Abstract
Multi-scale permutation entropy (MPE) is an effective nonlinear dynamic approach for complexity measurement of time series and it has been widely applied to fault feature representation of rolling bearing. However, the coarse-grained time series in MPE becomes shorter and shorter with the increase of the scale factor, which causes an imprecise estimation of permutation entropy. In addition, the different amplitudes of the same patterns are not considered by the permutation entropy used in MPE. To solve these issues, the time-shift multi-scale weighted permutation entropy (TSMWPE) approach is proposed in this paper. The inadequate process of coarse-grained time series in MPE was optimized by using a time shift time series and the process of probability calculation that cannot fully consider the symbol mode is solved by introducing a weighting operation. The parameter selections of TSMWPE were studied by analyzing two different noise signals. The stability and robustness were also studied by comparing TSMWPE with TSMPE and MPE. Based on the advantages of TSMWPE, an intelligent fault diagnosis method for rolling bearing is proposed by combining it with gray wolf optimized support vector machine for fault classification. The proposed fault diagnostic method was applied to two cases of experimental data analysis of rolling bearing and the results show that it can diagnose the fault category and severity of rolling bearing accurately and the corresponding recognition rate is higher than the rate provided by the existing comparison methods.
Highlights
Rolling bearing is one of the most important parts of rotating machinery and the one most prone to failure [1]
In literature [13], permutation entropy (PE) was applied to experiment data analysis of rolling bearings and the result concluded that PE is a randomness and dynamic behavior detection method of vibration signals and that it can effectively identify the bearing fault types and degrees
Multi-scale sample entropy (MSE) [14], multi-scale fuzzy entropy (MFE) [15] and multi-scale permutation (MPE) were developed by the scholars to measure the complexity of time series in different scales
Summary
Rolling bearing is one of the most important parts of rotating machinery and the one most prone to failure [1]. In literature [13], PE was applied to experiment data analysis of rolling bearings and the result concluded that PE is a randomness and dynamic behavior detection method of vibration signals and that it can effectively identify the bearing fault types and degrees. The entropy-based indicators mentioned above are generally limited to single-scale analysis of time series and the information of time series on other scales is ignored, which results in a serious loss of information For this reason, multi-scale sample entropy (MSE) [14], multi-scale fuzzy entropy (MFE) [15] and multi-scale permutation (MPE) were developed by the scholars to measure the complexity of time series in different scales.
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