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.

Significant wave height forecasts integrating ensemble empirical mode decomposition with sequence-to-sequence model

As wave height is an important parameter in marine climate measurement,its accurate prediction is crucial in ocean engineering.It also plays an important role in marine disaster early warning and ship design,etc.However,challenges in the large demand for computing resources and the improvement of accuracy are currently encountered.To resolve the above mentioned problems,sequence-to-sequence deep learning model(Seq-to-Seq)is applied to intelligently explore the internal law between the continuous wave height data output by the model,so as to realize fast and accurate predictions on wave height data.Simultaneously,ensemble empirical mode decomposition(EEMD)is adopted to reduce the non-stationarity of wave height data and solve the problem of modal aliasing caused by empirical mode decomposition(EMD),and then improves the prediction accuracy.A significant wave height forecast method integrating EEMD with the Seq-to-Seq model(EEMD-Seq-to-Seq)is proposed in this paper,and the prediction models under different time spans are established.Compared with the long short-term memory model,the novel method demonstrates increased continuity for long-term prediction and reduces prediction errors.The experiments of wave height prediction on four buoys show that the EEMD-Seq-to-Seq algorithm effectively improves the prediction accuracy in short-term(3-h,6-h,12-h and 24-h forecast horizon)and long-term(48-h and 72-h forecast horizon)predictions.

A novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise,minimum mean square variance criterion and least mean square adaptive filter

Underwater acoustic signal processing is one of the research hotspots in underwater acoustics.Noise reduction of underwater acoustic signals is the key to underwater acoustic signal processing.Owing to the complexity of marine environment and the particularity of underwater acoustic channel,noise reduction of underwater acoustic signals has always been a difficult challenge in the field of underwater acoustic signal processing.In order to solve the dilemma,we proposed a novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN),minimum mean square variance criterion(MMSVC) and least mean square adaptive filter(LMSAF).This noise reduction technique,named CEEMDAN-MMSVC-LMSAF,has three main advantages:(i) as an improved algorithm of empirical mode decomposition(EMD) and ensemble EMD(EEMD),CEEMDAN can better suppress mode mixing,and can avoid selecting the number of decomposition in variational mode decomposition(VMD);(ii) MMSVC can identify noisy intrinsic mode function(IMF),and can avoid selecting thresholds of different permutation entropies;(iii) for noise reduction of noisy IMFs,LMSAF overcomes the selection of deco mposition number and basis function for wavelet noise reduction.Firstly,CEEMDAN decomposes the original signal into IMFs,which can be divided into noisy IMFs and real IMFs.Then,MMSVC and LMSAF are used to detect identify noisy IMFs and remove noise components from noisy IMFs.Finally,both denoised noisy IMFs and real IMFs are reconstructed and the final denoised signal is obtained.Compared with other noise reduction techniques,the validity of CEEMDAN-MMSVC-LMSAF can be proved by the analysis of simulation signals and real underwater acoustic signals,which has the better noise reduction effect and has practical application value.CEEMDAN-MMSVC-LMSAF also provides a reliable basis for the detection,feature extraction,classification and recognition of underwater acoustic signals.

Pressure fluctuation signal analysis of pump based on ensemble empirical mode decomposition method

Pressure fluctuations, which are inevitable in the operation of pumps, have a strong non-stationary characteristic and contain a great deal of important information representing the operation conditions. With an axial-flow pump as an example, a new method for time-frequency analysis based on the ensemble empirical mode decomposition （EEMD） method is proposed for research on the characteristics of pressure fluctuations. First, the pressure fluctuation signals are preprocessed with the empirical mode decomposition （EMD） method, and intrinsic mode functions （IMFs） are extracted. Second, the EEMD method is used to extract more precise decomposition results, and the number of iterations is determined according to the number of IMFs produced by the EMD method. Third, correlation coefficients between IMFs produced by the EMD and EEMD methods and the original signal are calculated, and the most sensitive IMFs are chosen to analyze the frequency spectrum. Finally, the operation conditions of the pump are identified with the frequency features. The results show that, compared with the EMD method, the EEMD method can improve the time-frequency resolution and extract main vibration components from pressure fluctuation signals.

A method for extracting human gait series from accelerometer signals based on the ensemble empirical mode decomposition

In this paper, the ensemble empirical mode decomposition （EEMD） is applied to analyse accelerometer signals collected during normal human walking. First, the self-adaptive feature of EEMD is utilised to decompose the ac- celerometer signals, thus sifting out several intrinsic mode functions （IMFs） at disparate scales. Then, gait series can be extracted through peak detection from the eigen IMF that best represents gait rhythmicity. Compared with the method based on the empirical mode decomposition （EMD）, the EEMD-based method has the following advantages： it remarkably improves the detection rate of peak values hidden in the original accelerometer signal, even when the signal is severely contaminated by the intermittent noises; this method effectively prevents the phenomenon of mode mixing found in the process of EMD. And a reasonable selection of parameters for the stop-filtering criteria can improve the calculation speed of the EEMD-based method. Meanwhile, the endpoint effect can be suppressed by using the auto regressive and moving average model to extend a short-time series in dual directions. The results suggest that EEMD is a powerful tool for extraction of gait rhythmicity and it also provides valuable clues for extracting eigen rhythm of other physiological signals.

Source Separation of Diesel Engine Vibration Based on the Empirical Mode Decomposition and Independent Component Analysis

Vibration signals from diesel engine contain many different components mainly caused by combustion and mechanism operations,several blind source separation techniques are available for decomposing the signal into its components in the case of multichannel measurements,such as independent component analysis（ICA）.However,the source separation of vibration signal from single-channel is impossible.In order to study the source separation from single-channel signal for the purpose of source extraction,the combination method of empirical mode decomposition（EMD） and ICA is proposed in diesel engine signal processing.The performance of the described methods of EMD-wavelet and EMD-ICA in vibration signal application is compared,and the results show that EMD-ICA method outperforms the other,and overcomes the drawback of ICA in the case of single-channel measurement.The independent source signal components can be separated and identified effectively from one-channel measurement by EMD-ICA.Hence,EMD-ICA improves the extraction and identification abilities of source signals from diesel engine vibration measurements.

Study on the Improvement of the Application of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise in Hydrology Based on RBFNN Data Extension Technology

The complex nonlinear and non-stationary features exhibited in hydrologic sequences make hydrological analysis and forecasting difficult.Currently,some hydrologists employ the complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)method,a new time-frequency analysis method based on the empirical mode decomposition(EMD)algorithm,to decompose non-stationary raw data in order to obtain relatively stationary components for further study.However,the endpoint effect in CEEMDAN is often neglected,which can lead to decomposition errors that reduce the accuracy of the research results.In this study,we processed an original runoff sequence using the radial basis function neural network(RBFNN)technique to obtain the extension sequence before utilizing CEEMDAN decomposition.Then,we compared the decomposition results of the original sequence,RBFNN extension sequence,and standard sequence to investigate the influence of the endpoint effect and RBFNN extension on the CEEMDAN method.The results indicated that the RBFNN extension technique effectively reduced the error of medium and low frequency components caused by the endpoint effect.At both ends of the components,the extension sequence more accurately reflected the true fluctuation characteristics and variation trends.These advances are of great significance to the subsequent study of hydrology.Therefore,the CEEMDAN method,combined with an appropriate extension of the original runoff series,can more precisely determine multi-time scale characteristics,and provide a credible basis for the analysis of hydrologic time series and hydrological forecasting.

Denoising of chaotic signal using independent component analysis and empirical mode decomposition with circulate translating

In this paper, a new method to reduce noises within chaotic signals based on ICA （independent component analysis） and EMD （empirical mode decomposition） is proposed. The basic idea is decomposing chaotic signals and constructing multidimensional input vectors, firstly, on the base of EMD and its translation invariance. Secondly, it makes the indepen- dent component analysis on the input vectors, which means that a self adapting denoising is carried out for the intrinsic mode functions （IMFs） of chaotic signals. Finally, all IMFs compose the new denoised chaotic signal. Experiments on the Lorenz chaotic signal composed of different Gaussian noises and the monthly observed chaotic sequence on sunspots were put into practice. The results proved that the method proposed in this paper is effective in denoising of chaotic signals. Moreover, it can correct the center point in the phase space effectively, which makes it approach the real track of the chaotic attractor.

HARMONIC COMPONENT EXTRACTION FROM A CHAOTIC SIGNAL BASED ON EMPIRICAL MODE DECOMPOSITION METHOD

A novel approach of signal extraction of a harmonic component fRom a chaotic signal generated by a Duffing oscillator was proposed. Based on empirical mode decomposition （EMD） and concept that any signal is composed of a series of the simple intrinsic modes, the harmonic components were extracted f^om the chaotic signals. Simulation results show the approach is satisfactory.

Effective forecast of Northeast Pacific sea surface temperature based on a complementary ensemble empirical mode decomposition–support vector machine method

The sea surface temperature （SST） has substantial impacts on the climate; however, due to its highly nonlinear nature, evidently non-periodic and strongly stochastic properties, it is rather difficult to predict SST. Here, the authors combine the complementary ensemble empirical mode decomposition （CEEMD） and support vector machine （SVM） methods to predict SST. Extensive tests from several different aspects are presented to validate the effectiveness of the CEEMD-SVM method. The results suggest that the new method works well in forecasting Northeast Pacific SST at a 12-month lead time, with an average absolute error of approximately 0.3℃ and a correlation coefficient of 0.85. Moreover, no spring predictability barrier is observed in our experiments.

Chirplet Signal and Empirical Mode Decompositions of Ultrasonic Signals for Echo Detection and Estimation

In this study, the performance of chirplet signal decomposition (CSD) and empirical mode decomposition (EMD) coupled with Hilbert spectrum have been evaluated and compared for ultrasonic imaging applications. Numerical and experimental results indicate that both the EMD and CSD are able to decompose sparsely distributed chirplets from noise. In case of signals consisting of multiple interfering chirplets, the CSD algorithm, based on successive search for estimating optimal chirplet parameters, outperforms the EMD algorithm which estimates a series of intrinsic mode functions (IMFs). In particular, we have utilized the EMD as a signal conditioning method for Hilbert time-frequency representation in order to estimate the arrival time and center frequency of chirplets in order to quantify the ultrasonic signals. Experimental results clearly exhibit that the combined EMD and CSD is an effective processing tools to analyze ultrasonic signals for target detection and pattern recognition.

Feature Layer Fusion of Linear Features and Empirical Mode Decomposition of Human EMG Signal

To explore the influence of the fusion of different features on recognition,this paper took the electromyography(EMG)signals of rectus femoris under different motions(walk,step,ramp,squat,and sitting)as samples,linear features(time-domain features(variance(VAR)and root mean square(RMS)),frequency-domain features(mean frequency(MF)and mean power frequency(MPF)),and nonlinear features(empirical mode decomposition(EMD))of the samples were extracted.Two feature fusion algorithms,the series splicing method and complex vector method,were designed,which were verified by a double hidden layer(BP)error back propagation neural network.Results show that with the increase of the types and complexity of feature fusions,the recognition rate of the EMG signal to actions is gradually improved.When the EMG signal is used in the series splicing method,the recognition rate of time-domain+frequency-domain+empirical mode decomposition(TD+FD+EMD)splicing is the highest,and the average recognition rate is 92.32%.And this rate is raised to 96.1%by using the complex vector method,and the variance of the BP system is also reduced.

Application of Empirical Mode Energy to the Analysis of Fluctuating Signals

After an aerial object enters the water, physical changes to sounds in the water caused by the accompanying bubbles are quite complex. As a result, traditional signal analyzing methods cannot identify the real physical object. In view of this situation, a novel method for analyzing the sounds caused by an aerial object’s entry into water was proposed. This method analyzes the vibrational mode of the bubbles by using empitical mode decomposition. Experimental results showed that this method can efficiently remove noise and extract the broadband pulse signal and low-frequency fluctuating signal, producing an accurate resolution of entry time and frequency. This shows the improved performance of the proposed method.

Missing interpolation model for wind power data based on the improved CEEMDAN method and generative adversarial interpolation network

Randomness and fluctuations in wind power output may cause changes in important parameters(e.g.,grid frequency and voltage),which in turn affect the stable operation of a power system.However,owing to external factors(such as weather),there are often various anomalies in wind power data,such as missing numerical values and unreasonable data.This significantly affects the accuracy of wind power generation predictions and operational decisions.Therefore,developing and applying reliable wind power interpolation methods is important for promoting the sustainable development of the wind power industry.In this study,the causes of abnormal data in wind power generation were first analyzed from a practical perspective.Second,an improved complete ensemble empirical mode decomposition with adaptive noise(ICEEMDAN)method with a generative adversarial interpolation network(GAIN)network was proposed to preprocess wind power generation and interpolate missing wind power generation sub-components.Finally,a complete wind power generation time series was reconstructed.Compared to traditional methods,the proposed ICEEMDAN-GAIN combination interpolation model has a higher interpolation accuracy and can effectively reduce the error impact caused by wind power generation sequence fluctuations.

A Hybrid BPNN-GARF-SVR Prediction Model Based on EEMD for Ship Motion

Accurate prediction of shipmotion is very important for ensuringmarine safety,weapon control,and aircraft carrier landing,etc.Ship motion is a complex time-varying nonlinear process which is affected by many factors.Time series analysis method and many machine learning methods such as neural networks,support vector machines regression(SVR)have been widely used in ship motion predictions.However,these single models have certain limitations,so this paper adopts amulti-model prediction method.First,ensemble empirical mode decomposition(EEMD)is used to remove noise in ship motion data.Then the randomforest(RF)prediction model optimized by genetic algorithm(GA),back propagation neural network(BPNN)prediction model and SVR prediction model are respectively established,and the final prediction results are obtained by results of three models.And the weights coefficients are determined by the correlation coefficients,reducing the risk of prediction and improving the reliability.The experimental results show that the proposed combined model EEMD-GARF-BPNN-SVR is superior to the single predictive model and more reliable.The mean absolute percentage error(MAPE)of the proposed model is 0.84%,but the results of the single models are greater than 1%.

De-noising of radiation pressure signal generated by bubble oscillation based on ensemble empirical mode decomposition

The radiation pressure signals generated by the bubble oscillation are often utilized to recognize the characteristics of the target objects in many fields.However,these signals are easily contaminated by complex background noises.In order to accurately extract the effective components of the radiation pressure signal generated by the bubble oscillation,this paper proposes a de-noising procedure for the radiation pressure signal,based on the ensemble empirical mode decomposition(EEMD),the autocorrelation function and the modified wavelet soft-threshold de-noising method.In order to verify the effectiveness of the procedure,the typical radiation pressure signal generated based on the Keller-Miksis model under the acoustic excitation is employed for the subsequent de-noising analysis.The results of the qualitative analysis show that the amplitude and the period of the bubble oscillation can be clearly observed in the time-domain diagram of the de-noised signal based on the EEMD.In the quantitative analysis,the de-noised signal based on the EEMD has better performance with higher signal-to-noise ratio(SNR),smaller root-mean-square error,and larger correlation coefficient than that based on the wavelet transform(WT)and the empirical mode decomposition(EMD).Furthermore,with the increase of the complexity of the radiation pressure signal(e.g.,the increase of the dimensionless pressure amplitude of the acoustic wave and the decrease of the SNR of the input signal),the above three evaluation indexes of the de-noised signal based on the EEMD are all better than those based on the other two methods.When the signal is more complex,the de-noising capabilities of the WT,the EMD are greatly reduced,but the EEMD can still maintain the good de-noising capability,which shows the superiority of the signal de-noising procedure proposed in the present paper.

An Enhanced Ensemble-Based Long Short-Term Memory Approach for Traffic Volume Prediction

With the advancement of artificial intelligence,traffic forecasting is gaining more and more interest in optimizing route planning and enhancing service quality.Traffic volume is an influential parameter for planning and operating traffic structures.This study proposed an improved ensemble-based deep learning method to solve traffic volume prediction problems.A set of optimal hyperparameters is also applied for the suggested approach to improve the performance of the learning process.The fusion of these methodologies aims to harness ensemble empirical mode decomposition’s capacity to discern complex traffic patterns and long short-term memory’s proficiency in learning temporal relationships.Firstly,a dataset for automatic vehicle identification is obtained and utilized in the preprocessing stage of the ensemble empirical mode decomposition model.The second aspect involves predicting traffic volume using the long short-term memory algorithm.Next,the study employs a trial-and-error approach to select a set of optimal hyperparameters,including the lookback window,the number of neurons in the hidden layers,and the gradient descent optimization.Finally,the fusion of the obtained results leads to a final traffic volume prediction.The experimental results show that the proposed method outperforms other benchmarks regarding various evaluation measures,including mean absolute error,root mean squared error,mean absolute percentage error,and R-squared.The achieved R-squared value reaches an impressive 98%,while the other evaluation indices surpass the competing.These findings highlight the accuracy of traffic pattern prediction.Consequently,this offers promising prospects for enhancing transportation management systems and urban infrastructure planning.

Detection of time varying pitch in tonal languages: an approach based on ensemble empirical mode decomposition

A method based on ensemble empirical mode decomposition (EEMD) is proposed for accurately detecting the time varying pitch of speech in tonal languages. Unlike frame-, event-, or subspace-based pitch detectors, the time varying information of pitch within the short duration, which is of crucial importance in speech processing of tonal languages, can be accurately extracted. The Chinese Linguistic Data Consortium (CLDC) database for Mandarin Chinese was employed as standard speech data for the evaluation of the effectiveness of the method. It is shown that the proposed method provides more accurate and reliable results, particularly in estimating the tones of non-monotonically varying pitches like the third one in Mandarin Chinese. Also, it is shown that the new method has strong resistance to noise disturbance.

Regional features of topographic relief over the Loess Plateau,China:evidence from ensemble empirical mode decomposition

Landforms with similar surface matter compositions,endogenic and exogenic forces,and development histories tend to exhibit significant degrees of self-similarity in morphology and spatial variation.In loess hill-gully areas,ridges and hills have similar topographic relief characteristics and present nearly periodic variations of similar repeating structures at certain spatial scales,which is termed the topographic relief period(TRP).This is a relatively new concept,which is different from the degree of relief,and describes the fluctuations of the terrain from both horizontal and vertical(cross-section)perspectives,which can be used for in-depth analysis of 2-D topographic relief features.This technique provides a new perspective for understanding the macro characteristics and differentiation patterns of loess landforms.We investigate TRP variation features of different landforms on the Loess Plateau,China,by extracting catchment boundary profiles(CBPs)from 5 m resolution digital elevation model(DEM)data.These profiles were subjected to temporal-frequency analysis using the ensemble empirical mode decomposition(EEMD)method.The results showed that loess landforms are characterized by significant regional topographic relief;the CBP of 14 sample areas exhibited an overall pattern of decreasing TRPs and increasing topographic relief spatial frequencies from south to north.According to the TRPs and topographic relief characteristics,the topographic relief of the Loess Plateau was divided into four types that have obvious regional differences.The findings of this study enrich the theories and methods for digital terrain data analysis of the Loess Plateau.Future study should undertake a more in-depth investigation regarding the complexity of the region and to address the limitations of the EEMD method.

A hybrid approach based on complete ensemble empirical mode decomposition with adaptive noise for multi-step-ahead solar radiation forecasting

Accurate measurements of solar radiation are required to ensure that power and energy systems continue to function effectively and securely.On the other hand,estimating it is extremely challenging due to the non-stationary behaviour and randomness of its components.In this research,a novel hybrid forecasting model,namely complete ensemble empirical mode decomposition with adaptive noise-Gaussian process regression(CEEMDAN-GPR),has been developed for daily global solar radiation prediction.The non-stationary global solar radiation series is transformed by CEEMDAN into regular subsets.After that,the GPR model uses these subsets as inputs to perform its prediction.According to the results of this research,the performance of the developed hybrid model is superior to two widely used hybrid models for solar radiation forecasting,namely wavelet-GPR and wavelet packet-GPR,in terms of mean square error,root mean square error,coefficient of determination and relative root mean square error values,which reached 3.23 MJ/m^(2)/day,1.80 MJ/m^(2)/day,95.56%,and 8.80%,respectively(for one-step forward forecasting).The proposed hybrid model can be used to ensure the safe and reliable operation of the electricity system.