Box-Cox sparsity measure-based impulse extraction for gearbox condition monitoring

Vibration impulses from gearboxes are crucial for fault diagnosis but are often obscured by strong meshing components and background noise. This paper proposes Box-Cox Sparsity Measure-Based Impulse Extraction (BCIE), which advances beyond the existing Optimal Weighted Impulse Extraction (OWIE) method by: (1) generalizing the kurtosis criterion in OWIE to Box-Cox sparsity measures (BCSM) parameterized by λ[jls-end-space/], where (Formula presented) corresponds to the original OWIE formulation; and (2) introducing an optimized window-length selection strategy absent in OWIE. The efficacy of the proposed BCIE is validated through both numerical simulation experiments and gearbox run-to-failure datasets. The results demonstrate that the proposed BCIE exhibits strong sensitivity to incipient gear faults and is well-suited for gearbox impulse extraction and health monitoring, particularly when (Formula presented) (negative relative entropy), which optimally balances early fault detection sensitivity with false alarm suppression. Parameter analysis reveals: (1) large λ values ((Formula presented) ) increase false alarms while showing minimal BCSM changes during faults; and (2) small λ values ((Formula presented) ) yield insignificant fault indications while weakening healthy-state signals.