Refined 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.

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.

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.

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.

Cross‐domain bearing fault diagnosis with refined composite multiscale fuzzy entropy and the self organizing fuzzy classifier

AbstractIn this article, the use of refined composite multiscale fuzzy entropy (RCMFE) for cross‐domain diagnosis of bearings is introduced and verified with two publicly available datasets of varying operating conditions, a factor that challenges the diagnostic ability of trained models. For classification, the self organizing fuzzy (SOF) classifier is used. The diagnostic framework which primarily only involves extracting RCMFE feature and training the SOF classifier, is able to detect and isolate faults with over 97% accuracy when the classes are comprised of a single fault type and size. Compared to related works, the proposed approach does not require deep learning for feature extraction nor any domain adaptation technique as the RCMFE feature is robust against changing operating conditions. Furthermore, the method does not need target domain data during training. With regard to fault isolation, when the classes in the training data contain all the available fault sizes instead of a single size, the classifier can distinguish inner race faults from outer race and ball fault with an average accuracy of 96%. However, the accuracy for differentiating ball and outer race faults falls slightly to an average of 86%. Thus even for the latter arrangement which poses a tougher transfer learning problem, the proposed approach still performs very well.

Improvement in classification accuracy and computational speed in bearing fault diagnosis using multiscale fuzzy entropy

The operation of ball bearings under varying faulty conditions comprises complex time-varying modulations in the acquired vibration signals. In such circumstances, the extraction of nonlinear dynamic parameters based on multiscale fuzzy entropy (MFE) and refined composite multiscale fuzzy entropy (RCMFE) have proved to be more efficient in fault recognition than the conventional feature extraction methods. However, the accuracy of the methods in classifying several fault classes should not arrive at the expense of higher computational cost. The two major factors responsible for affecting the computational cost are the sampling length and number of features. This paper investigates the capabilities of MFE and RCMFE methods to estimate several health states of bearing at a different range of sampling lengths and scale factors. The bearing condition comprises normal and defective states, where the defective state considers incipient and severe faulty conditions of bearing. The diagnosis capability of both methods is verified by employing the support vector machine classifier. Although the results demonstrate higher fault classification ability of RCMFE for both incipient and severe bearing faults, the results are more impressive, especially at a higher range of scale factors as well as at lower sampling lengths.

Rolling Bearings Fault Diagnosis under Variable Conditions Using RCMFE and Improved Support Vector Machine

As critical components, rolling bearings are widely used in a variety of rotating machinery. It is necessary to develop a suitable fault diagnosis method to prevent malfunctions and breakages of bearings during operation. However, the current methods for the fault diagnosis of rolling bearings are too cumbersome to be applied in practical engineering. In addition, the working condition of rolling bearings is generally tough, complex, and especially variable. These conditions cause fault diagnosis methods to be less effective. This paper aims to provide a simple and effective method for the fault diagnosis of rolling bearings under variable conditions. The main contribution of this paper is as follows: (1) The refined composite multiscale fuzzy entropy (RCMFE) is applied in bearing fault feature extraction because of its simplicity and high efficiency; (2) The improved support vector machine (ISVM), based on the whale optimization algorithm (WOA), is proposed to identify the fault pattern of rolling bearings. The ISVM is proposed in this paper to solve the problem that parameter setting affects the classification effect of SVM. In the ISVM, the WOA is employed to optimize both the regularization and kernel parameters of the SVM. Compared with the traditional optimization methods, the WOA has the advantages of high optimization speed and better optimization ability; (3) Combining the RCMFE and the ISVM to diagnose bearing fault under variable working conditions. The effectiveness of the RCMFE-ISVM has been validated via experimental vibration signal of bearings faults under variable working conditions.

Using the entropy of the corneal pulse signal to distinguish healthy eyes from eyes affected by primary open-angle glaucoma

Objective: The purpose of this study was to evaluate whether the complexity of the corneal pulse (CP) signal can be used to differentiate patients with primary open-angle glaucoma (POAG) from healthy subjects. Approach: The study sample consisted of 28 patients with POAG and a control, age-matched group of 30 subjects. After standard ophthalmic examination, the CP signal from a randomly selected eye of each participant was measured using non-contact ultrasonic micro-displacement measurement technology. After pre-processing, the complexity of the CP signal was estimated using refined composite multiscale fuzzy entropy (RCMFE) up to scale factor 50. The average RCMFE values were computed from three repeated measurements of the CP signals for each participant and each scale factor. Main results: The complexity of the CP signal in glaucomatous eyes was higher than that observed in healthy ones. Also, RCMFE of the CP signal was found to differentiate (statistically significantly) between the two groups for scales in the range from 26 to 43. For these scales, the one for which the lowest p-value (t-test, p = 0.017) was obtained when comparing RCMFE between the two groups was selected as the optimal scale. Next, a receiver operating characteristic analysis for the optimal scale showed that the proposed approach of calculating the multiscale entropy of the CP signal has some potential to discriminate between patients with POAG and healthy controls (sensitivity, specificity and accuracy of 0.643, 0.700 and 0.672, respectively). Significance: In conclusion, RCMFE, as a complexity measure, may be considered an auxiliary indicator to support glaucoma diagnostics.

Fractional Refined Composite Multiscale Fuzzy Entropy of International Stock Indices

Fractional refined composite multiscale fuzzy entropy (FRCMFE), which aims to relieve the large fluctuation of fuzzy entropy (FuzzyEn) measure and significantly discriminate different short-term financial time series with noise, is proposed to quantify the complexity dynamics of the international stock indices in the paper. To comprehend the FRCMFE, the complexity analyses of Gaussian white noise with different signal lengths, the random logarithmic returns and volatility series of the international stock indices are comparatively performed with multiscale fuzzy entropy (MFE), composite multiscale fuzzy entropy (CMFE) and refined composite multiscale fuzzy entropy (RCMFE). The empirical results show that the FRCMFE measure outperforms the traditional methods to some extent.

A method combining refined composite multiscale fuzzy entropy with PSO-SVM for roller bearing fault diagnosis

Combining refined composite multiscale fuzzy entropy (RCMFE) and support vector machine (SVM) with particle swarm optimization (PSO) for diagnosing roller bearing faults is proposed in this paper. Compared with refined composite multiscale sample entropy (RCMSE) and multiscale fuzzy entropy (MFE), the smoothness of RCMFE is superior to that of those models. The corresponding comparison of smoothness and analysis of validity through decomposition accuracy are considered in the numerical experiments by considering the white and 1/f noise signals. Then RCMFE, RCMSE and MFE are developed to affect extraction by using different roller bearing vibration signals. Then the extracted RCMFE, RCMSE and MFE eigenvectors are regarded as the input of the PSO-SVM to diagnose the roller bearing fault. Finally, the results show that the smoothness of RCMFE is superior to that of RCMSE and MFE. Meanwhile, the fault classification accuracy is higher than that of RCMSE and MFE.

Refined composite multiscale fuzzy entropy: Localized defect detection of rolling element bearing

We proposed an appealing method based on refined composite multiscale fuzzy entropy (RCMFE), infinite feature selection (Inf-FS) algorithm, and support vector machine (SVM) for implementing localized defect detection to keep the downtime and extended damage caused by incipient failure of bearing at a minimum. As a useful approach, multiscale fuzzy entropy (MFE) was utilized to measure the complexity and dynamic changes of signals. However, an inaccurate entropy value would be yielded with the increase of scale factor. Here, as an improvement version of MFE, the RCMFE was proposed to address the shortcomings in the case of short time series. For this novel method, we conducted a full investigation of the effects and robustness by comparing the proposed method with two other entropy-based approaches using synthetic signals and real data. Results indicate that the proposed algorithm outperforms the other approaches in terms of reliability and stability. The RCMFE values of bearing signals from one healthy condition and seven fault states are calculated as diagnostic information. Moreover, an intelligent fault identification method was constructed by combining the Inf-FS algorithm and SVM classifier. Experimental results show the usefulness of the proposed strategy.

Analyzing the Dynamics of Lung Cancer Imaging Data Using Refined Fuzzy Entropy Methods by Extracting Different Features

Lung cancer is the major cause of cancer-related deaths worldwide with poor survival due to the poor diagnostic system at the advanced cancer stage. In the past, researchers developed computer-aided diagnosis (CAD) systems, which were greatly used by the radiologist for identifying the abnormalities and applied few features extracting methods. The physiology and behavior of various physiological systems can be best investigated using nonlinear dynamical measures for capturing the intrinsic dynamics, which is influenced due to multiple pathologies by the degradation of structural and functional components. As cancer images contain hidden information, which can be best analyzed using these dynamical measures. In this paper, we proposed multiscale sample entropy (MSE) with a mean and KD-tree algorithmic approach, multiscale permutation entropy (MPE), multiscale fuzzy entropy (MFE), and refined composite multiscale fuzzy entropy (RCMFE) with mean, variance, and standard deviation. The statistically significant results were computed to distinguish non-small-cell lung cancer (NSCLC) from SCLC by extracting morphological, texture, and elliptic Fourier descriptors (EFDs). The highest significant results obtained based on texture features using MFE with standard deviation give the P-value of 1.95E-50, morphological features using RCMFE with mean provide the P-value of 3.01E-14, and EFDs features using MFE with variance give the P-value of 1.04E-13. The results reveal that the improved complexity measures based on refined fuzzy entropy outperformed in analyzing the dynamics of lung cancer and will provide a new insight into extract meaningful hidden information present in the Lung cancer images, which will be very helpful to further distinguish NSCLC and SCLC for early diagnosis and prognosis.

Refined Multiscale Fuzzy Entropy to Analyse Post-Exercise Cardiovascular Response in Older Adults With Orthostatic Intolerance.

Orthostatic intolerance syndrome occurs when the autonomic nervous system is incapacitated and fails to respond to the demands associated with the upright position. Assessing this syndrome among the elderly population is important in order to prevent falls. However, this problem is still challenging. The goal of this work was to determine the relationship between orthostatic intolerance (OI) and the cardiovascular response to exercise from the analysis of heart rate and blood pressure. More specifically, the behavior of these cardiovascular variables was evaluated in terms of refined composite multiscale fuzzy entropy (RCMFE), measured at different scales. The dataset was composed by 65 older subjects, 44.6% (n = 29) were OI symptomatic and 55.4% (n = 36) were not. Insignificant differences were found in age and gender between symptomatic and asymptomatic OI participants. When heart rate was evaluated, higher differences between groups were observed during the recovery period immediately after exercise. With respect to the blood pressure and other hemodynamic parameters, most significant results were obtained in the post-exercise stage. In any case, the symptomatic OI group exhibited higher irregularity in the measured parameters, as higher RCMFE levels in all time scales were obtained. This information could be very helpful for a better understanding of cardiovascular instability, as well as to recognize risk factors for falls and impairment of functional status.

Fault Diagnosis of Rolling Bearing Under Speed Fluctuation Condition Based on Vold-Kalman Filter and RCMFE

Rolling bearings’ operation under variable speed conditions exhibits complex time-varying modulations and spectral structures, resulting in difficulty in the fault diagnosis. In order to effectively remove the influence of the rotational speed and extract the fault characteristics, this paper develops a fault diagnosis scheme based on the Vold–Kalman filter (VKF), refined composite multi-scale fuzzy entropy (RCMFE), and Laplacian score (LS). In the proposed method, the VKF is first adopted to remove the fault-unrelated components and give a clear representation of the fault symptoms. Second, the RCMFE is applied to extract fault features from the denoised vibration signal. Third, the LS approach is introduced to refine the fault features by sorting the scale factors. In the end, the selected features are fed into the logistic regression to automatically complete the fault pattern identifications. The proposed method is experimentally demonstrated to be able to recognize the localized defect on the inner race, outer race, and rolling element under variable speed conditions.