Effective and intelligent fault diagnosis is essential for ensuring the operational safety and reliability of gearbox systems. In practical engineering environments, however, weak fault-related features are often obscured by strong background noise, pronounced nonstationarity, and time-varying operating conditions, which significantly degrade the performance of conventional feature extraction techniques. To address these challenges, this paper proposes an adaptive feature extraction approach that integrates the complementary advantages of variational mode decomposition (VMD), Teager energy operator (TEO), and multi-scale permutation entropy (MPE) to enhance the characterization of weak and transient fault signatures. Vibration signals associated with different fault conditions are first adaptively decomposed into a series of intrinsic mode functions (IMFs) using VMD, enabling the effective separation of fault-sensitive components and enrichment of fault-related information. Subsequently, an enhanced multi-scale permutation entropy (EMPE) method is developed to emphasize transient impulsive characteristics and capture fault-induced complexity variations across multiple temporal scales. By jointly exploiting instantaneous energy modulation and multi-scale dynamical complexity analysis, the proposed approach exhibits improved sensitivity to weak fault signatures and enhanced robustness against variable operating conditions. The effectiveness and generalization capabilities of the proposed framework are validated using three experimental datasets involving gearboxes and rolling bearings under diverse operating conditions. Comparative results demonstrate that the proposed method outperforms conventional entropy-based approaches in terms of fault feature separability and diagnostic performance, highlighting its potential for practical condition monitoring and fault diagnosis of rotating machinery.
Zeng et al. (Mon,) studied this question.