Hierarchical diversity entropy for the early fault diagnosis of rolling bearing

Intelligent fault diagnosis provides great convenience for the prognostic and health management of the rotating machinery. Recently, the multiscale diversity entropy has been proven to be a promising feature extraction tool for the intelligent fault diagnosis. Compared with the existing entropy methods, the multiscale diversity entropy has advantages of high consistency, strong robustness, and high calculation efficiency. However, the multiscale diversity entropy encounters the challenge to extract features from early fault signals with weak fault symptoms and strong noise. This can be attributed to the multiscale diversity entropy that only concerns the fault information embedded in the low frequency, which ignores the information hidden in the high frequency. To address this defect, the hierarchical diversity entropy (HDE) is proposed, which can synchronously extract fault information hidden in both high and low frequencies. Based on HDE and random forest, a novel intelligent fault diagnosis frame has been proposed. The effectiveness of the proposed method has been evaluated through simulated and experimental bearing signals. The results show that the proposed HDE has the best feature extraction ability compared with multiscale sample entropy, multiscale permutation entropy, multiscale fuzzy entropy, and multiscale diversity entropy.