surpasses other comparative methods in extracting and enhancing fault features.

Acoustic Mode Analysis (AMA) for aero-engines can offer valuable insights for the design of silent engines as well as for fault diagnosis. Commonly, this is done in the (spatial) Fourier domain, necessitating the use of multiple uniformly spaced microphones to ensure adequate resolution. Recent works show that sub-Nyquist estimation is feasible using sparse reconstruction frameworks, although such modelling generally introduces an estimation bias that has to be compensated for. Moreover, there is a growing interest in monitoring mode amplitude over continuous time, as it can offer crucial insights for diagnosing operational conditions. In this work, we introduce a Block Orthogonal Matching Pursuit (BOMP) method for continuous time mode analysis, exploiting the underlying structural sparsity of the signal model. Specifically, the (pseudo) ℓ₀−norm penalty is employed to induce sparsity in the wavenumber domain, whereas a block structure is imposed as a constraint to monitor the amplitude variation in the time domain. The effectiveness of the BOMP is evaluated using both numerical simulations and experimental measurements, indicating the proposed method’s preferable performance as compared to the classic Least Absolute Shrinkage and Selection Operator (LASSO) and Orthogonal Matching Pursuit (OMP) methods.