Multiscale Fuzzy Entropy Research Articles

Intelligent Fault Diagnosis of Rolling Bearings Based on a Complete Frequency Range Feature Extraction and Combined Feature Selection Methodology

The utilization of multiscale entropy methods to characterize vibration signals has proven to be promising in intelligent diagnosis of mechanical equipment. However, in the current multiscale entropy methods, only the information in the low-frequency range is utilized and the information in the high-frequency range is discarded. In order to take full advantage of the information, in this paper, a fault feature extraction method utilizing the bidirectional composite coarse-graining process with fuzzy dispersion entropy is proposed. To avoid the redundancy of the full frequency range feature information, the Random Forest algorithm combined with the Maximum Relevance Minimum Redundancy algorithm is applied to feature selection. Together with the K-nearest neighbor classifier, a rolling bearing intelligent diagnosis framework is constructed. The effectiveness of the proposed framework is evaluated by a numerical simulation and two experimental examples. The validation results demonstrate that the extracted features by the proposed method are highly sensitive to the bearing health conditions compared with hierarchical fuzzy dispersion entropy, composite multiscale fuzzy dispersion entropy, multiscale fuzzy dispersion entropy, multiscale dispersion entropy, multiscale permutation entropy, and multiscale sample entropy. In addition, the proposed method is able to identify the fault categories and health states of rolling bearings simultaneously. The proposed damage detection methodology provides a new and better framework for intelligent fault diagnosis of rolling bearings in rotating machinery.

A hybrid model for multistep-ahead significant wave height prediction using an innovative decomposition–reconstruction framework and E-GRU

As waves are exploited as renewable energy, developing new forecasting technologies is essential to accurately predict significant wave height. In this study, a wave height prediction model is proposed that includes a decomposition–reconstruction framework and ensemble gated recurrent unit (E-GRU). First, variational mode decomposition (VMD) decomposes the original wave height series into multiple subsequences to decrease the uncertainty and nonstationarity of the data. Second, the refined composite multiscale fuzzy entropy (RCMFE) is adopted to reconstruct subsequences into several components to reduce the computational complexity. A GRU is then used to predict each component individually to capture more temporal information from historical data. Finally, we predict all the subresults by E-GRU and obtain the final result. We test the proposed hybrid model using wave height data from three buoy stations. The comparative evaluation of prediction accuracy across four models is achieved through the utilization of key performance metrics, namely, the coefficient of determination (R2), Nash–Sutcliffe efficiency coefficient (ENS), Legates and McCabe index (ELM), Willmott's index (WI), root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE). Among these metrics, the VMD-RCMFE-E-GRU model distinctly emerges as the superior performer for forecasting hourly wave height across all stations and future temporal intervals, as evidenced by its notably lowest RMSE, MAE, and MAPE values, coupled with the highest R2, ENS, ELM, and WI scores. The case results show that the proposed hybrid model is more effective for wave height prediction.

Study on the optimization of the classification method of rolling bearing fault type and damage degree based on SFO–VMD

Currently, rolling bearings operate in harsh environments, resulting in acquired signals with a low signal-to-noise ratio. In light of this, this paper proposes an improved variational modal decomposition(VMD) combined with refine composite multi-scale fuzzy entropy (RCMFE) and linear support vector machine (LSVM) for fault diagnosis. Firstly, the sailfish optimization (SFO) algorithm is employed to optimize the important parameter combinations in the VMD algorithm, using the envelope entropy as its objective function. The analysis includes both simulated and real measured signals with varying signal-to-noise ratios. The results demonstrate that, compared to traditional manual parameter setting and empirical modal decomposition methods, this approach effectively addresses the parameter setting issue of VMD in the signal decomposition process. Additionally, it successfully eliminates noise to extract the fault characteristic signal hidden within the original signal. Secondly, the RCMFE algorithm is introduced to overcome the problem of commonly used dimensioned and dimensionless indicators being influenced by load and speed when used as characteristic indicators. By analyzing the influence of load and speed on the RCMFE value, the results demonstrate its strong stability as a feature indicator, unaffected by these factors. For the intelligent classification of failure type and damage degree, LSVM is chosen as the classification method. Analysis results indicate that the distribution characteristics of RCMFE values align better with LSVM compared to the common radial basis function support vector machine, resulting in a significant improvement in diagnosis accuracy.

Short-term wind speed forecasting based on a hybrid model of ICEEMDAN, MFE, LSTM and informer.

Wind energy, as a kind of environmentally friendly renewable energy, has attracted a lot of attention in recent decades. However, the security and stability of the power system is potentially affected by large-scale wind power grid due to the randomness and intermittence of wind speed. Therefore, accurate wind speed prediction is conductive to power system operation. A hybrid wind speed prediction model based on Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), Multiscale Fuzzy Entropy (MFE), Long short-term memory (LSTM) and INFORMER is proposed in this paper. Firstly, the wind speed data are decomposed into multiple intrinsic mode functions (IMFs) by ICEEMDAN. Then, the MFE values of each mode are calculated, and the modes with similar MFE values are aggregated to obtain new subsequences. Finally, each subsequence is predicted by informer and LSTM, each sequence selects the one with better performance than the two predictors, and the prediction results of each subsequence are superimposed to obtain the final prediction results. The proposed hybrid model is also compared with other seven related models based on four evaluation metrics under different prediction periods to verify its validity and applicability. The experimental results indicate that the proposed hybrid model based on ICEEMDAN, MFE, LSTM and INFORMER exhibits higher accuracy and greater applicability.

Multiscale Fuzzy Entropy-Based Feature Selection

In practice, it is common that there will be the same decision results under different scale conditions. Therefore, knowledge representation based on a single scale feature framework is far from meeting the needs of practical applications. Based on this, multi-scale data has received extensive attention. Feature selection is an important application of fuzzy multigranularity data analysis model. The existing multi-scale fuzzy granulation-based feature selection methods remove redundant or irrelevant features by selecting the optimal scale. However, this will lose the information corresponding to the remaining scale fuzzy granules, which will affect the classification results or learning tasks. Inspired by this, multi-scale fuzzy entropy is defined to fuse the granule information at different scales, and applied to feature selection. First, the feature with maximum multi-scale fuzzy mutual information is first selected. Then, the most significant features are gradually selected by evaluation metric that simultaneously considers the redundancy, relevance and complementary. A multi-scale fuzzy entropy-based feature selection (MFEFS) algorithm by means of this evaluation index is further designed. Finally, the proposed method is compared with some state-of-the-art methods. The experimental results show that the proposed algorithm has higher reduction efficiency than the comparison algorithms.

The Partial Reconstruction Symplectic Geometry Mode Decomposition and Its Application in Rolling Bearing Fault Diagnosis.

Extracting the fault characteristic information of rolling bearings from intense noise disturbance has been a heated research issue. Symplectic geometry mode decomposition (SGMD) has already been adopted for bearing fault diagnosis due to its advantages of no subjective customization of parameters and the ability to reconstruct existing modes. However, SGMD suffers from rapidly decreasing calculation efficiency as the amount of data increases, in addition to invalid symplectic geometry components affecting decomposition accuracy. The regularized composite multiscale fuzzy entropy (RCMFE) operator is constructed to evaluate the complexity of each initial single component and minimize the residual energy. Combined with the partial reconstruction threshold indicator to filter out specific significant initial single components, the raw signal can be decomposed into multiple physically meaningful symplectic geometric mode components. Therefore, the decomposition efficiency and accuracy can be enhanced. Thus, a rolling bearing fault diagnosis method is proposed based on partial reconstruction symplectic geometry mode decomposition (PRSGMD). Both simulated and experimental analysis results show that PRSGMD can improve the speed of SGMD analysis while increasing the decomposition accuracy, thereby augmenting the robustness and effectiveness of the algorithm.

Studying Dynamical Characteristics of Oxygen Saturation Variability Signals Using Haar Wavelet.

An aim of the analysis of biomedical signals such as heart rate variability signals, brain signals, oxygen saturation variability (OSV) signals, etc., is for the design and development of tools to extract information about the underlying complexity of physiological systems, to detect physiological states, monitor health conditions over time, or predict pathological conditions. Entropy-based complexity measures are commonly used to quantify the complexity of biomedical signals; however novel complexity measures need to be explored in the context of biomedical signal classification. In this work, we present a novel technique that used Haar wavelets to analyze the complexity of OSV signals of subjects during COVID-19 infection and after recovery. The data used to evaluate the performance of the proposed algorithms comprised recordings of OSV signals from 44 COVID-19 patients during illness and after recovery. The performance of the proposed technique was compared with four, scale-based entropy measures: multiscale entropy (MSE); multiscale permutation entropy (MPE); multiscale fuzzy entropy (MFE); multiscale amplitude-aware permutation entropy (MAMPE). Preliminary results of the pilot study revealed that the proposed algorithm outperformed MSE, MPE, MFE, and MMAPE in terms of better accuracy and time efficiency for separating during and after recovery the OSV signals of COVID-19 subjects. Further studies are needed to evaluate the potential of the proposed algorithm for large datasets and in the context of other biomedical signal classifications.

Regionalized fault line in distribution networks based on an improved SSA-VMD and multi-scale fuzzy entropy

Regionalized fault line in distribution networks based on an improved SSA-VMD and multi-scale fuzzy entropy

A new rotating machinery fault diagnosis method for different speeds based on improved multivariate multiscale fuzzy distribution entropy

A new rotating machinery fault diagnosis method for different speeds based on improved multivariate multiscale fuzzy distribution entropy

Use of Composite Multivariate Multiscale Permutation Fuzzy Entropy to Diagnose the Faults of Rolling Bearing.

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.

Fault Diagnosis Method of Planetary Gearbox Based on ISSA-VME and Multi-scale Fuzzy Entropy

To solve the problem of noise interference and difficulty in feature extraction of vibration signals of planetary gearbox, propose a fault diagnosis method of planetary gearbox based on improved sparrow search algorithm optimized variational mode extraction (ISSA-VME) and multi-scale fuzzy entropy (MFE). The vibration signal was decomposed by ISSA-VME, and the multi-scale fuzzy entropy of the original signal was calculated according to the IMF component. The fault feature set composed of MFE was applied to the SVM classifier optimized by the improved sparrow search algorithm for fault pattern recognition. The experimental results demonstrate that compared with ICEEMDAN and VMD methods, ISSA-VME has a better effect and higher efficiency on vibration signal decomposition. The identification rate of missing teeth, cracks, wear, and other faults of planetary gearbox sun gear by the proposed method reaches 97.50%.

Resting state EEG complexity as a predictor of cognitive performance

Sustained spontaneous activity in the resting state brain represents the intrinsic state of the brain during most cognitive tasks. Electroencephalogram (EEG) measures of the resting state have shown potential as biomarkers for the evaluation of cognitive performance, but there is a lack of validation across health and different diseased populations. This study aims to decode cognitive function from resting-state EEG activity, and demonstrates that nonlinear dynamic features of EEG signals can be used to predict cognitive performance in healthy young adults, elderly adults with mild cognitive impairment (MCI), and patients with major depressive disorder (MDD) using the extreme gradient boosting (XGBoost) prediction model. In particular, the results showed that performance in cognitive task can be predicted by the resting-state EEG-based measures in these three populations (correlation coefficients between predicted values and observed true values were: r=0.39, p < 0.01; r=0.76, p < 0.001; and r=0.40, p < 0.001; respectively). Furthermore, we observed a U-shaped or inverted U-shaped distribution of multiscale fuzzy entropy index (MFEI) in healthy, aging and diseased populations, which symbolizes the law of complexity and health. The results suggest that the dynamic complexity of resting state EEG oscillations can predict certain dimensions of cognitive function in both health and mental illness, and highlights the nonlinear relationship between neurological measures and cognitive health status. These findings may provide insights into the development of treatments to improve cognition.

Continuous monitoring of rolling element bearing health by nonlinear weighted squared envelope-based fuzzy entropy

Fuzzy entropy (FE) can be regarded as an effective measure for nonlinear characterization of rolling element bearing (REB) health condition by quantifying the complexity of vibration signals. However, during continuous monitoring operation under heavy noise, transient impulses corresponding to a REB fault get submerged under unnecessary random noise components. As a consequence, FE algorithm not only fails to detect a REB fault at the earliest point of inception but also performs poorly in monitoring the development of the incepted fault in an efficient manner. Aiming at solving the aforementioned limitations of FE in continuous monitoring of REB health, background noise associated with collected vibration signals is eliminated by weighting the corresponding square envelope signal. Due to the utilization of weighted squared envelope signal, the proposed measure is termed as weighted square envelope-based FE (WSEFE). One simulated case and two different run-to-failure experimental cases are used for validation. The comparison results demonstrate that the proposed WSEFE not only overcomes the limitations of original FE but also performs better than conventional permutation entropy and advanced FE-based measure multiscale FE (MFE) in continuous monitoring of REB health.

Evaluation on game concentration with multi-scale fuzzy entropy based on EEG signals

Concentration is the index to measure a person concentrating on certain thing or activity. Finding a valid physiological characteristic index to represent concentration level is important for attention training and experience improvement. In this study, the multi-scale fuzzy entropy (MSFEn) was proposed as an EEG feature to evaluate concentration level. Firstly, a game platform was designed independently to arouse the players’ concentration during the game, and the physical characteristics index Rect_y was defined to directly represent the players’ emotional concentration. Secondly, a portable single-channel EEG device was adopted to collect EEG signals of players during the experiment. Hilbert–Huang transform, the MSFEn and Grey correlation analysis were used for signal processing. The behavioral performances of participants were investigated with a questionnaire after each participant playing game. The statistical results showed that the MSFEn maintained a high correlation with the Rect_y at different game speeds and different scale factors for each player, with the median of about 70%. Compared with conditional entropies, the MSFEn can better reflect relatively short-term concentration and long-term overall game concentration of participants during the game.

Uncovering the Correlation between COVID-19 and Neurodegenerative Processes: Toward a New Approach Based on EEG Entropic Analysis.

COVID-19 is an ongoing global pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Although it primarily attacks the respiratory tract, inflammation can also affect the central nervous system (CNS), leading to chemo-sensory deficits such as anosmia and serious cognitive problems. Recent studies have shown a connection between COVID-19 and neurodegenerative diseases, particularly Alzheimer's disease (AD). In fact, AD appears to exhibit neurological mechanisms of protein interactions similar to those that occur during COVID-19. Starting from these considerations, this perspective paper outlines a new approach based on the analysis of the complexity of brain signals to identify and quantify common features between COVID-19 and neurodegenerative disorders. Considering the relation between olfactory deficits, AD, and COVID-19, we present an experimental design involving olfactory tasks using multiscale fuzzy entropy (MFE) for electroencephalographic (EEG) signal analysis. Additionally, we present the open challenges and future perspectives. More specifically, the challenges are related to the lack of clinical standards regarding EEG signal entropy and public data that can be exploited in the experimental phase. Furthermore, the integration of EEG analysis with machine learning still requires further investigation.

Intelligent fault detection scheme for constant-speed wind turbines based on improved multiscale fuzzy entropy and adaptive chaotic Aquila optimization-based support vector machine

Timely and effective fault detection is essential to ensure the safe and reliable operation of wind turbines. However, due to the complex kinematic mechanisms and harsh working environments of wind turbine equipment, it is difficult to extract sensitive features and detect faults from acquired wind turbine signals. To address this challenge, a novel intelligent fault detection scheme for constant-speed wind turbines based on refined time-shifted multiscale fuzzy entropy (RTSMFE), supervised isometric mapping (SI), and adaptive chaotic Aquila optimization-based support vector machine (ACAOSVM) is proposed. In the first step, the RTSMFE method is used to fully extract features of the wind turbine system. The time-shifted coarse-grained construction technique and a refined computing technique are adopted in the RTSMFE method to enhance the capability of traditional multiscale fuzzy entropy for measuring the complexity of signals. Subsequently, an effective manifold learning approach, SI, is applied to obtain the important and low-dimensional feature set from the high-dimensional feature set. Finally, sensitive features are fed into the ACAOSVM classifier to identify faults. The proposed ACAO algorithm is used to optimize important parameters of the SVM, thereby improving its detection performance. Simulations and wind turbine experiments verified that the proposed RTSMFE outperforms existing entropy techniques in terms of complexity measurement and feature extraction. Furthermore, the proposed ACAOSVM classifier is superior to existing advanced classifiers for fault pattern recognition. Finally, the proposed intelligent fault detection scheme can more correctly and efficiently detect wind turbine single/hybrid faults than other recently published schemes.

Forecasting carbon price in China using a novel hybrid model based on secondary decomposition, multi-complexity and error correction

As global warming intensifies, the reduction of carbon emissions is imminent. Carbon price is directly related to whether carbon can be effectively reduced. Therefore, accurately forecasting carbon price has important practical significance. Aiming at the nonstationary and nonlinear characteristics of carbon price, this paper proposes a novel hybrid model for forecasting carbon price, which is based on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), multiscale fuzzy entropy (MFE), complete ensemble empirical mode decomposition (CEEMD), improved random forest by salp swarm algorithm (SSARF), improved back propagation by cuckoo search (CSBP), improved extreme learning machine by whale optimization algorithm (WOAELM) and error correction (EC), named ICEEMDAN-MFE-CEEMD-SSARF-CSBP-WOAELM-EC. Firstly, carbon price is decomposed by ICEEMDAN, divided into high-, medium-, and low-complexity components by MFE. Secondly, high-complexity components are merged and secondarily decomposed by CEEMD, which are still recorded as high-complexity components. Then, SSARF, CSBP and WOAELM are used to forecast high-, medium-, and low-complexity components, respectively, and forecasting results are reconstructed. Finally, EC is carried out using an extreme learning machine to obtain the final forecasting results, and the Diebold-Mariano test is introduced for a comprehensive evaluation of the model. Taking carbon price in the pilot cities of Shenzhen and Hubei as examples, after 6 aspects and 20 comparative experiments, the results show that the proposed model has higher forecast accuracy, with MAPE, MAE and RMSE up to 0.03131, 0.00089 and 4.02e-06 in Hubei, and its forecasting ability is better than other commonly used international carbon financial price forecasting models, providing a theoretical and data basis for carbon pricing and formulating carbon reduction policies in China. The main contributions of this paper are the improved primary decomposition, the use of secondary decomposition, and the innovative combination of three optimal models to forecast carbon price, but it still needs to be optimized for practice.

Which Multivariate Multi-Scale Entropy Algorithm Is More Suitable for Analyzing the EEG Characteristics of Mild Cognitive Impairment?

So far, most articles using the multivariate multi-scale entropy algorithm mainly use algorithms to analyze the multivariable signal complexity without clearly describing what characteristics of signals these algorithms measure and what factors affect these algorithms. This paper analyzes six commonly used multivariate multi-scale entropy algorithms from a new perspective. It clarifies for the first time what characteristics of signals these algorithms measure and which factors affect them. It also studies which algorithm is more suitable for analyzing mild cognitive impairment (MCI) electroencephalograph (EEG) signals. The simulation results show that the multivariate multi-scale sample entropy (mvMSE), multivariate multi-scale fuzzy entropy (mvMFE), and refined composite multivariate multi-scale fuzzy entropy (RCmvMFE) algorithms can measure intra- and inter-channel correlation and multivariable signal complexity. In the joint analysis of coupling and complexity, they all decrease with the decrease in signal complexity and coupling strength, highlighting their advantages in processing related multi-channel signals, which is a discovery in the simulation. Among them, the RCmvMFE algorithm can better distinguish different complexity signals and correlations between channels. It also performs well in anti-noise and length analysis of multi-channel data simultaneously. Therefore, we use the RCmvMFE algorithm to analyze EEG signals from twenty subjects (eight control subjects and twelve MCI subjects). The results show that the MCI group had lower entropy than the control group on the short scale and the opposite on the long scale. Moreover, frontal entropy correlates significantly positively with the Montreal Cognitive Assessment score and Auditory Verbal Learning Test delayed recall score on the short scale.

Multiscale Fuzzy Entropy Analysis of Balance: Evidences of Scale-Dependent Dynamics on Diabetic Patients With and Without Neuropathy.

Postural control is usually assessed by examining the fluctuations of the center of pressure (COP). Balance maintenance is based on sensory feedback and neural interactions, deployed over multiple temporal scales and producing less complex outputs with aging and disease. This paper aims to investigate postural dynamics and complexity on diabetic patients, since diabetic neuropathy (DN) affects the somatosensory system and impairs postural steadiness. A multiscale fuzzy entropy (MSFEn) analysis, over a wide range of temporal scales, was performed on COP timeseries during unperturbed stance in a group of diabetic individuals without neuropathy and two groups of DN patients, with and without symptoms. A parameterization of the MSFEn curve is also proposed. A significant loss of complexity was recognized for the medial-lateral direction in DN groups with respect to non-neuropathic population. For the anterior-posterior direction, symptomatic DN group showed a lowered sway complexity for longer time scales with respect to non neuropathic and asymptomatic patients. The MSFEn approach and the related parameters highlighted that the loss of complexity might be attributed to different factors depending on sway direction, i.e. related to the presence of neuropathy along the medial-lateral axis and to a symptomatic state on the anterior-posterior direction. Results of this study support the use of the MSFEn for gaining insights into balance control mechanisms for diabetic patients, in particular when comparing non neuropathic with neuropathic asymptomatic patients, whose identification by posturographic analysis would be of great value.

Rolling Bearing Fault Diagnosis Method Based on MCMF and SAIMFE

Fault diagnosis of rolling bearing is important for ensuring the safe operation of industrial machinery. In order to improve diagnosis accuracy of bearing fault, a rolling bearing fault diagnosis method based on multiscale combined morphological filter (MCMF) and self-adaption improved multiscale fuzzy entropy (SAIMFE) is proposed in this paper. First, the MCMF is designed to eliminate noise and preserve fault information more effectively. Second, SAIMFE is proposed to extract bearing fault features, and the optimized scale factor of SAIMFE is determined based on the absolute skewness. Third, some experiments are completed to demonstrate the effectiveness and superiority of the proposed method. The experimental results show that the proposed method not only has high diagnosis accuracy but also less dependent on the diagnosis model.