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

Abstract

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 may lack the capability to fully describe dynamics of complex signals since compressing all the information into a single parameter. Afterwards, multiscale PeEn (MPeEn) is put forward for coping with nonstationarity, outliers and artifacts emerging in complex signals. In MPeEn, a set of parameters serve to describe dynamics of a complex signal in different time scales. Nonetheless, an average procedure in MPeEn may withhold local information of a complex signal. To overcome deficiencies of PeEn and MPeEn, this paper proposes generalized PeEn (GPeEn) by introducing different time lags and orders into PeEn. In GPeEn, a complex signal is compressed into one matrix rather than a single parameter. Moreover, minimal, maximal and average values of a matrix obtained by GPeEn serve to briefly describe conditions of rotating machinery. Next, a numerical experiment proves that GPeEn outperforms PeEn and MPeEn in characterizing conditions of a Lorenz model. Subsequently, the performance of GPeEn is benchmarked against that of 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 has a clear advantage over PeEn and MPeEn in condition monitoring of rotating machinery.

A Novel Feature for Fault Classification of Rotating Machinery: Ternary Approximate Entropy for Original, Shuffle and Surrogate Data

“…The principal contribution of this paper is to develop the ternary entropy approach by integrating ApEn of original, shuffle, and surrogate data into a three-dimensional vector for characterizing the properties of complex data. Indeed, the shuffle and surrogate methods of treating data, distinct from EMD or WD, can take the original data apart [15,16,22,23,30,31]. In this way, shuffle data and surrogate data simply contain PDF information and spectral information of the original data, respectively.…”

“…In addition, chaotic and fractal methods were adopted to explore complex vibration data [13,14]. However, chaotic methods typically face difficulties in determining embedding dimensions and time lags, while traditional fractal methods are frequently disturbed by non-stationary trends [15,16]. Detrended fluctuation analysis (DFA) was proposed for analyzing complex vibration data [17].…”

A novel feature dimensionality reduction method for gearbox fault diagnosis with HMSDE, DANCo-DDMA and KELM

“…0.2729 [4,3] 0.3168 [6,3] 0.3039 [11,2] 0.2794 [16,2] 0.2647 [3,3] 0.2938 [4,4] 0.3266 [7,2] 0.2906 [12,2] 0.2754 [17,2] 0.2579 [3,4] 0.3097 [5,2] 0.2824 [8,2] 0.2878 [13,2] 0.2752 [18,2] 0.2538 [3,5] 0.3145 [5,3] It can be seen that from Fig. 4, the HMSDE features with nine states are effectively distinguished with a high discrimination degree.…”

“…For a given time series, the complexity is not fully described by a single scale entropy. Various multiscale and hierarchical entropy variants have been proposed to extract more complex features from time series [15][16][17][18][19][20][21][22]. However, the above two types of methods still have some shortcomings.…”