The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 5) HIERARCHICAL FUZZY ENTROPY <s> We introduce complexity parameters for time series based on comparison of neighboring values. The definition directly applies to arbitrary real-world data. For some well-known chaotic dynamical systems it is shown that our complexity behaves similar to Lyapunov exponents, and is particularly useful in the presence of dynamical or observational noise. The advantages of our method are its simplicity, extremely fast calculation, robustness, and invariance with respect to nonlinear monotonous transformations. <s> BIB001 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 5) HIERARCHICAL 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> BIB002 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 5) HIERARCHICAL FUZZY ENTROPY <s> Aiming at the non-linear characteristics of bearing vibration signals as well as the complexity of condition-indicating information distribution in the signals, a new rolling element bearing fault diagnosis method based on hierarchical fuzzy entropy and support vector machine is proposed in this paper. By incorporating the advantages of both the concept of fuzzy sets and the hierarchical decomposition of hierarchical entropy, hierarchical fuzzy entropy is developed to extract the fault features from the bearing vibration signals, which can provide more useful information reflecting bearing working conditions than hierarchical entropy. After feature extraction with hierarchical fuzzy entropy, a multi-class support vector machine is trained and then employed to fulfill an automated bearing fault diagnosis. The experimental results demonstrate that the proposed approach can identify different bearing fault types as well as severities precisely. <s> BIB003
Similar with MSE, MFE only considers the fault information embedded in the low frequency region, which loses fault information in the high frequency part. To tackle this problem of MFE, hierarchical fuzzy entropy (HFE) is proposed by Li et al. BIB002 by combing hierarchical decomposition analysis with FE. Because the averaging and differential processes are both utilized in the hierarchical decomposition, the HFE can characterize more information than the MFE. The effectiveness of HFE is validated using experimental signals from CWRU. The results demonstrate that the HFE has a better performance than MFE. Meanwhile, Zhu and Li BIB003 combined with HFE with SVM to recognize bearing fault types and a satisfactory classification accuracy (100%) was achieved. The concept of HFE is given as follows. (1) Calculate the hierarchical component Z e k through the hierarchical decomposition analysis (details are given in Section V. C. 4). (2) Calculate the FE value of each hierarchical component and the HSDE can be obtained using Eq. BIB001 .