Feature extraction based on generalized permutation entropy for condition monitoring of rotating machinery

Defective rotating machinery usually exhibits complex dynamic behavior. Therefore, feature representation of machinery vibration signals is always critical for condition monitoring of rotating machinery. Permutation entropy (PeEn), an adaptive symbolic description, can measure complexities of signals. However, PeEn, which compresses all the information into a single parameter, may lack the capability to fully describe the dynamics of complex signals. Afterward, multiscale PeEn (MPeEn) is put forward for coping with nonstationarity, outliers and artifacts emerging in complex signals. In MPeEn, a set of parameters serves to describe the dynamics of complex signals in different time scales. Nonetheless, an average procedure in MPeEn may withhold local information of complex signals and destroy internal structures of complex signals. To overcome deficiencies of PeEn and MPeEn, this paper proposes generalized PeEn (GPeEn) by introducing different orders and time lags into PeEn. In GPeEn, a complex signal is converted into a PeEn matrix rather than a single parameter. Moreover, minimal, maximal and average values of the PeEn matrix serve to briefly describe conditions of rotating machinery. Next, a numerical experiment proves that the proposed method in this paper performs better than skewness, kurtosis, PeEn and MPeEn in characterizing conditions of a Lorenz model. Subsequently, the proposed method in this paper is compared with skewness, kurtosis, PeEn and MPeEn by investigating gear and roll-bearing vibration signals containing different types and severity of faults. The results show that the proposed method in this paper outperforms the other four methods in distinguishing between different types and severity of faults of rotating machinery.