Fluctuation-based Dispersion Entropy Research Articles

Vibration-Based Fault Diagnosis for Railway Point Machines Using VMD and Multiscale Fluctuation-Based Dispersion Entropy

Vibration-Based Fault Diagnosis for Railway Point Machines Using VMD and Multiscale Fluctuation-Based Dispersion Entropy

Improved DBO-VMD and optimized DBN-ELM based fault diagnosis for control valve

Control valves play a vital role in process production. In practical applications, control valves are prone to blockage and leakage faults. At the small control valve openings, the vibration signals exhibit the drawbacks of significant interference and weak fault characteristics, which causes subpar fault diagnosis performance. To address the issue, a diagnostic model based on optimized variational mode decomposition (VMD) and improved deep belief network-extreme learning machine (DBN-ELM) is proposed. Firstly, good point set population initialization, nonlinear convergence factor, and adaptive Gaussian–Cauchy mutation strategies are applied in the dung beetle optimization algorithm (DBO) to escape local optima. Then, the improved DBO (IDBO) is used to optimize VMD parameters to obtain a series of modal components. Next, the generalized dispersion entropy (GDE) is formed by the combination of generalized Gaussian distribution and refined composite multiscale fluctuation-based dispersion entropy. The maximum correlation coefficient modal components are applied to extract GDE. Finally, the IDBO is applied to optimize the parameters of the DBN-ELM network to improve the classification performance of control valve faults. The comparative experiment results demonstrate that the proposed model can extract effective features and the diagnostic accuracy reaches 99.87%.

A Time Series Decomposition and Reinforcement Learning Ensemble Method for Short-Term Passenger Flow Prediction in Urban Rail Transit

Short-term passenger flow prediction (STPFP) helps ease traffic congestion and optimize the allocation of rail transit resources. However, the nonlinear and nonstationary nature of passenger flow time series challenges STPFP. To address this issue, a hybrid model based on time series decomposition and reinforcement learning ensemble strategies is proposed. Firstly, the improved arithmetic optimization algorithm is constructed by adding sine chaotic mapping, a new dynamic boundary strategy, and adaptive T distribution mutations for optimizing variational mode decomposition (VMD) parameters. Then, the original passenger flow data containing nonlinear and nonstationary irregular changes of noise is decomposed into several intrinsic mode functions (IMFs) by using the optimized VMD technology, which reduces the time-varying complexity of passenger flow time series and improves predictability. Meanwhile, the IMFs are divided into different frequency series by fluctuation-based dispersion entropy, and diverse models are utilized to predict different frequency series. Finally, to avoid the cumulative error caused by the direct superposition of each IMF’s prediction result, reinforcement learning is adopted to ensemble the multiple models to acquire the multistep passenger flow prediction result. Experiments on four subway station passenger flow datasets proved that the prediction performance of the proposed method was better than all benchmark models. The excellent prediction effect of the proposed model has important guiding significance for evaluating the operation status of urban rail transit systems and improving the level of passenger service.

Hierarchical refined composite multiscale fluctuation-based dispersion entropy: application to feature extraction of underwater target signal

Hierarchical refined composite multiscale fluctuation-based dispersion entropy: application to feature extraction of underwater target signal

Dual feature extraction system for ship-radiated noise and its application extension

The complexity of maritime noise and the time-variability of hydroacoustic channels make it more and more difficult to extract feature from ship-radiated noise effectively. To accurately recognize ship-radiated noise, a dual feature extraction and recognition system based on pre-processing-dual feature extraction-recognition is proposed. Pre-processing: The primary decomposition and secondary decomposition are performed for the first time using variational mode decomposition optimized by giant trevally optimizer, in which the threshold is adaptively determined. Dual feature extraction: Grey relational analysis is calculated for the intrinsic mode function component after primary decomposition and the high-intrinsic mode function component after secondary decomposition, and two eigenvectors are selected separately. Then entropy of the combination of weighted fluctuation-based dispersion entropy and Lempel-Ziv complexity is proposed to calculate the eigenvalues for classification. Recognition: The feature values are recognized using random forest recognizer optimized by tuna swarm optimization to obtain the final recognition rate. The experimental results show that the proposed entropy has an overwhelming advantage over the others, such as permutation entropy, and dispersion entropy. It is proved that the proposed system for ship-radiated noise has good classification performance and the recognition rate is up to 97.5%. In addition, it is successfully applied to simulated chaotic signals as well as measured aquatic life signals.

A new feature extraction method of ship radiated noise based on variational mode decomposition, weighted fluctuation-based dispersion entropy and relevance vector machine

Due to the changeable circumstance and the continuous improvement of ship manufacturing technique, ship radiated noise (SRN) has become more and more complex, which makes it more essential to extract its features. Moreover, the target ships can be quickly classified by feature extraction, thus occupying the advantage of maritime confrontation. For the sake of improved feature extraction technology, a new feature extraction method of SRN based on optimized variational mode decomposition by tuna swarm optimization (TSO-VMD), weighted fluctuation-based dispersion entropy (WFDE) and optimized relevance vector machine by sparrow search algorithm (SSA-RVM) is proposed, moreover, the features of seven types of SRN are extracted respectively. To solve the weakness that decomposition level K and penalty factor α must to be preset artificially in VMD, TSO-VMD is proposed. To select optimal width factor and super parameter of RVM, SSA-RVM is proposed. In the first place, decompose SRN into a range of intrinsic modal functions (IMFs) by TSO-VMD, calculate the K-nearest neighbor mutual information (KNN-MI) value between each IMF and the original signal, and normalize it to obtain normalized KNN-MI (nor-KNNMI). Next, select the IMF with the largest nor-KNNMI value as the feature vector, and 60 samples are randomly selected from the feature vector and their fluctuation-based dispersion entropy (FDE) are calculated. Afterwards, select the nor-KNNMI value corresponding to the feature vector to weight the FDE value to obtain the WFDE value, and use the WFDE value to classify SRN. In the end, input the WFDE value of each sample into SSA-RVM for identification. The experimental results show that the identification rate of the proposed method is over 90%. Therefore, the proposed method can accurately and efficiently extract the features of SRN.

Bearing Fault Diagnosis Method Based on RCMFDE-SPLR and Ocean Predator Algorithm Optimizing Support Vector Machine.

For the problem that rolling bearing fault characteristics are difficult to extract accurately and the fault diagnosis accuracy is not high, an unsupervised characteristic selection method of refined composite multiscale fluctuation-based dispersion entropy (RCMFDE) combined with self-paced learning and low-redundant regularization (SPLR) is proposed, for which the fault diagnosis is carried out by support vector machine (SVM) optimized by the marine predator algorithm (MPA). First, we extract the entropy characteristics of the bearings under different fault states by RCMFDE and the introduction of the fine composite multiscale coarse-grained method and fluctuation strategy improves the stability and estimation accuracy of the bearing characteristics; then, a novel dimensionality-reduction method, SPLR, is used to select better entropy characteristics, and the local flow structure of the fault characteristics is preserved and the redundancy is constrained by two regularization terms; finally, using the MPA-optimized SVM classifier by combining Levy motion and Eddy motion strategies, the preferred RCMFDE is fed into the MPA-SVM model for fault diagnosis, for which the obtained bearing fault diagnosis accuracy is 97.67%. The results show that the RCMFDE can effectively improve the stability and accuracy of the bearing characteristics, the SPLR-based low-dimensional characteristics can suppress the redundancy characteristics and improve the effectiveness of the characteristics, and the MPA-based adaptive SVM model solves the parameter randomness problem and, therefore, the proposed method has outstanding superiority.

Underwater acoustic signal denoising model based on secondary variational mode decomposition

Due to the complexity of marine environment, underwater acoustic signal will be affected by complex background noise during transmission. Underwater acoustic signal denoising is always a difficult problem in underwater acoustic signal processing. To obtain a better denoising effect, a new denoising method of underwater acoustic signal based on optimized variational mode decomposition by black widow optimization algorithm (BVMD), fluctuation-based dispersion entropy threshold improved by Otsu method (OFDE), cosine similarity stationary threshold (CSST), BVMD, fluctuation-based dispersion entropy (FDE), named BVMD-OFDE-CSST-BVMD-FDE, is proposed. In the first place, decompose the original signal into a series of intrinsic mode functions (IMFs) by BVMD. Afterwards, distinguish pure IMFs, mixed IMFs and noise IMFs by OFDE and CSST, and reconstruct pure IMFs and mixed IMFs to obtain primary denoised signal. In the end, decompose primary denoising signal into IMFs by BVMD again, use the FDE value to distinguish noise IMFs and pure IMFs, and reconstruct pure IMFs to obtain the final denoised signal. The proposed mothod has three advantages: (i) BVMD can adaptively select the decomposition layer and penalty factor of VMD. (ii) FDE and CS are used as double criteria to distinguish noise IMFs from useful IMFs, and Otsu algorithm and CSST algorithm can effectively avoid the error caused by manually selecting thresholds. (iii) Secondary decomposition can make up for the deficiency of primary decomposition and further remove a small amount of noise. The chaotic signal and real ship signal are denoised. The experiment result shows that the proposed method can effectively denoise. It improves the denoising effect after primary decomposition, and has good practical value.

A Novel Fault Diagnosis Method for Rolling Bearing Based on Hierarchical Refined Composite Multiscale Fluctuation-Based Dispersion Entropy and PSO-ELM

This paper proposes a novel fault diagnosis method for rolling bearing based on hierarchical refined composite multiscale fluctuation-based dispersion entropy (HRCMFDE) and particle swarm optimization-based extreme learning machine (PSO-ELM). First, HRCMFDE is used to extract fault features in the vibration signal at different time scales. By introducing the hierarchical theory algorithm into the vibration signal decomposition process, the problem of missing high-frequency signals in the coarse-grained process is solved. Fluctuation-based dispersion entropy (FDE) has the characteristics of insensitivity to noise interference and high computational efficiency based on the consideration of nonlinear time series fluctuations, which makes the extracted feature vectors more effective in describing the fault information embedded in each frequency band of the vibration signal. Then, PSO is used to optimize the input weights and hidden layer neuron thresholds of the ELM model to improve the fault identification capability of the ELM classifier. Finally, the performance of the proposed rolling bearing fault diagnosis method is verified and analyzed by using the CWRU dataset and MFPT dataset as experimental cases, respectively. The results show that the proposed method has high identification accuracy for the fault diagnosis of rolling bearings with varying loads and has a good load migration effect.

A Novel Acoustic Method for Cavitation Identification of Propeller

When a propeller is under a state of cavitation, it will experience negative effects, including strong noise, vibration, and even damage to the blades. Accordingly, the detection of propeller cavitation has attracted the attention of researchers. Propeller noise signal contains a wealth of cavitation information, which is a powerful method to identify the cavitation state. Considering the nonlinear characteristics of propeller noise, a feature describing the complexity of nonlinear signals, which is called refined composite multiscale fluctuation-based dispersion entropy (RCMFDE), is adopted as the indicator of propeller cavitation, and a framework for the identification of propeller cavitation state is established in this paper. Firstly, the propeller noise signal is decomposed by the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method, and the intrinsic mode function (IMF) components with cavitation characteristics are extracted. Secondly, the RCMFDE of the IMF components is computed. Finally, a hybrid optimization support vector machine (SVM) is established to classify the features, in which a Relief-F filter is utilized to reduce the feature dimension, and a particle swarm optimization (PSO) wrapper is utilized to optimize the parameters of the SVM. The experimental results demonstrate encouraging accuracy to apply this approach to identify the propeller cavitation states, with an identification accuracy of 91.11%.

MVME-RCMFDE framework for discerning hyper-responsivity in Autism Spectrum Disorders

BackgroundAutism Spectrum Disorder (ASD), characterized by impaired sensory processing, has a wide range of clinical heterogeneity, which handicaps effective therapeutic interventions. Therefore, it is imperative to develop potential mechanisms for delineating clinically meaningful subgroups, so as to provide individualised medical treatment. In this study, an attempt is being made to differentiate the hyper-responsive subgroup from ASD by analysing the complexity pattern of Visual Evoked Potentials (VEPs), recorded from a group of 30 ASD participants, in the presence of vertical achromatic sinewave gratings at varying contrast conditions of low (5%), medium (50%) and high (90%). MethodThis study proposes a new diagnostic framework incorporating a novel signal decomposition method termed as Modified Variational Mode Extraction (MVME) and a multiscale entropy approach. MVME segments the signal into five constituent modes with less spectral overlap in lower frequencies. Refined Composite Multiscale Fluctuation-based Dispersion entropy (RCMFDE) is extracted from these constituent modes, thereby facilitating the identification of hyper-responsive subgroup in ASD. ResultsWhen tested on both simulated and real VEPs, MVME displays appreciable performance in terms of root mean square error and minimal spectral overlap in the lower frequencies, in comparison with the other state-of-the-art techniques. Relative Complexity analysis with RCMFDE exhibits a rising trend in 43%–50% of ASD in modes 1, 2, 3 and 4. ConclusionThe proposed MVME-RCMFDE approach is efficient in discriminating the hyper-responsive subgroup in ASD in multiple modes namely mode 1, 2, 3 and 4, which correspond to delta, theta, alpha and beta frequency bands of brain signals.

Functional Connectivity and Complexity in the Phenomenological Model of Mild Cognitive-Impaired Alzheimer's Disease.

BackgroundFunctional connectivity and complexity analysis has been discretely studied to understand intricate brain dynamics. The current study investigates the interplay between functional connectivity and complexity using the Kuramoto mean-field model.MethodFunctional connectivity matrices are estimated using the weighted phase lag index and complexity measures through popularly used complexity estimators such as Lempel-Ziv complexity (LZC), Higuchi's fractal dimension (HFD), and fluctuation-based dispersion entropy (FDispEn). Complexity measures are estimated on real and simulated electroencephalogram (EEG) signals of patients with mild cognitive-impaired Alzheimer's disease (MCI-AD) and controls. Complexity measures are further applied to simulated signals generated from lesion-induced connectivity matrix and studied its impact. It is a novel attempt to study the relation between functional connectivity and complexity using a neurocomputational model.ResultsReal EEG signals from patients with MCI-AD exhibited reduced functional connectivity and complexity in anterior and central regions. A simulation study has also displayed significantly reduced regional complexity in the patient group with respect to control. A similar reduction in complexity was further evident in simulation studies with lesion-induced control groups compared with non-lesion-induced control groups.ConclusionTaken together, simulation studies demonstrate a positive influence of reduced connectivity in the model imparting a reduced complexity in the EEG signal. The study revealed the presence of a direct relation between functional connectivity and complexity with reduced connectivity, yielding a decreased EEG complexity.

Classification of ECG signal-based cardiac abnormalities using fluctuation-based dispersion entropy and first-order statistics

The heart is one of the most important organs in the human body. The presence of abnormalities in the heart can be fatal for a person. One way to detect heart abnormalities is an Electrocardiogram (EKG) signal examination. To facilitate the detection of ECG signal abnormalities, an automatic classification method is needed. Therefore, in this study, a method for classifying ECG signals using FdispEn (Fluctuation-based dispersion Entropy) and first-order statistics is proposed. FdispEn measures the uncertainty in the signal and is expected to be able to distinguish the physiological state of the ECG signal time series. In this study FdispEn and statistical computing were used as feature extraction of the ECG signal and combined with the Support Vector Machine (SVM) for the classification process of Normal ECG, AFIB (Atrial Fibrilation), and CHF (Congestive Heart Failure). The method proposed in this study generates an accuracy of 91.5%. The system proposed in this study is expected to assist in the clinical diagnosis of abnormalities in the heart.

A Novel Method for Fault Diagnosis of Rotating Machinery.

When rotating machinery fails, the consequent vibration signal contains rich fault feature information. However, the vibration signal bears the characteristics of nonlinearity and nonstationarity, and is easily disturbed by noise, thus it may be difficult to accurately extract hidden fault features. To extract effective fault features from the collected vibration signals and improve the diagnostic accuracy of weak faults, a novel method for fault diagnosis of rotating machinery is proposed. The new method is based on Fast Iterative Filtering (FIF) and Parameter Adaptive Refined Composite Multiscale Fluctuation-based Dispersion Entropy (PARCMFDE). Firstly, the collected original vibration signal is decomposed by FIF to obtain a series of intrinsic mode functions (IMFs), and the IMFs with a large correlation coefficient are selected for reconstruction. Then, a PARCMFDE is proposed for fault feature extraction, where its embedding dimension and class number are determined by Genetic Algorithm (GA). Finally, the extracted fault features are input into Fuzzy C-Means (FCM) to classify different states of rotating machinery. The experimental results show that the proposed method can accurately extract weak fault features and realize reliable fault diagnosis of rotating machinery.

A novel feature extraction method based on weighted multi-scale fluctuation based dispersion entropy and its application to the condition monitoring of rotary machines

Features describing the state of industrial gearboxes and their extraction from the mixed noisy signal are always an issue of concern. Unfortunately, traditional feature extraction methods are not equally useful for both adaptive and non-adaptive decomposition techniques. In the present study, a novel feature extraction method named weighted multi-scale fluctuation-based dispersion entropy (wtMFDE) is proposed for the condition monitoring of planetary gearbox (PGB). It is equally useful for adaptive (ensemble empirical mode decomposition) and non-adaptive (flexible analytical wavelet transform) signal denoising techniques. Four state-of-the-art classifiers viz. support vector machine (SVM), random forest (RF), K-nearest neighbor (KNN), and multilayer perceptron (MLP), which have extensive applications in machine condition monitoring, are used for the classification of the chipped sun gear, pitted planet gear as well as the combined effect for these faults. It is observed that the extracted features are highly sensitive and effective in a way that they can recognize faults with comparable accuracy with all the selected classifiers.

Carbon price combination prediction model based on improved variational mode decomposition

Carbon price is one of the core factors in the carbon trading process, so it is of great significance to establish a carbon price prediction model for guiding the carbon trading market to make scientific and reasonable decision. In order to improve the accuracy of carbon price prediction, a carbon price combination prediction model with variational mode decomposition based on seagull optimization algorithm (SVMD), fluctuation-based dispersion entropy (FDE), extreme learning machine (ELM) and kernel extreme learning machine (KELM) optimized by JAYA algorithm (JAYA-KELM), named SVMD-FDE-ELM-JAYA-KELM, is proposed. To solve the selection of mode number K and the penalty factor α of VMD, SVMD is proposed, which realizes adaptive determination of the parameter K and α. The idea of the SVMD-FDE-ELM-JAYA-KELM is roughly as follows. Firstly, SVMD decomposes carbon price into a series of intrinsic mode functions (IMFs). According to the FDE value, these IMFs are divided into high frequency IMFs or low frequency IMFs. Secondly, JAYA-KELM is established for high frequency IMFs and ELM is established for low frequency IMFs. Finally, the predicted value of carbon price is reconstructed to complete the prediction. The experimental results show that the proposed model has best prediction accuracy, and provides a new method for carbon price prediction.

Spectrum Sensing Implemented with Improved Fluctuation-Based Dispersion Entropy and Machine Learning.

Spectrum sensing is an important function in radio frequency spectrum management and cognitive radio networks. Spectrum sensing is used by one wireless system (e.g., a secondary user) to detect the presence of a wireless service with higher priority (e.g., a primary user) with which it has to coexist in the radio frequency spectrum. If the wireless signal is detected, the second user system releases the given frequency to maintain the principle of not interfering. This paper proposes a machine learning implementation of spectrum sensing using the entropy measure as a feature vector. In the training phase, the information about the activity of the wireless service with higher priority is gathered, and the model is formed. In the classification phase, the wireless system compares the current sensing report to the created model to calculate the posterior probability and classify the sensing report into either the presence or absence of wireless service with higher priority. This paper proposes the novel application of the Fluctuation Dispersion Entropy (FDE) measure recently introduced in the research community as a feature vector to build the model and implement the classification. An improved implementation of the FDE (IFDE) is used to enhance the robustness to noise. IFDE is further enhanced with an adaptive method (AIFDE) to automatically select the hyper-parameter introduced in IFDE. Then, this paper combines the machine learning approach with the entropy measure approach, which are both recent developments in spectrum sensing research. The approach is compared to similar approaches in literature and the classical energy detection method using a generated radar signal data set with different conditions of SNR(dB) and fading conditions. The results show that the proposed approach is able to outperform the approaches from literature based on other entropy measures or the Energy Detector (ED) in a consistent way across different levels of SNR and fading conditions.

Comparative study of feature extraction and classification based on dispersion Lempel‐Ziv complexity

AbstractAs an important complexity feature of signal, Lempel‐Ziv complexity (LZC) has the advantage of simple‐to‐calculate, but it ignores amplitude information, and has low sensitivity at low amplitude. Dispersion Lempel‐Ziv complexity (DLZC) is a recently proposed nonlinear dynamic method, it has the advantage of immunity to noise even at relatively large proportion of noise and has been used to describe different pathological states. In view of its good performance in the field of biomedicine, we introduce DLZC into the field of underwater acoustic and fault diagnosis, and propose a feature extraction method for ship and gear fault signals based on DLZC, then an intelligent classification method was proposed by combining DLZC with K‐Nearest Neighbor (KNN) to further verify the effectiveness of the proposed feature extraction method, termed DLZC‐KNN. We conducted comparative experiments on feature extraction and classification, respectively: for the feature extraction comparison experiment, we compared the proposed feature extraction method with other feature extraction methods, which are based on Lempel‐Ziv complexity (LZC), permutation entropy (PE), dispersion entropy (DE), and fluctuation‐based dispersion entropy (FDE); for the classification comparison experiment, we compare the impact of different features and different classifiers on the recognition rate and also discussed the influence of different parameters on the experiment. The results show that DLZC has a better representation of signal complexity, and the DLZC‐KNN classification method gets a higher recognition rate than other comparative methods both in the field of fault diagnosis and underwater acoustic.

Multi-distance fluctuation based dispersion fractal for epileptic seizure detection in EEG signal

The developmental methods for evaluating the complexity of univariate signals has attracted extensive attention. Therefore, entropy was discovered to be one of the best methods for evaluating the complexity of a biological signal. Recent studies on signal complexity using fractal dimension have been able to tackle the domination of entropy measurement. It was found that Fluctuation-based dispersion entropy (FDispEn) is one of the recently proposed methods based on permutation (PE) and Shannon entropies (SE). This method analyzes the signal’s uncertainty and deals with its fluctuations. FDispEn mainly calculates the differences between adjacent elements of the dispersion patterns based on Shannon entropy, however, it is limited by distance. Therefore, this study proposes a new feature extraction method based on FDispEn by expanding adjacent elements’ measurement distance using the multi-distance signal level differences (MSLD) method. MSLD is an upgrade of the gray-level difference (GLD) that is used to evaluate one-dimensional signals. Furthermore, it is used to calculate several distances of adjacent dispersion patterns. The MSLD is also applied in FDispEn to form multi-distance FDispEn (MFDispEn). Other signal complexity evaluations involving two fractal dimension methods, namely Higuchi and Katz’s were used in forming the multi-distance fluctuation-based dispersion fractal (MFDF). The performance of FDispEn, MFDispEn, and three variations of MFDF were compared to evaluate the epileptic EEG signals. The results showed that the multi-distance application on MFDispEn and MFDF produced a better separability than FDispEn. Meanwhile, the MFDF outperformed the FDispEn and MFDispEn as it showed a higher accuracy, sensitivity, and specificity in classifying epileptic EEG signals.

Data-driven fault diagnosis for wind turbines using modified multiscale fluctuation dispersion entropy and cosine pairwise-constrained supervised manifold mapping

Condition monitoring and fault diagnosis of wind turbines is an attractive yet challenging task. This paper presents a novel data-driven fault diagnosis scheme for wind turbines, using refined time-shift multiscale fluctuation-based dispersion entropy (RTSMFDE) and cosine pairwise-constrained supervised manifold mapping (CPCSMM). The developed RTSMFDE can improve multiscale dispersion entropy in complexity measurement of time series, by employing the refined time-shift analysis approach. Moreover, the proposed CPCSMM combines cosine distance metric, supervised theory and sparse global manifold structure, to obtain the most important features, resulting in a low dimensional representation. In this fault diagnosis scheme, a high-dimensional fault feature set is first constructed using RTSMFDE. Then, sensitive features are extracted using CPCSMM. Finally, the low-dimensional feature set is fed to a beetle antennae search-based support vector machine for fault identification. Simulation experiments and wind turbine fault diagnosis experiments were used, to show that the proposed RTSMFDE can comprehensively mine the wind turbine features and outperforms the existing state-of-the-art entropy methods. The visualization results and classification effects of the proposed CPCSMM approach are better than existing unsupervised and supervised dimensionality reduction methods. The proposed data-driven fault diagnosis method can effectively and accurately identify multi-faults and outperforms existing fault diagnosis techniques.