Band-limited Intrinsic Mode Functions Research Articles

A novel vibro-acoustic fault diagnosis approach of planetary gearbox using intrinsic wavelet integrated GE-EfficientNet

Planetary gearbox operates under complex working conditions involving high speed, heavy load, and corrosion. When the planetary gearbox is in tight spaces, it is difficult to measure its signal by conventional methods. In this case, acoustic sensors can measure signal with the noncontact method. This paper proposes a vibro-acoustic fault diagnosis method with respect to planetary gearbox. The method addresses challenges related to weak vibro-acoustic signal, difficulty in extracting fault features, and low diagnostic accuracy and efficiency. Firstly, vibro-acoustic signal is captured by a unidirectional microphone. Next, intrinsic wavelet analysis extracts intrinsic features of the planetary gears. The band-limited intrinsic mode functions (BLIMFs) of the acoustic signal are obtained by optimized variational mode decomposition, and the BLIMFs are then transformed into time-frequency map features. Finally, these time-frequency map features are utilized as the inputs for Ghost module and Efficient channel attention module (GE)-improved EfficientNet model, namely GE-EfficientNet model, to achieve fault diagnosis of planetary gearbox. The superiority of the proposed method is verified by the experimental results which show that the diagnostic accuracy of GE-EfficientNet reached 100%, and the floating-point operations and parameter numbers are only 5.1 G and 0.4 MB, respectively. The results demonstrate that the proposed vibro-acoustic fault diagnosis method achieves good diagnostic accuracy and efficiency.

A novel fault diagnosis approach of rolling bearing using intrinsic feature extraction and CBAM-enhanced InceptionNet

Rolling bearings play a crucial role as components in mechanical equipment. Malfunctioning rolling bearings can disrupt the normal operation of the equipment and pose safety hazards. Traditional deep learning-based methods for diagnosing faults in rolling bearings present several issues, such as insufficient feature information of fault samples, high model complexity and low accuracy. To overcome these challenges, this paper introduces an intelligent approach for rolling bearing fault diagnosis using intrinsic feature extraction and convolutional block attention module (CBAM)-enhanced InceptionNet. In our researches, variational mode decomposition (VMD) is adopted to decompose the original signal into multiple band-limited intrinsic mode functions (BLIMFs). In the decomposition process of VMD, the number of decomposition layers k is determined by center frequency method and the optimal BLIMF is chosen based on minimum envelope entropy. Subsequently, the continuous wavelet transform is employed to transform the optimal BLIMFs into time-frequency images. Finally, the obtained time-frequency images are fed into the proposed CBAM-enhanced InceptionNet for fault state diagnosis. Experiments on two different datasets prove that the method has stable and reliable accuracy. Comparative experiments have demonstrated that this method can reduce network model parameters and improve diagnosis efficiency while achieving high accuracy.

Fault diagnosis of low‐speed rolling bearing based on weighted reconstruction of vibration envelopes

AbstractThe main bearing supports the rotation of the main shaft of a wind turbine. It bears heavy dead weights as well as variable speed dynamic loading during operations; thus, it is a vulnerable part in a wind turbine drive train. Because of the low speed and time‐varying operations of the main bearing, vibrations generated by bearing faults are often weak in response amplitudes, low in frequency range, and smeared in damage feature energy. As a result, the applicability of the conventional acceleration envelope analysis (AEA) technique, a traditionally effective technology for bearing fault diagnosis, is limited in such cases. In order to resolve this, a modified AEA method specially designed for bearings with low and variable speed operation is proposed in this paper. First, the structural response is decomposed by means of variational mode decomposition (VMD) for the low frequency components to form a series of band‐limited intrinsic mode functions (BLIMFs). Next, weighting factors are determined for the BLIMFs by defined energy ratios. Finally, a new envelope is reconstructed by weighting the envelopes of each BLIMF for bearing fault diagnosis. The effectiveness and practicality of the proposed method for the diagnosis of main bearing faults in wind turbines is verified through the analysis of measured data from a wind turbine in the field. The proposed method provides an effective way for bearing fault diagnosis at low and variable rotational speeds.

Seismic Signal Analysis Based on Variational Mode Decomposition and Hilbert Transform for Ground Intrusion Activity Classification.

The identification of ground intrusion is a key and important technology in the national public security field. In this paper, a novel variational mode decomposition (VMD) and Hilbert transform (HT) is proposed for the classification of seismic signals generated by ground intrusion activities using a seismic sensing system. Firstly, the representative seismic data, including bicycles, vehicles, footsteps, excavations, and environmental noises, were collected through the designed experiment. Secondly, each original datum is decomposed through VMD and five Band-limited intrinsic mode functions (BIMF) are obtained, respectively, which will be used to generate a corresponding marginal spectrum that can reflect the actual frequency component of the signal accurately by HT. Then, three features related to the marginal spectrum, including marginal spectrum energy, marginal spectrum entropy, and marginal spectrum dominant frequency, are extracted for the analysis of the multi-classification using the support vector machine (SVM) classifier with the LIBSVM library. For the sake of testing and verifying the effectiveness of the proposed variational mode decomposition and Hilbert transform (VMD-HT) technique, the evaluation indicators including accuracy, precision, recall, and F1-Score are used and the results are compared with the time domain, frequency domain, ensemble empirical mode decomposition (EEMD), and empirical wavelet transform (EWT) combined with the HT analysis method. The performance of the VMD-HT method for ground intrusion activity classification provides an average value of 99.50%, 98.76%, 98.76%, and 98.75% for the four evaluation indicators, which are higher than all the other contrasted methods.

ResNet-integrated very early bolt looseness monitoring based on intrinsic feature extraction of percussion sounds

Very early bolt looseness monitoring has been a challenge in the field of structural health monitoring. The authors have conducted a further study of the previous researches, with the aim of detecting very early bolt looseness conditions. The intrinsic features of vibro-acoustic signals contain the underlying dynamic characteristics denoting full range bolt looseness conditions. Correspondingly, this paper proposes a novel ResNet-integrated very early bolt looseness monitoring approach based on intrinsic feature extraction of percussion sounds. The intrinsic features of percussion-caused sound signals were extracted by variational mode decomposition (VMD), where the parameters of VMD were determined by grey wolf optimization algorithm. The optimal band-limited intrinsic mode functions were converted into two-dimensional time–frequency maps by continuous wavelet transform. The (red green blue) RGB images were adopted as the input of residual network (ResNet) to monitor very early bolt looseness conditions. The results and analysis illustrate the validity and superiority of the novel ResNet-integrated very early bolt looseness monitoring approach. The proposed approach in our researches provides a novel solution for very early bolt looseness monitoring in the field of structural health monitoring. The strategy can also be extended to other nonlinear signal processing-involved fields.

Error Compensation for Optical Encoder Based on Variational Mode Decomposition With a Coarse-to-Fine Selection Scheme

To further improve the compensation performance of the optical encoder at a reasonable speed, a novel error compensation method is proposed based on variational mode decomposition (VMD) with a coarse-to-fine selection scheme. We make the first attempt to introduce the VMD into error compensation for the optical encoder due to its excellent abilities of mode-mixing suppression and low computational cost. First, the VMD with an adaptive parameter selection scheme is proposed to decompose the measurement error into several band-limited intrinsic mode functions (BLIMFs). Then, a coarse-to-fine selection scheme is proposed to adaptively select eligible BLIMFs, which are used to reconstruct the systematic error from the measurement error. The coarse selection scheme is proposed based on permutation entropy (PE) to select the candidate BLIMFs with low randomness and complexity. Also, a contribution factor is defined to finely select the eligible BLIMFs from the candidate BLIMFs, which is defined by combining PE and optimal effective singular rank of each candidate BLIMF. Experimental results indicate that the proposed method is superior to the existing compensation methods, which can achieve an excellent compensation precision of root-mean-square error (RMSE) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.335 ~\mu \text{m}$ </tex-math></inline-formula> and 95% confidence interval (−0.015, 0.014) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> .

A Novel Multivariate Cutting Force-Based Tool Wear Monitoring Method Using One-Dimensional Convolutional Neural Network.

Tool wear condition monitoring during the machining process is one of the most important considerations in precision manufacturing. Cutting force is one of the signals that has been widely used for tool wear condition monitoring, which contains the dynamical information of tool wear conditions. This paper proposes a novel multivariate cutting force-based tool wear monitoring method using one-dimensional convolutional neural network (1D CNN). Firstly, multivariate variational mode decomposition (MVMD) is used to process the multivariate cutting force signals. The multivariate band-limited intrinsic mode functions (BLIMFs) are obtained, which contain a large number of nonlinear and nonstationary tool wear characteristics. Afterwards, the proposed modified multiscale permutation entropy (MMPE) is used to measure the complexity of multivariate BLIMFs. The entropy values on multiple scales are calculated as condition indicators in tool wear condition monitoring. Finally, the one-dimensional feature vectors are constructed and employed as the input of 1D CNN to achieve accurate and stable tool wear condition monitoring. The results of the research in this paper demonstrate that the proposed approach has broad prospects in tool wear condition monitoring.

Fault diagnosis of planetary gears based on intrinsic feature extraction and deep transfer learning

The planetary gearbox is a key transmission apparatus used to change speed and torque. The planetary gear is one of the most failure-prone components in a planetary gearbox. Due to the complexity of working environments, collected vibration signals contain a lot of noise and interference; fault characteristic frequencies are usually submerged or even lost. Thus, feature extraction from the vibration signal is beneficial to subsequent fault diagnosis. As a fault identification approach that has been increasingly popular in the field of fault diagnosis, deep learning requires a large number of samples to train the model. Insufficient samples lead to low diagnostic accuracy for deep learning models. This paper proposes a novel fault diagnosis approach for planetary gears based on intrinsic feature extraction and deep transfer learning. The original vibration signals are decomposed into a series of band-limited intrinsic mode functions (BLIMFs) by variational mode decomposition. BLIMF with the most apparent fault characteristics is selected to generate two-dimensional time-frequency maps by continuous wavelet transform. The preprocessed time-frequency maps are adopted as the input of the pretrained VGG16 model. The bottom layers are frozen, and the top layers are fine-tuned to achieve fault diagnosis for planetary gears. Applications to planetary gear datasets verify the superiority of the proposed method.

Intelligent Timber Damage Monitoring Using PZT-Enabled Active Sensing and Intrinsic Multiscale Entropy Analysis

Timber has been commonly used in the field of civil engineering, and the health condition of timber is of great significance for the whole structure in practical scenarios. However, due to mechanical load and environmental impact, timber-based constructions are vulnerable to termite attack, microbial corrosion and fractures within their service lives. Thus, the damage monitoring of timber structures is very challenging under real situations. This paper presents an intelligent timber damage monitoring approach using Lead Zirconate Titanate (PZT)-enabled active sensing and intrinsic multiscale entropy analysis. The proposed approach adopts PZT-enabled active sensing to collect the signals depicting dynamic characteristics of the timber structure. The proposed intrinsic multiscale entropy analysis utilizes variational mode decomposition (VMD) to deal with the collected response signals. Decomposition of the response signals into a set of band-limited intrinsic mode functions (BLIMFs) denoting nonlinear and nonstationary characteristics. Then multiscale sample entropy (MSE) is employed to extract quantitative features, which are adopted as health condition indicators of timber structures. Finally, the convolutional neural network (CNN) fulfills the intelligent timber damage monitoring by using the quantitative features as the effective input. The research findings reveal the efficacy and superiority of the proposed method.

A Novel Noise Suppression and Artifact Removal Method of Mechanomyography Based on RLS, IGWO-VMD, and CEEMDAN

Mechanomyography (MMG) signals have extensive applications in muscle function assessment and human intention recognition. However, during signal acquisition, MMG signals are easily contaminated by noise and artifacts, which seriously affects the recognition of their characteristics. To address these issues, a novel noise suppression and artifact removal method based on recursive least square (RLS), improved Gray Wolf Optimizer-optimized variable mode decomposition (IGWO-VMD), and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is proposed. In this paper, the RLS algorithm is first applied to adaptively filter out the power line interference (PLI). Then, IGWO is designed to select the appropriate VMD parameters and use the VMD to decompose the noisy signal into band-limited intrinsic mode functions (BLIMFs). In addition, the BLIMFs are classified into the low-frequency part and high-frequency part according to the given correlation coefficient (CC) threshold value. The effective components of the low-frequency part are identified by the center frequency. Meanwhile, the high-frequency part is decomposed by CEEMDAN, and its effective components are obtained according to the proposed sample entropy threshold range. Finally, the effective components of the low and high-frequency parts are reconstructed to obtain the denoised signal to realize the extraction of useful signals. Simulation experiment results demonstrate that the proposed method outperforms the classical methods and the designed IGWO-VMD method in terms of denoising performance. The effectiveness of the proposed method is verified through the measured MMG signal experiments. The proposed method not only effectively suppresses noise and artifacts but also overcomes the limitations of VMD and CCEMDAN.

Fault Diagnosis of Rolling Bearings Based on Variational Mode Decomposition and Genetic Algorithm-Optimized Wavelet Threshold Denoising

Fault diagnosis of rolling bearings can be a serious challenge, as rolling bearings often work under complex conditions and their vibration signals are typically nonlinear and nonstationary. This paper proposes a novel approach to diagnosing faults of rolling bearings based on variational mode decomposition (VMD) and genetic algorithm-optimized wavelet threshold denoising. First, VMD was used to decompose the vibration signals of faulty rolling bearings into a series of band-limited intrinsic mode functions (BLIMFs). During the decomposition, the parameters of VMD were selected by Kullback–Leibler (K–L) divergence. Then, the effective BLIMFs were determined by the analysis of their correlation coefficients and variance contributions. Finally, genetic algorithm-optimized wavelet threshold denoising was proposed to optimize the selection of important parameters, and the optimized threshold function used not only ensures the continuity of the threshold function but also avoids the fixed deviation of the soft threshold. The validity and superiority of the proposed approach were verified by theoretical calculations, numerical simulations and application studies. The results indicate that the proposed approach is promising in fault diagnosis of rotary machinery.

Phase retrieval for objects in rain based on a combination of variational image decomposition and variational mode decomposition in FPP.

As far as we know, there is no paper reported to retrieve the phase of an object in rain by the fringe projection profilometry (FPP) method. The fringe projection pattern taken in rain contains much rain noise, which makes it difficult to accurately retrieve the phase of the object. In this paper, we focus on the phase retrieval of the object in rain by the FPP method. We first decompose the original fringe projection pattern into a series of band-limited intrinsic mode functions by the two-dimensional variational mode decomposition (2D-VMD) method. Then we screen out fringe-associated modes adaptively based on mutual information and reconstruct the fringe projection pattern. Next, we decompose the reconstructed fringe projection pattern by the TGV-Hilbert-BM3D variational model to obtain the de-rained fringe component. Finally, we use the Fourier transform method, phase unwrapping method, and carrier-removal method to obtain the unwrapped phase. We test the proposed method on three fringe projection patterns taken in simulated rain weather, and we compare our proposed method with the phase-shifting method, windowed Fourier method, morphological operation-based bidimensional empirical mode decomposition method, 2D-VMD method, and the TGV-Hilbert-BM3D method. The experimental results demonstrate that, for the first time to our knowledge, our method can effectively retrieve the phase of an object in rain from a single fringe projection pattern.

An improved variational mode decomposition for seismic random noise attenuation using grasshopper optimization via shape dynamic time warping

In seismic signal processing, attenuation of noise is one of the most difficult challenges. Variational mode decomposition (VMD) is a recently developed adaptable signal processing technique that subdivides a signal into bandlimited intrinsic mode functions (BIMFs). In VMD, the key elements are the number of intrinsic modes and the quadratic penalty factor for better denoising. In this paper, we have applied the Grasshopper optimization algorithm (GOA) to determine the key elements of VMD and decomposes the signal into optimized BIMFs. Then, the Shape dynamic time warping (shapeDTW) is applied for determining the relevant modes. Finally, the relevant modes are deal with Wavelet thresholding (WT) to obtain a better result of signal to noise ratio (SNR). Initially, the analysis is made on the synthetic signals to represent the dominance of the new approaching method with Empirical mode decomposition (EMD) based and VMD based methods. We also applied new approaching method to a 1D real seismic signal from the Pacific Earthquake Engineering Research Center (PEER) ground motion database to suppress the random noise interferences. The proposed approach is also tested in a 2D synthetic seismic section corrupted by random noise, and also with a 2D real Forrest seismic survey in South Australia's resources information gateway. Application of the proposed GOA-VMD-shapeDTW-WT method on both the synthetic and the real seismic signal shows supremacy with other denoising techniques.

Enhanced Discrimination of Seismic Geological Channels Based on Multi-Trace Variational Mode Decomposition

The spectral decomposition is a valuable tool for improving the resolution of seismic interpretation, and thus can improve the accuracy of the subtle geo-features (thin and narrow channels, thin reservoirs, etc.). Variational mode decomposition (VMD) is an adaptive signal decomposition algorithm that non-recursively decomposes multicomponent signals into several band-limited intrinsic mode functions, which is competitive in enhancing time-frequency resolution. However, discontinuity is normally caused by the trace-by-trace process, making the 3D seismic interpretation difficult. To address this issue, we present a novel seismic geological channel detection method for 3D seismic dataset based on multi-trace variational mode decomposition (MTVMD). The proposed method decomposes the broadband seismic data into several intrinsic mode functions and then computes seismic attributes from each component for geological feature analysis. Further tested by field seismic case, the proposed method demonstrates strength in depicting the detailed edges and sedimentary signatures of paleochannels. Overall, the proposed method provides an alternative approach to identifying seismic channels, especially for the detailed portrayals of subtle geo-features in low-quality seismic data.

Looseness monitoring of multiple M1 bolt joints using multivariate intrinsic multiscale entropy analysis and Lorentz signal-enhanced piezoelectric active sensing

Bolts are widely used in the fields of mechanical, civil, and aerospace engineering. The condition of bolt joints has a significant impact on the safe and reliable operation of the whole equipment. The failure of bolt joints monitoring leads to severe accidents or even casualties. This paper proposes a novel bolt joints monitoring method using multivariate intrinsic multiscale entropy (MIME) analysis and Lorentz signal-enhanced piezoelectric active sensing. Lorentz signal is used as excitation signal in piezoelectric active sensing to expose nonlinear dynamical characteristics of the bolt joints. Multivariate variational mode decomposition (MVMD) is employed to decompose multiple components of the collected Lorentz signal into multivariate band-limited intrinsic mode functions (BLIMFs). Afterward, improved multiscale sample entropy (IMSE) values of each channel’s BLIMFs are computed to measure its irregularity and complexity. IMSE values are taken as quantitative features, reflecting dynamical characteristics of bolt joints. Further, the constructed 3-layer feature matrices are adopted as the input of the convolutional neural network (CNN) to achieve accurate bolt joint monitoring. The multiple M1 bolt joints are used during the experiment to verify the effectiveness and superiority of the proposed approach. The results demonstrate the proposed novel approach is promising in bolt joints monitoring.

Improving seismic resolution based on enhanced multi-channel variational mode decomposition

The attenuation and dispersion of seismic waves change with frequency. So, it is unreasonable to compensate absorption and attenuation using the full-frequency band seismic data directly. In this study, we propose a seismic high-resolution processing workflow based on the enhanced multi-channel variational mode decomposition (EMVMD). Frist, we aim to adopt the multi-channel variational mode decomposition (MVMD) to decompose seismic data into several band-limited intrinsic mode functions (IMFs). Then, we explain the relationship between the IMFs and the different scale structures, and propose a strategy to determine the number of IMFs by introducing the contraction operator mapping (COM) and the scale-space representation (SSR). Note that we name the MVMD with a number selection strategy as the enhanced MVMD (EMVMD). Next, we adopt the adaptive spectrum-broadening method (ASBM) to separately improve the resolution of each decomposed IMF. Afterward, we can easily obtain the enhanced seismic data with a high resolution by summing the processed IMFs. Finally, we apply the proposed workflow (EMVMD-ASBM) to synthetic and field data to testify its validity and effectiveness for enhancing the resolution of the post-stack seismic data.

Denoising and Feature Extraction for Space Infrared Dim Target Recognition Utilizing Optimal VMD and Dual-Band Thermometry

Space target feature extraction and space infrared target recognition are important components of space situational awareness (SSA). However, owing to far imaging distance between the space target and infrared detector, the infrared signal of the target received by the detector is dim and easily contaminated by noise. To effectively improve the accuracy of feature extraction and recognition, it is essential to suppress the noise of the infrared signal. Hence, a novel denoising and extracting feature method combinating optimal variational mode decomposition (VMD) and dual-band thermometry (DBT) is proposed. It takes the mean weighted fuzzy-distribution entropy (FuzzDistEn) of the band-limited intrinsic mode functions (BLIMFs) as the optimization index of dragonfly algorithm (DA) to obtain the optimal parameters (K, α) of VMD. Then the VMD is utilized to decompose the noisy signal to obtain a series of BLIMFs and the Pearson correlation coefficient (PCC) is proposed to determine the effective modes to reconstructe the denoising signal. Finally, based on the denoising signal, the feature of temperature and emissivity-area product are calculated using the DBT. The simulation and experiment results show that the proposed method has better noise reduction performance compared with the other denoising methods, and the accuracy of feature extraction is improved at different noise equivalent irradiance. This provides more accurate feature of temerpature and emissivity-area product for space infrared dim target recognition.

An Open-Circuit Faults Diagnosis Approach for Three-Phase Inverters Based on an Improved Variational Mode Decomposition, Correlation Coefficients, and Statistical Indicators

To ensure the reliability and robustness of the three-phase inverter, it is important to accurately detect the faults of insulated gate bipolar transistor (IGBT) switches. Signal processing is widely used for monitoring and fault diagnosis of the three-phase inverters. The current signals are usually noisy, which can lead to a loss of fault information. This article proposes a new approach for identifying and detecting the IGBTs open-circuit faults of a three-phase inverter. This approach is based on an improved version of the variational mode decomposition (IVMD) technique associated with correlation coefficients and statistical indicators (variance and mean value). First, the IVMD is applied to the three-phase current signals to obtain an elementary function called the band-limited intrinsic mode functions (BLIMFs). Second, the correlation coefficients between the original signals and theirs BLIMFs are used to select the relevant modes. The variances of the modes that have the highest correlation coefficients among those selected are calculated to detect the faulty phase and, therefore, the faulty leg. Finally, the mean value of the mode that has the lowest correlation coefficients among those selected of the faulty phase is calculated to localize the fault position in either the upper or the lower IGBTs of the faulty leg. Different experimental data are used to test the effectiveness of the proposed approach. The results obtained show the merits of the proposed approach for the diagnosis and detection of open-circuit IGBTs compared to the conventional method.

Application of nonlinear system identification for EEG modelling using VMD-based deep random vector functional link network

In this paper, the EEG signal is considered for the development of the model. As the signal is nonlinear and non-stationary, the model is designed accordingly which is similar to nonlinear dynamic system identification. Initially, the signal is decomposed by a robust variational mode decomposition method for which the basic noise components are eliminated. Later, a kurtosis index method is applied to choose the best band-limited intrinsic mode functions (BLIMFs) based on their clean coefficient the model is developed using a random vector functional link neural network (RVFLN) for identification. The use of deep RVFLN provides better results as compared to simple RVFLN as explained in the result section. For verification of the system's robustness, three different epileptic signals known as pre-ictal, inter-ictal and ictal are experienced in this piece of work.

Multiscale Coherence Attribute and Its Application on Seismic Discontinuity Description

Geologic structure characterization is a key step for seismic structure interpretation, such as fluvial channels, faults, and fractures. The coherence attribute is a widely used tool for describing seismic discontinuities, which is usually calculated based on the similarity and dissimilarity of the adjacent seismic traces. However, accurately extracting coherence attribute is a difficult task in field data applications because seismic signal is one of the typical nonstationary, non-Gaussian, and wideband signals. To describe seismic discontinuities at different scales, we propose a workflow to extract the multiscale coherence (MSC) attribute. We first decompose seismic data into several band-limited intrinsic mode functions (IMFs) with different dominant frequencies via the multichannel variational mode decomposition (MVMD). Afterward, we develop a Cauchy kernel correlation-based coherence algorithm to extract the coherence attributes at different scales based on the decomposed IMFs. Finally, we can compute the MSC attribute by utilizing the calculated coherence attributes. Field data applications demonstrate that the proposed MSC attribute characterizes seismic discontinuities, such as faults and fluvial channels, more accurately and more clearly than the traditional coherence attribute and the 1-D variational mode decomposition (VMD)-based coherence attribute.