Refined time-shift multiscale slope entropy: a new nonlinear dynamic analysis tool for rotating machinery fault feature extraction

Slope entropy (SlE) is an effective nonlinear dynamic analysis method, which has been used in mechanical fault diagnosis field. However, SlE only analyzes the time series on a single scale with much important information on other scales being ignored. Inspired by the multiscale analysis, the multiscale slope entropy (MSlE) is developed to extract the multiscale features of time series. Nevertheless, MSlE is susceptible to the loss of important information of original time series due to insufficient coarse-graining. In this paper, a novel algorithm termed refined time-shift multiscale slope entropy (RTSMSlE) is further proposed for enhancing the performance of MSlE. RTSMSlE changes the original coarse-grained computation and effectively improves the nonlinear analysis performance of MSlE, which has higher discriminating power and is less affected by mutant signals. After that, a novel fault diagnosis method for rotating machinery is proposed based on the RTSMSlE and DBO-SVM classifier. The effectiveness and superiority of the proposed fault diagnosis method is verified via the simulated signals and the measured data analysis with comparison to the MSlE, refined time-shift multiscale sample entropy (RTSMSE), refined time-shift multiscale fuzzy entropy (RTSMFE), refined composite multiscale sample entropy (RCMSE) and refined composite multiscale dispersion entropy (RCMDE). The analysis results show that the proposed method provides better diagnostic effect and more stable performance in analyzing the vibration signals of rotating machinery than the compared methods.