The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> A. SYMBOLIC DYNAMIC ENTROPY <s> Abstract Health condition identification of planetary gearboxes is crucial to reduce the downtime and maximize productivity. This paper aims to develop a novel fault diagnosis method based on modified multi-scale symbolic dynamic entropy (MMSDE) and minimum redundancy maximum relevance (mRMR) to identify the different health conditions of planetary gearbox. MMSDE is proposed to quantify the regularity of time series, which can assess the dynamical characteristics over a range of scales. MMSDE has obvious advantages in the detection of dynamical changes and computation efficiency. Then, the mRMR approach is introduced to refine the fault features. Lastly, the obtained new features are fed into the least square support vector machine (LSSVM) to complete the fault pattern identification. The proposed method is numerically and experimentally demonstrated to be able to recognize the different fault types of planetary gearboxes. <s> BIB001 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> A. SYMBOLIC DYNAMIC ENTROPY <s> Abstract Early fault diagnosis of rolling bearings is crucial to operating and maintenance cost reduction of the equipment with bearings. This paper aims to propose a novel early fault feature extraction method based on the proposed hierarchical symbol dynamic entropy (HSDE) and the binary tree support vector machine (BT-SVM). Multiscale symbolic dynamic entropy (MSDE) has been recently proposed to characterize the dynamical behavior of time series. MSDE has several merits comparing with multiscale sample entropy (MSE) and multiscale permutation entropy (MPE), such as high computational efficiency and robustness to noise. However, MSDE only utilizes the fault information in the low frequency components and consequently the fault information hidden in the high frequency components is discarded. To address this shortcoming, a new method, namely HSDE, is proposed to extract the fault information in the high frequency components. Then, the BT-SVM is utilized to automatically complete the fault type identification. The effectiveness of the proposed method is validated using simulated and experimental vibration signals. Meanwhile, a comparison is conducted between MPE, hierarchical permutation entropy (HPE), MSE, hierarchical sample entropy (HSE), MSDE and HSDE. Results show that the proposed method performs best to recognize the early fault types of rolling bearings. <s> BIB002 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> A. SYMBOLIC DYNAMIC ENTROPY <s> Abstract The fault diagnosis of planetary gearboxes is crucial to reduce the maintenance costs and economic losses. This paper proposes a novel fault diagnosis method based on adaptive multi-scale morphological filter (AMMF) and modified hierarchical permutation entropy (MHPE) to identify the different health conditions of planetary gearboxes. In this method, AMMF is firstly adopted to remove the fault-unrelated components and enhance the fault characteristics. Second, MHPE is utilized to extract the fault features from the denoised vibration signals. Third, Laplacian score (LS) approach is employed to refine the fault features. In the end, the obtained features are fed into the binary tree support vector machine (BT-SVM) to accomplish the fault pattern identification. The proposed method is numerically and experimentally demonstrated to be able to recognize the different fault categories of planetary gearboxes. <s> BIB003 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> A. SYMBOLIC DYNAMIC ENTROPY <s> Abstract This paper proposes a novel fault diagnosis method based on variational mode decomposition (VMD) and generalized composite multi-scale symbol dynamic entropy (GCMSDE) to identify the different health conditions of planetary gearboxes. First, VMD is adopted to remove the noises and highlight the fault symptoms. Second, GCMSDE is utilized to extract the fault features from the denoised vibration signals. Third, the Laplacian score (LS) approach is employed to refine the fault features. Finally, the new features are fed into Softmax regression to identify the health conditions of planetary gearboxes. The proposed method is numerically and experimentally demonstrated to be able to differentiate seven localized fault types on the sun gear, planet gear and ring gear of planetary gearboxes. <s> BIB004
Recently, Li et al. BIB001 proposed a new entropy method, namely symbolic dynamic entropy (SDE), to assess the dynamical characteristics of time series. Known that SampEn and PE are two most widely used entropy methods. However, SampEn is not fast enough especially in the analysis of long time duration signals. PE, though faster than SampEn, only utilizes the amplitude information of the time series, which is easily affected by the noises BIB002 . To fill this research gap, SDE utilizes the symbolization procedure to eliminate background noise. Also, SDE reserve the fault information using the probability of state pattern and the state transition BIB001 . SDE has been demonstrated to have better performance in detecting the dynamical change of time series using both simulated and experimental signals. SDE has obvious advantages, such as high calculation efficiency and robust to noise. The main calculation steps can be seen in Figure 14 . Details about SDE can refer to BIB001 . In addition, SDE is extended to multiscale symbolic dynamic entropy (MSDE) BIB001 , refined composite multiscale symbolic dynamic entropy BIB003 , hierarchical symbol dynamic entropy BIB002 , and generalized multiscale symbolic dynamic entropy (GCMSDE) BIB004 for comprehensive analysis of vibration signals of rotating machinery. Until now, SDE and its various improvements have been successfully applied in the fault diagnosis of rolling bearings and gearboxes.