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.

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.

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.

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.

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).

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.

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.

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.

Dynamic mode decomposition of the geomagnetic field over the last two decades

Earth’s magnetic field,which is generated in the liquid outer core through the dynamo action,undergoes changes on timescales of a few years to several million years,yet the underlying mechanisms responsible for the field variations remain to be elucidated.In this study,we apply a novel data analysis technique developed in fluid dynamics,namely the dynamic mode decomposition,to analyze the geomagnetic variations over the last two decades when continuous satellite observations are available.The dominant dynamic modes are extracted by solving an eigen-value problem,so one can identify modes with periods longer than the time span of data.Our analysis show that similar dynamic modes are extracted from the geomagnetic secular variation and secular acceleration,justifying the validity of applying the dynamic mode decomposition method to geomagnetic field.We reveal that the geomagnetic field variations are characterized by a global mode with period of 58 years,a localized mode with period of 16 years and an equatorially trapped mode with period of 8.5 years.These modes are possibly related to magnetohydrodynamic waves in the Earth’s outer core.

Wind Speed Prediction Based on Improved VMD-BP-CNN-LSTM Model

Amid the randomness and volatility of wind speed, an improved VMD-BP-CNN-LSTM model for short-term wind speed prediction was proposed to assist in power system planning and operation in this paper. Firstly, the wind speed time series data was processed using Variational Mode Decomposition (VMD) to obtain multiple frequency components. Then, each individual frequency component was channeled into a combined prediction framework consisting of BP neural network (BPNN), Convolutional Neural Network (CNN) and Long Short-Term Memory Network (LSTM) after the execution of differential and normalization operations. Thereafter, the predictive outputs for each component underwent integration through a fully-connected neural architecture for data fusion processing, resulting in the final prediction. The VMD decomposition technique was introduced in a generalized CNN-LSTM prediction model;a BPNN model was utilized to predict high-frequency components obtained from VMD, and incorporated a fully connected neural network for data fusion of individual component predictions. Experimental results demonstrated that the proposed improved VMD-BP-CNN-LSTM model outperformed other combined prediction models in terms of prediction accuracy, providing a solid foundation for optimizing the safe operation of wind farms.

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.

基于POA-VMD-WT的MEMS去噪方法

针对MEMS传感器所测得的加速度和角速度输出信号噪声较大问题,提出一种基于鹈鹕优化算法(pelican optimization algorithm,POA)的变分模态分解(variational mode decomposition,VMD)结合小波阈值(wavelet threshold,WT)的去噪方法。首先利用POA对VMD的参数组合进行优化选择,然后应用POA-VMD将含噪信号自适应、非递归地分解为一系列本征模态函数(intrinsic mode function,IMF)。再通过计算每个IMF的余弦相似度对IMFs进行分类,根据计算结果将IMFs分为噪声主导分量与信号主导分量,对分类后的噪声主导分量进行改进小波阈值去噪处理,最后对处理后的噪声分量与信号主导分量进行重构,获得降噪后的MEMS传感器信号。静态和动态实验结果表明,该方法去噪处理后信号的信噪比分别提高12和10 dB,均方误差分别降低75.5%和46.6%,去噪效果显著,能够提高MEMS传感器的精度。

基于VMD-GA-BiLSTM的月降水量预测方法

利用辽宁省气象局提供的地面观测降水资料,构建了具有多元时间特征的降水数据,采用变分模态分解方法(variational mode decomposition,VMD)组合遗传算法(genetic algorithm,GA)对双向长短时记忆神经网络(bidirectional long short-term memory,BiLSTM)进行优化,建立基于VMD-GA-BiLSTM的月降水量预测模型,并与BiLSTM、VMD-BiLSTM和GA-BiLSTM进行实验对比,应用均方根误差(root mean square error,RMSE)、平均绝对误差(mean absolute error,MAE)和R 2决定系数作为模型评价指标。实验结果表明:VMD-GA-BiLSTM模型的R 2决定系数达到0.98,RMSE和MAE表现更低,验证了VMD-GA-BiLSTM模型在时间序列预测方面的优势。

基于VMD-ISSA-GRU组合模型的短期风电功率预测

为解决风速不确定性和波动性造成风电功率预测精度不高的问题,提出一种基于变分模态分解(VMD)、改进麻雀搜索算法(ISSA)和门控循环神经网络(GRU)的VMD-ISSA-GRU组合模型。首先,利用中心频率法确定采用VMD分解后的模态分量个数,这样有效避免了过分解或者分解不充分。其次引入混沌映射、非线性递减权重以及一个突变策略来改进麻雀搜索算法,用于优化门控循环神经网络,然后对分解得到的各个子序列建立ISSA-GRU预测模型,最后叠加每个子序列的预测值得到最终的预测值。将该模型用于实际风电功率预测,实验结果表明:VMD-ISSA-GRU组合模型的平均绝对误差、平均绝对百分比误差、均方根误差分别为1.2118MW、1.8900及1.5916MW;相较于传统的GRU、长短时记忆(LSTM)神经网络、BiLSTM(Bi-directional LSTM)神经网络模型以及其他组合模型在预测精度上都有明显的提升,能很好地解决风电功率预测精度不高的问题.

基于Spearman相关性阈值寻优和VMD-LSTM的用户级综合能源系统超短期负荷预测

由于用户级综合能源系统(integrated energy system,IES)的多元负荷序列之间复杂的耦合关系及易受外部因素影响等原因,综合能源系统多元负荷的精准预测面临很大困难。为此,提出一种基于Spearman相关性分析阈值寻优(threshold optimization,TO)和变分模态分解结合长短期记忆网络(variational mode decomposition based long short-term memory network,VMD-LSTM)的多元负荷预测方法。首先,使用斯皮尔曼等级(Spearman rank,SR)相关系数定量计算多元负荷间以及负荷与其他气候因素间的相关关系并通过循环寻优确定最优相关阈值,然后采用VMD算法将以最优阈值筛选出的负荷特征序列分解成更简单、平稳、有规律性的本征模态函数(intrinsic mode function,IMF)后与最优气象特征一起输入LSTM模型进行负荷预测。通过某用户级IES的实际数据对所提方法的有效性进行了验证,结果表明,所提方法能有效提高IES的多元负荷预测精度。

基于参数自适应SVR和VMD-TCN的水电机组劣化趋势预测

针对水电机组难以利用实时监测数据对机组劣化状态进行有效评估,以及水电机组不同运行工况对运行状态指标趋势预测模型参数影响显著的问题,提出一种基于参数自适应支持向量回归机(SVR)、变分模态分解(VMD)和时间卷积网络(TCN)的水电机组劣化趋势预测方法;首先按照功率和水头将机组运行工况细化为若干典型工况,在此基础上采用改进天鹰算法建立SVR模型,对各个工况下的预测参数进行寻优,建立起工况与最优参数的数据;再通过神经网络对工况和最优预测参数进行拟合,构建出映射两者复杂关系的非线性函数,然后将构建出的映射关系加入到传统的SVR中,实现适应于水电机组工况变化的自适应SVR健康模型;其次,根据健康模型输出的标准值和监测数据,计算出劣化趋势序列;最后,考虑到劣化趋势序列的非线性因素,建立了一个基于VMD-TCN的时间序列预测模型,以实现对劣化趋势的准确预测。并设计多组对比实验,验证所提出模型的精度更高,时间更快。

基于双层优化VMD-LSTM的农村超短期电力负荷预测

稳定的供电是农村发展建设的有力保障,而电力负荷水平是建设效果的重要衡量标准,因此建立精确的负荷预测模型可以更准确直观显现电力负荷情况,为供电公司制定决策提供有力支撑。由于LSTM负荷预测模型在数据预测方面存在收敛性差、预测精度不高等问题,为提高模型的预测精度,提出一种基于双层优化VMD-LSTM的超短期电力负荷预测方法。首先提出麻雀算法优化变分模态分解(sparrow variational mode decomposition,SVMD),通过SVMD将原始数据转化为模态分量(intrinsic mode functions,IMF);其次采用改进樽海鞘群算法(association salp swarm algorithm,ASSSA)优化LSTM模型。通过引入4种策略增强标准樽海鞘算法优化能力;最后将各模态分量分别代入到新模型并进行叠加预测。选取辽宁省某市某乡村10kV变压器真实历史负荷数据,以均方根误差(RMSE)、平均绝对误差(MAE)、平均绝对百分比误差(MAPE)、拟合度(R^(2))作为评价指标,并与其他基础预测模型进行对比,结果表明,改进后的算法在计算精度、稳定性方面均优于其他基础预测模型。

基于VMD-TCN-GRU模型的水质预测研究

为充分挖掘水质数据在短时震荡中的变化特征,提升预测模型的精度,提出一种基于VMD(变分模态分解)、TCN(卷积时间神经网络)及GRU(门控循环单元)组成的混合水质预测模型,采用VMD-TCN-GRU模型对汾河水库出水口高锰酸盐指数进行预测,并与此类研究中常见的SVR(支持向量回归)、LSTM(长短期记忆神经网络)、TCN和CNN-LSTM(卷积神经网络-长短期记忆神经网络)这4种模型预测结果对比表明:VMD-TCN-GRU模型能更好挖掘水质数据在短时震荡过程中的特征信息,提升水质预测精度;VMD-TCN-GRU模型的MAE(平均绝对误差)、RMSE(均方根误差)下降,R^(2)(确定系数)提高,其MAE、RMSE、R^(2)分别为0.0553、0.0717、0.9351;其预测性能优越,预测精度更高且拥有更强的泛化能力,可以应用于汾河水质预测。