Weighted Permutation Entropy Research Articles

Optimized Variational Mode Decomposition and Permutation Entropy with Their Application in Feature Extraction of Ship-Radiated Noise.

The complex and changeable marine environment surrounded by a variety of noise, including sounds of marine animals, industrial noise, traffic noise and the noise formed by molecular movement, not only interferes with the normal life of residents near the port, but also exerts a significant influence on feature extraction of ship-radiated noise (S-RN). In this paper, a novel feature extraction technique for S-RN signals based on optimized variational mode decomposition (OVMD), permutation entropy (PE), and normalized Spearman correlation coefficient (NSCC) is proposed. Firstly, with the mode number determined by reverse weighted permutation entropy (RWPE), OVMD decomposes the target signal into a set of intrinsic mode functions (IMFs). The PE of all the IMFs and SCC between each IMF with the raw signal are then calculated, respectively. Subsequently, feature parameters are extracted through the sum of PE weighted by NSCC for the IMFs. Lastly, the obtained feature vectors are input into the support vector machine multi-class classifier (SVM) to discriminate various types of ships. Experimental results indicate that five kinds of S-RN samples can be accurately identified with a recognition rate of 94% by the proposed scheme, which is higher than other previously published methods. Hence, the proposed method is more advantageous in practical applications.

Fault diagnosis of rolling bearing using a refined composite multiscale weighted permutation entropy

The health status information of rolling bearings is often contained in vibration signals, but it is difficult to detect bearing defects directly through vibration signals. To effectively extract the key feature information hidden in the original signal, this paper proposes the refined composite multiscale weighted permutation entropy (RCMWPE) method to efficiently characterize the operating state of the bearing. The proposed method focuses on two aspects: the improved version reduces the dependence of entropy on the length of the original time series, and the error caused by considering the amplitude information is suppressed. The performance of the proposed method is evaluated by synthetic signals and real bearing data, and compared with other traditional methods. By analyzing bearing signals of different fault types and different degrees of damage, it is verified that the proposed method can obtain more stable and reliable results and achieve higher fault diagnosis accuracy.

On the Behaviour of Weighted Permutation Entropy on Fractional Brownian Motion in the Univariate and Multivariate Setting

The estimation of the qualitative behaviour of fractional Brownian motion is an important topic for modelling real-world applications. Permutation entropy is a well-known approach to quantify the complexity of univariate time series in a scalar-valued representation. As an extension often used for outlier detection, weighted permutation entropy takes amplitudes within time series into account. As many real-world problems deal with multivariate time series, these measures need to be extended though. First, we introduce multivariate weighted permutation entropy, which is consistent with standard multivariate extensions of permutation entropy. Second, we investigate the behaviour of weighted permutation entropy on both univariate and multivariate fractional Brownian motion and show revealing results.

Refined Composite Multi-Scale Reverse Weighted Permutation Entropy and Its Applications in Ship-Radiated Noise.

Ship-radiated noise is one of the important signal types under the complex ocean background, which can well reflect physical properties of ships. As one of the valid measures to characterize the complexity of ship-radiated noise, permutation entropy (PE) has the advantages of high efficiency and simple calculation. However, PE has the problems of missing amplitude information and single scale. To address the two drawbacks, refined composite multi-scale reverse weighted PE (RCMRWPE), as a novel measurement technology of describing the signal complexity, is put forward based on refined composite multi-scale processing (RCMP) and reverse weighted PE (RWPE). RCMP is an improved method of coarse-graining, which not only solves the problem of single scale, but also improves the stability of traditional coarse-graining; RWPE has been proposed more recently, and has better inter-class separability and robustness performance to noise than PE, weighted PE (WPE), and reverse PE (RPE). Additionally, a feature extraction scheme of ship-radiated noise is proposed based on RCMRWPE, furthermore, RCMRWPE is combined with discriminant analysis classifier (DAC) to form a new classification method. After that, a large number of comparative experiments of feature extraction schemes and classification methods with two artificial random signals and six ship-radiated noise are carried out, which show that the proposed feature extraction scheme has better performance in distinguishing ability and stability than the other three similar feature extraction schemes based on multi-scale PE (MPE), multi-scale WPE (MWPE), and multi-scale RPE (MRPE), and the proposed classification method also has the highest recognition rate.

Repetitive anodal transcranial direct current stimulation improves neurological recovery by preserving the neuroplasticity in an asphyxial rat model of cardiac arrest

BackgroundNon-shockable rhythms present an increasing proportion of out-of-hospital cardiac arrest (CA) patients, but are associated with poor prognosis and received limited therapeutic effect of targeted temperature management (TTM). Previous study showed repetitive anodal transcranial direct current stimulation (tDCS) improved neurological outcomes in animals with ventricular fibrillation. Here, we examine the effectiveness of tDCS on neurological recovery and the potential mechanisms in a rat model of asphyxial CA. MethodCardiopulmonary resuscitation was initiated after 5 min of untreated asphyxial CA. Animals were randomized to three experimental groups immediately after successful resuscitation (n = 12/group, 6 males): no-treatment control (NTC) group, TTM group, and tDCS group. Post resuscitation hemodynamics, quantitative electroencephalogram (EEG), neurological deficit score, and 96-h survival were evaluated. Brain tissues of additional animals undergoing same experimental procedure was harvested for enzyme-linked immunoassay-based quantification assays of neuroplasticity-related biomarkers and compared with the sham-operated rats (n = 6/group). ResultsWe observed that after resuscitation tDCS-treated animals exhibited significantly higher mean arterial pressure and left ventricular ejection fraction than NTC group and showed greatly improved EEG characteristics including weighted-permutation entropy and gamma band power, and neurologic deficit scores and 96-h survival rates compared to NTC and TTM groups. Furthermore, neuroplastic biomarkers including microtubule-associated protein 2, growth-associated protein 43, postsynaptic density protein 95 and synaptophysin, were significantly higher in tDCS group when compared with NTC and TTM groups. ConclusionIn this rat model of asphyxial CA, repetitive anodal tDCS commenced after resuscitation improved neurological recovery, and it may exert a neuroprotective effect by preserving the neuroplasticity.

A multi-step ahead photovoltaic power prediction model based on similar day, enhanced colliding bodies optimization, variational mode decomposition, and deep extreme learning machine

Accurate photovoltaic power prediction is important to ensure the safety, stability, and economic operation of the power system after high photovoltaic demand. However, due to the intermittent and stochastic volatility characteristics of photovoltaic power, it is difficult to build satisfactory photovoltaic power prediction models. In this study, a similar day-based ultrashort-term multi-step ahead prediction model of photovoltaic power is proposed, which combines enhanced colliding bodies optimization (ECBO), variational mode decomposition (VMD), and a deep extreme learning machine (DELM). First, a new training data selection method based on grey correlation analysis and a Pearson correlation coefficient is proposed to find days that are similar to the predicted day. Second, the variational mode decomposition, based on enhanced colliding bodies optimization, is used to decompose the original photovoltaic power data into an ensemble of components with different amplitudes and frequencies, in which a new fitness function is designed based on a weighted-permutation entropy algorithm. Finally, the deep extreme learning machine network is employed to complete the prediction of each component, and the enhanced colliding bodies optimization algorithm is utilized again to obtain the optimal neuron numbers in hidden layers of the deep extreme learning machine; the ultimate prediction results of the photovoltaic power is obtained by reconstructing the prediction value of each component. The proposed model is tested with data from a real-world photovoltaic power station located in Xinjiang, China. The experimental results show that: (a) among all the competing models, the proposed model can achieve the highest multi-step prediction accuracy; (b) a qualitative breakthrough on the prediction accuracy improvement has been made by the proposed model in the 1-step and 2-step ahead prediction; (c) only a few parameters need to be tuned manually in the whole prediction process; the proposed model has good intelligence capabilities and can be easily applied and popularized in the practical projects.

Intelligent fault diagnosis of rolling bearings based on refined composite multi-scale dispersion q-complexity and adaptive whale algorithm-extreme learning machine

In order to extract the non-linear fault characteristics of rolling bearings more accurately, a novel nonlinear dynamical analysis method, referred to as the refined composite multi-scale dispersion q-complexity (RCMSDQC), is proposed for fault feature extraction of rolling bearings. To improve further the overall performance of the extreme learning machine (ELM) algorithm, the adaptive whale optimization algorithm (AWOA) is used to determine the input weights and hidden layer biases of the ELM. The RCMSDQC has the advantages of strong feature extraction ability and stability compared to the composite multi-scale weighted permutation entropy (CMSWPE) and composite multi-scale permutation entropy (CMSPE) methods. Furthermore, compared to the whale optimization algorithm, particle swarm optimization, and genetic algorithm, the AWOA shows a superior performance in the benchmark function comparison experiment. Based on the experimental rolling bearing data from the Paderborn University, the performance of the proposed method is further evaluated. The experimental results indicate that the proposed fault diagnosis method can identify the type and severity of rolling bearing faults with an accuracy of 99.1%.

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

In order to improve the classification performance of ship-radiated noise effectively, a comparative study of four multi-scale entropies is carried out by combining with grey relational degree (GRD) and a novel classification method for ship-radiated noise is proposed based on multi-scale reverse dispersion entropy (MRDE) and GRD, named MRDE-GRD. In this paper, MRDE is applied to the complexity feature extraction of ship-radiated noise under different scales, and GRD is used to identify different kinds of ship-radiated noise by calculating the GRD of the ship to be identified and reference ships. Experimental results show that the proposed MRDE-GRD classification method can effectively extract the complexity features of ship-radiated noise, and has better classification performance than the other three classification methods based on multi-scale permutation entropy (MPE), multi-scale weighted permutation entropy (MWPE) and multi-scale dispersion entropy (MDE) combined with GRD, named MPE-GRD, MWPE-GRD, and MDE-GRD. It is proved that the proposed classification method for ship-radiated noise is effective and achieves a recognition rate of 97.75%.

Modified multiscale weighted permutation entropy and optimized support vector machine method for rolling bearing fault diagnosis with complex signals

The rolling bearing vibration signals are complex, non-linear, and non-stationary, it is difficult to extract the sensitive features and diagnose faults by conventional signal processing methods. This paper focuses on the sensitive features extraction and pattern recognition for rolling bearing fault diagnosis and proposes a novel intelligent fault-diagnosis method based on generalized composite multiscale weighted permutation entropy (GCMWPE), supervised Isomap (S-Iso), and marine predators algorithm-based support vector machine (MPA-SVM). Firstly, a novel non-linear technology named GCMWPE was presented, allowing the extraction of bearing features from multiple scales and enabling the construction of a high-dimensional feature set. The GCMWPE uses the generalized composite coarse-grained structure to overcome the shortcomings of the original structure in multiscale weighted permutation entropy and obtain more stable entropy values. Subsequently, the S-Iso algorithm was introduced to obtain the main features and reduce the GCMWPE set dimensionality. Finally, a combination of GCMWPE and S-Iso set was input to the MPA-SVM for diagnosis and identification. The marine predators algorithm (MPA) was used to obtain the optimal SVM parameters. The effectiveness of the proposed fault diagnosis method was confirmed through two bearing fault diagnosis experiments. The results have shown that the proposed method can be used to correctly diagnose bearing states with high diagnostic accuracy.

Feature Extraction of Surface Electromyography Using Wavelet Weighted Permutation Entropy for Hand Movement Recognition.

The feature extraction of surface electromyography (sEMG) signals has been an important aspect of myoelectric prosthesis control. To improve the practicability of myoelectric prosthetic hands, we proposed a feature extraction method for sEMG signals that uses wavelet weighted permutation entropy (WWPE). First, wavelet transform was used to decompose and preprocess sEMG signals collected from the relevant muscles of the upper limbs to obtain the wavelet sub-bands in each frequency segment. Then, the weighted permutation entropies (WPEs) of the wavelet sub-bands were extracted to construct WWPE feature set. Lastly, the WWPE feature set was used as input to a support vector machine (SVM) classifier and a backpropagation neural network (BPNN) classifier to recognize seven hand movements. Experimental results show that the proposed method exhibits remarkable recognition accuracy that is superior to those of single sub-band feature set and commonly used time-domain feature set. The maximum recognition accuracy rate is 100% for hand movements, and the average recognition accuracy rates of SVM and BPNN are 100% and 98%, respectively.

A comparative study of four nonlinear dynamic methods and their applications in classification of ship-radiated noise

Refined composite multi-scale dispersion entropy (RCMDE), as a new and effective nonlinear dynamic method, has been applied in the field of medical diagnosis and fault diagnosis. In this paper, we first introduce RCMDE into the field of underwater acoustic signal processing for complexity feature extraction of ship radiated noise, and then propose a novel classification method for ship-radiated noise based on RCMDE and k-nearest neighbor (KNN), termed RCMDE-KNN. The results of a comparative experiment show that the proposed RCMDE-KNN classification method can effectively extract the complexity features of ship-radiated noise, and has better classification performance under one and two scales than the other three classification methods based on multi-scale permutation entropy (MPE) and KNN, multi-scale weighted-permutation entropy (MW-PE) and KNN, and multi-scale dispersion entropy (MDE) and KNN, termed MPE-KNN, MW-PE-KNN, and MDE-KNN. It is proved that the RCMDE-KNN classification method for ship-radiated noise is feasible and effective, and can obtain a very high recognition rate.

Ground reaction force complexity in hallux valgus

BackgroundInvestigating the complexity of movement systems can be insightful in clinical decision making. The study conducted to evaluate whether complexity of ground reaction force is affected by hallux valgus grades and footwear or foot side conditions. MethodsA sample of 120 females including 30 participants in each group of healthy and mild, moderate, and severe hallux valgus were recruited in this case-control study. Hallux valgus grades were assessed using Manchester scale. Ground reaction force were measured in bare foot and shod conditions for both feet and weighted permutation entropy was used to calculate the complexity. Nonparametric tests were employed for statistical inference. FindingsThe first important result was that hallux valgus caused loss of complexity of ground reaction force with a medium to large effect size. However, we did not find any difference between three grades of hallux valgus entropy. The second finding was that entropy of healthy group decreased from barefoot to shod condition with a large effect size and the third finding was that ground reaction force entropy were similar in both feet. InterpretationThe findings are aligned with the theory that loss of complexity appears when the biological systems become functionally impaired. As soon as hallux valgus initiates, all potential risks related to the reduction of complexity appear. So, we suggest to administer conservative treatments in the early stages of hallux valgus. The study outcomes can be used for evaluation of foot function, classification of the foot types, or footwear selection.

An Improved Hybrid Highway Traffic Flow Prediction Model Based on Machine Learning

For intelligent transportation systems (ITSs), reliable and accurate real-time traffic flow prediction is an important step and a necessary prerequisite for alleviating traffic congestion and improving highway operation efficiency. In this paper, we propose an improved hybrid predicting model including two steps: decomposition and prediction to predict highway traffic flow. First, we adopted the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method to adaptively decompose the original nonlinear, nonstationary, and complex highway traffic flow data. Then, we used the improved weighted permutation entropy (IWPE) to obtain new reconstructed components. In the prediction step, we used the gray wolf optimizer (GWO) algorithm to optimize the least-squares support vector machine (LSSVM) prediction model established for each reconstruction component and integrate the prediction results of each subsequence to obtain the final prediction result. We experimentally validated the effectiveness of the proposed approach. The research results reveal that the proposed model is useful for predicting traffic flow and its changing trends and also allowing transportation officials to make more effective traffic decisions.

Rescaled Range Permutation Entropy: A Method for Quantifying the Dynamical Complexity of Extreme Volatility in Chaotic Time SeriesSupported by the National Natural Science Foundation of China (Grant Nos. 51527805 and 11572220).

Information entropy, as a quantitative measure of complexity in nonlinear systems, has been widely researched in a variety of contexts. With the development of a nonlinear dynamic, the entropy is faced with severe challenges in dealing with those signals exhibiting extreme volatility. In order to address this problem of weighted permutation entropy, which may result in the inaccurate estimation of extreme volatility, we propose a rescaled range permutation entropy, which selects the ratio of range and standard deviation as the weight of different fragments in the time series, thereby effectively extracting the maximum volatility. By analyzing typical nonlinear systems, we investigate the sensitivities of four methods in chaotic time series where extreme volatility occurs. Compared with sample entropy, fuzzy entropy, and weighted permutation entropy, this rescaled range permutation entropy leads to a significant discernibility, which provides a new method for distinguishing the complexity of nonlinear systems with extreme volatility.

Adaptive carrier fringe pattern enhancement for wavelet transform profilometry through modifying intrinsic time-scale decomposition.

The uneven background illumination and random noise will degrade the quality of the optical fringe pattern, resulting in reduced accuracy or errors in phase extraction of wavelet transform profilometry (WTP). An adaptive fringe pattern enhancement method is proposed in this paper, which can effectively solve the above problems and improve the robustness of WTP. First, a modified intrinsic time-scale decomposition (MITD) algorithm is used to decompose each row of the fringe pattern adaptively, which can obtain a set of reasonable and pure proper rotation components (PRCs) with a frequency ranging from high to low and a monotonic trend. The MITD algorithm can overcome the mode mixing problem while ensuring the completeness of decomposition. Then, based on the obtained pure PRCs, an innovative background-carrier signal-noise automatic grouping strategy is proposed. Specifically, weighted-permutation entropy (WPE) is adopted to handle noise removal, and fuzzy gray correlation analysis (FGCA) is used to separate the background and carrier signal. Finally, the desired phase information can be easily and accurately extracted from the enhanced carrier signal component by a direct wavelet ridge detection method. Both the simulation and experimental results demonstrate the effectiveness and functionality of the proposed method.

Experimental study on early detection of cascade flutter in turbo jet fans using combined methodology of symbolic dynamics, dynamical systems theory, and machine learning

Cascade flutter driven by aerodynamic instability leads to severe structural destruction of turbine blades in aircraft engines. The development of a sophisticated methodology for detecting a precursor of cascade flutter is one of the most important topics in current aircraft engineering and related branches of nonlinear physics. A novel detection methodology combining symbolic dynamics, dynamical systems, and machine learning is proposed in this experimental study to detect a precursor of cascade flutter in a low-pressure turbine. Two important measures, the weighted permutation entropy in terms of symbolic dynamics and the determinism in recurrence plots in terms of dynamical systems theory, are estimated for the strain fluctuations on turbine blades to capture the significant changes in the dynamical state during a transition to cascade flutter. A feature space consisting of the two measures obtained by a support vector machine, can appropriately be classified into three dynamical states: a stable state, a transition state, and a cascade flutter state. The proposed methodology is valid for detecting a precursor of cascade flutter.

An Improved VMD-Based Denoising Method for Time Domain Load Signal Combining Wavelet with Singular Spectrum Analysis

Measured load data play a crucial role in the fatigue durability analysis of mechanical structures. However, in the process of signal acquisition, time domain load signals are easily contaminated by noise. In this paper, a signal denoising method based on variational mode decomposition (VMD), wavelet threshold denoising (WTD), and singular spectrum analysis (SSA) is proposed. Firstly, a simple criterion based on mutual information entropy (MIE) is designed to select the proper mode number for VMD. Detrended fluctuation analysis (DFA) is adopted to obtain the noise level of the noisy signal, which can optimize the selection of MIE threshold. Meanwhile, the noisy signal is adaptively decomposed into band-limited intrinsic mode functions (BLIMFs) by using VMD. In addition, weighted-permutation entropy (WPE) is applied to divide the BLIMFs into signal-dominant BLIMFs and noise-dominant BLIMFs. Then, the signal-dominant BLIMFs are reconstructed with the noise-dominant BLIMFs processed by WTD. Finally, SSA is implemented for the reconstructed signal. Experimental results of synthetic signals demonstrate that the presented method outperforms the conventional digital signal denoising methods and the related methods proposed recently. Effectiveness of the proposed method is verified through experiments of the measured load signals.

A novel method of composite multiscale weighted permutation entropy and machine learning for fault complex system fault diagnosis

A novel fault diagnosis method is proposed for rolling bearing by combining extreme-point symmetric mode decomposition (ESMD) composite multiscale weighted permutation entropy (CMWPE) and gravitational search algorithm based on multiple adaptive constraint strategy (MACGSA) optimized least squares support vector machine (LSSVM). In order to solve the problem of intrinsic mode function (IMF) modal aliasing and small differences in fault features, ESMD and CMWPE are used to obtain a more sensitive high-dimensional feature vector set. Aiming at the low accuracy of LSSVM fault diagnosis, MACGSA was used to optimize LSSVM to improve the accuracy of fault diagnosis. ESMD is used to process the rolling bearing data to obtain a series of IMFs; Then, extracting the CMWPE values of IMFs to form a high-dimensional feature vector set; Finally, the MACGSA-LSSVM model is adopted to achieve fault classification. Compared with other diagnostic methods, this method has higher diagnostic accuracy.

A Novel Microwave Treatment for Sleep Disorders and Classification of Sleep Stages Using Multi-Scale Entropy.

The aim of this study was to develop an integrated system of non-contact sleep stage detection and sleep disorder treatment for health monitoring. Hence, a method of brain activity detection based on microwave scattering technology instead of scalp electroencephalogram was developed to evaluate the sleep stage. First, microwaves at a specific frequency were used to penetrate the functional sites of the brain in patients with sleep disorders to change the firing frequency of the activated areas of the brain and analyze and evaluate statistically the effects on sleep improvement. Then, a wavelet packet algorithm was used to decompose the microwave transmission signal, the refined composite multiscale sample entropy, the refined composite multiscale fluctuation-based dispersion entropy and multivariate multiscale weighted permutation entropy were obtained as features from the wavelet packet coefficient. Finally, the mutual information-principal component analysis feature selection method was used to optimize the feature set and random forest was used to classify and evaluate the sleep stage. The results show that after four times of microwave modulation treatment, sleep efficiency improved continuously, the overall maintenance was above 80%, and the insomnia rate was reduced gradually. The overall classification accuracy of the four sleep stages was 86.4%. The results indicate that the microwaves with a certain frequency can treat sleep disorders and detect abnormal brain activity. Therefore, the microwave scattering method is of great significance in the development of a new brain disease treatment, diagnosis and clinical application system.

Coded Permutation Entropy: A Measure for Dynamical Changes Based on the Secondary Partitioning of Amplitude Information.

An improved permutation entropy (PE) algorithm named coded permutation entropy (CPE) is proposed in this paper to optimize the problems existing in PE based on the secondary partitioning. The principle of CPE algorithm is given, and the performance of it for dynamical change detection is analyzed using synthetic signal, logistic map and Lorenz map. The detection ability of CPE algorithm in different signal-to-noise ratios (SNR) is studied and the algorithm complexity is discussed. The results show that CPE can accurately capture minor feature information and amplify the detection results of dynamical changes compared with PE, weighted permutation entropy (WPE) and amplitude-aware permutation entropy (AAPE), but it has less robustness to noise and requires a higher computation cost than the others. Finally, we use the new algorithm to analyze the rolling bearing fault signals. The application of actual signals illustrates that CPE performs better in detecting abnormal pulse of the rolling bearing when the embedded dimension is small. From all the analyses in this paper, we find that CPE has a better performance for dynamical change detection compared with the other three algorithms when there is a larger repetition rate of permutation pattern in the position sequences.