The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy

On the Genuine Relevance of the Data-Driven Signal Decomposition-Based Multiscale Permutation Entropy

Ordinal pattern-based approaches have great potential to capture intrinsic structures of dynamical systems, and therefore, they continue to be developed in various research fields. Among these, the permutation entropy (PE), defined as the Shannon entropy of ordinal probabilities, is an attractive time series complexity measure. Several multiscale variants (MPE) have been proposed in order to bring out hidden structures at different time scales. Multiscaling is achieved by combining linear or nonlinear preprocessing with PE calculation. However, the impact of such a preprocessing on the PE values is not fully characterized. In a previous study, we have theoretically decoupled the contribution of specific signal models to the PE values from that induced by the inner correlations of linear preprocessing filters. A variety of linear filters such as the autoregressive moving average (ARMA), Butterworth, and Chebyshev were tested. The current work is an extension to nonlinear preprocessing and especially to data-driven signal decomposition-based MPE. The empirical mode decomposition, variational mode decomposition, singular spectrum analysis-based decomposition and empirical wavelet transform are considered. We identify possible pitfalls in the interpretation of PE values induced by these nonlinear preprocessing, and hence, we contribute to improving the PE interpretation. The simulated dataset of representative processes such as white Gaussian noise, fractional Gaussian processes, ARMA models and synthetic sEMG signals as well as real-life sEMG signals are tested.

Experimental Investigation and Fault Diagnosis for Buckled Wet Clutch Based on Multi-Speed Hilbert Spectrum Entropy

The multi-disc wet clutch is widely used in transmission systems as it transfers the torque and power between the gearbox and the driving engine. During service, the buckling of the friction components in the wet clutch is inevitable, which can shorten the lifetime of the wet clutch and decrease the vehicle performance. Therefore, fault diagnosis and online monitoring are required to identify the buckling state of the friction components. However, unlike in other rotating machinery, the time-domain features of the vibration signal lack efficiency in fault diagnosis for the wet clutch. This paper aims to present a new fault diagnosis method based on multi-speed Hilbert spectrum entropy to classify the buckling state of the wet clutch. Firstly, the wet clutch is classified depending on the buckling degree of the disks, and then a bench test is conducted to obtain vibration signals of each class at varying speeds. By comparing the accuracy of different classifiers with and without entropy, Hilbert spectrum entropy shows higher efficiency than time-domain features for the wet clutch diagnosis. Thus, the classification results based on multi-speed entropy achieve even better accuracy.

The Refined Composite Downsampling Permutation Entropy Is a Relevant Tool in the Muscle Fatigue Study Using sEMG Signals

Surface electromyography (sEMG) is a valuable technique that helps provide functional and structural information about the electric activity of muscles. As sEMG measures output of complex living systems characterized by multiscale and nonlinear behaviors, Multiscale Permutation Entropy (MPE) is a suitable tool for capturing useful information from the ordinal patterns of sEMG time series. In a previous work, a theoretical comparison in terms of bias and variance of two MPE variants—namely, the refined composite MPE (rcMPE) and the refined composite downsampling (rcDPE), was addressed. In the current paper, we assess the superiority of rcDPE over MPE and rcMPE, when applied to real sEMG signals. Moreover, we demonstrate the capacity of rcDPE in quantifying fatigue levels by using sEMG data recorded during a fatiguing exercise. The processing of four consecutive temporal segments, during biceps brachii exercise maintained at 70% of maximal voluntary contraction until exhaustion, shows that the 10th-scale of rcDPE was capable of better differentiation of the fatigue segments. This scale actually brings the raw sEMG data, initially sampled at 10 kHz, to the specific 0–500 Hz sEMG spectral band of interest, which finally reveals the inner complexity of the data. This study promotes good practices in the use of MPE complexity measures on real data.

Coal and Rock Hardness Identification Based on EEMD and Multi-Scale Permutation Entropy

This study offers an efficient hardness identification approach to address the problem of poor real-time performance and accuracy in coal and rock hardness detection. To begin, Ensemble Empirical Mode Decomposition (EEMD) was performed on the current signal of the cutting motor to obtain a number of Intrinsic Mode Functions (IMFs). Further, the target signal was selected among the IMFs to reconstruct the current signal according to the energy density and correlation coefficient criteria. After that, the Multi-scale Permutation Entropy (MPE) of the reconstructed signal was trained by the Adaboost improved Back Propagation (BP) neural network, in order to establish the hardness recognition model. Finally, the cutting arm’s swing speed and the cutting head’s rotation speed were adjusted based on the coal and rock hardness. The simulation results indicated that using the energy density and correlation criterion to reconstruct the signal can successfully filter out noise interference. Compared to the BP model, the relative root-mean-square error of the Adaboost-BP model decreased by 0.0633, and the prediction results were more accurate. Additionally, the speed control strategy based on coal and rock hardness can ensure the efficient cutting of the roadheader.