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.

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.

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.

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.

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.

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.

A debris-flow forecasting method with infrasound-based variational mode decomposition and ARIMA

Infrasound,known for its strong penetration and low attenuation,is extensively used in monitoring and warning systems for debris flows.Here,a debris-flow forecasting method was proposed by combining infrasound-based variational mode decomposition and Autoregressive Integrated Moving Average(ARIMA)model.High-precision infrasound sensor was utilized in experiments to record signals under twelve varying conditions of debris flow volume and velocity.Variational mode decomposition was performed on the detected raw signals,and the optimal decomposition scale and penalty factor were obtained through the sparrow search algorithm.The Hilbert transform,rescaled range analysis,power spectrum analysis,and Pearson correlation coefficients judgment criteria were employed to separate and reconstruct the signals.Based on the reconstructed infrasound signals,an ARIMA model was constructed to forecast the trend of debris flow infrasound signal.Results reveal that the Hilbert transform effectively separated noise,and the predictive model’s results fell within a 95%confidence interval.The Mean Absolute Percentage Error(MAPE)across four experiments were 4.87%,5.23%,5.32%and 4.47%,respectively,showing a satisfactory accuracy and providing an alternative for predicting debris flow by infrasound signals.

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.

Hybrid data decomposition-based deep learning for Bitcoin prediction and algorithm trading

In recent years,Bitcoin has received substantial attention as potentially high-earning investment.However,its volatile price movement exhibits great financial risks.Therefore,how to accurately predict and capture changing trends in the Bitcoin market is of substantial importance to investors and policy makers.However,empirical works in the Bitcoin forecasting and trading support systems are at an early stage.To fill this void,this study proposes a novel data decomposition-based hybrid bidirectional deep-learning model in forecasting the daily price change in the Bitcoin market and conducting algorithmic trading on the market.Two primary steps are involved in our methodology framework,namely,data decomposition for inner factors extraction and bidirectional deep learning for forecasting the Bitcoin price.Results demonstrate that the proposed model outperforms other benchmark models,including econometric models,machine-learning models,and deep-learning models.Furthermore,the proposed model achieved higher investment returns than all benchmark models and the buy-and-hold strategy in a trading simulation.The robustness of the model is verified through multiple forecasting periods and testing intervals.

Forecasting hourly PM_(2.5)concentrations based on decomposition-ensemble-reconstruction framework incorporating deep learning algorithms

Accurate predictions of hourly PM_(2.5)concentrations are crucial for preventing the harmful effects of air pollution.In this study,a new decomposition-ensemble framework incorporating the variational mode decomposition method(VMD),econometric forecasting method(autoregressive integrated moving average model,ARIMA),and deep learning techniques(convolutional neural networks(CNN)and temporal convolutional network(TCN))was developed to model the data characteristics of hourly PM_(2.5)concentrations.Taking the PM_(2.5)concentration of Lanzhou,Gansu Province,China as the sample,the empirical results demonstrated that the developed decomposition-ensemble framework is significantly superior to the benchmarks with the econometric model,machine learning models,basic deep learning models,and traditional decomposition-ensemble models,within one-,two-,or three-step-ahead.This study verified the effectiveness of the new prediction framework to capture the data patterns of PM_(2.5)concentration and can be employed as a meaningful PM_(2.5)concentrations prediction tool.

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.

Wind power prediction based on variational mode decomposition multi-frequency combinations

Because of the uncertainty and randomness of wind speed, wind power has characteristics such as nonlinearity and multiple frequencies. Accurate prediction of wind power is one effective means of improving wind power integration. Because the traditional single model cannot fully characterize the fluctuating characteristics of wind power, scholars have attempted to build other prediction models based on empirical mode decomposition(EMD) or ensemble empirical mode decomposition(EEMD) to tackle this problem. However, the prediction accuracy of these models is affected by modal aliasing and illusive components. Aimed at these defects, this paper proposes a multi-frequency combination prediction model based on variational mode decomposition(VMD). We use a back propagation neural network(BPNN),autoregressive moving average(ARMA)model, and least square support vector machine(LS-SVM) to predict high, intermediate,and low frequency components,respectively. Based on the predicted values of each component, the BPNN is applied to combine them into a final wind power prediction value.Finally,the prediction performance of the single prediction models(ARMA,BPNN and LS-SVM)and the decomposition prediction models(EMD and EEMD) are used to compare with the proposed VMD model according to the evaluation indices such as average absolute error, mean square error,and root mean square error to validate its feasibility and accuracy. The results show that the prediction accuracy of the proposed VMD model is higher.

Variational mode decomposition based modal parameter identification in civil engineering

An out-put only modal parameter identification method based on variational mode decomposition (VMD) is developed for civil structure identifications. The recently developed VMD technique is utilized to decompose the free decay response (FDR) of a structure into to modal responses. A novel procedure is developed to calculate the instantaneous modal frequencies and instantaneous modal damping ratios. The proposed identification method can straightforwardly extract the mode shape vectors using the modal responses extracted from the FDRs at all available sensors on the structure. A series of numerical and experimental case studies are conducted to demonstrate the efficiency and highlight the superiority of the proposed method in modal parameter identification using both free vibration and ambient vibration data. The results of the present method are compared with those of the empirical mode decomposition-based method, and the superiorities of the present method are verified. The proposed method is proved to be efficient and accurate in modal parameter identification for both linear and nonlinear civil structures, including structures with closely spaced modes, sudden modal parameter variation, and amplitude-dependent modal parameters, etc.

Wind Power Prediction Based on Variational Mode Decomposition and Feature Selection

Accurate wind power prediction can scientifically arrange wind power output and timely adjust power system dispatching plans. Wind power is associated with its uncertainty,multi-frequency and nonlinearity for it is susceptible to climatic factors such as temperature, air pressure and wind speed.Therefore, this paper proposes a wind power prediction model combining multi-frequency combination and feature selection.Firstly, the variational mode decomposition(VMD) is used to decompose the wind power data, and the sub-components with different fluctuation characteristics are obtained and divided into high-, intermediate-, and low-frequency components according to their fluctuation characteristics. Then, a feature set including historical data of wind power and meteorological factors is established, which chooses the feature sets of each component by using the max-relevance and min-redundancy(m RMR) feature selection method based on mutual information selected from the above set. Each component and its corresponding feature set are used as an input set for prediction afterwards. Thereafter, the high-frequency input set is predicted using back propagation neural network(BPNN), and the intermediate-and low-frequency input sets are predicted using least squares support vector machine(LS-SVM). After obtaining the prediction results of each component, BPNN is used for integration to obtain the final predicted value of wind power, and the ramping rate is verified. Finally, through the comparison, it is found that the proposed model has higher prediction accuracy.

Wind power forecasting based on improved variational mode decomposition and permutation entropy

Due to the significant intermittent,stochastic and non-stationary nature of wind power generation,it is difficult to achieve the desired prediction accuracy.Therefore,a wind power prediction method based on improved variational modal decomposition with permutation entropy is proposed.First,based on the meteorological data of wind farms,the Spearman correlation coefficient method is used to filter the meteorological data that are strongly correlated with the wind power to establish the wind power prediction model data set;then the original wind power is decomposed using the improved variational modal decomposition technique to eliminate the noise in the data,and the decomposed wind power is reconstructed into a new subsequence by using the permutation entropy;with the meteorological data and the new subsequence as input variables,a stacking deeply integrated prediction model is developed;and finally the prediction results are obtained by optimizing the hyperparameters of the model algorithm through a genetic algorithm.The validity of the model is verified using a real data set from a wind farm in north-west China.The results show that the mean absolute error,root mean square error and mean absolute percentage error are improved by at least 33.1%,56.1%and 54.2%compared with the autoregressive integrated moving average model,the support vector machine,long short-term memory,extreme gradient enhancement and convolutional neural networks and long short-term memory models,indicating that the method has higher prediction accuracy.