Composite Multiscale Fuzzy Entropy Research Articles

Refined offshore wind speed prediction: Leveraging a two-layer decomposition technique, gated recurrent unit, and kernel density estimation for precise point and interval forecasts

Precise forecasting of offshore wind speeds is paramount for various applications, including offshore wind energy production, disaster prevention and mitigation, and maritime navigation. This study introduces a novel model for point and interval prediction of offshore wind speed, incorporating an innovative two-layer decomposition technique, gated recurrent unit (GRU), and kernel density estimation (KDE). Initially, the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is utilized to decompose the raw series into multiple subsequences, thus alleviating the inherent data nonstationarity. Subsequently, we employ the refined composite multiscale fuzzy entropy (RCMFE) to reconstruct the subsequences into multiple components, thereby reducing the computational complexity. Variational mode decomposition (VMD) is utilized to enhance the modeling accuracy to decompose the high-frequency component, thereby generating a set of submodels. The GRU, a specialized recurrent neural network architecture, is leveraged to forecast the remaining components and submodels, producing a series of subresults. The subresults are linearly summed to obtain the final point prediction result. Finally, based on point prediction, employing KDE to gauge the probability density distribution of prediction errors culminates in the derivation of the offshore wind speed prediction interval. The experimental results substantiate the superior predictive performance of the proposed prediction model.

Adaptive DBSCAN Clustering and GASA Optimization for Underdetermined Mixing Matrix Estimation in Fault Diagnosis of Reciprocating Compressors.

Underdetermined blind source separation (UBSS) has garnered significant attention in recent years due to its ability to separate source signals without prior knowledge, even when sensors are limited. To accurately estimate the mixed matrix, various clustering algorithms are typically employed to enhance the sparsity of the mixed matrix. Traditional clustering methods require prior knowledge of the number of direct signal sources, while modern artificial intelligence optimization algorithms are sensitive to outliers, which can affect accuracy. To address these challenges, we propose a novel approach called the Genetic Simulated Annealing Optimization (GASA) method with Adaptive Density-Based Spatial Clustering of Applications with Noise (DBSCAN) clustering as initialization, named the CYYM method. This approach incorporates two key components: an Adaptive DBSCAN to discard noise points and identify the number of source signals and GASA optimization for automatic cluster center determination. GASA combines the global spatial search capabilities of a genetic algorithm (GA) with the local search abilities of a simulated annealing algorithm (SA). Signal simulations and experimental analysis of compressor fault signals demonstrate that the CYYM method can accurately calculate the mixing matrix, facilitating successful source signal recovery. Subsequently, we analyze the recovered signals using the Refined Composite Multiscale Fuzzy Entropy (RCMFE), which, in turn, enables effective compressor connecting rod fault diagnosis. This research provides a promising approach for underdetermined source separation and offers practical applications in fault diagnosis and other fields.

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.

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.

Bearing fault diagnosis method based on refined composite multiscale fuzzy entropy

In this paper, a new fuzzy C-mean (FCM) clustering method based on refined composite multiscale fuzzy entropy (RCMFE) is proposed and applied to the bearing fault diagnosis of rotating machinery. The RCMFE adds multiscale processing, which can not only characterize the complex changes of time sequences at several different scales but also solve the problems of information loss caused by the process of coarse granulation and large fluctuation of entropy value when the scale becomes large. This method uses RCMFE to extract fault features, that are inputted into the Fuzzy C-mean clustering algorithm to achieve rolling bearing fault identification. Comparing the method with Multiscale Fuzzy Entropy (MFE) and Composite Multiscale Fuzzy Entropy (CMFE), the method used was experimentally proven to have better diagnostic results.

Refined composite multiscale fuzzy entropy based fault diagnosis of diesel engine

Due to complicated transfer paths and strong background noise interference, the fault pattern information deeply hides in common features of the vibration signal at the engine surface. In this study, the refined composite multiscale fuzzy entropy (RCMFE) used to measure the irregularity and self-similarity of time series is proposed to quantify the feature of various fault patterns. Followed by RCMFE, the features dug out are recognized by a parameter-adaptive support vector machine based on the firefly algorithm (FASVM). After putting forward the diagnosing schematics, the RCMFE-FASVM is applied to a fault diagnosis case of a diesel engine on a test rig. A comparative analysis of the four methods to extract features and the four methods to recognize fault patterns are conducted. Results indicate the proposed method has superior recognition performance and can effectively identify the working states of the diesel engine, contrasting the existing methods. Under the small samples and features task of identifying the working states of a diesel engine, the recognition rate of the proposed method with more stability can reach 98.2%, which is larger than other methods. Given the superior performance of the proposed method, the number of input features and training samples should vary from 8 to 20 and from 35 to 50.

A two-stage fault diagnosis methodology for rotating machinery combining optimized support vector data description and optimized support vector machine

Most intelligent fault diagnosis methods of rotating machinery generally consider that normal samples and fault samples as equally important for pattern recognition training. It ignores that the rotating machinery is in a normal state most of the time, and the collected normal samples are far more than the fault samples. Considering this situation, this paper proposes a two-stage intelligent fault diagnosis methodology for rotating machinery combing optimized support vector data description (SVDD) and optimized support vector machine (SVM). Specifically, SVDD is applied for fault detection, and SVM is applied for fault identification. The parameters of SVDD and SVM are optimized by the grasshopper optimization algorithm (GOA). Multiscale entropy (ME) is used for feature extraction, which is the input feature vector of SVDD and SVM. Under the framework of the proposed methodology, the strengths and weaknesses of 8 different entropy-based indicators in feature extraction are explored. The analysis results of three cases prove the availability and universality of the proposed methodology. According to the analysis results of three case analyses, the permutation entropy (PE)-based indicators are not promising for fault detection. Refined composite multiscale fuzzy entropy (RCMFE) is recommended for fault detection and fault identification to generalize the universality. Based on RCMFE, the fault detection accuracy in the three cases is more than 99%, and the fault identification accuracy is more than 94%. This methodology, therefore, provides a powerful tool for rotating machinery fault diagnosis, which is beneficial to practical application.

Multiscale complexity fluctuation behaviours of stochastic interacting cryptocurrency price model

The price dynamics of the emerging cryptocurrency market become an important factor affecting the current global investment market. To investigate its microscopic nonlinear dynamics mechanism, we develop a novel financial agent-based price model by combining the stochastic interacting system and two opposite directions of random jump processes, in which the attribute interactions between particles in the interacting system are utilized to imitate the influence of information transmission on investor’s investment attitude in the cryptocurrency market. Return series of the model, generated by Monte Carlo simulations, can reproduce a number of “stylized facts” of real cryptocurrency data. Additionally, we apply the composite multiscale fuzzy entropy algorithm and the matching energy method to detecting the complexity of price volatility behaviours in both actual and simulated cryptocurrency markets. The similarity of empirical results indicates that the proposed model can replicate the properties of price volatility in actual cryptocurrency market to some extent.

Photovoltaic Power Quality Analysis Based on the Modulation Broadband Mode Decomposition Algorithm

The Broadband Mode Decomposition (BMD) method was previously proposed to solve the Gibbs phenomenon that occurs during photovoltaic signal decomposition; its main idea is to build a dictionary which contains signal features, and to search in the dictionary to solve the problem. However, BMD has some shortcomings; especially if the relative bandwidth of the decomposed signal is not small enough, it may treat a square wave signal as several narrowband signals, resulting in a deviation in the decomposition effect. In order to solve the problem of relative bandwidth, the original signal is multiplied by a high-frequency, single-frequency signal, and the wideband signal is processed as an approximate wideband signal. This is the modulation broadband mode decomposition algorithm (MBMD) proposed in this article. In order to further identify and classify the disturbances in the photovoltaic direct current (DC) signal, the experiment uses composite multi-scale fuzzy entropy (CMFE) to calculate the components after MBMD decomposition, and then uses the calculated value in combination with the back propagation (BP) neural network algorithm. Simulation and experimental signals verify that the method can effectively extract the characteristics of the square wave component in the DC signal, and can successfully identify various disturbance signals in the photovoltaic DC signal.

Refined Composite Multivariate Multiscale Fractional Fuzzy Entropy: Measuring the Dynamical Complexity of Multichannel Financial Data

Refined composite multivariate multiscale fractional fuzzy entropy (RCmvMFFE), which aims to sensitively discriminate different short noisy multichannel financial data, is proposed as a new measure to quantify the complexity dynamics of multichannel time series in this work. To better comprehend the RCmvMFFE measure, the dynamical complexity analyses of multichannel synthetic dataset are comparatively studied with multivariate multiscale fuzzy entropy (mvMFE), refined composite multivariate multiscale fuzzy entropy (RCmvMFE), and refined composite multivariate multiscale fractional fuzzy entropy (RCmvMFFE). Then, these measures are firstly employed to explore actual multichannel financial index series to the best of our knowledge. The empirical analyses report that RCmvMFFE measure is able to deeply and sensitively dig up the market information hidden in the multichannel financial data and can better discriminate markets in different area compared to the traditional measures to some extent.

The Relationship Between Blood Perfusion in the Lower Extremities and Heart Rate Variability at Different Positions.

Previous studies have explored the relationship between the complexity of local blood flow signals and heart rate variability (HRV) under different thermal stimulations. However, the relationship between the complexity of local blood flow signals and HRV in different positions is not clear. In this study, healthy participants were placed in different body positions. The bilateral blood flux and ECG were monitored, and refined composite multiscale entropy (RC MSE) and refined composite multiscale fuzzy entropy (RC MFE) were used to measure the complexity of the local blood flux. The sample entropy was calculated to evaluate the HRV complexity. The change of body position did not affect the time domain or frequency domain of HRV, but did reverse the blood flux laterality of the lower extremities. Furthermore, there was a negative correlation between the complexity of right-side blood flux and sample entropy of HRV when the participant was in the -10 degrees position. These results provide a new perspective of the relationship between skin blood flux signals and cardiac function.

Generalized refined composite multiscale fuzzy entropy and multi-cluster feature selection based intelligent fault diagnosis of rolling bearing

Extracting the failure related information from vibration signals is a very important aspect of vibration-based fault detection for rolling bearing Multiscale entropy and its improvement, multiscale fuzzy entropy (MFE), are significant complexity measure tools of time series. They have been successfully applied to extract vibration failure features for rolling bearing condition monitoring . However, MFE over different scales will fluctuate with increase of scale factor. A new nonlinear dynamic parameter termed generalized refined composite multiscale fuzzy entropy (GRCMFE) is firstly developed to enhance the performance of MSE and MFE in data complexity measurement. Then three algorithms are developed and compared with MSE and MFE, as well as two algorithms of generalized MFE to verify the availability and superiority by analyzing two kinds of noise signals. In addition, based on three algorithms of GRCMFE, a novel fault diagnosis approach for rolling bearing is proposed with linking multi-cluster feature selection for supervised learning and the gravitational search algorithm optimized support vector machine for failure pattern recognition. Last, the proposed fault diagnostic approach was utilized to analyze two kinds of bearing test data sets. Analysis results indicate that our proposed fault diagnosis approach could effectively extract nonlinear dynamic complexity information and gets the highest identifying rate and the best performance among the comparative approaches.

A novel automated seizure detection system from EMD-MSPCA denoised EEG: Refined composite multiscale sample, fuzzy and permutation entropies based scheme

This paper investigates three complexity measures namely, refined composite multiscale sample entropy (RCMSE), refined composite multiscale fuzzy entropy (RCMFE), and refined composite multiscale permutation entropy (RCMPE) as features for the automated detection of epileptic seizures from electroencephalograms (EEGs). Generally, the EEG signals contain unwanted frequency components and superimposed trends that may influence their complexity evaluation. Therefore, we propose a denoising technique based on empirical mode decomposition (EMD) and multiscale principal component analysis (MSPCA) called EMD-MSPCA, and explore its impact on the performance of RCMSE, RCMFE, and RCMPE features for seizure diagnosis. Additionally, we put forward a novel automated seizure detection methodology based on EMD-MSPCA denoised EEG and combined RCMSE, RCMFE, and RCMPE features to characterize healthy, seizure-free, and seizure EEG signals. The experimental results demonstrate that all the three entropy features can successfully characterize the abnormal dynamics related to epileptic EEG signals with RCMPE being the best feature; applying the proposed EMD-MSPCA denoising technique prior to feature extraction using RCMSE, RCMFE and, RCMPE not only improved the performances of various classifiers but also reduced the computational time of these three entropy features significantly; and the proposed seizure detection scheme yielded good classification accuracies on two widely used EEG databases as compared to state-of-the-art works, hence emerges as a robust model for automated detection of epileptic seizures.

Fault diagnosis of rolling bearing using marine predators algorithm-based support vector machine and topology learning and out-of-sample embedding

The long-term safe operation of rotating machinery is closely related to the stability of rolling bearings. This paper proposes a rolling bearing fault diagnosis method based on refined composite multiscale fuzzy entropy (RCMFE), topology learning and out-of-sample embedding (TLOE), and the marine predators algorithm based-support vector machine (MPA-SVM). First, the RCMFE algorithm is used to extract the features of the original rolling bearing fault signal and to construct the original high-dimensional fault feature set. Then, TLOE is used to reduce the dimensionality of the high-dimensional fault feature set. The low-dimensional sensitive fault features are extracted to construct a low-dimensional fault feature subset. Finally, fault-type discrimination is performed using the MPA-SVM. The Case Western Reserve University dataset and data from fault diagnosis experiments performed on 1210 self-aligning ball bearings were used to verify the proposed method. The results demonstrate the effectiveness of the fault diagnosis method, which can diagnose bearing faults with up to 100% accuracy.

Rolling Bearing Fault Diagnosis Based on CEEMDAN and Refined Composite Multiscale Fuzzy Entropy

Considering the nonlinear and nonstationary characteristics of rolling bearing vibration signals, we propose a rolling bearing fault diagnosis method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), refined composite multiscale fuzzy entropy (RCMFE), Laplace score (LS), and the particle swarm optimization-probabilistic neural network (PSO-PNN). First, the method employs CEEMDAN to decompose the vibration signal and select the intrinsic mode functions (IMFs) containing the primary fault information via the frequency-domain correlation coefficient method. Then, it uses RCMFE to extract the characteristic information from the selected IMF. In addition, it uses LS to select and construct low-dimensional sensitive feature vectors, which are incorporated into the PSO-PNN model for diagnostic analysis to realize the state recognition of rolling bearing. Finally, the effectiveness of the method is verified by the analysis of the experimental data.

Identification of denatured and normal biological tissues based on compressed sensing and refined composite multi-scale fuzzy entropy during high intensity focused ultrasound treatment* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11774088 and 11474090).

In high intensity focused ultrasound (HIFU) treatment, it is crucial to accurately identify denatured and normal biological tissues. In this paper, a novel method based on compressed sensing (CS) and refined composite multi-scale fuzzy entropy (RCMFE) is proposed. First, CS is used to denoise the HIFU echo signals. Then the multi-scale fuzzy entropy (MFE) and RCMFE of the denoised HIFU echo signals are calculated. This study analyzed 90 cases of HIFU echo signals, including 45 cases in normal status and 45 cases in denatured status, and the results show that although both MFE and RCMFE can be used to identify denatured tissues, the intra-class distance of RCMFE on each scale factor is smaller than MFE, and the inter-class distance is larger than MFE. Compared with MFE, RCMFE can calculate the complexity of the signal more accurately and improve the stability, compactness, and separability. When RCMFE is selected as the characteristic parameter, the RCMFE difference between denatured and normal biological tissues is more evident than that of MFE, which helps doctors evaluate the treatment effect more accurately. When the scale factor is selected as 16, the best distinguishing effect can be obtained.

A rotating machinery fault diagnosis method using composite multiscale fuzzy distribution entropy and minimal error of convex hull approximation

Rotating machinery plays an increasingly crucial role in mechanical systems. For its normal operation, a novel fault diagnosis method is proposed in this paper, using composite multiscale fuzzy distribution entropy (CMFDE) and minimal error of convex hull approximation (MECHA). In this paper, CMFDE is utilized to extract essential information and measure time series complexity for vibration signals. Results indicate the CMFDE has less information loss and better stability. Then, to fulfill the classification tasks, the first several main features obtained by principal components analysis are fed into the proposed MECHA-based classifier. Results show MECHA has better classification performance. Using the laboratory data, we validate the feasibility and superiority of the proposed fault diagnosis method through two cases consisting of different fault types or fault severity degrees.

An Improved Composite Multiscale Fuzzy Entropy for Feature Extraction of MI-EEG.

Motor Imagery Electroencephalography (MI-EEG) has shown good prospects in neurorehabilitation, and the entropy-based nonlinear dynamic methods have been successfully applied to feature extraction of MI-EEG. Especially based on Multiscale Fuzzy Entropy (MFE), the fuzzy entropies of the τ coarse-grained sequences in τ scale are calculated and averaged to develop the Composite MFE (CMFE) with more feature information. However, the coarse-grained process fails to match the nonstationary characteristic of MI-EEG by a mean filtering algorithm. In this paper, CMFE is improved by assigning the different weight factors to the different sample points in the coarse-grained process, i.e., using the weighted mean filters instead of the original mean filters, which is conductive to signal filtering and feature extraction, and the resulting personalized Weighted CMFE (WCMFE) is more suitable to represent the nonstationary MI-EEG for different subjects. All the WCMFEs of multi-channel MI-EEG are fused in serial to construct the feature vector, which is evaluated by a back-propagation neural network. Based on a public dataset, extensive experiments are conducted, yielding a relatively higher classification accuracy by WCMFE, and the statistical significance is examined by two-sample t-test. The results suggest that WCMFE is superior to the other entropy-based and traditional feature extraction methods.