Adaptive Variational Mode Decomposition with Improved Greylag Goose Optimization and Refined Composite Multiscale Permutation Entropy for Weak Fault Feature Extraction of Hydropower Units

Incipient fault signatures of hydropower units are weak and easily masked by strong background noise and dominant harmonic components. This paper proposes a weak fault feature extraction method combining adaptively optimized variational mode decomposition (VMD) with refined composite multiscale permutation entropy (RCMPE). An improved greylag goose optimization (IGGO) algorithm is developed by introducing Tent chaotic stratified initialization, refraction-based opposition learning, and an adaptively weighted Lévy-flight mutation. A composite fitness function augments the minimum envelope entropy with spectral-overlap and normalized-bandwidth constraints, eliminating the boundary-solution problem of a single sparsity objective. A comprehensive evaluation index fusing the energy ratio, the correlation coefficient, and the envelope-spectrum harmonic energy proportion automatically screens sensitive modes for RCMPE feature construction. On eight benchmark functions, IGGO attains the lowest average Friedman rank among eight algorithms, with no statistically significant difference from GWO, SSA and EGGO and a significant improvement over WOA, GGO and PSO; under the same evaluation budget as the VMD optimization task, it hits the global optimum with a success rate of 96%, which is significantly higher than the 82% of the standard GGO. On measured data of four states from a shafting simulation test rig, the proposed method achieves 100% recognition accuracy and maintains 82.6% under −6 dB noise. On rubbing data from a 200 MW hydropower unit, the leading sensitive mode automatically shifts from the 4.02× rotational-frequency band to the 12.01× band, and the normal, pre-warning, and fault states are reliably distinguished. The method stably extracts weak fault features under strong noise and dominant harmonic interference.