Rolling Bearing Fault Diagnosis Based on Wavelet Packet Decomposition and Multi-Scale Permutation Entropy

Abstract

This paper presents a rolling bearing fault diagnosis approach by integrating wavelet packet decomposition (WPD) with multi-scale permutation entropy (MPE). The approach uses MPE values of the sub-frequency band signals to identify faults appearing in rolling bearings. Specifically, vibration signals measured from a rolling bearing test system with different defect conditions are decomposed into a set of sub-frequency band signals by means of the WPD method. Then, each sub-frequency band signal is divided into a series of subsequences, and MPEs of all subsequences in corresponding sub-frequency band signal are calculated. After that, the average MPE value of all subsequences about each sub-frequency band is calculated, and is considered as the fault feature of the corresponding sub-frequency band. Subsequently, MPE values of all sub-frequency bands are considered as input feature vectors, and the hidden Markov model (HMM) is used to identify the fault pattern of the rolling bearing. Experimental study on a data set from the Case Western Reserve University bearing data center has shown that the presented approach can accurately identify faults in rolling bearings.

Analog Circuit Fault Diagnosis via Joint Cross-Wavelet Singular Entropy and Parametric t-SNE

“…Here, nine kinds of entropy techniques, including approximate entropy (Apen) [9], sampEn entropy (Samp) [22], fuzzy entropy (Fen) [23], permutation entropy (Per) [42], fuzzy approximate entropy (Fapen) [43], corrected conditional entropy (Cce) [43], Tsallis entropy [28] and shannon entropy [26], are employed to extract fault features, and these features are directly imported into SVM classifiers. The dimension of features is varied from 1 to 16 and finally, the resultant feature set without feature reduction are employed as the input vectors of SVM classifier.…”

Multi-Scale Permutation Entropy Based on Improved LMD and HMM for Rolling Bearing Diagnosis

“…Then, the phase space reconstruction of the PF1 is carried out by using the MI and the FNN to calculate the delay time and embedding dimension, and then we can set the scale to obtain the MPE of PF1. In Figure 3, MI [17][18][19][20] determines the optimal delay time.…”

“…In the formula: ( ) h x and ( ) h y respectively correspond to ( ) x i and ( ) y j of the entropy in the specified system and measure the average amount of information; ( , ) h x y is a joint information entropy. In Figure 3, MI [17][18][19][20] determines the optimal delay time. x = {x i , i = 1, 2, · · · , N} represents a group of signals, the probability density function of the point is p x [x(i)], the signal is mapped to the probability y = y j , j = 1, 2, · · · , N .…”

Railway rolling bearing fault diagnosis based on multi-scale intrinsic mode function permutation entropy and extreme learning machine classifier

“…Multi-scale permutation entropy (MPE), which is based on PE, can describe the complexity of time series within different scales. 8 EMD performs well when it used to process nonlinear, non-stationary signals, but it can cause mode mixing during such processes. PE is a measure of complexity.…”