Multiscale symbolic fuzzy entropy: An entropy denoising method for weak feature extraction of rotating machinery

The entropy-based method has been demonstrated to be an effective approach to extract the fault features by estimating the complexity of signals, but how to remove the strong background noises in analyzing early weak impulsive signal remains unexplored. To solve this problem, this paper proposes symbolic fuzzy entropy (SFE) based on symbolic dynamic filtering and fuzzy entropy to eliminate the noises and improve the calculation efficiency. The main idea of SFE is to use symbolic dynamic filtering to remove the noise-related fluctuations while significantly simplifying the circulation calculation, thereby, generating better performance in resisting the background noises and high computation efficiency. The superiority of SFE is verified via two simulated signals and other three entropy methods. For comprehensive feature description, we further extend SFE into multiscale analysis by incorporating with the coarse gaining process, called MSFE. Experimental results demonstrate that the proposed MSFE method has the best performance in extracting weak fault characteristics compared with three existing MSE, MFE, and MPE methods.