The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 2) WAVELET ENTROPY <s> Since traditional electrical brain signal analysis is mostly qualitative, the development of new quantitative methods is crucial for restricting the subjectivity in the study of brain signals. These methods are particularly fruitful when they are strongly correlated with intuitive physical concepts that allow a better understanding of brain dynamics. Here, new method based on orthogonal discrete wavelet transform (ODWT) is applied. It takes as a basic element the ODWT of the EEG signal, and defines the relative wavelet energy, the wavelet entropy (WE) and the relative wavelet entropy (RWE). The relative wavelet energy provides information about the relative energy associated with different frequency bands present in the EEG and their corresponding degree of importance. The WE carries information about the degree of order:disorder associated with a multi-frequency signal response, and the RWE measures the degree of similarity between different segments of the signal. In addition, the time evolution of the WE is calculated to give information about the dynamics in the EEG records. Within this framework, the major objective of the present work was to characterize in a quantitative way functional dynamics of order:disorder microstates in short duration EEG signals. For that aim, spontaneous EEG signals under different physiological conditions were analyzed. Further, specific quantifiers were derived to characterize how stimulus affects electrical events in terms of frequency synchronization (tuning) in the event related potentials. © 2001 Published by Elsevier Science B.V. <s> BIB001 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 2) WAVELET ENTROPY <s> Abstract Planetary gearboxes significantly differ from fixed-axis gearboxes and exhibit unique behaviors, which invalidate fault diagnosis methods working well for fixed-axis gearboxes. Much work has been done for condition monitoring and fault diagnosis of fixed-axis gearboxes, while studies on planetary gearboxes are not that many. However, we still notice that a number of publications on condition monitoring and fault diagnosis of planetary gearboxes have appeared in academic journals, conference proceedings and technical reports. This paper aims to review and summarize these publications and provide comprehensive references for researchers interested in this topic. The structures of a planetary gearbox as well as a fixed-axis one are briefly introduced and contrasted. The unique behaviors and fault characteristics of planetary gearboxes are identified and analyzed. Investigations on condition monitoring and fault diagnosis of planetary gearboxes are summarized based on the adopted methodologies. Finally, open problems are discussed and potential research topics are pointed out. <s> BIB002 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 2) WAVELET ENTROPY <s> Abstract In order to improve the accuracy of fault diagnosis, this article proposes a multi-fault diagnosis method for rotating machinery based on orthogonal supervised linear local tangent space alignment (OSLLTSA) and least square support vector machine (LS-SVM). First, the collected vibration signals are decomposed by empirical model decomposition (EMD), and a high-dimensional feature set is constructed by extracting statistical features, autoregressive (AR) coefficients and instantaneous amplitude Shannon entropy from those intrinsic model functions (IMFs) that contain most fault information. Then, the high-dimensional feature set is inputted into OSLLTSA for dimension reduction to yield more sensitive low-dimensional fault features, which not only achieves the combination of intrinsic structure information and class label information of dataset but also improves the discrimination of the low-dimensional fault features. Further, the low-dimensional fault features are inputted to LS-SVM to recognize machinery faults according to the LS-SVM parameters selected by enhanced particle swarm optimization (EPSO). Finally, the performance of the proposed method is verified by a fault diagnosis case in a rolling element bearing, and the results confirm the improved accuracy of fault diagnosis. <s> BIB003
Wavelet entropy (WaEn) estimates the complexity of time series by quantifying the degree of similarity between different fractions of signals. In other words, WaEn is a indicator of the disorder degree associated with the multi-frequency signal response BIB003 . WaEn can recognize the underlying episodic dynamic behavior of a signal. Also, WaEn can provide an accurate complexity estimation for a periodic mono-frequency signal BIB001 . The definition of wavelet entropy is given in Eq. BIB002 . where p i denotes the probability distribution of time series. i represents different resolution levels.