Envelope Entropy Research Articles

A Novel Lower-Limb Coordination Assessment Scheme Using Multi-Scale Nonlinear Coupling Characteristics With sEMG

Motor dysfunction (e.g., incoordination of upper or lower limb) significantly limits the individuals’ ability of daily living, and thus the provisioning of a motion coordination assessment method becomes of vital importance. As a quantitative indicator, inter-muscular coupling strength could assess limb coordination. Since surface electromyography (sEMG) signals cover nonlinear coupling characteristics, in this paper, a lower-limb motion coordination assessment scheme with intermuscular coherence (IMC) analysis and optimization variational mode decomposition (VMD) is proposed. First, sEMG signals are decomposed into several intrinsic mode functions (IMFs) using optimized VMD. Then, the nonlinear coupling feature vector in the beta-band frequency domian (15-35Hz) is extracted by the G-P algorithm from optimal IMF, thereby estimating intermuscular coupling strength by IMC. In particular, differential evolution (DE) algorithm’s global optimization capability and envelope entropy (EE)’s sparsity are adopted to provide the basis for optimization VMD and screening optimal IMF, respectively. Finally, signals are collected from four muscle pairs of the 12 male and 12 female subjects to assess lower-limb motions coordination. Simultaneously, the independent sample T test is leveraged to compare the effects of gender on groups’ characteristics (e.g., age, height, and body mass). Results demonstrate not only the effectiveness of the proposed approach (i.e., p < 0.01 with both “S-walking” and “Running” motions, p < 0.05 with “Q-walking”), but also the difference of motion coordination relationship between male and female adults as well as the significance of muscle selection.

An Improved VME Technique via Heap Based Optimization Algorithm and AWIT Method for PLI and MA Noise Elimination in ECG

Diagnosing cardiac conditions require careful examination of an electrocardiogram (ECG). However, a significant issue arises when capturing an ECG due to interference from various noises. Noises like power line interference (PLI) and muscle artifact (MA) change the morphology, making it difficult to interpret the original signal. Our research proposes an improved variational mode extraction (IVME) technique using a Heap-based optimization (HBO) algorithm and an automatic wavelet interval-dependent thresholding (AWIT) method to eliminate such noises. First, HBO uses the envelope entropy spectrum (EES) as the objective function to find the best fitness value for optimizing the VME parameter, known as penalty factor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> . Then, we extract a specific mode using the optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> value in VME to accurately remove PLI from the signal. Finally, the AWIT method automatically computes the intervals and their respective threshold values to remove excessive MA noise from the PLI-filtered ECG signal. We evaluate the efficiency of ten random real-time ECG signals from the MIT-BIH arrhythmia database. The result analysis proves that our algorithm can accurately extract the mode containing PLI and eradicate MA from the noisy ECG signal. It also shows improvement in signal parameters like signal-to-noise ratio (SNR <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\mathrm {improvement}}$ </tex-math></inline-formula> ), mean square error (MSE), and correlation coefficients (CC) with 36.7968 dB, 0.00030901, and 99.7278%, respectively.

A Novel Denoising Method for Partial Discharge Signal Based on Improved Variational Mode Decomposition

Partial discharge (PD) online monitoring is a common technique for high-voltage equipment diagnosis. However, due to field interference, the monitored PD signal contains a lot of noise. Therefore, this paper proposes a novel method by integrating the flower pollination algorithm, variational mode decomposition, and Savitzky–Golay filter (FPA-VMD-SG) to effectively suppress white noise and narrowband noise in the PD signal. Firstly, based on the mean envelope entropy (MEE), the decomposition number and quadratic penalty term of the VMD were optimized by the FPA. The PD signal containing noise was broken down into intrinsic mode functions (IMFs) by optimized parameters. Secondly, the IMFs were classified as the signal component, the noise dominant component, and the noise component according to the kurtosis value. Thirdly, the noise dominant component was denoised using the SG filter, and the denoised signal was mixed with the signal component to reconstruct a new signal. Finally, threshold denoising was used to eliminate residual white noise. To verify the performance of the FPA-VMD-SG method, compared with empirical mode decomposition with wavelet transform (EMD-WT) and adaptive singular value decomposition (ASVD), the denoising results of simulated and real PD signals indicated that the FPA-VMD-SG method had excellent performance.

Feature extraction method of ship radiated noise based on BOA-VMD and slope entropy

Although the technical requirements for the feature extraction of ship radiated noise (SRN) in the fields of national defense and economy increase with each passing day, the complexity of the marine environment makes the feature extraction of SRN difficult. The traditional feature extraction method based on variational mode decomposition (VMD) is widely used in the feature extraction of SRN. Nevertheless, the use of VMD is greatly affected by parameters. In this paper, the butterfly optimization algorithm (BOA) is introduced to optimize VMD, which is called BOA-VMD algorithm, and realizes the optimal selection of VMD parameters K and α. To further improve the efficiency of feature extraction method, combined with slope entropy (SE), a feature extraction method of SRN based on BOA-VMD and SE is proposed. The experimental results of the simulated signal show that the BOA-VMD algorithm has a smaller envelope entropy value and better decomposition effect than the genetic algorithm (GA) and particle swarm optimization (PSO). The experimental results of feature extraction of SRN show that the highest recognition rate of the four entropy values improve with the increase of the number of extracted features, compared with the three entropy values of dispersion entropy (DE), fluctuation dispersion entropy (FDE) and permutation entropy (PE), the SRN feature extraction method based on BOA-VMD and SE has the highest recognition rate under different quantity features, and the recognition rate has reached 100% under three features.

An improved method for fault diagnosis of rolling bearings of power generation equipment in a smart microgrid

In the construction of smart microgrids for petrochemical enterprises, the generating unit is an important part, and the rolling bearings are one of the key components of the generator. The condition of the rolling bearing directly affects the safe operation of the entire generating unit and an accurate fault diagnosis of the bearing not only can improve the stability of the smart microgrid, but also can reduce the risk of loss of the factory. This study proposes an improved fault diagnosis method based on variational modal decomposition (VMD) and a convolutional neural network (CNN). The VMD algorithm was used to remove random noise in the original signal and a CNN was used to extract useful data from the vibration signal processed by VMD. Since the modal number and penalty parameter of the VMD are difficult to choose and they have a profound impact on the decomposition results, differential evolution (DE) was used as the optimization method and envelope entropy was used as the fitness function to optimize the VMD parameters. Since it is difficult to ensure the best fit of the hyper-parameters of CNN, this study proposes a method for using the DE algorithm to obtain suitable hyper-parameters for the CNN, and then used the CNN to diagnose a fault. The test results using the vibration data of Case Western Reserve University show that the combination of VMD and CNN can improve the convergence speed more than 10% and the accuracy to over 99.6%.

Improved Variational Mode Decomposition and One-Dimensional CNN Network with Parametric Rectified Linear Unit (PReLU) Approach for Rolling Bearing Fault Diagnosis

As a critical component of rotating machinery, rolling bearings are essential for the safe and efficient operation of machinery. Sudden faults of rolling bearings can lead to unscheduled downtime and substantial economic costs. Therefore, diagnosing and identifying the equipment status is essential for ensuring the operation and decreasing the additional maintenance costs of the machines. However, extracting the features from the early bearing fault signals is challenging under background noise interference. With the purpose of solving the above problem, we propose an integrated rolling bearing fault diagnosis model based on the improved grey wolf optimized variational modal decomposition (IGVMD) and an improved 1DCNN with a parametric rectified linear unit (PReLU). Firstly, an improved grey wolf optimizer (IGWO) with the fitness function, the minimum envelope entropy, is designed for adaptively searching the optimal parameter values of the VMD model. The performance of the basic grey wolf optimizer (GWO) algorithm by introducing three improvement strategies, the non-linear convergence factor adjustment strategy, the grey wolf adaptive position update strategy, and the Levy flight strategy in the IGWO algorithm, is improved. Then, an improved 1DCNN model with the PReLU activation function is proposed, which extracts the bearing fault features, and a grid search to optimize the model parameters of the 1DCNN is introduced. Finally, the effectiveness of the proposed model is demonstrated well by employing two experimental datasets. The preliminary comparative results of the average identification accuracy in the proposed method in two datasets are 99.98% and 99.50%, respectively, suggesting that this proposed method has a relatively higher recognition accuracy and application values.

A Denoising Method for Ship-Radiated Noise Based on Optimized Variational Mode Decomposition with Snake Optimization and Dual-Threshold Criteria of Correlation Coefficient

The ship-radiated noise (SN) is easily affected by other hydroacoustic objects or complex ocean noise when it spreads through water. In order to reduce the impact from the environment, a denoising method for SN based on optimized variational mode decomposition with snake optimization (SO-VMD) and dual-threshold criteria of correlation coefficient (CC) is proposed in this paper. The first step is to optimize the parameter combination, that is, decomposition number K and penalty factor α, of variational mode decomposition (VMD) by snake optimization (SO) with envelope entropy (EE). Then, the input signal using the optimized results is decomposed and the intrinsic mode functions (IMFs) are obtained. After that, the IMFs are classified into three classes with the dual-threshold criteria of CC, including signal components, signal-noise components, and noise components. Finally, all the signal components and the processed signal-noise components denoised by wavelet threshold (WT) are reconstructed together. Simulations performed in this paper demonstrate that SO is the more appropriate optimization for VMD and the proposed method has the more outstanding performance in denoising different kinds of test signals. In addition, experiments on measured SNs show that the proposed method is effective and accurate in denoising.

Mechanical Fault Diagnosis of a Disconnector Operating Mechanism Based on Vibration and the Motor Current

The mechanical fault diagnosis of a disconnector operating mechanism using a single signal is not sufficiently accurate and reliable. To address this problem, this paper proposes a new fault diagnosis method based on the vibration signal and the motor current signal. First, based on the analysis of the motor stator current signal envelope, segmented envelope RMS values are extracted. Then, the vibration signal of the operating mechanism is processed with VMD (Variational Mode Decomposition). In this paper, the number of modal decompositions K is selected according to the envelope entropy. Second, the effective value of the current segment envelope is fused with the energy entropy value of each IMF component to construct the feature parameters for fault identification. Finally, a fusion weighting algorithm using AdaBoost is proposed to train an SVM as a strong classifier to improve the correct fault diagnosis rate. In this paper, the proposed new diagnosis method is applied to a 220 kV disconnector operating mechanism. The algorithm can effectively identify three operating states of a disconnector operating mechanism.

An Optimized VMD Method for Predicting Milling Cutter Wear Using Vibration Signal

Tool wear has a negative impact on machining quality and efficiency. As for the nonlinear and non-stationary characteristics of vibration signals and strong background noises during the milling process, an identification method of the milling cutter wear state based on the optimized Variational Mode Decomposition (VMD) was proposed, in which the objective function is to minimize the Envelope Entropy (Ep); the various modes of the vibration signal are decomposed using the self-adaptive optimization parameters with Differential Evolution (DE). According to the cross-correlation coefficient in the frequency domain between Intrinsic Mode Function (IMF) and the original signals, the informative IMF components were selected as the sensitive IMF components to superimpose the reconstruction signal and extract the eigenvalues. The mapping relationship between the eigenvalues and the milling cutter wear degree is established by the Naive Bayes classifier method. The experimental results under the various operation conditions indicate that the proposed optimized VMD method possesses an excellent generalization performance. Compared with Empirical Mode Decomposition (EMD) and Ensemble Empirical Mode Decomposition (EEMD), it has better denoising capacity, and so can improve the identification accuracy of the milling cutter wear. Therefore, the processing quality and production efficiency are ensured effectively.

Ultra-Short-Term Wind Speed Forecasting Using the Hybrid Model of Subseries Reconstruction and Broad Learning System

The traditional decomposition–combination wind speed forecasting model has high complexity and a long calculation time. As a result, an ultra-short-term wind speed hybrid forecasting model based on a broad learning system (BLS) that combines improved variational mode decomposition (EPSO-VMD, EVMD) and subseries reconstruction (SR) is proposed in this work. The values of K and α in the EVMD are determined by minimum mean envelope entropy (MMEE) and enhanced particle swarm optimization (EPSO), and EVMD is used to decompose the original wind speed data. SR is applied to recombine the subseries obtained by EVMD to improve the forecasting efficiency. The sample entropy (SE) is used to quantify the subseries’ complexity, and they are then adaptively divided into high-entropy and low-entropy subseries. Adjacent high-entropy subseries of approximate entropy values are merged to obtain a new group of reconstructed high-entropy subseries, while the low-entropy subseries merge into a new subseries as well. Then, the forecasting results of the reconstructed high- and low-entropy subseries are calculated via the BLS and ARIMA models. Numerical simulation results show that the proposed method is more effective than traditional methods.

Pipeline signal feature extraction method based on multi-feature entropy fusion and local linear embedding

This paper considers the problem of effective feature extraction of acoustic signals from oil and gas pipelines under different working conditions. A feature extraction of pipeline leakage detection method is proposed based on multi-feature entropy fusion and local linear embedding (LLE). First, seven kinds of commonly used entropy which can reflect the characteristics of the signal better are extracted from the pipeline signal through experiments, including permutation entropy, envelope entropy, approximate entropy, fuzzy entropy, energy entropy, sample entropy and dispersion entropy. The seven-dimensional feature vectors are obtained by feature fusion. Second, the LLE algorithm is used to reduce the dimension of the feature vector to complete the secondary feature extraction. Finally, the support vector machine (SVM) is used to identify the working conditions of the pipeline. The experimental results show that, compared with other dimensionality reduction methods, single-feature entropy method and multi-feature entropy fusion method, the proposed method can identify the types of pipeline working conditions effectively and reduce the problems of false negatives and false positives in pipeline leakage detection.

An Adaptive Graph Morlet Wavelet Transform for Railway Wayside Acoustic Detection

Monitoring condition of train axle bearings is significant for ensuring the safety of train operation. Wayside acoustic detection technology is a promising tool for early fault detection of train axle bearings. However, the strong background noise exists in collected acoustic signals, which normally masks the fault feature of axle bearings. In this work, a novel method called adaptive graph Morlet wavelet transform (AGMWT), is proposed for fault feature extraction in railway wayside acoustic detection. In AGMWT, acoustic signals are firstly transformed into horizontal visibility graphs. Next, the inner product operation is conducted to measure the similarity between the graph and daughter wavelets which are translated and scaled versions of the mother Morlet wavelet. An adaptive wavelet threshold and a shrinkage strategy are then proposed to shrink the graph Morlet wavelet coefficient, and finally the denoised signal can be obtained using inverse transform. To improve denoising performance, parameters of the mother Morlet wavelet are then optimised according to the Hilbert envelope spectrum fault feature ratio and the Hilbert envelope entropy. The effectiveness of the proposed method has been verified by conducting simulation, laboratory and field experiments. In addition, the denoising ability of AGMWT has advantages comparing other methods.

A frequency-weighted energy operator and swarm decomposition for bearing fault diagnosis

The weak fault characteristics of rolling bearings are difficult to identify due to strong background noise. To address this issue, a bearing fault detection scheme combining swarm decomposition (SWD) and frequency-weighted energy operator (FWEO) is presented. First, SWD is applied to decompose the bearing fault signal into single mode components. Then, a new evaluation index termed LEP is constructed by combining the advantages of envelope entropy, Pearson correlation coefficient and L-kurtosis, and it is utilized to choose the sensitive component containing the richest bearing fault characteristics. Finally, FWEO is employed for extracting the bearing fault features from the sensitive component. Simulation and experimental analyses indicate that the LEP index has better performance than the L-kurtosis index in determining the sensitive component. The method has the effect of suppressing noise and enhancing impulse characteristics, which is superior to the SWD-based envelope demodulation method.

Bearing Fault Feature Extraction Method Based on GA-VMD and Center Frequency

To promote the effect of variational mode decomposition (VMD) and further enhance the recognition performances of bearing fault signals, genetic algorithm (GA) is applied to optimize the combination of VMD parameters in this paper, and GA-VMD algorithm is put forward to improve the decomposition accuracy of VMD. In addition, combined with the center frequency, a feature extraction method based on GA-VMD and center frequency is proposed to ameliorate the difficulty of bearing fault feature extraction. Firstly, the bearing signal is decomposed into a series of intrinsic mode components (IMFs) by GA-VMD. Then, the Center Frequency of IMFs is extracted, and the recognition rate is calculated by k-nearest neighbor (KNN) algorithm. Simulation signal experiments state clearly that, compared with manual parameter setting-VMD algorithm and parameter optimization VMD algorithm based on particle swarm optimization (PSO), the decomposition result of GA-VMD has a smaller root mean square error and higher decomposition accuracy, which verifies the effectiveness of GA-VMD. The experimental results demonstrate that, by comparison with the feature extraction method based on envelope entropy, the feature extraction method based on center frequency has better inter class separability and higher mean recognition rate (the highest recognition rate of single feature is 94.5%, and in the case of multiple features, the recognition rate reaches 100% when four features are extracted) and can realize the accurate identification of different bearing fault signals.

Fault diagnosis of rolling bearings based on improved direct fast iterative filtering and spectral amplitude modulation

As the transient impulse components in early fault signals are weak and easily buried by strong background noise, the fault features of rolling bearings are difficult to be extracted effectively. Focusing on this issue, a novel method based on improved direct fast iterative filtering and spectral amplitude modulation (IDFIF-SAM) is presented for detecting the early fault of rolling bearings. First, the ratio of the average crest factor of autocorrelation envelope spectrum to the average envelope entropy is taken as the fitness function to search the optimal parameters of direct fast iterative filtering (DFIF) adaptively via particle swarm optimization (PSO). Then, the efficient kurtosis entropy (EKE) index is being employed to choose the suitable components to reconstruct the signal. Finally, the reconstructed signal is subjected to spectral amplitude modulation (SAM) to strengthen the impulse features. The superiority of improved direct fast iterative filtering (IDFIF) over fixed-parameter DFIF, fast iterative filtering (FIF), and hard thresholding fast iterative filtering (HTFIF) is clarified through the simulated signal. Moreover, the comparative experimental analysis shows that the proposed IDFIF-SAM method can identify the early fault feature of rolling bearings more effectively.

A New Feature Extraction Technique for Early Degeneration Detection of Rolling Bearings

Feature extraction technology is an important part of bearing diagnosis, especially for early degradation detection. However, the traditional feature extraction technology can not effectively remove noise or is not sensitive to periodic weak faults, which leads to be inclined to raise false alarms and prediction delay for early degradation detection. In order to solve these two issues, a new feature extraction technique is presented based on Envelope Harmonic-to-noise Ratio (EHNR) and Adaptive Variational Mode Decomposition (AVMD). First of all, the minimum average envelope entropy is used as the objective function to search the optimal parameters of the Variational Modal Decomposition (VMD) adaptively by the Grey Wolf Optimization (GWO) algorithm. The problem of under-decomposition or over-decomposition caused by improper parameter setting is avoided. Then, a new index called Effective Weighted Sparseness Kurtosis (EWSK) is proposed. This index can separate the effective modal components and noise modal components only by the positive and negative results, so as to achieve the purpose of removing noise interference and retaining a large amount of fault information. Finally, the EHNR of the reconstructed signal is calculated, and its sensitivity to periodic fault shock is utilized to detect the early degradation starting point of the rolling bearing. Experimental results show that the proposed method outperforms several state-of-the-art detection methods in terms of early degradation point detection, false alarm rate and computational complexity. The superior performances of the presented AVMD-EHNR method can provide the basis for early fault diagnosis and remaining useful life prediction of rolling bearings.

A novel method for online real-time forecasting of crude oil price

Improving the accuracy of crude oil price forecasting is helpful for stabilizing financial markets and oil import and export trade. However, the extant models rarely focus on the online forecasting and uncertainty of crude oil price. Motivated by these, a new forecasting method is proposed. Firstly, the price sequence is decomposed to get the regular sub-sequences and noise sequence by the improved variational mode decomposition, whose parameters are optimized by particle swarm optimization based on average maximum envelope entropy. Secondly, the proposed hybrid model of point prediction is established by the characteristics of sub-sequences, and the interval prediction model is constructed by combining the point prediction model and Bootstrap sampling. Finally, the proposed point prediction model and interval prediction model are formed into a predictor to realize online real-time prediction. The empirical results show that, compared with other competing models, the proposed model for point prediction improves basically by over 10% on loss functions in the different frequency data, which verifies that it is superior to other models in accuracy and robustness. The coverage rate and fluctuation consistency are almost all more than 70% in the interval prediction results. In a word, the proposed method has high flexibility and accuracy, which can provide referring information for practitioners working with oil.

Radar signals modulation recognition based on bispectrum feature processing

Modulation recognition of radar signals is an important part of modern electronic intelligence reconnaissance and electronic support systems. In this paper, to solve the problem of low recognition accuracy and low noise resistance of radar signals under low signal-to-noise ratio(SNR), a recognition method based on variational mode decomposition(VMD) and bispectrum feature extraction is proposed. Based on the feature that bispectrum can suppress Gaussian noise, the feasibility of signals modulation recognition under low SNR is analyzed and the noise item is introduced. Due to the interference of noise item, the noise suppression effect of bispectrum is worse under 0dB. An improved VMD algorithm based on artificial bee colony(ABC) algorithm optimization and envelope entropy evaluation is proposed to preprocess the signal to improve the SNR. Finally, we designed a convolution neural network(CNN) classifier to recognize signals of different modulation types. The simulation results show that this method has better noise resistance than traditional methods, and can effectively identify different types of signals under low SNR.

Research on unknown fault diagnosis of rolling bearings based on parameter-adaptive maximum correlation kurtosis deconvolution.

Maximum correlation kurtosis deconvolution (MCKD) is an effective means of identifying the periodic impulses of fault signals. However, the multiple input parameters required by MCKD complicate the process of fault diagnosis. To overcome this drawback, a new method for identifying fault types based on a parameter-adaptive MCKD method is proposed. First, an improved adaptive variational mode decomposition is developed to denoise the raw signal. The improved method adopts the weighted envelope entropy, which is constructed by combining the envelope entropy with the kurtosis, allowing the salience of the denoising performance to be evaluated. Furthermore, the mean maximum correlation kurtosis is constructed to allow the specification of fault types and the corresponding parameters. Finally, two rolling bearing test datasets are used to demonstrate the strong adaptability of this method compared with other adaptive techniques.

A Method for Pulse Signal Denoising Based on VMD Parameter Optimization and Grey Wolf Optimizer

Aiming at the difficulty of parameter determination when using variational modal decomposition algorithm (VMD) to decompose photoplethysmographic(PPG) pulse wave signals, α VMD parameter optimization method based on Grey Wolf Optimizer (GWO) is proposed. In this paper, the envelope entropy of the K eigenmode component (IMF) after VMD decomposition is used as the fitness function, and the grey wolf optimization algorithm (GWO) is used to find the K sum corresponding to the minimum envelope entropy of the eigenmode component α, to determine the optimal value of the VMD algorithm parameters, and then use the parameter optimized VMD algorithm to filter out the noise in the PPG signal. The experimental results show that after decomposing the PPG signal using the algorithm in this paper, the effective component and the noise component of the signal are well separated. After selecting the appropriate IMF component for reconstruction, the noise in the PPG signal is effectively filtered out.