Composite Multiscale Permutation Entropy Research Articles

Combined ICEEMDAN and CMPE noise reduction algorithm for dynamic deformation data

Abstract To effectively segregate complex noise components within Global Navigation Satellite System (GNSS) deformation data, a noise reduction algorithm is proposed, which integrates the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and composite multiscale permutation entropy (CMPE). The algorithm initially employs the ICEEMDAN algorithm to decompose the observed data into a series of intrinsic modal functions (IMFs), and then develops a CMPE-based effective coefficient sieving method to accurately classify the IMF that contains effective information components, thus obtaining the GNSS deformation data after noise separation. The processing outcomes of both simulated and empirically measured data reveal that the adopted approach surpasses a solitary filtering algorithm in achieving optimal noise mitigation. Notably, the application of this method leads to a diminution of the root mean square error (RMSE) metric associated with the sequence of elevation coordinates, resulting in a reduction to 2.837 mm post-denoising and an enhancement of 32.9% in overall precision.

Remaining useful life prediction of rolling bearing via composite multiscale permutation entropy and Elman neural network

Accurate prediction of remaining useful life (RUL) is very important for the maintenance of mechanical equipment. With the latest development in sensor technology and artificial intelligence, the data-driven prediction method of mechanical equipment RUL has been widely concerned. However, in the past, the research on data mining was not sufficient, and the method of extracting degradation features was single. In order to solve this problem, this paper proposes a new method to extract the degradation features of bearings. This method creatively combines image with entropy methods and uses the Symmetrized Dot Pattern (SDP) method and Composite Multiscale Permutation Entropy (CMPE) to extract degradation features. Through five evaluation indexes, the degradation feature extracted by the SDP-CMPE method is compared with five common degradation features in time domain. Finally, a simple Elman neural network is used to predict RUL. Through the case study of bearing data set, it is verified that the degradation features extracted by the SDP-CMPE method are superior in prediction accuracy and conservatism.

Multivariate variational mode decomposition and generalized composite multiscale permutation entropy for multichannel fault diagnosis of hoisting machinery system

Due to the harsh working environment of hoisting machinery system, the fault information of the important components is significantly complex, which leads to the fault signals not being collected completely by using only single channel. To alleviate this problem, acoustic emission (AE) experiments are applied to collect multichannel AE signal of hoisting machinery system. Additionally, a new intelligent fault diagnosis method based on multivariate variational mode decomposition (MVMD) and generalized composite multiscale permutation entropy (GCMPE) is proposed to extract multichannel AE fault features and implement multichannel fault diagnosis of hoisting machinery system. Firstly, based on variational mode decomposition (VMD) and the idea of multichannel AE data processing, MVMD is proposed to process the original multichannel AE signals collected from hoisting machinery system, which can obtain adaptively several multichannel modal components containing discriminative information. Meanwhile, GCMPE is presented to extract the fault information of multichannel modal components obtained by MVMD, which can improve the feature extraction performance of the original multiscale permutation entropy. The experimental results demonstrate the effectiveness and superiority of the proposed method in multichannel fault diagnosis of hoisting machinery system compared with some traditional single-channel analysis and other multichannel analysis methods.

Method for Locating Single-Phase Disconnection Faults in a Smart Distribution System Based on Refined Composite Multiscale Permutation q-Complexity Entropy and Random Forest

In this paper, a novel hybrid method of combining refined composite multi-scale permutation <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -complexity entropy (RCMPQE) and random forest (RF) is developed to locate disconnection faults in a power distribution system. As a feature extraction method, RCMPQE is used to analyze the negative-sequence current to obtain fault features, and then they are input into RF to build a fault location model. The effectiveness of the proposed method is corroborated by referencing a three-feeder distribution network. The results demonstrate that compared with multi-scale permutation entropy (MPE), refined composite multi-scale permutation entropy (RCMPE), and generalized multi-scale permutation entropy (GMPE), the RCMPQE has stronger feature extraction ability and can abstract more prominent fault information from negative-sequence current signals. The proposed method for locating faults significantly outperforms other commonly employed machine learning models, and it is immune to various levels of noise. Furthermore, the proposed method can perform well with a high fault location accuracy in a new system.

The Refined Composite Downsampling Permutation Entropy Is a Relevant Tool in the Muscle Fatigue Study Using sEMG Signals.

Surface electromyography (sEMG) is a valuable technique that helps provide functional and structural information about the electric activity of muscles. As sEMG measures output of complex living systems characterized by multiscale and nonlinear behaviors, Multiscale Permutation Entropy (MPE) is a suitable tool for capturing useful information from the ordinal patterns of sEMG time series. In a previous work, a theoretical comparison in terms of bias and variance of two MPE variants—namely, the refined composite MPE (rcMPE) and the refined composite downsampling (rcDPE), was addressed. In the current paper, we assess the superiority of rcDPE over MPE and rcMPE, when applied to real sEMG signals. Moreover, we demonstrate the capacity of rcDPE in quantifying fatigue levels by using sEMG data recorded during a fatiguing exercise. The processing of four consecutive temporal segments, during biceps brachii exercise maintained at 70% of maximal voluntary contraction until exhaustion, shows that the 10th-scale of rcDPE was capable of better differentiation of the fatigue segments. This scale actually brings the raw sEMG data, initially sampled at 10 kHz, to the specific 0–500 Hz sEMG spectral band of interest, which finally reveals the inner complexity of the data. This study promotes good practices in the use of MPE complexity measures on real data.

Series Arc Fault Detection of Grid-Connected PV System via SVD Denoising and IEWT-TWSVM

Series arc fault (SAF) is one of the most harmful faults during the operation of photovoltaic (PV) systems. It is a challenging task to find SAFs promptly for avoiding the PV fire. Aiming at the SAFs under different operating conditions, a novel detection algorithm by combining the Hankel singular value decomposition (Hankel-SVD) denoising method and the improved empirical wavelet transform–twin support vector machine (IEWT-TWSVM) is proposed. The Hankel-SVD algorithm is used to denoise the dc-bus current, which alleviates the influence of switching frequency and irrelevant background noise effectively. Then, the denoised current is decomposed by the IEWT, and the composite multiscale permutation entropy of each frequency band is input into the TWSVM classifier of the salp swarm optimization for completing the fault detection. The proposed algorithm not only can detect SAFs at various fault locations, but also resist dynamic shading, inverter startup, strong wind, and other interference phenomena. Moreover, the detection performance due to the arc transient process, a long-line fault, a single string array fault, a multiply string array fault, and different sampling rates of this model is verified in this study, and the corresponding results are relatively ideal. Experimental results show that the detection accuracy of the proposed method is as high as 98.10% for the measured data, which is more superior than other methods, such as wavelet decomposition, empirical mode decomposition, statistics methods including mean, standard deviation, and entropy.

A Cutting Pattern Recognition Method for Shearers Based on ICEEMDAN and Improved Grey Wolf Optimizer Algorithm-Optimized SVM

When the shearer is cutting, the sound signal generated by the cutting drum crushing coal and rock contains a wealth of cutting status information. In order to effectively process the shearer cutting sound signal and accurately identify the cutting mode, this paper proposed a shearer cutting sound signal recognition method based on an improved complete ensemble empirical mode decomposition with adaptive noise (ICCEMDAN) and an improved grey wolf optimizer (IGWO) algorithm-optimized support vector machine (SVM). First, the approach applied ICEEMDAN to process the cutting sound signal and obtained several intrinsic mode function (IMF) components. It used the correlation coefficient to select the characteristic component. Meanwhile, this paper calculated the composite multi-scale permutation entropy (CMPE) of the characteristic components as the eigenvalue. Then, the method introduced a differential evolution algorithm and nonlinear convergence factor to improve the GWO algorithm. It used the improved GWO algorithm to realize the adaptive selection of SVM parameters and established a cutting sound signal recognition model. According to the proportioning plan, the paper made several simulation coal walls for cutting experiments and collected cutting sound signals for cutting pattern recognition. The experimental results show that the method proposed in this paper can effectively process the cutting sound signal of the shearer, and the average accuracy of the cutting pattern recognition model reached 97.67%.

Application of the refined multiscale permutation entropy method to fault detection of rolling bearing

To detect the fault status and identify the fault category of rolling bearings in a timely manner, a method based on refined composite multiscale permutation entropy (RCMPE) and a support vector machine is proposed. Multiscale permutation entropy (MPE) is an improved method based on permutation entropy. Although this method can effectively perform dynamic analysis of nonlinear signals and fault monitoring of rolling bearings, the method is likely to lose some key information when shortening the time series during the identification of coarse-grained fault signals, which reduces the reliability of the results. To overcome this obstacle, the RCMPE algorithm is utilized to extract bearing feature information, and it is compared and analyzed with MPE and the multiscale entropy (MSE). Through simulation and experimental verification of the signal, it is found that as the scale factor increases, RCMPE can retain more useful information. The calculation results of fault identification are more accurate and have better robustness and stability. This method has less dependence on data length and is more stable in entropy estimation. This new diagnostic method is verified by actual bearing test data. The results show that the method can successfully distinguish the fault type and damage degree of rolling bearings and verify the effectiveness and superiority of the proposed method.

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.

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%.

Improvement of Statistical Performance of Ordinal Multiscale Entropy Techniques Using Refined Composite Downsampling Permutation Entropy.

Multiscale Permutation Entropy (MPE) analysis is a powerful ordinal tool in the measurement of information content of time series. MPE refinements, such as Composite MPE (cMPE) and Refined Composite MPE (rcMPE), greatly increase the precision of the entropy estimation by modifying the original method. Nonetheless, these techniques have only been proposed as algorithms, and are yet to be described from the theoretical perspective. Therefore, the purpose of this article is two-fold. First, we develop the statistical theory behind cMPE and rcMPE. Second, we propose an alternative method, Refined Composite Downsampling Permutation Entropy (rcDPE) to further increase the entropy estimation’s precision. Although cMPE and rcMPE outperform MPE when applied on uncorrelated noise, the results are higher than our predictions due to inherent redundancies found in the composite algorithms. The rcDPE method, on the other hand, not only conforms to our theoretical predictions, but also greatly improves over the other methods, showing the smallest bias and variance. By using MPE, rcMPE and rcDPE to classify faults in bearing vibration signals, rcDPE outperforms the multiscaling methods, enhancing the difference between faulty and non-faulty signals, provided we apply a proper anti-aliasing low-pass filter at each time scale.

Detection of ICE states from mechanical vibrations using entropy measurements and machine learning algorithms

1. Zheng P, Yang H. Generalized composite multiscale permutation entropy and laplacian score based rolling bearing fault diagnosis. Mechanical Systems and Signal Processing. 2018; 99: 229–243. https://doi.org/10.1016/j.ymss.... CrossRef Google Scholar

Rolling bearing fault diagnosis based on composite multiscale permutation entropy and reverse cognitive fruit fly optimization algorithm – Extreme learning machine

Rolling bearings usually work in complex environments, which makes them more prone to mechanical failures. Aiming at the non-stationary and nonlinear characteristics of its vibration signals, a fault diagnosis model based on composite multiscale permutation entropy (CMPE) and reverse cognitive fruit fly optimization algorithm optimized extreme learning machine (RCFOA-ELM) is proposed. Firstly, the particle swarm optimization optimized variational mode decomposition (PSO-VMD) is used to decompose the bearing vibration signal. Then the composite multiscale permutation entropy (CMPE) is used to calculate and compose the fault feature vector. Finally, input the feature sets into the optimized extreme learning machine (ELM) model for training and testing. Different types and different degrees of rolling bearing fault diagnosis experiments have proved that this model has a higher fault diagnosis recognition rate than other models. Therefore, this model can effectively improve the accuracy of fault classification and provide a new solution for rolling bearing fault diagnosis.

Multi-Feature Fusion-Based Mechanical Fault Diagnosis for On-Load Tap Changers in Smart Grid With Electric Vehicles

With the proliferation of electric vehicles (EVs), the supporting facilities and infrastructure become new components in conjunction with conventional electrical appliances. These novel appliances, e.g., charging piles and energy storage devices, bring new features as well as challenges to the existing power grid. To enhance the accuracy of mechanical fault identification for on-load tap changers (OLTCs) in smart grid with EVs, a feature selection method for OLTC mechanical fault identification is proposed in this paper. This method relies on the multi-feature fusion and the joint application of the K-nearest neighbors algorithm (KNN) and the improved whale optimization algorithm (IWOA). By multi-feature fusion, the high-dimensional set of time-domain and frequency-domain characteristics as well as energy and composite multi-scale permutation entropy can be constructed. As a result, the maximum correlation minimum redundancy (mRMR) principle can be used to screen the sensitive feature subsets. Finally, IWOA is used to optimize the sensitive feature subsets, and KNN is used to classify the different types of optimal feature subsets. The experimental results show that the proposed method is at least 8% more accurate than the existing methods. The high-accuracy nature of the proposed method can accelerate the promotion of EVs and the establishment of intelligent transportation environments.

Optimal Denoising and Feature Extraction Methods Using Modified CEEMD Combined with Duffing System and Their Applications in Fault Line Selection of Non-Solid-Earthed Network

As the non-solid-earthed network fails, the zero-sequence current of each line is highly non-stationary, and the noise component is serious. This paper proposes a fault line selection method based on modified complementary ensemble empirical mode decomposition (MCEEMD) and the Duffing system. Here, based on generalized composite multiscale permutation entropy (GCMPE) and support vector machine (SVM) for signal randomness detection, the complementary ensemble empirical mode decomposition is modified. The MCEEMD algorithm has good adaptability, and it can restrain the modal aliasing of empirical mode decomposition (EMD) at a certain level. The Duffing system is highly sensitive when the frequency of the external force signal is the same as that of the internal force signal. For automatically identifying chaotic characteristics, by using the texture features of the phase diagram, the method can quickly obtain the numerical criterion of the chaotic nature. Firstly, the zero-sequence current is decomposed into a series of intrinsic mode functions (IMF) to complete the first noise-reduction. Then an optimized smooth denoising model is established to select optimal IMF for signal reconstruction, which can complete the second noise-reduction. Finally, the reconstructed signal is put into the Duffing system. The trisection symmetry phase estimation is used to determine the relative phase of the detection signal. The faulty line in the non-solid-earthed network is selected with the diagram outputted by the Duffing system.

Fault Diagnosis for Rail Vehicle Axle-Box Bearings Based on Energy Feature Reconstruction and Composite Multiscale Permutation Entropy

The fault response signals of an axle-box bearing of a rail vehicle have strongly non-linear and non-stationary characteristics, which can reflect the operating state of the running gears. This paper proposes a novel method for bearing fault diagnosis based on frequency-domain energy feature reconstruction (EFR) and composite multiscale permutation entropy (CMPE). First, a wavelet packet transform (WPT) is applied to decompose the vibration signals into multiple frequency bands. Then, considering that the bearing-localized defects cause the axle-box bearing system to resonate at a high frequency, which will lead to uneven energy distribution of the signal in the frequency domain, the energy factors of each frequency band are calculated by an energy feature extraction algorithm, from which the frequency band with maximum energy factor (which contains abundant fault information) is reconstructed to the time-domain signal. Next, the complexity of the reconstructed signals is calculated by CMPE as fault feature vectors. Finally, the feature vectors are input into a medium Gaussian support vector machine (MG-SVM) for bearing condition classification. The proposed method is validated by a public bearing data set and a wheelset-bearing system test bench data set. The experimental results indicate that the proposed method can effectively extract bearing fault features and provides a new solution for condition monitoring and fault diagnosis of rail vehicle axle-box bearings.

A feature extraction method based on composite multi-scale permutation entropy and Laplacian score for shearer cutting state recognition

In the field of coal mining, accurate cutting state recognition of shearer is the basis and premise for achieving automatic coal cutting. In this paper, a novel shearer cutting state recognition method is presented based on composite multi-scale permutation (CMPE), Laplacian score (LS) and fly optimization algorithm-based support vector machine classification (FOA-SVM). CMPE is proposed to overcome the shortcomings of MPE and can extract the hidden state characteristics from the vibration signals of shearer rocker arm. Some simulations are provided to select the appropriate parameter settings and prove the superiority of CMPE to MPE. In addition, LS algorithm is employed to sort the extracted features over different scales according to their importance and the sensitive feature combinations can be generated scientifically. The FOA-SVM classifier is constructed to achieve intelligent recognition of shearer cutting state. Finally, some experiments are presented and the comparison results indicated that the proposed method can realize the recognition of shearer cutting state with higher accuracy than the existing methods.

A New Bearing Fault Diagnosis Method Based on Fine-to-Coarse Multiscale Permutation Entropy, Laplacian Score and SVM

Fault diagnosis of rotating machinery is vital to identify incipient failures and avoid unexpected downtime in industrial systems. This paper proposes a new rolling bearing fault diagnosis method by integrating the fine-to-coarse multiscale permutation entropy (F2CMPE), Laplacian score (LS) and support vector machine (SVM). A novel entropy measure, named F2CMPE, was proposed by calculating permutation entropy via multiple-scale fine-grained and coarse-grained signals based on the wavelet packet decomposition. The entropy measure estimates the complexity of time series from both low- and high-frequency components. Moreover, the F2CMPE mitigates the drawback of producing time series with sharply reduced data length via the coarse-grained procedure in the conventional composite multiscale permutation entropy (CMPE). The comparative performance of the F2CMPE and CMPE is investigated by analyzing the synthetic and experimental signals for entropy-based feature extraction. In the proposed bearing fault diagnosis method, the F2CMPE is first used to extract the entropy-based features from bearing vibration signals. Then, LS and SVM are used for selection of features and fault classification, respectively. Finally, the effectiveness of the proposed method is verified for rolling bearing fault diagnosis using experimental vibration data sets, and the results have demonstrated the capability of the proposed method to recognize and identify the bearing fault patterns under different fault states and severity levels.

A method based on refined composite multi-scale symbolic dynamic entropy and ISVM-BT for rotating machinery fault diagnosis

Multiscale symbolic dynamic entropy (MSDE) has been recently proposed to characterize the dynamical behavior of time series, which has merits of high computational efficiency and robustness to noise comparing with multiscale sample entropy (MSE) and multiscale permutation entropy (MPE). However, the variance of the MSDE values increases as the length of a time series becomes shorter using multiscale analysis. To address this shortcoming, a new method, namely refined composite multi-scale symbolic dynamic entropy (RCMSDE), is proposed to extract the fault information of rotating machinery. Then, Laplacian score (LS) is utilized to reduce the dimension of eigenvectors. In the end, the selected features are taken as the input of the improved support vector machine based on binary tree (ISVM-BT) for fault type identification. The effectiveness of the proposed method is validated using both the simulation and two experimental tests. Results demonstrate that the proposed method generates highest classification accuracy in comparison with existing methods such as MSDE, refined composite multiscale sample entropy (RCMSE) and refined composite multiscale permutation entropy (RCMPE).

Generalized composite multiscale permutation entropy and Laplacian score based rolling bearing fault diagnosis

Abstract Multiscale permutation entropy (MPE) is a recently proposed nonlinear dynamic method for measuring the randomness and detecting the nonlinear dynamic change of time series and can be used effectively to extract the nonlinear dynamic fault feature from vibration signals of rolling bearing. To solve the drawback of coarse graining process in MPE, an improved MPE method called generalized composite multiscale permutation entropy (GCMPE) was proposed in this paper. Also the influence of parameters on GCMPE and its comparison with the MPE are studied by analyzing simulation data. GCMPE was applied to the fault feature extraction from vibration signal of rolling bearing and then based on the GCMPE, Laplacian score for feature selection and the Particle swarm optimization based support vector machine, a new fault diagnosis method for rolling bearing was put forward in this paper. Finally, the proposed method was applied to analyze the experimental data of rolling bearing. The analysis results show that the proposed method can effectively realize the fault diagnosis of rolling bearing and has a higher fault recognition rate than the existing methods.