Multi-scale entropy analysis of acoustic emission for gearbox fault severity classification

Acoustic emission (AE) sensors offer significant potential for early fault detection in rotating machinery through the monitoring of high-frequency transients. However, extracting effective features from complex AE signals remains challenging for automated fault severity classification across multiple damage mechanisms. This study investigates multi-scale entropy methods for extracting a computationally efficient set of 16 non-linear information entropy features from AE signals to diagnose gearbox fault severity. Three approaches were systematically compared: Composite Multi-Scale Entropy (CMSE), Hierarchical Multi-Scale Entropy (HMSE), and Composite Hierarchical Multi-Scale Entropy (CHMSE). Experimental data were collected from a spur gearbox test rig operating under controlled conditions, with artificially induced faults representing four damage mechanisms (pitting, broken teeth, root cracks, and scuffing) at nine severity levels each, providing the most granular assessment reported in the entropy-based fault diagnosis literature. Features extracted using each multi-scale method were classified using several classical machine learning models. The CHMSE combined with Random Forests (RF) models achieved the highest classification accuracy (97.37-99.50%), representing a 1-4% improvement over conventional single-scale methods and demonstrating superior performance compared to statistical features and alternative machine learning models. SHAP-based interpretability analysis revealed that generalized entropy measures, specifically Rényi entropy and Tsallis entropy, emerge as primary discriminators across CMSE, HMSE, and CHMSE approaches, with threshold entropy and log energy entropy demonstrating substantial discriminative power when combined with hierarchical decomposition methods (HMSE and CHMSE). Statistical analysis confirmed significant performance improvements (p <0.05) for the hierarchical approaches. These findings demonstrate that CHMSE-based feature extraction enables reliable AE-based condition-monitoring systems for predictive maintenance in industrial gearboxes.