Dynamic characteristics of absence EEG recordings with multiscale permutation entropy analysis

A method based on compound multiscale permutation entropy, support vector machine, and particle swarm optimization for roller bearings fault diagnosis was presented in this study. Firstly, the roller bearings vibration signals under different conditions were decomposed into permutation entropy values by the multiscale permutation entropy and compound multiscale permutation entropy methods. The compound multiscale permutation entropy model combined the different graining sequence information under each scale factor. The average value of each scale factor was regarded as the final entropy value in the compound multiscale permutation entropy model. The compound multiscale permutation entropy model suppressed the shortcomings of poor stability caused by the length of the original signals in the multiscale permutation entropy model. Validity and accuracy are considered in the numerical experiments, and then compared with the computational efficiency of the multiscale permutation entropy method. Secondly, the entropy values of the multiscale permutation entropy/compound multiscale permutation entropy under different scales are regarded as the input of the particle swarm optimization–support vector machine models for fulfilling the fault identification, the classification accuracy is used to verify the effectiveness of the multiscale permutation entropy/compound multiscale permutation entropy with particle swarm optimization–support vector machine. Finally, the experimental results show that the classification accuracy of the compound multiscale permutation entropy model is higher than that of the multiscale permutation entropy.

In this study, we investigate multiscale entropy (MSE) as a tool to evaluate the dynamic characteristics of electroencephalogram (EEG) during seizure-free, pre-seizure and seizure state, respectively, in epileptic rats. The results show that MSE method is able to reveal that EEG signals are more complex in seizure-free state than in seizure state, and can successfully distinguish among different seizure states. The classification ability of the MSE measures is tested using the linear discriminant analysis (LDA). Test results confirm that the classification accuracy of MSE method is superior to traditional single-scale entropy method. MSE method has potential in classifying the epileptic EEG signals.

A comparative study of four multi-scale entropies combined with grey relational degree in classification of ship-radiated noise

Financial time series analysis using the relation between MPE and MWPE

Variational mode decomposition is a new signal decomposition method, which can process non-linear and non-stationary signals. It can overcome the problems of mode mixing and compensate for the shortcomings in empirical mode decomposition. Permutation entropy is a method which can detect the randomness and kinetic mutation behavior of a time series. It can be considered for use in fault diagnosis. The complexity of wind power generation systems means that the randomness and kinetic mutation behavior of their vibration signals are displayed at different scales. Multi-scale permutation entropy analysis is therefore needed for such vibration signals. This research investigated a method based on variational mode decomposition and permutation entropy for the fault diagnosis of a wind turbine roller bearing. Variational mode decomposition was adopted to decompose the bearing vibration signal into its constituent components. The components containing key fault information were selected for the extraction of their permutation entropy. This entropy was used as a bearing fault characteristic value. The nearest neighbor algorithm was employed as a classifier to identify faults in a roller bearing. The experimental data showed that the proposed method can be applied to wind turbine roller bearing fault diagnosis.

It is an important practical problem to accurately recognize whether biological tissue is denatured during high intensity focused ultrasound (HIFU) treatment. Ultrasonic scattering echo signals are related to some physical properties of biological tissues. According to the characteristics of ultrasonic scattering echo signals, the recognition of denatured biological tissues is studied based on the variational mode decomposition (VMD) and multi-scale permutation entropy (MPE) in this paper. The ultrasonic echo signals are decomposed into various modal components by the VMD. The noise components and the useful components are separated according to the power spectrum information entropy of various modal components. The separated useful signals are reconstructed and the MPE are extracted. Furthermore, Gustafson-Kessel (GK) fuzzy clustering analysis is employed to obtain the standard clustering center, and the recognition of denatured biological tissues is carried out by Euclid approach degree and principle of proximity. The proposed method is applied to ultrasonic scattering echo signal during HIFU treatment. In order to determine the parameters of MPE algorithm for ultrasonic scattering echo signals, the embedding dimension of the MPE is discussed, and the scale factor of the MPE algorithm is optimized by genetic algorithm. When the delay time and the embedding dimension are 2 and 7 respectively, the MPE values decrease with scale factor increasing. Assuming that the scale factor is 12 from optimization results, the 293 ultrasonic scattering echo signals from normal tissues and denatured tissues are analyzed by the MPE. It is found that the MPE values of the denatured tissues are higher than those of the normal tissues. The MPE can be used to distinguish normal tissues and denatured tissues. Comparing with the recognition methods of the EMD-MPE-GK fuzzy clustering method and the VMD-WE-GK fuzzy clustering, the proposed method has good clustering performance and separability. Its partition coefficient (PC) is close to 1 and the Xie-Beni (XB) index is smaller. There are fewer feature points in the overlap region between MPE features of denatured tissues and normal tissues. The recognition results of denatured biological tissues in this experimental environment show that the recognition rate based on this method is higher, reaching up to 93.81%.

Fault diagnosis of rotating machinery is vital to identify incipient failures and avoid unexpected downtime in industrial systems. This paper proposes a new rolling bearing fault diagnosis method by integrating the fine-to-coarse multiscale permutation entropy (F2CMPE), Laplacian score (LS) and support vector machine (SVM). A novel entropy measure, named F2CMPE, was proposed by calculating permutation entropy via multiple-scale fine-grained and coarse-grained signals based on the wavelet packet decomposition. The entropy measure estimates the complexity of time series from both low- and high-frequency components. Moreover, the F2CMPE mitigates the drawback of producing time series with sharply reduced data length via the coarse-grained procedure in the conventional composite multiscale permutation entropy (CMPE). The comparative performance of the F2CMPE and CMPE is investigated by analyzing the synthetic and experimental signals for entropy-based feature extraction. In the proposed bearing fault diagnosis method, the F2CMPE is first used to extract the entropy-based features from bearing vibration signals. Then, LS and SVM are used for selection of features and fault classification, respectively. Finally, the effectiveness of the proposed method is verified for rolling bearing fault diagnosis using experimental vibration data sets, and the results have demonstrated the capability of the proposed method to recognize and identify the bearing fault patterns under different fault states and severity levels.

Quantifying the complexity of the EEG signal during prolonged wakefulness and during sleep is gaining interest as an additional mean to characterize the mechanisms associated with sleep and wakefulness regulation. Here, we characterized how EEG complexity, as indexed by Multiscale Permutation Entropy (MSPE), changed progressively in the evening prior to light off and during the transition from wakefulness to sleep. We further explored whether MSPE was able to discriminate between wakefulness and sleep around sleep onset and whether MSPE changes were correlated with spectral measures of the EEG related to sleep need during concomitant wakefulness (theta power-Ptheta: 4-8 Hz). To address these questions, we took advantage of large datasets of several hundred of ambulatory EEG recordings of individual of both sexes aged 25-101 years. Results show that MSPE significantly decreases before light off (i.e. before sleep time) and in the transition from wakefulness to sleep onset. Furthermore, MSPE allows for an excellent discrimination between pre-sleep wakefulness and early sleep. Finally, we show that MSPE is correlated with concomitant Ptheta. Yet, the direction of the latter correlation changed from before light-off to the transition to sleep. Given the association between EEG complexity and consciousness, MSPE may track efficiently putative changes in consciousness preceding sleep onset. An MSPE stands as a comprehensive measure that is not limited to a given frequency band and reflects a progressive change brain state associated with sleep and wakefulness regulation. It may be an effective mean to detect when the brain is in a state close to sleep onset.

Multiscale Permutation Entropy (MPE) analysis is a powerful ordinal tool in the measurement of information content of time series. MPE refinements, such as Composite MPE (cMPE) and Refined Composite MPE (rcMPE), greatly increase the precision of the entropy estimation by modifying the original method. Nonetheless, these techniques have only been proposed as algorithms, and are yet to be described from the theoretical perspective. Therefore, the purpose of this article is two-fold. First, we develop the statistical theory behind cMPE and rcMPE. Second, we propose an alternative method, Refined Composite Downsampling Permutation Entropy (rcDPE) to further increase the entropy estimation’s precision. Although cMPE and rcMPE outperform MPE when applied on uncorrelated noise, the results are higher than our predictions due to inherent redundancies found in the composite algorithms. The rcDPE method, on the other hand, not only conforms to our theoretical predictions, but also greatly improves over the other methods, showing the smallest bias and variance. By using MPE, rcMPE and rcDPE to classify faults in bearing vibration signals, rcDPE outperforms the multiscaling methods, enhancing the difference between faulty and non-faulty signals, provided we apply a proper anti-aliasing low-pass filter at each time scale.

A new rolling bearing fault diagnosis approach based on multiscale permutation entropy (MPE), Laplacian score (LS), and support vector machines (SVMs) is proposed in this paper. Permutation entropy (PE) was recently proposed and defined to measure the randomicity and detect dynamical changes of time series. However, for the complexity of mechanical systems, the randomicity and dynamic changes of the vibration signal will exist in different scales. Thus, the definition of MPE is introduced and employed to extract the nonlinear fault characteristics from the bearing vibration signal in different scales. Besides, the SVM is utilized to accomplish the fault feature classification to fulfill diagnostic procedure automatically. Meanwhile, in order to avoid a high dimension of features, the Laplacian score (LS) is used to refine the feature vector by ranking the features according to their importance and correlations with the main fault information. Finally, the rolling bearing fault diagnosis method based on MPE, LS, and SVM is proposed and applied to the experimental data. The experimental data analysis results indicate that the proposed method could identify the fault categories effectively.

Considering the diversity, complexity and uncertainty existing in bearing vibrations, an extended intelligent identification paradigm for bearing faults was proposed based on multiscale permutation entropy (MPE) and extension theory. MPE can reflect the random degree and detect the dynamic mutation of time series over subsequent scales, while extension theory provides an approach to address the extensibility and regularity of complicated problems. In the present paradigm, MPE was employed to compute the entropies over multiple scales as an original feature vector to represent bearing vibrations, which were then graded using Fisher ratio to choose the most informative features. The chosen features were exploited to determine the classical domain and joint domain of matter elements associated with various bearing health conditions. Bearing fault pattern was assigned to the one with maximum dependence degree among the afore-constructed matter elements. An experiment was conducted on an electrical motor involving four bearing conditions including normal, inner race, outer race and rolling element faults. The test was repeated 100 times with an averaged rate of 92.2% by the proposed method which outperforms the method using multiscale sample entropy and extension theory.

Automatic detection of absence seizures with compressive sensing EEG

In order to solve the shortcoming of multi-scale weighted permutation entropy ignoring high-frequency components, this paper proposes a new nonlinear dynamics analysis method, which is called hierarchical weighted permutation entropy. This method can fully and accurately reflect the low-frequency and high-frequency information of the time series. Based on this, a new intelligent fault diagnosis method for common rail injector based on hierarchical weighted permutation entropy and LSSVM is proposed. Through simulation signal and experimental data analysis, the proposed method is compared with the fault diagnosis method based on multi-scale permutation entropy and multi-scale weighted permutation entropy. The results show that HWPE can more comprehensively reflect the fault information and the proposed diagnosis method has a higher fault recognition rate and stronger robustness.

Aiming to address the nonlinear and non-stationary characteristics of rolling bearing fault vibration signals, traditional diagnostic methods face challenges such as mode mixing, insufficient feature discrimination, and sensitivity to classifier parameters, which limit further improvements in diagnostic accuracy. This paper proposes a comprehensive optimization framework for fault diagnosis, covering signal decomposition and fault feature classification. First, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is applied to decompose the signal into intrinsic mode functions (IMF), effectively suppressing mode mixing. Next, the correlation coefficient and multiscale permutation entropy (MPE) are employed to quantify the dynamic complexity of each IMF across multiple scales, enabling the extraction of highly discriminative multidimensional feature vectors. Finally, the black-winged kite algorithm (BKA) is used to optimize the penalty factor and kernel parameters of the least squares support vector machine (LSSVM). BKA achieves a dynamic balance between local exploitation and global exploration, and its integration with Cauchy mutation improves robustness to noise, thereby enhancing convergence speed and stability. Experimental results from publicly available datasets and a custom experimental platform show that the proposed approach effectively distinguishes among various fault types, offering superior performance, improved interpretability, and enhanced robustness.

The slope fitting line between MPE (multi-scale permutation entropy) and MWPE (multi-scale weighted permutation entropy) is recently proposed as a discriminant statistic for testing the nonlinearity of a time series. The main objective of this paper is to demonstrate that the selection of the optimal parameters of the non-uniform embedding is essential for the proposed discriminant statistic. In particular, the presented case studies indicate that the modified discriminant statistic based on non-uniform embedding can detect differences between such time series which remain indistinguishable if the original approach is used.