Refined time-shift multiscale normalised dispersion entropy and its application to fault diagnosis of rolling bearing

Multiscale entropy (MSE) and multiscale permutation entropy (MPE) are two effective nonlinear dynamic complexity measurement methods of time series that have been applied to many areas for complexity feature extraction in recent years. To overcome the inherent defects of sample entropy and permutation entropy, together with the coarse graining process used in MSE and MPE, based on the recently proposed dispersion entropy (DisEn), the refined time-shift multiscale normalised dispersion entropy (RTSMNDE) is proposed here for the complexity measurement of time series. In the RTSMNDE method, first, to expand DisEn to the multiscale framework, the time-shift multiscale method is used to replace the traditional coarse graining multiscale method. The refining approach is adopted to alleviate the fluctuation of DisEns in larger scale factors, and a normalisation operation is implemented on all entropies to restrain the influence of the parameters on RTSMNDE values. Furthermore, the RTSMNDE is compared with the multiscale dispersion entropy (MDE) by analysing synthetic simulation signals to verify its effectiveness. Based on that, an intelligent fault diagnosis method for rolling bearings is proposed by combining the RTSMNDE for fault feature extraction with the particle swarm optimisation support vector machine for feature classification. Finally, the proposed method is applied to rolling bearing experimental data analysis, and the analysis results show that the proposed method can effectively diagnose the locations and degrees of rolling bearing failures and obtain a higher recognition rate than those of the MPE and MDE-based methods.