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.

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.

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.

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.

Random noise attenuation by f–x spatial projection-based complex empirical mode decomposition predictive filtering

The frequency–space（f–x） empirical mode decomposition（EMD） denoising method has two limitations when applied to nonstationary seismic data. First, subtracting the first intrinsic mode function（IMF） results in signal damage and limited denoising. Second, decomposing the real and imaginary parts of complex data may lead to inconsistent decomposition numbers. Thus, we propose a new method named f–x spatial projection-based complex empirical mode decomposition（CEMD） prediction filtering. The proposed approach directly decomposes complex seismic data into a series of complex IMFs（CIMFs） using the spatial projection-based CEMD algorithm and then applies f–x predictive filtering to the stationary CIMFs to improve the signal-to-noise ratio. Synthetic and real data examples were used to demonstrate the performance of the new method in random noise attenuation and seismic signal preservation.

Improved random noise attenuation using f-x empirical mode decomposition and local similarity

Conventional f-x empirical mode decomposition（EMD） is an effective random noise attenuation method for use with seismic profiles mainly containing horizontal events.However,when a seismic event is not horizontal,the use of f-x EMD is harmful to most useful signals.Based on the framework of f-x EMD,this study proposes an improved denoising approach that retrieves lost useful signals by detecting effective signal points in a noise section using local similarity and then designing a weighting operator for retrieving signals.Compared with conventional f-x EMD,f-x predictive filtering,and f-x empirical mode decomposition predictive filtering,the new approach can preserve more useful signals and obtain a relatively cleaner denoised image.Synthetic and field data examples are shown as test performances of the proposed approach,thereby verifying the effectiveness of this method.

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.

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.

Improvement of the Mirror Extending in Empirical Mode Decomposition Method and the Technology for Eliminating Frequency Mixing

The mirror extending approach proposed by Zhao and Huang in EMD method is improved in this paper. Mirror extending manner of data is kept unchanged, but the approach for determining envelopes is changed. When the end of data is obviously not extremum, the envelope is determined by the first inner extremum and the image value in the mirror, ignoring the value on the end. This improvement eliminates the frequency compression near the end and decreases the error. Meanwhile, tridiagonal equations are used and the calculation speed is much increased. The temporal process curve is more important in reflecting the real physical process and comparable with other phenomena. Frequency mixing in IMFs makes it impossible. A high frequency reconstruction (HFR) approach is proposed to eliminate common frequency mixing and reconstruct an IMF with all high frequency portions. By this approach, the IMFs without frequency mixing are obtained to express significative processes. The high frequency information restored in high frequency IMF can be extracted by general spectrum method. After obtaining IMFs by EMD method, some of the theoretical and technological issues still exist when using the IMFs. The consistency of IMFs with real physical process is discussed in detail. By virtue of the approach proposed in this paper, the EMD method can be widely used in various fields.

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.

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.

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.

Application of empirical mode decomposition based energy ratio to vortex flowmeter state diagnosis

To improve the measurement performance, a method for diagnosing the state of vortex flowmeter under various flow conditions was presented. The raw sensor signal of the vortex flowmeter was adaptively decomposed into intrinsic mode functions using the empirical mode decomposition approach. Based on the empirical mode decomposition results, the energy of each intrinsic mode function was extracted, and the vortex energy ratio was proposed to analyze how the perturbation in the flow affected the measurement performance of the vortex flowmeter. The relationship between the vortex energy ratio of the signal and the flow condition was established. The results show that the vortex energy ratio is sensitive to the flow condition and ideal for the characterization of the vortex flowmeter signal. Moreover, the vortex energy ratio under normal flow condition is greater than 80%, which can be adopted as an indicator to diagnose the state of a vortex flowmeter.

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.

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.

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.

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.