The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 4) MODIFIED MULTISCALE FUZZY ENTROPY <s> Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series. <s> BIB001 </s> The Entropy Algorithm and Its Variants in the Fault Diagnosis of Rotating Machinery: A Review <s> 4) MODIFIED 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> BIB002
Modified multiscale fuzzy entropy (MMFE) is proposed by Li et al. BIB002 to overcome the data length decreasing during the coarse-graining procedure in MFE method. Combined local mean decomposition (LMD) and SVM, the LMD-MMFE method is demonstrated to be effective in recognizing 10 bearing fault types and severities BIB002 . The concept of MMFE is defined as follows. (1) The modified multiscale time series can be obtained using Eq. BIB001 . (2) Calculate the FE for each improved coarse-grained time series.