Variational Mode Decomposition-Informed Empirical Wavelet Transform for Electric Vibrator Noise Analysis

Electric vibrators find wide applications in reliability testing, waveform generation, and vibration simulation, making their noise characteristics a topic of significant interest. While Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) offer valuable support for studying signal components, they also present certain limitations. This article integrates the strengths of both methods and proposes an enhanced approach that integrates VMD into the frequency band division principle of EWT. Initially, the method decomposes the signal using VMD, determining the mode count based on residuals, and subsequently employs EWT decomposition based on this information. This addresses mode aliasing issues in the original method while capitalizing on VMD’s adaptability. Feasibility was confirmed through simulation signals and ultimately applied to noise signals from vibrators. Experimental results demonstrate that the improved method not only resolves EWT frequency band division challenges but also effectively decomposes signal components compared to the VMD method.

Research on Modulation Signal Denoising Method Based on Improved Variational Mode Decomposition

In order to further analyze the micro-motion modulation signals generated by rotating components and extract micro-motion features,a modulation signal denoising algorithm based on improved variational mode decomposition(VMD)is proposed.To improve the time-frequency performance,this method decomposes the data into narrowband signals and analyzes the internal energy and frequency variations within the signal.Genetic algorithms are used to adaptively optimize the mode number and bandwidth control parameters in the process of VMD.This approach aims to obtain the optimal parameter combination and perform mode decomposition on the micro-motion modulation signal.The optimal mode number and quadratic penalty factor for VMD are determined.Based on the optimal values of the mode number and quadratic penalty factor,the original signal is decomposed using VMD,resulting in optimal mode number intrinsic mode function(IMF)components.The effective modes are then reconstructed with the denoised modes,achieving signal denoising.Through experimental data verification,the proposed algorithm demonstrates effective denoising of modulation signals.In simulation data validation,the algorithm achieves the highest signal-to-noise ratio(SNR)and exhibits the best performance.

Underwater acoustic signal denoising model based on secondary variational mode decomposition

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

Cloud Resource Integrated Prediction Model Based on Variational Modal Decomposition-Permutation Entropy and LSTM

Predicting the usage of container cloud resources has always been an important and challenging problem in improving the performance of cloud resource clusters.We proposed an integrated prediction method of stacking container cloud resources based on variational modal decomposition(VMD)-Permutation entropy(PE)and long short-term memory(LSTM)neural network to solve the prediction difficulties caused by the non-stationarity and volatility of resource data.The variational modal decomposition algorithm decomposes the time series data of cloud resources to obtain intrinsic mode function and residual components,which solves the signal decomposition algorithm’s end-effect and modal confusion problems.The permutation entropy is used to evaluate the complexity of the intrinsic mode function,and the reconstruction based on similar entropy and low complexity is used to reduce the difficulty of modeling.Finally,we use the LSTM and stacking fusion models to predict and superimpose;the stacking integration model integrates Gradient boosting regression(GBR),Kernel ridge regression(KRR),and Elastic net regression(ENet)as primary learners,and the secondary learner adopts the kernel ridge regression method with solid generalization ability.The Amazon public data set experiment shows that compared with Holt-winters,LSTM,and Neuralprophet models,we can see that the optimization range of multiple evaluation indicators is 0.338∼1.913,0.057∼0.940,0.000∼0.017 and 1.038∼8.481 in root means square error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE)and variance(VAR),showing its stability and better prediction accuracy.

Adaptive Variational Mode Decomposition for Bearing Fault Detection

Rolling element bearings are commonly used in rotary mechanical and electrical equipment. According to investigation, more than half of rotating machinery defects are related to bearing faults. However, reliable bearing fault detection still remains a challenging task, especially in industrial applications. The objective of this work is to propose an adaptive variational mode decomposition (AVMD) technique for non-stationary signal analysis and bearing fault detection. The AVMD includes several steps in processing: 1) Signal characteristics are analyzed to determine the signal center frequency and the related parameters. 2) The ensemble-kurtosis index is suggested to decompose the target signal and select the most representative intrinsic mode functions (IMFs). 3) The envelope spectrum analysis is performed using the selected IMFs to identify the characteristic features for bearing fault detection. The effectiveness of the proposed AVMD technique is examined by experimental tests under different bearing conditions, with the comparison of other related bearing fault techniques.

Application of sparse time-frequency decomposition to seismic data

The Gabor and S transforms are frequently used in time-frequency decomposition methods. Constrained by the uncertainty principle, both transforms produce low-resolution time-frequency decomposition results in the time and frequency domains. To improve the resolution of the time-frequency decomposition results, we use the instantaneous frequency distribution function（IFDF） to express the seismic signal. When the instantaneous frequencies of the nonstationary signal satisfy the requirements of the uncertainty principle, the support of IFDF is just the support of the amplitude ridges in the signal obtained using the short-time Fourier transform. Based on this feature, we propose a new iteration algorithm to achieve the sparse time-frequency decomposition of the signal. The iteration algorithm uses the support of the amplitude ridges of the residual signal obtained with the short-time Fourier transform to update the time-frequency components of the signal. The summation of the updated time-frequency components in each iteration is the result of the sparse timefrequency decomposition. Numerical examples show that the proposed method improves the resolution of the time-frequency decomposition results and the accuracy of the analysis of the nonstationary signal. We also use the proposed method to attenuate the ground roll of field seismic data with good results.

Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

Variational Mode Decomposition for Rotating Machinery Condition Monitoring Using Vibration Signals

The failure of rotating machinery applications has major time and cost effects on the industry.Condition monitoring helps to ensure safe operation and also avoids losses.The signal processing method is essential for ensuring both the efficiency and accuracy of the monitoring process.Variational mode decomposition(VMD)is a signal processing method which decomposes a non-stationary signal into sets of variational mode functions(VMFs)adaptively and non-recursively.The VMD method offers improved performance for the condition monitoring of rotating machinery applications.However,determining an accurate number of modes for the VMD method is still considered an open research problem.Therefore,a selection method for determining the number of modes for VMD is proposed by taking advantage of the similarities in concept between the original signal and VMF.Simulated signal and online gearbox vibration signals have been used to validate the performance of the proposed method.The statistical parameters of the signals are extracted from the original signals,VMFs and intrinsic mode functions(IMFs)and have been fed into machine learning algorithms to validate the performance of the VMD method.The results show that the features extracted from VMD are both superior and accurate for the monitoring of rotating machinery.Hence the proposed method offers a new approach for the condition monitoring of rotating machinery applications.

An improved proximal-based decomposition method for structured monotone variational inequalities

The proximal-based decomposition method was originally proposed by Chen and Teboulle （Math. Programming, 1994, 64：81-101 for solving corrvex minimization problems. This paper extends it to solving monotone variational inequalities associated with separable structures with the improvements that the restrictive assumptions on the involved parameters are much relaxed, and thus makes it practical to solve the subproblems easily. Without additional assumptions, global convergence of the new method is proved under the same mild assumptions on the problem＇s data as the original method.

Microseismic signal denoising by combining variational mode decomposition with permutation entropy

Remarkable progress has been achieved on microseismic signal denoising in recent years,which is the basic component for rock-burst detection.However,its denoising effectiveness remains unsatisfactory.To extract the effective microseismic signal from polluted noisy signals,a novel microseismic signal denoising method that combines the variational mode decomposition(VMD)and permutation entropy(PE),which we denote as VMD–PE,is proposed in this paper.VMD is a recently introduced technique for adaptive signal decomposition,where K is an important decomposing parameter that determines the number of modes.VMD provides a predictable eff ect on the nature of detected modes.In this work,we present a method that addresses the problem of selecting an appropriate K value by constructing a simulation signal whose spectrum is similar to that of a mine microseismic signal and apply this value to the VMD–PE method.In addition,PE is developed to identify the relevant effective microseismic signal modes,which are reconstructed to realize signal filtering.The experimental results show that the VMD–PE method remarkably outperforms the empirical mode decomposition(EMD)–VMD filtering and detrended fl uctuation analysis(DFA)–VMD denoising methods of the simulated and real microseismic signals.We expect that this novel method can inspire and help evaluate new ideas in this field.

Adaptive variational models for image decomposition combining staircase reduction and texture extraction

New models for image decomposition are proposed which separate an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed models are given in a variational formulation with adaptive regularization norms for both the cartoon and texture parts. The adaptive behavior preserves key features such as object boundaries and textures while avoiding staircasing in what should be smooth regions. This decomposition is computed by minimizing a convex functional which depends on the two variables u and v, alternatively in each variable. Experimental results and comparisons to validate the proposed models are presented.

An extraction method for pressure beat vibration characteristics of hydraulic drive system based on variational mode decomposition

In the pump-controlled motor hydraulic transmission system,when the pressure pulsation frequencies seperately generated by the pump and the motor are close to each other,the hydraulic system will generate a strong pressure beat vibration phenomenon,which will seriously affect the smooth running of the hydraulic system.However,the modulated pressure signal also carries information related to the operating state of the hydraulic system,and a accurate extraction of pressure vibration characteristics is the key to obtain the operating state information of the hydraulic system.In order to extract the pressure beat vibration signal component effectively from the multi-component time-varying aliasing pressure signal and reconstruct the time domain characteristics,an extraction method of the pressure beat vibration characteristics of the hydraulic transmission system based on variational mode decomposition(VMD)is proposed.The experimental results show that the VMD method can accurately extract the pressure beat vibration characteristics from the high-pressure oil pressure signal of the hydraulic system,and the extraction effect is preferable to that of the traditional signal processing methods such as empirical mode decomposition(EMD).

A Unification of the Concepts of the Variational Iteration, Adomian Decomposition and Picard Iteration Methods;and a Local Variational Iteration Method

This paper compares the variational iteration method(VIM),the Adomian decomposition method(ADM)and the Picard iteration method(PIM)for solving a system of first o rder n onlinear o rdinary d ifferential e quations(ODEs).A unification of the concepts underlying these three methods is attempted by considering a very general iterative algorithm for VIM.It is found that all the three methods can be regarded as special cases of using a very general matrix of Lagrange multipliers in the iterative algorithm of VIM.The global variational iteration method is briefly reviewed,and further recast into a Local VIM,which is much more convenient and capable of predicting long term complex dynamic responses of nonlinear systems even if they are chaotic.

Anchoring Bolt Detection Based on Morphological Filtering and Variational Modal Decomposition

The pull test is a damaging detection method that fails to measure the actual length of a bolt.Thus,the ultrasonic echo is an important non?destructive testing method for bolt quality detection.In this research,the variational modal decomposition(VMD)method is introduced into the bolt detection signal analysis.On the basis of morphological filtering(MF)and the VMD method,a VMD?combined MF principle is established into a bolt detection signal analysis method(MF?VMD).MF?VMD is used to analyze the vibration and actual bolt detection signals of the simulation.Results show that MF?VMD effectively separates intrinsic mode function,even under strong interference.In comparison with conventional VMD method,the proposed method can remove noise interference.An intrinsic mode function of the field detection signal can be effectively identified by reflecting the signal at the bottom of the bolt.

Removal of Ocular Artifacts from Electroencephalo-Graph by Improving Variational Mode Decomposition

Ocular artifacts in Electroencephalography(EEG)recordings lead to inaccurate results in signal analysis and process.Variational Mode Decomposition(VMD)is an adaptive and completely nonrecursive signal processing method.There are two parameters in VMD that have a great influence on the result of signal decomposition.Thus,this paper studies a signal decomposition by improving VMD based on squirrel search algorithm(SSA).It’s improved with abilities of global optimal guidance and opposition based learning.The original seasonal monitoring condition in SSA is modified.The feedback of whether the optimal solution is successfully updated is used to establish new seasonal monitoring conditions.Opposition-based learning is introduced to reposition the position of the population in this stage.It is applied to optimize the important parameters of VMD.GOSSA-VMD model is established to remove ocular artifacts from EEG recording.We have verified the effectiveness of our proposal in a public dataset compared with other methods.The proposed method improves the SNR of the dataset from-2.03 to 2.30.

A Study of Some Nonlinear Partial Differential Equations by Using Adomian Decomposition Method and Variational Iteration Method

In this paper, a numerical solution of nonlinear partial differential equation, Benjamin-Bona-Mahony (BBM) and Cahn-Hilliard equation is presented by using Adomain Decomposition Method (ADM) and Variational Iteration Method (VIM). The results reveal that the two methods are very effective, simple and very close to the exact solution.

Distributed Sea Clutter Denoising Algorithm Based on Variational Mode Decomposition

In order to improve the detection accuracy of chaotic small signal prediction models under the background of sea clutter,a distributed sea clutter denoising algorithm is proposed,on the basis of variational modal decomposition(VMD).The sea clutter signal is decomposed into variational modal functions(VMF)with different center bandwidths by means of VMD.By analyzing the autocorrelation characteristics of the deco mposed signal,we perform instantaneous half-period(IHP)and wavelet threshold denoising processing on the high-frequency and low-frequency components respectively,and regain the sea clutter signals.Based on LSSVM sea clutter prediction model,this research compares and analyzes the denoising effects of VMD.Experi ment results show that,the RMSE after denoising is reduced by two orders of magnitude,approximating 0.00034,with an apparently better denoising effect,compared with the root mean square error(RMSE)of the prediction before denoising.

Application of He’s Variational Iteration Method and Adomian Decomposition Method to Solution for the Fifth Order Caudrey-Dodd-Gibbon (CDG) Equation

In this work we use the He’s variational iteration method and Adomian decomposition method to solution N-soliton solutions for the fifth order Caudrey-Dodd-Gibbon (CDG) Equation.

Spatio-Temporal Wind Speed Prediction Based on Variational Mode Decomposition

Improving short-term wind speed prediction accuracy and stability remains a challenge for wind forecasting researchers.This paper proposes a new variational mode decomposition(VMD)-attention-based spatio-temporal network(VASTN)method that takes advantage of both temporal and spatial correlations of wind speed.First,VASTN is a hybrid wind speed prediction model that combines VMD,squeeze-and-excitation network(SENet),and attention mechanism(AM)-based bidirectional long short-term memory(BiLSTM).VASTN initially employs VMD to decompose the wind speed matrix into a series of intrinsic mode functions(IMF).Then,to extract the spatial features at the bottom of the model,each IMF employs an improved convolutional neural network algorithm based on channel AM,also known as SENet.Second,it combines BiLSTM and AM at the top layer to extract aggregated spatial features and capture temporal dependencies.Finally,VASTN accumulates the predictions of each IMF to obtain the predicted wind speed.This method employs VMD to reduce the randomness and instability of the original data before employing AM to improve prediction accuracy through mapping weight and parameter learning.Experimental results on real-world data demonstrate VASTN’s superiority over previous related algorithms.

Ultrasonic echo denoising in liquid density measurement based on improved variational mode decomposition

The ultrasonic echo in liquid density measurement often suffers noise,which makes it difficult to obtain the useful echo waveform,resulting in low accuracy of density measurement.A denoising method based on improved variational mode decomposition(VMD)for noise echo signals is proposed.The number of decomposition layers of the traditional VMD is hard to determine,therefore,the center frequency similarity factor is firstly constructed and used as the judgment criterion to select the number of VMD decomposition layers adaptively;Secondly,VMD algorithm is used to decompose the echo signal into several modal components with a single modal component,and the useful echo components are extracted based on the features of the ultrasonic emission signal;Finally,the liquid density is calculated by extracting the amplitude and time of the echo from the modal components.The simulation results show that using the improved VMD to decompose the echo signal not only can improve the signal-to-noise ratio of the echo signal to 20.64 dB,but also can accurately obtain the echo information such as time and amplitude.Compared with the ensemble empirical mode decomposition(EEMD),this method effectively suppresses the modal aliasing,keeps the details of the signal to the maximum extent while suppressing noise,and improves the accuracy of the liquid density measurement.The density measurement accuracy can reach 0.21%of full scale.