Fault diagnosis of rotating machinery bearings under strong noise backgrounds using refined composite wavelet packet fuzzy diversity entropy

In recent years, multiscale fuzzy diversity entropy (MFDE) has been demonstrated as a highly promising feature extraction tool for intelligent fault diagnosis. Compared to existing entropy methods, MFDE offers the advantages of high consistency, strong robustness, and excellent computational efficiency. However, the coarse-graining process within MFDE exclusively accounts for fault information concealed in low-frequency bands, neglecting high-frequency components and thereby leading to incomplete feature extraction. To address these critical pain points, this article proposes a fault feature extraction and diagnosis framework based on hierarchical FDE, which can synchronously extract fault information embedded in both high- and low-frequency bands. Furthermore, refined composite wavelet packet FDE (RCWPFDE) is introduced as an advanced enhancement to MFDE. By integrating the wavelet packet transform to replace the traditional hierarchical operator, RCWPFDE enables finer full-band frequency partitioning and reduces energy leakage between adjacent frequency bands. Additionally, a refined composite mechanism is embedded into the probability distribution calculation phase of the FDE, significantly improving the statistical stability of the extracted features. The proposed method is systematically evaluated through bearing fault classification experiments under varying noise conditions and benchmarked against existing state-of-the-art entropy methods. Experimental results derived from two distinct test rigs demonstrate that the proposed methodology achieves optimal performance in both signal feature extraction capability and fault recognition accuracy. Notably, at a signal-to-noise ratio of 3 dB, the average diagnostic accuracy consistently exceeds 97%, comprehensively illustrating its superior capability for extracting weak bearing fault features in heavily noise-corrupted environments.