Rolling bearing signal monitoring and diagnosis based on global arc length entropy

In the fault diagnosis of rolling bearings, information entropy has become one of the promising tools for feature extraction. To further enhance the ability of information entropy to track the internal structure of signals, the global arc length entropy (GAE) has been proposed. Currently, most entropy calculations based on the Takens theory in specific embedding dimensions do not consider the variation trend of individual subvectors in the global space, only calculating the relationship between adjacent subvectors. To address this issue, this study introduces a new algorithmic structure and entropy concept to explore the relationship between adjacent embedding dimensions and the variation of each subvector in all spaces. Meanwhile, through the logistic map function and testing of different signal styles and robustness, GAE demonstrates superior capabilities compared to other entropy methods. On the other hand, to improve the discrimination ability of fault signals, the concept of multiscale is introduced, called multiscale global arc length entropy (MGAE). Through monitoring and diagnosing different fault data, the MGAE demonstrates excellent scale shape and recognition rates, reaching 99.7% in both real experimental data validations.