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.

Studies of Variational Assimilation for the Inversion of the Coupled Air-sea Model

For the prediction of ENSO, the accuracy of the model including the parameters, initial value and others of the model is important, which can be retrieved by the variational data assimilation methods developed in recent years. However, when the nonlinearity of the model is quite strong, the effect of the improvement made by the 4-D variational data assimilation may be poor due to the bad approximation of the tangent linear model to the original model. So in the paper the ideas in the optimal control is introduced to improve the effect of 4-DVAR in the inversion of the parameters of a nonlinear dynamic ENSO model. The results indicate that when the terminal controlling term is added to the cost functional of 4DVAR, which originated from the optimal control, the effect of the inversion may be largely improved comparing to the traditional 4DVAR, as can be especially obvious from the phase orbit of the model variables. The results in the paper also suggest that the method of 4DVAR in combination with optimal control cannot only reduce the error resulting from the inaccuracy of the model parameters but also can correct the parameters itself. This gives a good method in modifying the model and improving the quality of prediction of ENSO.

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.

Water Gauge Image Denoising Model Based on Improved Adaptive Total Variation

As an important part of water level warning in water conservancy projects,often due to the influence of environmental factors such as light and stains,the acquired water gauge images have sticky,broken and bright spot conditions,which affect the identification of water gauges.To solve this problem,a water gauge image denoising model based on improved adaptive total variation is proposed.Firstly,the regular term exponent in the adaptive total variational equation is changed to an inverse cosine function;secondly,the differential curvature is used to distinguish the image noise points and increase the smoothing strength at the noise points;finally,according to the characteristics of the gradient mode and adaptive gradient threshold after Gaussian filtering,the New model can adaptively denoise in the smooth area and protect the edge area,so as to have the characteristics of both edge-preserving denoising.The experimental results show that the new model has a great improvement in image vision,higher iteration efficiency and an average increase of 1.6 dB in peak signal-to-noise ratio,and an average increase of 9%in structural similarity,which is more beneficial to practical applications.

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.

The connection of phytoplankton biomass in the Marguerite Bay polynya of the western Antarctic Peninsula to the Southern Annular Mode

Antarctic coastal polynyas are biological hotspots in the Southern Ocean that support the abundance of hightrophic-level predators and are important for carbon cycling in the high-latitude oceans.In this study,we examined the interannual variation of summertime phytoplankton biomass in the Marguerite Bay polynya(MBP)in the western Antarctic Peninsula area,and linked such variability to the Southern Annular Mode(SAM)that dominated the southern hemisphere extratropical climate variability.Combining satellite data,atmosphere reanalysis products and numerical simulations,we found that the interannual variation of summer chlorophyll-a(Chl-a)concentration in the MBP is significantly and negatively correlated with the spring SAM index,and weakly correlated with the summer SAM index.The negative relation between summer Chl-a and spring SAM is due to weaker spring vertical mixing under a more positive SAM condition,which would inhibit the supply of iron from deep layers into the surface euphotic layer.The negative relation between spring mixing and spring SAM results from greater precipitation rate over the MBP region in positive SAM phase,which leads to lower salinity in the ocean surface layer.The coupled physical-biological mechanisms between SAM and phytoplankton biomass revealed in this study is important for us to predict the future variations of phytoplankton biomasses in Antarctic polynyas under climate change.

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.

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.

The Variations of Dominant Convection Modes over Asia, Indian Ocean, and Western Pacific Ocean during the Summers of 1997-2004

The NOAA daily outgoing longwave radiation （OLR） and the Global Precipitation Climatology Project （GPCP）daily precipitation data are used to study the variation of dominant convection modes and their relationships over Asia, the Indian Ocean, and the western Pacific Ocean during the summers from 1997 to 2004. Major findings are as follows： （1） Regression analysis with the OLR indicates the convective variations over Asian monsoon region are more closely associated with the convective activities over the western subtropical Pacific （WSP） than with those over the northern tropical Indian Ocean （NTIO）. （2） The EOF analysis of OLR indicates the first mode （EOF1） exhibits the out-of-phase variations between eastern China and India, and between eastern China and the WSP. The OLR EOF1 primarily exhibits seasonal and even longer-term variations. （3） The OLR EOF2 mostly displays in-phase convective variations over India, the Bay of Bengal, and southeastern China. A wavelet analysis reveals intraseasonal variation （ISV） features in 2000, 2001, 2002, and 2004. However, the effective ISV does not take place in every year and it seems to occur only when the centers of an east-west oriented dipole reach enough intensity over the tropical Indian and western Pacific Oceans. （4） The spatial patterns of OLR EOF3 are more complicated than those of EOF1 and EOF2, and an effective ISV is noted from 1999 to 2004. The OLR EOF3 implies there is added complexity of the OLR pattern when the effective ISV occurs. （5） The correlation analysis suggests the precipitation over India is more closely associated with the ISV, seasonal variations, and even longer-term variations than precipitation occurring over eastern China.

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.

Dominant variation modes associated with Yangtze–Huai River Basin summer heavy rainfall events

The Yangtze–Huai River Basin(YHRB)always suffers from anomalously heavy rainfall during the warm season,and has been well explored as a whole area during the past several decades.In this study,the YHRB is divided into two core regions-the northern YHRB(nYHRB)and southern YHRB(sYHRB)-based on 29-year(1979–2007)June–July–August(JJA)temporally averaged daily rainfall rates and the standard deviation of rainfall.A spectral analysis of JJA daily rainfall data over these 29 years reveals that a 3–7-day synoptic-timescale high-frequency mode is absolutely dominant over the nYHRB,with 10–20-day and 15–40-day modes playing a secondary role.By contrast,3–7-day and 10–20-day modes are both significant over the sYHRB,with 7–14-day,15–40-day,and 20–60-day modes playing secondary roles.Based on a comparison between bandpass-filtered rainfall anomalies and original rainfall series,a total of 42,1,5,and 3 heavy rainfall events(daily rainfall amounts in the top 5%of rainy days)are detected over the nYHRB,corresponding to 3–7-day,7–14-day,10–20-day,and 15–40-day variation disturbances.Meanwhile,a total of 28,8,12,and 6 heavy rainfall events are detected over the sYHRB,corresponding to 3–7-day,7–14-day,10–20-day,and 20–60-day variation disturbances.The results have important implications for understanding the duration of summer heavy rainfall events over both regions.

A PRINCIPAL MODE OF CIRCULATION COVARIATION BETWEEN THE NORTHERN AND SOUTHERN HEMISPHERES AND ITS ASSOCIATION WITH ENSO DURING BOREAL WINTER

By employing the singular value decomposition(SVD) analysis, we have investigated in the present paper the covariations between circulation changes in the Northern(NH) and Southern Hemispheres(SH) and their associations with ENSO by using the NCEP/NCAR reanalysis, the reconstructed monthly NOAA SST, and CMAP precipitation along with NOAA Climate Prediction Center(CPC) ENSO indices. A bi-hemispheric covariation mode(hereafter BHCM) is explored, which is well represented by the first mode of the SVD analysis of sea surface pressure anomaly(SLPA-SVD1). This SVD mode can explain 57.36% of the total covariance of SLPA. BHCM varies in time with a long-term trend and periodicities of 3—5 years. The long term trend revealed by SVD1 shows that the SLP increases in the equatorial central and eastern Pacific but decreases in the western Pacific and tropical Indian Ocean, which facilitates easterlies in the lower troposphere to be intensified and El Ni觡o events to occur with lower frequency. The spatial pattern of the BHCM looks roughly symmetric about the equator in the tropics, whereas it is characterized by zonal disturbances in the mid-latitude of NH and is highly associated with AAO in the mid-latitude of SH. On inter-annual time scales, the BHCM is highly correlated with ENSO. The atmosphere in both the NH and SH responds to sea surface temperature anomalies in the equatorial region, while the contemporaneous circulation changes in the NH and SH in turn affect the occurrence of El Ni觡o/La Ni觡a. In boreal winter, significant temperature and precipitation anomalies associated with the BHCM are found worldwide. Specifically, in the positive phase of the BHCM,temperature and precipitation are anomalously low in eastern China and some other regions of East Asia. These results are helpful for us to better understand interactions between circulations in the NH and SH and the dynamical mechanisms behind these interactions.

SPATIAL VARIATION OF WINTER SEA SURFACE TEMPERATURE IN NORTH PACIFIC AND ITS RELATION TO ATMOSPHERIC OSCILLATION MODES

The spatial variation of sea surface temperature anomalies(SSTA) in the North Pacific Ocean during winter is investigated using the EOF decomposition method.The first two main modes of SSTA are associated with Pacific Decadal Oscillation(PDO) mode and North Pacific Gyre Oscillation(NPGO) mode,respectively.Moreover,the first mode(PDO) is switched to the second mode(NPGO),a dominant mode after mid-1980.The mechanism of the modes' transition is analyzed.As the two oceanic modes are forced by the Aleutian Low(AL) and North Pacific Oscillation(NPO) modes,the AR-1 model is further used to examine the possible effect and mechanism of AL and NPO in generating the PDO and NPGO.The results show that compared to the NPO,the AL plays a more important role in generating the NPGO mode since the 1970s.Likewise,both the AL and NPO affect the PDO mode since the 1980s.

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.