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The study focuses on the fault signals of rolling bearings, which are characterized by nonlinearity, periodic impact, and low signal-to-noise ratio. The advantages of entropy calculation in analyzing time series data were combined with the high calculation accuracy of Multiscale Fuzzy Entropy (MFE) and the strong noise resistance of Multiscale Permutation Entropy (MPE), a multivariate coarse-grained form was introduced, and the coarse-grained process was improved. The Composite Multivariate Multiscale Permutation Fuzzy Entropy (CMvMPFE) method was proposed to solve the problems of low accuracy, large entropy perturbation, and information loss in the calculation process of fault feature parameters. This method extracts the fault characteristics of rolling bearings more comprehensively and accurately. The CMvMPFE method was used to calculate the entropy value of the rolling bearing experimental fault data, and Support Vector Machine (SVM) was used for fault diagnosis analysis. By comparing with MPFE, the Composite Multiscale Permutation Fuzzy Entropy (CMPFE) and the Multivariate Multiscale Permutation Fuzzy Entropy (MvMPFE) methods, the results of the calculations show that the CMvMPFE method can extract rolling bearing fault characteristics more comprehensively and accurately, and it also has good robustness.

The vibration signals of rolling bearings are often nonlinear and non-stationary. Multiscale entropy (MSE) has been widely applied to measure the complexity of nonlinear mechanical vibration signals, however, at present only the single channel vibration signals are used for fault diagnosis by many scholars. In this paper multiscale entropy in multivariate framework, i.e., multivariate multiscale entropy (MMSE) is introduced to machinery fault diagnosis to improve the efficiency of fault identification as much as possible through using multi-channel vibration information. MMSE evaluates the multivariate complexity of synchronous multi-channel data and is an effective method for measuring complexity and mutual nonlinear dynamic relationship, but its statistical stability is poor. Refined composite multivariate multiscale fuzzy entropy (RCMMFE) was developed to overcome the problems existing in MMSE and was compared with MSE, multiscale fuzzy entropy, MMSE and multivariate multiscale fuzzy entropy by analyzing simulation data. Finally, a new fault diagnosis method for rolling bearing was proposed based on RCMMFE for fault feature extraction, Laplacian score and particle swarm optimization support vector machine (PSO-SVM) for automatic fault mode identification. The proposed method was compared with the existing methods by analyzing experimental data analysis and the results indicate its effectiveness and superiority.

To abstract the fault features from multivariate vibration signals of the rotating machinery under different speeds, an improved multivariate multiscale fuzzy distribution entropy (IMMFDE) is proposed. Based on multivariate empirical mode decomposition, the IMMFDE can determine the maximum scale adaptively, meanwhile eliminate the frequency aliasing and avoid the loss of potentially useful information in the multiscale process. The trait of IMMFDE is verified by calculating the sequences and their amplitude spectrums at each scale of the simulated multivariate signals. Further, the fault diagnosis method is proposed for the rotating machinery under different speeds based on IMMFDE. In the method, the statistical parameters and IMMFDE are calculated as fault feature set; then, support vector machine is used for fault diagnosis. Applying the method to two types of the rotating machinery multi-fault diagnosis under different speeds, the results show the proposed method can obtain better fault diagnosis results.

The recently introduced multivariate multiscale entropy (MMSE) has been successfully used to quantify structural complexity in terms of nonlinear within- and cross-channel correlations as well as to reveal complex dynamical couplings and various degrees of synchronization over multiple scales in real-world multichannel data. However, the applicability of MMSE is limited by the coarse-graining process which defines scales, as it successively reduces the data length for each scale and thus yields inaccurate and undefined entropy estimates at higher scales and for short length data. To that cause, we propose the multivariate multiscale fuzzy entropy (MMFE) algorithm and demonstrate its superiority over the MMSE on both synthetic as well as real-world uterine electromyography (EMG) short duration signals. Based on MMFE features, an improvement in the classification accuracy of term-preterm deliveries was achieved, with a maximum area under the curve (AUC) value of 0.99.

The results showed that during reactive hyperemia and the biphasic response induced by local heating, the modified sample entropy in diabetics presents only small changes compared to baseline but undergoes significant changes in controls. [...]during baseline and skin blood flow responses—except for the pressure loading period—the modified sample entropy at small scales exhibits different transitions between the two groups. [...]different multiclass classifiers were tested: logistic discriminant analysis (LDA), quadratic discriminant analysis (QDA), and multilayer perceptron neural network (MLP). The authors showed that their approach significantly improved the classification recognition rate compared with the traditional sample entropy, fuzzy entropy, and combination entropy. [...]fuzzy entropy and combination entropy associated with kernel principal component analysis give worse results than those obtained with sample entropy and kernel principal component analysis. The authors also concluded that downsampling within the coarse-graining procedure may not be needed to quantify the complexity of signals, especially for short ones. [...]the authors showed that dispersion entropy leads to more stable results than sample entropy in the estimations based on coefficient of variation values and ensures that the entropy values are defined at all temporal scales.

Pattern synchronization (PS) can capture one aspect of the dynamic interactions between bivariate physiological systems. It can be tested by several entropy-based measures, e.g., cross sample entropy (X-SampEn), cross fuzzy entropy (X-FuzzyEn), multivariate multiscale entropy (MMSE), etc. A comprehensive comparison on their distinguishability is currently missing. Besides, they are highly dependent on several pre-defined parameters, the threshold value r in particular. Thus, their consistency also needs further elucidation. Based on the well-accepted assumption that a tight coupling necessarily leads to a high PS, we performed a couple of evaluations over several simulated coupled models in this study. All measures were compared to each other with respect to their consistency and distinguishability, which were quantified by two pre-defined criteria—degree of crossing (DoC) and degree of monotonicity (DoM). Results indicated that X-SampEn and X-FuzzyEn could only work well over coupled stochastic systems with meticulously selected r . It is thus not recommended to apply them to the intrinsic complex physiological systems. However, MMSE was suitable for both, indicating by relatively higher DoC and DoM values. Final analysis on the cardiorespiratory coupling validated our results.