The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 1) MULTISCALE FUZZY ENTROPY <s> Abstract When the fault happens, the complexity of the intrinsic oscillation from the mechanical system will change. Fuzzy entropy (FuzzyEn), which is defined to measure the complexity and self-similarity of the time series, can be utilized to measure the complexity of vibration signal and reflect changes of complexity of the intrinsic oscillation. Since the changes distribute in different scales, a new non-stationary signal analysis method, local characteristic-scale decomposition (LCD), is proposed and used to decompose the vibration signal adaptively into series of intrinsic scale components (ISC) in different scales. And then a new rolling bearing fault diagnosis approach based on LCD and FuzzyEn is proposed. Namely, firstly, by using the LCD rolling bearing vibration signal is decomposed into numbers of ISCs; then the FuzzyEns of the first few ISCs that contain main failure information are extracted. Thirdly, the FuzzyEns obtained are taken as the inputs to the adaptive neuro-fuzzy inference systems (ANFIS) classifier. Finally, the proposed method is applied to experimental data, and the analysis results show that the proposed method performs effectively for the rolling bearing fault diagnosis. <s> BIB001 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 1) MULTISCALE FUZZY ENTROPY <s> Abstract A new rolling bearing fault diagnosis method based on multi-scale fuzzy entropy (MFE), Laplacian Score (LS) and variable predictive model-based class discrimination (VPMCD) is proposed in this paper. Compared with previous approximate entropy (ApEn) and sample entropy (SampEn), MFE has taken into account the dynamic nonlinearity, interaction and coupling effects among mechanical components and thus it provides much more hidden information in different scales of vibration signal. Hence, MFE is employed to characterize the complexity and irregularity of rolling bearing vibration signals. Besides, to fulfill an automatical fault diagnosis, the VPMCD, as a new classification approach, is employed to construct a multi-fault classifier for making decision. Also, Laplacian Score (LS) for feature selection is utilized to refine the feature vector by sorting the features according to their importance and correlations with the fault information to eschew a high dimension of feature vector. Finally, the proposed method is implemented to rolling bearing experimental data and the results indicate that the proposed method is able to discriminate the different fault categories and degrees effectively. <s> BIB002 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 1) MULTISCALE FUZZY ENTROPY <s> Abstract This paper presents a new rolling bearing fault diagnosis method based on local mean decomposition (LMD), improved multiscale fuzzy entropy (IMFE), Laplacian score (LS) and improved support vector machine based binary tree (ISVM-BT). When the fault occurs in rolling bearings, the measured vibration signal is a multi-component amplitude-modulated and frequency-modulated (AM–FM) signal. LMD, a new self-adaptive time-frequency analysis method can decompose any complicated signal into a series of product functions (PFs), each of which is exactly a mono-component AM–FM signal. Hence, LMD is introduced to preprocess the vibration signal. Furthermore, IMFE that is designed to avoid the inaccurate estimation of fuzzy entropy can be utilized to quantify the complexity and self-similarity of time series for a range of scales based on fuzzy entropy. Besides, the LS approach is introduced to refine the fault features by sorting the scale factors. Subsequently, the obtained features are fed into the multi-fault classifier ISVM-BT to automatically fulfill the fault pattern identifications. The experimental results validate the effectiveness of the methodology and demonstrate that proposed algorithm can be applied to recognize the different categories and severities of rolling bearings. <s> BIB003 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 1) MULTISCALE FUZZY ENTROPY <s> Abstract A novel rolling bearing fault diagnosis method based on hierarchical fuzzy entropy (HFE), Laplacian score (LS) and improved support vector machine based binary tree (ISVM-BT) is proposed in this paper. Focus on the difficulty of extracting fault feature from the non-linear and non-stationary vibration signal under complex operating conditions, HFE method is utilized for fault feature extraction. Compared with multi-scale fuzzy entropy (MFE) method, HFE method considers both the low and high frequency components of the vibration signals, which can provide a much more accurate estimation of entropy. Besides, Laplacian score (LS) method is introduced to refine the fault feature by sorting the scale factors. Subsequently, the obtained features are fed into the multi-fault classifier ISVM-BT to automatically fulfill the fault pattern identifications. The experimental results demonstrate that the proposed method is effective in recognizing the different categories and severities of rolling bearings faults. <s> BIB004 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 1) MULTISCALE FUZZY ENTROPY <s> Abstract Multiscale permutation entropy (MPE) is a recently proposed nonlinear dynamic method for measuring the randomness and detecting the nonlinear dynamic change of time series and can be used effectively to extract the nonlinear dynamic fault feature from vibration signals of rolling bearing. To solve the drawback of coarse graining process in MPE, an improved MPE method called generalized composite multiscale permutation entropy (GCMPE) was proposed in this paper. Also the influence of parameters on GCMPE and its comparison with the MPE are studied by analyzing simulation data. GCMPE was applied to the fault feature extraction from vibration signal of rolling bearing and then based on the GCMPE, Laplacian score for feature selection and the Particle swarm optimization based support vector machine, a new fault diagnosis method for rolling bearing was put forward in this paper. Finally, the proposed method was applied to analyze the experimental data of rolling bearing. The analysis results show that the proposed method can effectively realize the fault diagnosis of rolling bearing and has a higher fault recognition rate than the existing methods. <s> BIB005
Because applying FE of single scale entropy may generate the unreliable results, MFE method was proposed by combining multiscale analysis and FE method BIB002 . MFE algorithm contains two steps as follows BIB002 , BIB003 . (1) For a given original time series · · · , X N }, it can be divided into several coarse-grained time series y τ j using Eq. BIB001 . where τ = 1, 2, · · · , N is a positive integer. (2) Calculate FuzzyEn of each coarse-grained time series y τ j using Eqs. (21)- (23) and describe FuzzyEn as a function of scale factor τ using Eq. (25) BIB003 . A flowchart of the MFE method is shown in Figure 11 . For convenience, the applications of MFE in fault diagnosis of rotating machinery are summarized in Table 10 . However, there are two main problems in the MFE method. First, the statistical stability of MFE is poor for the analysis of short time series. Since the coarse-graining procedure in the multi-scale analysis shortens the length of the time series as the scale factor τ increases, it may generate the inaccurate or undefined estimation of entropy and loose statistical reliability at larger scale factors BIB003 . Second, the averaging operation used in the coarse-graining procedure to generate a new time series only considers the fault information embedded in the low frequency region, which loses fault information in the high frequency part BIB005 , BIB004 .