Empirical Wavelet Research Articles

Peak envelope spectrum Fourier decomposition method and its application in fault diagnosis of rolling bearings

The Fourier decomposition method (FDM) is a useful method for signal decomposition. However, FDM has the problems of over decomposition and time-consuming. Therefore, a peak envelope spectrum Fourier decomposition method (PESFDM) is proposed in this paper. Firstly, the upper peak envelope is used to process the signal spectrum and obtain the peak envelope spectrum. Secondly, the segmentation boundaries are adaptively determined on the peak envelope spectrum using a modified “Locmaxmin” spectrum segmentation method. The bands between the segmentation boundaries are then reconstructed into several single-component signals. Finally, the proposed method is used to decompose the simulated and actual bearing fault signals. The results are compared against the other four signal processing methods: empirical mode decomposition, empirical wavelet transform, FDM, and adaptive power spectrum Fourier decomposition method. The results show that the proposed method has a more effective spectrum segmentation and a better effect of fault diagnosis.

Research on the Prediction Model of Blasting Vibration Velocity in the Dahuangshan Mine

In order to improve the prediction accuracy of blast vibration velocity, the model for predicting the peak particle velocity of blast vibration using the XGBoost (Extreme Gradient Boosting) method is improved, and the EWT–XGBoost model is established to predict the peak particle velocity of blast vibration by combining it with the EWT (Empirical Wavelet Transform) method. Calculate the relative error and root mean square error between the predicted value and measured value of each test sample, and compare the prediction performance of the EWT–XGBoost model with the original model. There is a large elevation difference between each vibration measurement location of high and steep slopes, but high and steep slopes are extremely dangerous, which is not conducive to the layout of blasting vibration monitoring equipment. The vibration velocity prediction model adopts the numerical simulation method, selects the center position of the small platform as the measurement point of the peak particle velocity, and studies the variation law of the blasting vibration velocity of the high and steep slopes under the action of top blasting. The research results show that the EWT–XGBoost model has a higher accuracy than the original model in the prediction of blasting vibration velocity; the simultaneous detonation method on adjacent high and steep slopes cannot meet the relevant requirements of safety regulations, and the delayed detonation method can effectively reduce the blasting vibration of high and steep slopes. The shock absorption effect of the elevation difference within 45 m is obvious.

Cyanobacteria blue-green algae prediction enhancement using hybrid machine learning-based gamma test variable selection and empirical wavelet transform.

This study aims to evaluate the usefulness and effectiveness of four machine learning (ML) models for modelling cyanobacteria blue-green algae (CBGA) at two rivers located in the USA. The proposed modelling framework was based on establishing a link between five water quality variables and the concentration of CBGA. For this purpose, artificial neural network (ANN), extreme learning machine (ELM), random forest regression (RFR), and random vector functional link (RVFL) are developed. First, the four models were developed using only water quality variables. Second, based on the results of the first, a new modelling strategy was introduced based on preprocessing signal decomposition. Hence, the empirical mode decomposition (EMD), the variational mode decomposition (VMD), and the empirical wavelet transform (EWT) were used for decomposing the water quality variables into several subcomponents, and the obtained intrinsic mode functions (IMFs) and multiresolution analysis (MRA) components were used as new input variables for the ML models. Results of the present investigation show that (i) using single models, good predictive accuracy was obtained using the RFR model exhibiting an R and NSE values of ≈0.914 and ≈0.833 for the first station, and ≈0.944 and ≈0.884 for the second station, while the others models, i.e., ANN, RVFL, and ELM, have failed to provide a good estimation of the CBGA; (ii) the decomposition methods have contributed to a significant improvement of the individual models performances; (iii) among the thee decomposition methods, the EMD was found to be superior to the VMD and EWT; and (iv) the ANN and RFR were found to be more accurate compared to the ELM and RVFL models, exhibiting high numerical performances with R and NSE values of approximately ≈0.983, ≈0.967, and ≈0.989 and ≈0.976, respectively.

A novel empirical wavelet SODP and spectral entropy based index for assessing the depth of anaesthesia

The requirement for anaesthesia during modern surgical procedures is unquestionable to ensure a safe experience for patients with successful recovery. Assessment of the depth of anaesthesia (DoA) is an important and ongoing field of research to ensure patient stability during and post-surgery. This research addresses the limitations of current DoA indexes by developing a new index based on electroencephalography (EEG) signal analysis. Empirical wavelet transformation (EWT) methods are employed to extract wavelet coefficients before statistical analysis. The features Spectral Entropy and Second Order Difference Plot are extracted from the wavelet coefficients. These features are used to train a new index, SSEDoA, utilising a Support Vector Machine (SVM) with a linear kernel function. The new index accurately assesses the DoA to illustrate the transition between different anaesthetic stages. Testing was undertaken with nine patients and an additional four patients with low signal quality. Across the nine patients we tested, an average correlation of 0.834 was observed with the Bispectral (BIS) index. The analysis of the DoA stage transition exhibited a Choen's Kappa of 0.809, indicative of a high agreement.

Variable step adaptive kurtogram method based on empirical wavelet transform for rolling bearing fault diagnosis

Variable step adaptive kurtogram method based on empirical wavelet transform for rolling bearing fault diagnosis

RUL prediction of rolling bearings based on improved empirical wavelet transform and convolutional neural network

Accurate prediction the remaining useful life (RUL) of rolling bearings under complex environmental conditions is crucial for prognostics and health management (PHM). In this paper, A new method for rolling bearing RUL prediction based on improved empirical wavelet transform (IEWT) and one-dimensional convolutional neural network (1D-CNN) is proposed to overcome the interference of noise and other disturbance signals. Firstly, in view of the problem of too many spectrum divisions in the traditional empirical wavelet transform (EWT) process, the mutual information value is used to re-determine the frequency band demarcation point in the EWT. The IEWT method is introduced to adaptively divide the original vibration signal to obtain a series of empirical mode functions (EMFs). Secondly, the effective components after IEWT decomposition are extracted by mutual information and kurtosis criteria and used to extract multi-dimensional time-frequency domain features. Finally, the 1D-CNN is constructed with the percentage of remaining life as the tracking metric to predict the RUL of the bearings. Based on two publicly available rolling bearing datasets, the model proposed in this paper have high prediction accuracy, which is better than other prediction models. Compared to other methods, its mean absolute error (MAE) and root mean square error (RMSE) are reduced.

Uterine Ultrasound Doppler Hemodynamics of Magnesium Sulfate Combined with Labetalol in the Treatment of Pregnancy-Induced Hypertension Using Empirical Wavelet Transform Algorithm.

The aim of this study was to explore the hemodynamic changes of magnesium sulfate combined with labetalol in the treatment of pregnancy-induced hypertension (PIH) under Doppler uterine ultrasound based on the empirical wavelet transform (EWT) algorithm. 500 patients with PIH in the hospital were selected and randomly divided into the control group (n = 250) and the observation group (n = 250). The control group was treated with conventional magnesium sulfate; the observation group was given labetalol based on magnesium sulfate drip in the control group. The uterine artery blood flow simulation model was established based on the EWT algorithm and compared with a short-time Fourier transform (STFT). The normalized root mean square error (NRMSE) of the STFT method was 0.19, and the NRMSE extracted by the EWT method was 0.13. After treatment, the blood pressure index, 24-hour urinary protein, and incidence of adverse birth outcomes in the observation group were lower than those in the control group; the effective rate of the control group (90.4%) was lower than that of the observation group (97.6%); the hemodynamic indexes of the uterine artery in the observation group were lower than those in the control group, and the differences were statistically significant (P < 0.05). The estimation accuracy of the EWT method was higher than that of the traditional STFT method; the combined treatment of magnesium sulfate and labetalol in patients with PIH had a remarkable effect, which could control the blood pressure index and reduce the 24-hour urinary protein; the uterine artery Doppler ultrasound examination could change hemodynamics and improve the adverse outcomes of mothers and infants.

Prediction of Fetal Growth Restriction for Fetal Umbilical Arterial/Venous Blood Flow Index Evaluated by Ultrasonic Doppler under Intelligent Algorithm

The empirical wavelet transform (EWT) algorithm was applied in ultrasound to explore the predictive value for fetal growth restriction (FGR) in fetal arteriovenous indexes. 142 pregnant women who received prenatal ultrasonic examination and delivered were selected. They were classified into control group and FGR group. There were 102 patients with normal pregnancy in the control group, and 40 patients with delayed fetal growth in the FGR group. The extended triple collocation (ETC) algorithm was employed to divide the Fourier spectrum of signals adaptively, and the constructed small filter banks were classified into corresponding intervals. The instantaneous frequency was analyzed, and the arterial blood flow indexes of the two groups were compared. The results showed that the time-frequency analysis method under EWT had lower normalization error and higher accuracy. The inner diameter and cross-sectional area of FGR were remarkably smaller than those of the control group, and the differences were statistically significant (P < 0.05). There were no significant differences in mean blood flow and mean blood velocity between the control group and FGR group (P > 0.05). The arterial blood flow parameters of the systolic flow velocity (VS) and the diastolic flow velocity (VD) in the FGR group were notably lower than those in the control group, and the differences were significant (P < 0.05). In conclusion, the frequency principal component extracted by EWT algorithm was less disturbed by noise, which could accurately and effectively evaluate fetal arteriovenous blood flow indexes and predict FGR.

Electricity price forecasting with high penetration of renewable energy using attention-based LSTM network trained by crisscross optimization

Accurate electricity price forecasts is the common concern of market participants. With the integration of high penetration of wind and solar energy resources into the power system, the renewable energy sources will have a great impact on the electricity price volatility undoubtedly. In this regard, a novel attention mechanism (AM) based electricity price forecasting model for electricity market with high proportion of renewable energy is proposed in this paper. In order to investigate the effect of renewable energy on the electricity price prediction, the wind power generation, solar power generation, predicted load and the historical price series are simultaneously taken as the input features. In the data preprocessing stage, the empirical wavelet transform (EWT) is applied to decompose each of the input features into multiple components to avoid learning the autocorrelation of the original sequence. In the model training stage, a hybrid AM-based long short-term memory network (LSTM) is proposed as the forecasting model, aiming to make full use of the AM to dynamically evaluate the importance of different input feature. Furthermore, the crisscross optimization algorithm (CSO) is adopted to retrain the parameters of fully-connected layer so as to further enhance the generalization ability. The proposed method is validated on the datasets of Danish electricity market with a high proportion of renewable energy, and the experimental results show that the proposed model is superior to other hybrid models involved in this study.

An effective wind speed prediction model combining secondary decomposition and regularised extreme learning machine optimised by cuckoo search algorithm

AbstractWind speed prediction has an important impact on the planning, economic operation and safe maintenance of wind power systems. However, the high volatility and intermittency of wind speed make it difficult to predict accurately. To improve the prediction accuracy, we developed a hybrid multistep wind speed prediction model named EWP‐CS‐RELM. In this model, a secondary decomposition technique of ensemble empirical mode decomposition (EEMD) and wavelet packet transform (WPT) is used, and it is called the EWP decomposition technique. This decomposition technique can achieve an adaptive processing of the data and accurately extract the characteristic components of the signal, avoiding the occurrence of pattern overlap and reducing the mutual interference between components. At the same time, the high and low‐frequency parts of the complex signal (component) can be decomposed into different frequency bands, and the corresponding frequency band can be selected adaptively to match the signal spectrum. The subsequence obtained after EWP decomposition is then predicted using a regularised extreme learning machine (RELM) optimised by the cuckoo search (CS) algorithm with strong global search ability to obtain the results. The hybrid prediction model is validated using four seasons of wind speed data from two wind farms in Shandong, China, and compared with seven other prediction models. Simulation results illustrate that the EWP‐CS‐RELM model outperforms the other seven models with the smallest statistical errors.

The Financial Market in China under the COVID-19

ABSTRACT The main aim of this study is to investigate the effects of COVID-19 on financial markets in China. Results of correlation analysis indicate that higher financial correlation among provinces emerged after the official announcement regarding COVID-19 in China. The Minimum Spanning Tree (MST) results after the pandemic announcement denote that Shanghai, Beijing, Jiangsu, Zhejiang, and Chongqing become the new cores, and the overall linking type exhibits cluster mode, which is varied from the intertwined connection mode. In addition, through Ensemble Empirical Mode Decomposition (EEMD) and Wavelet analysis, we found that financial markets in China are more susceptible to unexpected incidents.

Long-term multi-step ahead forecasting of root zone soil moisture in different climates: Novel ensemble-based complementary data-intelligent paradigms

The root zone soil moisture (RZSM) is essential for monitoring and forecasting agricultural, hydrological, and meteorological systems. Accordingly, researchers are determined to improve robust machine learning (ML) models to increase the accuracy of the RZSM predictions. This paper designed new complementary forecasting paradigms hybridizing Empirical Wavelet Transform (EWT) and two modern ensemble-based ML models, namely, extreme gradient boosting (XGBoost) and categorical boosting (CatBoost), to forecast long-term multi-step ahead daily RZSM in very cold and very warm semi-arid regions of Iran. For this purpose, the required datasets consisting of soil properties and meteorological information were extracted from the satellite datasets during 2005–2020 for Ardabil and Minab sites. Afterward, the significant lags of RZSM time series and optimal influence candidate inputs were sought based on the partial autocorrelation function (PACF) and mutual information techniques, respectively. Selected lagged components of RZSM time series were decomposed using EWT into different sub-sequences and consequently concatenated with candidate inputs to feed the ensemble ML models to forecast one-, three-, and seven-day-ahead RZSM at each case study. The performance of EWT-CatBoost and EWT-XGBoost and their counterpart standalone approaches was firstly evaluated in forecasting one-, three-, and seven-day-ahead RZSM using satellite data in this study and their accuracy were compared with a standalone kernel ridge regression (KRR) and complementary EWT-KRR models based on several statistical metrics (e.g., correlation coefficient (R), root mean square error (RMSE), Nash–Sutcliffe model efficiency coefficient (NSE)) and diagnostic analysis. The outcomes of testing phase in Ardabil site ascertained that the EWT-CatBoost (for RZSM(t + 1), R= 0.9979, RMSE= 0.0019, and NSE= 0.9985; for RZSM(t + 3), R= 0.9934, RMSE= 0.0035, and NSE= 0.9885; for RZSM(t + 7), R= 0.9489, RMSE= 0.0109, and NSE= 0.8634) outperformed the other models. On the other hand, the EWT-XGBoost model according to its best results (for RZSM(t + 1), R= 0.9911, RMSE= 0.0064, and NSE= 0.9805; for RZSM(t + 3), R= 0.9807, RMSE= 0.0092, and NSE= 0.9589; for RZSM(t + 7), R= 0.9680, RMSE= 0.0120, and NSE= 0.9309) yielded the most promising accuracy in forecasting multi-step ahead daily RZSM followed by the EWT-CatBoost, and EWT-KRR, respectively.

Half sine shock on random control method for multi-axial vibration testing

Control method for the multi-axial half sine shock on random vibration test is studied in this article. From the Fourier spectrum analysis, it is found that the power of the half sine shock is mainly concentrated within a specific frequency band, which is only related to the sine frequency of the half sine shock. Compared with the broadband random signal, the frequency band occupies a small range. Therefore, a mixed signal separation method is proposed for the shock on random vibration control test. Firstly, the Fourier spectrum is divided into two parts, and then the Empirical Wavelet Transform (EWT) is used to extract the shock component from the mixed signal. Afterward, the random component is obtained by subtracting the shock component from the mixed signal. According to the deviations between each component and the specified references, the amplitudes of the shock component and the Power Spectral Densities (PSDs) of the random component are controlled by the amplitude correction algorithm and the matrix power control algorithm, respectively. An experiment with tri-axial shaker is implemented and the results show that the proposed method is feasible for the multi-axial half sine shock on broadband random vibration control test.

Automated Detection of Pulmonary Diseases From Lung Sound Signals Using Fixed-Boundary-Based Empirical Wavelet Transform

In this letter, a promising method is proposed to automatically detect pulmonary diseases (PDs) from lung sound (LS) signals. The modes of the LS signal are evaluated using empirical wavelet transform with fixed boundary points. The time-domain (Shannon entropy) and frequency-domain (peak amplitude and peak frequency) features have been extracted from each mode. The classifiers, such as support vector machine, random forest, extreme gradient boosting, and light gradient boosting machine (LGBM), have been chosen to detect PDs using the features of LS signals automatically. The performance of the proposed method has been evaluated using LS signals obtained from a publicly available database. The detection accuracy values, such as 80.35, 83.27, 99.34, and 77.13%, have been obtained using the LGBM classifier with fivefold cross validation for normal versus asthma, normal versus pneumonia, normal versus chronic obstructive pulmonary disease (COPD), and normal versus pneumonia versus asthma versus COPD classification schemes. For the normal versus pneumonia versus asthma classification scheme, the proposed method has achieved an accuracy value of 84.76%, which is higher than that of the existing approaches using LS signals.

PowerCog: A Practical Method for Recognizing Power Quality Disturbances Accurately in a Noisy Environment

Currently, with the growing applicability of nonlinear electrical devices, power quality disturbances (PQDs) often occur in power systems. Previous works usually extracted statistical features from electrical signals manually and constructed classifiers with traditional machine learning methods for PQD monitoring. Furthermore, noisy tags or unlabeled data (different from noisy signals) are usually ignored in the traditional training stage, and these methods fail to meet the high accuracy and automation demands of real-world scenarios. To overcome the shortcomings of existing methods, this article proposes a practical method called PowerCog for accurately recognizing PQDs in noisy environments. First, an input voltage waveform signal is divided into several intrinsic mode functions by an empirical wavelet transform, and these functions are then aligned into columns to form a matrix. Second, tritraining is utilized for label refactoring to improve the generalization ability of the model in a noisy environment. Then, an optimized convolutional neural network structure combined with principal component analysis is deployed to extract and select the universal features automatically. Finally, a support vector machine classifier is constructed to recognize PQD patterns. Several comparative experiments are performed to verify the effectiveness and accuracy of PowerCog in complex environments.

RESCOVIDTCNnet: A residual neural network-based framework for COVID-19 detection using TCN and EWT with chest X-ray images

Since the advent of COVID-19, the number of deaths has increased exponentially, boosting the requirement for various research studies that may correctly diagnose the illness at an early stage. Using chest X-rays, this study presents deep learning-based algorithms for classifying patients with COVID illness, healthy controls, and pneumonia classes. Data gathering, pre-processing, feature extraction, and classification are the four primary aspects of the approach. The pictures of chest X-rays utilized in this investigation came from various publicly available databases. The pictures were filtered to increase image quality in the pre-processing stage, and the chest X-ray images were de-noised using the empirical wavelet transform (EWT). Following that, four deep learning models were used to extract features. The first two models, Inception-V3 and Resnet-50, are based on transfer learning models. The Resnet-50 is combined with a temporal convolutional neural network (TCN) to create the third model. The fourth model is our suggested RESCOVIDTCNNet model, which integrates EWT, Resnet-50, and TCN. Finally, an artificial neural network (ANN) and a support vector machine were used to classify the data (SVM). Using five-fold cross-validation for 3-class classification, our suggested RESCOVIDTCNNet achieved a 99.5 percent accuracy. Our prototype can be utilized in developing nations where radiologists are in low supply to acquire a diagnosis quickly.

Modal Identification of Structures with Closely Spaced Modes Based on Improved Empirical Wavelet Transform

Modal Identification of Structures with Closely Spaced Modes Based on Improved Empirical Wavelet Transform

An adaptive hierarchical decomposition-based method for multi-step cutterhead torque forecast of shield machine

Cutterhead torque is generated by interaction between geological environment and shield machine, which is one of the main load parameters of shield machine during the tunneling process. Its accurate forecast helps shield machine drivers adjust important operational parameters ahead of time for achieving safe and efficient tunneling. This paper presents an adaptive hierarchical decomposition-based method (AHDM) for multi-step forecast of cutterhead torque, where only original cutterhead torque signal is utilized as input and is decomposed adaptively to reduce its complexity and improve the forecast performance under complex geological environment and working conditions. First, matrix wavelet packet decomposition (MWPD) is developed to decompose original cutterhead torque signals into low-frequency and high-frequency sub-sequences. Then, an improved adaptive variational mode decomposition (IDVMD) is proposed for further decomposing the low-frequency sub-sequence into several simple series and residual series. Simultaneously, empirical wavelet transform is employed for dealing with the high-frequency sub-sequence. After adaptive hierarchical decomposition and significant complexity reduction of signal complexity, we design gated recurrent unit (GRU) based multi-step forecast network for each subsequence. Eventually, multi-step forecast of cutterhead torque is fulfilled by summing forecasting results for all sub-signals. To verify the developed AHDM, comparison with existing forecast methods in different five datasets is conducted. It is shown that the highest forecast accuracy obtained by the proposed AHDM reaches 99.030%, 98.721%, 98.653%, 98.113% and 97.674% from first-step to fifth-step, respectively. Moreover, the proposed AHDM outperforms current forecast methods on forecast accuracy for each step in 5 datasets. Especially, in the fifth-step forecast, forecast accuracy of AHDM is 6.424% higher on average than current methods. Meanwhile, when compared with current forecast methods, the RMSE and MAE indexes of the proposed AHDM reduce on average 72.937% and 71.315%, respectively. The results of k-fold cross validation show that proposed AHDM obtains strong robustness to different training and test set distributions. Therefore, for complex geological and working conditions, AHDM achieves high multi-step forecast accuracy, generalization ability and superiority.

Series Dc arc fault detection and location in wind-solar-storage hybrid system based on variational mode decomposition

As the main new energy, the wind-solar-storage hybrid system is widely used because of its excellent complementarity. However, due to the complexity of the system, series DC arc faults are prone to occur. This paper presents a method for series DC arc fault detection and location in wind-solar-storage hybrid system, which works mainly on the principle of threshold comparison in the time-frequency domain. Therein, an algorithm called variational mode decomposition (VMD) is employed. The voltage signal of the identical DC load under different operating conditions is decomposed by VMD, and the time-frequency domain characteristics of the normal operating conditions are used as thresholds. The series DC arc faults in different subsystems are detected and located by comparing the time-frequency domain features under different operating conditions with the threshold features. Compared with classical decomposition algorithms, Empirical Mode Decomposition (EMD) and Wavelet Transform (WT), the results show that VMD can eliminate the influence of noise and extract the fault signals of different systems more accurately, ensuring the precise localization of series DC arc faults.

Quaternion empirical wavelet transform and its applications in rolling bearing fault diagnosis

In view of the fact that it is difficult to predict the location and size of the failure of rotating machinery, the sensors sometimes cannot collect the fault information. When the fault location differs from the sensor direction by 180°, the fault information in the signal is weak and may be masked by noise. Multi-channel signal acquisition is one of the methods to solve the problem. Although existing algorithms can extract fault information from a single-channel signal, they are inefficient and sometimes fail to extract weak fault information. Therefore, the information in each channel needs to be associated and combined in advance. This paper proposes a multi-channel signal processing method called quaternion empirical wavelet transform (QEWT). QEWT based on the quaternion Fourier transform can process multiple groups of vibration signals at the same time, which realizes synchronous spectral division, fusion and modal decomposition. The modal separation method based on spectral trend avoids the problems of modal aliasing and low efficiency of scale-space representation. The proposed method combines spectral negentropy with the identification of the fault characteristics of the outer ring and the inner ring, and successfully realizes the fault diagnosis of the rolling bearing.