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.

Landslide displacement prediction based on optimized empirical mode decomposition and deep bidirectional long short-term memory network

There are two technical challenges in predicting slope deformation.The first one is the random displacement,which could not be decomposed and predicted by numerically resolving the observed accumulated displacement and time series of a landslide.The second one is the dynamic evolution of a landslide,which could not be feasibly simulated simply by traditional prediction models.In this paper,a dynamic model of displacement prediction is introduced for composite landslides based on a combination of empirical mode decomposition with soft screening stop criteria(SSSC-EMD)and deep bidirectional long short-term memory(DBi-LSTM)neural network.In the proposed model,the time series analysis and SSSC-EMD are used to decompose the observed accumulated displacements of a slope into three components,viz.trend displacement,periodic displacement,and random displacement.Then,by analyzing the evolution pattern of a landslide and its key factors triggering landslides,appropriate influencing factors are selected for each displacement component,and DBi-LSTM neural network to carry out multi-datadriven dynamic prediction for each displacement component.An accumulated displacement prediction has been obtained by a summation of each component.For accuracy verification and engineering practicability of the model,field observations from two known landslides in China,the Xintan landslide and the Bazimen landslide were collected for comparison and evaluation.The case study verified that the model proposed in this paper can better characterize the"stepwise"deformation characteristics of a slope.As compared with long short-term memory(LSTM)neural network,support vector machine(SVM),and autoregressive integrated moving average(ARIMA)model,DBi-LSTM neural network has higher accuracy in predicting the periodic displacement of slope deformation,with the mean absolute percentage error reduced by 3.063%,14.913%,and 13.960%respectively,and the root mean square error reduced by 1.951 mm,8.954 mm and 7.790 mm respectively.Conclusively,this model not only has high prediction accuracy but also is more stable,which can provide new insight for practical landslide prevention and control engineering.

Vehicle-Bridge Interaction Simulation and Damage Identification of a Bridge Using Responses Measured in a Passing Vehicle by Empirical Mode Decomposition Method

To prevent early bridge failures, effective Structural Health Monitoring (SHM) is vital. Vibration-based damage assessment is a powerful tool in this regard, as it relies on changes in a structure’s dynamic characteristics as it degrades. By measuring the vibration response of a bridge due to passing vehicles, this approach can identify potential structural damage. This dissertation introduces a novel technique grounded in Vehicle-Bridge Interaction (VBI) to evaluate bridge health. It aims to detect damage by analyzing the response of passing vehicles, taking into account VBI. The theoretical foundation of this method begins with representing the bridge’s superstructure using a Finite Element Model and employing a half-car dynamic model to simulate the vehicle with suspension. Two sets of motion equations, one for the bridge and one for the vehicle are generated using the Finite Element Method, mode superposition, and D’Alembert’s principle. The combined dynamics are solved using the Newmark-beta method, accounting for road surface roughness. A new approach for damage identification based on the response of passing vehicles is proposed. The response is theoretically composed of vehicle frequency, bridge natural frequency, and a pseudo-frequency component related to vehicle speed. The Empirical Mode Decomposition (EMD) method is applied to decompose the signal into its constituent parts, and damage detection relies on the Intrinsic Mode Functions (IMFs) corresponding to the vehicle speed component. This technique effectively identifies various damage scenarios considered in the study.

Determination of Instantaneous Frequencies of Low Plasma Waves in the Magnetosheath Using Empirical Mode Decomposition (EMD) and Hilbert Transform (HT)

The observations of in-situ spacecraft mission in the magnetosheath and a region of thermalized subsonic plasma behind the bow shock reveal a non-linear behaviour of plasma waves. The study of waves and optics in Physics has given the understanding of the effect of many waves coming together to form a wave field or wave packet. The common aspect of such study shows that two or more waves can superimpose constructively or destructively. The sudden high magnetic field data in the magnetosheath displays such possibility of superposition of waves. In this paper, we use the empirical mode decomposition (EMD) and Hilbert transform (HT) techniques to determine the instantaneous frequencies of low frequency plasma waves in the magnetosheath. Our analysis has shown that the turbulent behavior of magnetic field in the magnetosheath within the selected period is due to superposition of waves.

Improvement of the prediction accuracy of polar motion using empirical mode decomposition

Previous studies revealed that the error of pole coordinate prediction will significantly increase for a prediction period longer than 100 days, and this is mainly caused by short period oscillations. Empirical mode decomposition （EMD）, which is increasingly popular and has advantages over classical wavelet decomposition, can be used to remove short period variations from observed time series of pole co- ordinates. A hybrid model combing EMD and extreme learning machine （ELM）, where high frequency signals are removed and processed time series is then modeled and predicted, is summarized in this paper. The prediction performance of the hybrid model is compared with that of the ELM-only method created from original time series. The results show that the proposed hybrid model outperforms the pure ELM method for both short-term and long-term prediction of pole coordinates. The improvement of prediction accuracy up to 360 days in the future is found to be 24.91% and 26.79% on average in terms of mean absolute error （MAE） for the xp and yp components of pole coordinates, respectively.

Segmented second algorithm of empirical mode decomposition

A new algorithm, named segmented second empirical mode decomposition （EMD） algorithm, is proposed in this paper in order to reduce the computing time of EMD and make EMD algorithm available to online time-frequency analysis. The original data is divided into some segments with the same length. Each segment data is processed based on the principle of the first-level EMD decomposition. The algorithm is compared with the traditional EMD and results show that it is more useful and effective for analyzing nonlinear and non-stationary signals.

Weighing axle weight of moving vehicle based on empirical mode decomposition

Dynanfic forces are the main factor that influences the axle weight measurement accuracy of moving vehicle. Empirical mode decomposition （EMD） is presented to separate the dynamic forces contained in the axle weight signal. The concept and algorithm of EMD are introduced. The characteristic of the axle weight signal is analyzed. The method of judging pseudo intrinsic mode function （pseudo-IMF） is presented to improve the weighing accuracy. Numerical simulation and field experiments are conducted to evaluate the performance of EMD. The result shows effectiveness of the proposed method. Maximum weighing errors of the front axle, the rear axle and the gross weight at the speed of 15 km/h or lower are 2.22%, 6.26% and 4.11% respectively.

Satellite fault diagnosis method based on predictive filter and empirical mode decomposition

A novel satellite fault diagnosis scheme is presented based on the predictive filter and empirical mode composition（EMD）.First,the predictive filter is utilized to obtain the fault estimation,which is corrupted by noise.Then the EMD method is introduced to decompose the fault estimation into a finite number of intrinsic mode functions and extract the trend of faults for fault diagnosis.The proposed scheme has the ability of diagnosing both abrupt and incipient faults of the actuator in a satellite attitude control subsystem.A mathematical simulation is given to illustrate the effectiveness of the proposed scheme.

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.

A New Method of Wind Turbine Bearing Fault Diagnosis Based on Multi-Masking Empirical Mode Decomposition and Fuzzy C-Means Clustering

Based on Multi-Masking Empirical Mode Decomposition (MMEMD) and fuzzy c-means (FCM) clustering, a new method of wind turbine bearing fault diagnosis FCM-MMEMD is proposed, which can determine the fault accurately and timely. First, FCM clustering is employed to classify the data into different clusters, which helps to estimate whether there is a fault and how many fault types there are. If fault signals exist, the fault vibration signals are then demodulated and decomposed into different frequency bands by MMEMD in order to be analyzed further. In order to overcome the mode mixing defect of empirical mode decomposition (EMD), a novel method called MMEMD is proposed. It is an improvement to masking empirical mode decomposition (MEMD). By adding multi-masking signals to the signals to be decomposed in different levels, it can restrain low-frequency components from mixing in highfrequency components effectively in the sifting process and then suppress the mode mixing. It has the advantages of easy implementation and strong ability of suppressing modal mixing. The fault type is determined by Hilbert envelope finally. The results of simulation signal decomposition showed the high performance of MMEMD. Experiments of bearing fault diagnosis in wind turbine bearing fault diagnosis proved the validity and high accuracy of the new method.

Regional features of the temperature trend in China based on Empirical Mode Decomposition

By the Empirical Mode Decomposition method, we analyzed the observed monthly average temperature in more than 700 stations from 1951-2001 over China. Simultaneously, the temperature variability of each station is calculated by this method, and classification chart of long term trend and temperature variability distributing chart of China are obtained, supported by GIS, 1 kmxl km resolution. The results show that： in recent 50 years, the temperature has increased by more than 0.4~C/10a in most parts of northern China, while in Southwest China and the middle and lower Yangtze Valley, the increase is not significant. The areas with a negative temperature change rate are distributed sporadically in Southwest China. Meanwhile, the temperature data from 1881 to 2001 in nine study regions in China are also analyzed, indicating that in the past 100 years, the temperature has been increasing all the way in Northeast China, North China, South China, Northwest China and Xinjiang and declining in Southwest China. An inverse ‘V-shaped’ trend is also found in Central China. But in Tibet the change is less significant.

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.

FAULT DIAGNOSIS APPROACH FOR ROLLER BEARINGS BASED ON EMPIRICAL MODE DECOMPOSITION METHOD AND HILBERT TRANSFORM

Based upon empirical mode decomposition (EMD) method and Hilbert spectrum, a method for fault diagnosis of roller bearing is proposed. The orthogonal wavelet bases are used to translate vibration signals of a roller bearing into time-scale representation, then, an envelope signal can be obtained by envelope spectrum analysis of wavelet coefficients of high scales. By applying EMD method and Hilbert transform to the envelope signal, we can get the local Hilbert marginal spectrum from which the faults in a roller bearing can be diagnosed and fault patterns can be identified. Practical vibration signals measured from roller bearings with out-race faults or inner-race faults are analyzed by the proposed method. The results show that the proposed method is superior to the traditional envelope spectrum method in extracting the fault characteristics of roller bearings.

FAST IMPLEMENTATION OF ORTHOGONAL EMPIRICAL MODE DECOMPOSITION AND ITS APPLIGA-TION INTO HARMONIC DETECTION

Since the empirical mode decomposition （EMD） lacks strict orthogonality, the method of orthogonal empirical mode decomposition （OEMD） is innovationally proposed. The primary thought of this method is to obtain the intrinsic mode function （IMF） and the residual function by auto-adaptive band-pass filtering. OEMD is proved to preserve strict orthogonality and completeness theoretically, and the orthogonal basis function of OEMD is generated, then an algorithm to implement OEMD fast, IMF binary searching algorithm is built based on the point that the analytical band-pass filtering preserves perfect band-pass feature in the frequency domain. The application into harmonic detection shows that OEMD successfully conquers mode aliasing, avoids the occurrence of false mode, and is featured by fast computing speed. Furthermore, it can achieve harmonic detection accurately combined with the least square method.

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.

GEARBOX FAULTDIAGNOSIS BASED ON EMPIRICAL MODE DECOMPOSITION

Time synchronous averaging of vibration data is a fundament technique forgearbox diagnosis. Currently, this technique relies on hardware tachometer to give phase synchronousinformation. Empirical mode decomposition (EMD) is introduced to replace time synchronous averagingof gearbox vibration signal. With it, any complicated dataset can be decomposed into a finite andoften small number of intrinsic mode functions (IMF). The key problem is how to assure thatvibration signals deduced by gear defects could be sifted out by EMD. The characteristic vibrationsignals of gear defects are proved IMFs, which makes it possible to utilize EMD for the diagnosis ofgearbox faults. The method is validated by data from recordings of the vibration of a single-stagespiral bevel gearbox with fatigue pitting. The results show EMD is powerful to extractcharacteristic information from noisy vibration signals.

Remote Sensing Image Fusion Using Bidimensional Empirical Mode Decomposition and the Least Squares Theory

Due to the data acquired by most optical earth observation satellite such as IKONOS, QuickBird-2 and GF-1 consist of a panchromatic image with high spatial resolution and multiple multispectral images with low spatial resolution. Many image fusion techniques have been developed to produce high resolution multispectral image. Considering panchromatic image and multispectral images contain the same spatial information with different accuracy, using the least square theory could estimate optimal spatial information. Compared with previous spatial details injection mode, this mode is more accurate and robust. In this paper, an image fusion method using Bidimensional Empirical Mode Decomposition (BEMD) and the least square theory is proposed to merge multispectral images and panchromatic image. After multi-spectral images were transformed from RGB space into IHS space, next I component and Panchromatic are decomposed by BEMD, then using the least squares theory to evaluate optimal spatial information and inject spatial information, finally completing fusion through inverse BEMD and inverse intensity-hue-saturation transform. Two data sets are used to evaluate the proposed fusion method, GF-1 images and QuickBird-2 images. The fusion images were evaluated visually and statistically. The evaluation results show the method proposed in this paper achieves the best performance compared with the conventional method.

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.