Combination Of Empirical Mode Decomposition Research Articles

New formulation for predicting total dissolved gas supersaturation in dam reservoir: application of hybrid artificial intelligence models based on multiple signal decomposition

Total dissolved gas (TDG) concentration plays an important role in the control of the aquatic life. Elevated TDG can cause gas-bubble trauma in fish (GBT). Therefore, controlling TDG fluctuation has become of great importance for different disciplines of surface water environmental engineering.. Nowadays, direct estimation of TDG is expensive and time-consuming. Hence, this work proposes a new modelling framework for predicting TDG based on the integration of machine learning (ML) models and multiresolution signal decomposition. The proposed ML models were trained and validated using hourly data obtained from four stations at the United States Geological Survey. The dataset are composed from: (i) water temperature (Tw), (ii) barometric pressure (BP), and (iii) discharge (Q), which were used as the input variables for TDG prediction. The modelling strategy is conducted based on two different steps. First, six singles ML model namely: (i) multilayer perceptron neural network, (ii) Gaussian process regression, (iii) random forest regression, (iv) random vector functional link, (v) adaptive boosting, and (vi) Bootstrap aggregating (Bagging), were developed for predicting TDG using Tw, BP, and Q, and their performances were compared. Second, a new framework was introduced based on the combination of empirical mode decomposition (EMD), the variational mode decomposition (VMD), and the empirical wavelet transform (EWT) preprocessing signal decomposition algorithms with ML models for building new hybrid ML models. Hence, the Tw, BP, and Q signals were decomposed to extract the intrinsic mode functions (IMFs) by using the EMD and VMD methods and the multiresolution analysis (MRA) components by using the EWT method. Then after, the IMFs and MRA components were selected and regraded as new input variables for the ML models and used as an integral part thereof. The single and hybrid prediction models were compared using several statistical metrics namely, root mean square error, mean absolute error, coefficient of determination (R2), and Nash–Sutcliffe efficiency (NSE). The single and hybrid models were trained several times with high number of repetitions, depending on the kind of modeling process. The obtained results using single models gave good agreement between the predicted TDG and the situ measured dataset. Overall, the Bagging model performed better than the other five models with R2 and NSE values of 0.906 and 0.902, respectively. However, the extracted IMFs and MRA components using the EMD, VMD and the EWT have contributed to an improvement of the hybrid models’ performances, for which the R2 and NSE were significantly increased reaching the values of 0.996 and 0.995. Experimental results showed the superiority of hybrid models and more importantly the importance of signal decomposition in improving the predictive accuracy of TDG.Graphical abstract

EMD-BiLSTM Stock Price Trend Forecasting Model based on Investor Sentiment

The movement of stock prices is the focus of investors' attention in the stock market, so stock price trend prediction has always been a hot topic in quantitative investment research. Traditional machine learning forecasting models are difficult to process nonlinear, high-frequency, high-noise stock price time series, which makes the prediction accuracy of stock price trends low. In order to improve the prediction accuracy, according to the temporal characteristics of stock price data, it is proposed to use a combination of empirical mode decomposition (EMD), investor sentiment and two-way long short-term memory neural network to predict the rise and fall of stock prices. Firstly, the empirical mode decomposition algorithm is used to extract the characteristics of the stock price time series on different time scales, and the investor sentiment indicators of the text from the close of the previous stock trading day to the opening of the next trading day are extracted by constructing a financial sentiment dictionary, and finally the EMD-BiLSTM model is used to predict the rise and fall of the next index trading day. Experiments on the dataset of stock price series show that the optimized BiLSTM model has strong predictive ability for the trend of consumer sector indexes.

A novel intelligent approach for predicting meteorological drought based on satellite-based precipitation product: Application of an EMD-DFA-DBN hybrid model

This study uses the long-term Climate Hazards Group InfraRed Precipitation with Station (CHIRPS) dataset with 0.05° spatial resolution to calculate the Standardized Precipitation Index (SPI) signal. The combination of Empirical Mode Decomposition (EMD), Detrended Fluctuation Analysis (DFA) and Deep Belief Network (DBN) as a hybrid model is applied to predict the SPI in the short and long term, i.e. lead times of one, six and twelve months. The performance of the hybrid EMD-DFA-DBN prediction model is evaluated against the hybrid EMD-DFA-MLP model and the stand-alone MLP (Multi-Layer Perceptron) and DBN models. The SPI signal, reconstructed using the EMD-DFA pre-processing method, where the EMD method decomposes the SPI signal into Intrinsic Mode Functions (IMFs) and the DFA method separates high-frequency noisy IMFs from low-frequency useful ones (SNR ≈ 6.49, PSNR ≈ 15.85, CC ≈ 0.88), has lower noise than the original signal; this allows for more accurate predictions of the SPI signal: the DBN-based prediction, with the algorithm trained using the reconstructed SPI signal (CC ≈ 0.94–0.98, RMSE ≈ 0.23–0.38) is superior to that obtained with the algorithm trained using the original SPI signal (CC ≈ 0.87–0.90, RMSE ≈ 0.47–0.51), as well as the MLP-based prediction with training on the reconstructed SPI signal (CC ≈ 0.92–0.95, RMSE ≈ 0.24–0.42) or the original SPI signal (CC ≈ 0.87–0.88, RMSE ≈ 0.48–0.51). It is found that selecting an appropriate stopping criterion for the sifting process is crucial to correctly decompose and reconstruct SPI with the EMD-DFA method. Using the EMD-DFA-DBN hybrid model reduces the noise but preserves useful information in the SPI signal and allows for accurate prediction of drought through deep learning.

Investigating price fluctuations in copper futures: Based on EEMD and Markov-switching VAR model

Predictable global copper prices are crucial to the transition to a green economy. This paper examines the nonlinear characteristics between the international copper futures prices and their drivers, using combined Empirical Mode Decomposition (EEMD) and the Markov-switching VAR (MSVAR) models. We decompose the monthly international copper futures prices from January 2015 to October 2021 into its low-frequency and high-frequency components by using the EEMD method. In the next step, we employ the MSVAR to examine the nonlinear fluctuation of the international copper futures prices under different regimes. The results indicate that fluctuations of the international copper futures prices exhibit a dynamic regime switching patterns that is characterized as “expansion”, “plateau” and “contraction”. The long-term stability of the international copper futures prices is determined by factors associated with demand, especially demand for strategic metals. Both the London Metal Exchange (LME) copper stocks and the LME copper stock futures have a significant impact on the international copper futures prices in each regime. In several regimes, the global refined copper consumption has no significant effect on the international copper futures prices. The increase in copper turnover is the primary driver of the international copper futures prices during the contraction regime. Regarding the supply factor, an increase in global refined copper capacity would result in a rise in the international copper futures prices during the expansion regime. While a slump would occur during a plateau or contraction regime. The financial factor, reflected by non-commercial traders affects the international copper futures prices volatility differently under different regimes. The increase in speculation reduces the market volatility during regimes of expansion and contraction. In contrast, in plateau regime, speculation increases market volatility and activates the market. The broad dollar index has little impact on the international copper futures prices during each regime. The above conclusions indicate that we should focus on the fluctuations in the international copper futures prices that are caused by the demand for strategic metals and financial factors.

Combined empirical mode decomposition and phase space reconstruction based psychologically stressed and non-stressed state classification from cardiac sound signals

The psychological stress and associated mental health conditions causes high socioeconomic impacts on society and the onset of pandemic worsened the situation making it imperative to timely detect psychological stress. This paper presents a novel framework for using a combination of empirical mode decomposition (EMD) and phase space reconstruction (PSR) analysis to capture non-linear, non-stationary dynamics of cardiac sound signals acquired from fifty-four healthy male adults for detecting psychological stress. The time interval among successive S1 peaks of acquired cardiac sound signals is extracted to obtain Interbeat Interval signal used for decomposition to Intrinsic Mode Functions (IMFs) using EMD technique. Thereafter, the feature vectors namely- largest singular value, smallest singular value from two-dimensional PSRs of IMFs and the mean value of Euclidean distance, standard deviation of Euclidean distance from three-dimensional PSRs are extracted to detect psychologically stressed state. The non-parametric Kruskal-Wallis statistical test is applied to select statistically significant features that are fed to Decision Tree, Naïve Bayes and Support Vector Machine classifiers for classifying stressed and non-stressed state with fivefold cross-validation to make it a reliable system. The average accuracy, sensitivity and specificity achieved is 97.14%, 99.8% and 94% respectively using SVM and Radial Basis Function kernel function. The proposed framework performed better on the dataset in comparison to ratio of low-frequency to high-frequency (LF/HF) power parameter of Electrocardiography signal. The use of easy to acquire, cost-effective cardiac sound signals for detecting psychological stress makes proposed framework feasible for rural healthcare centres of developing economies, homecare and telemedicine.

Vibracije bloka motora - indikator kucanja u SI motoru

The factors influencing the onset of knocking have a significant impact on how well a SI engine performs. Hence, the efficacy in determining the onset and controlling of knock is a key factor in improving the SI engine's performance. This paper provides insight into the role of engine block vibrations in determining the occurrence of knock using Empirical Mode Decomposition and Short-Time Fourier Transform. To comprehend the behaviour of vibration amid normal combustion and knocking conditions, the engine block vibration signals are analyzed and compared with the incylinder pressure fluctuations. The features of knock are extracted from the engine block vibration signals using Empirical Mode Decomposition. The first Intrinsic Mode Function (IMF) thus obtained is used to generate the Hilbert spectrum for detecting the occurrence of knock. Similarly, ShortTime Fourier Transform is also performed on the first IMF to obtain the spectrogram. The findings demonstrate unequivocally that higher frequency variations are produced when knock occurs. These results also indicate that the combination of Empirical Mode Decomposition and Short-Time Fourier Transform can be used effectively for determining the occurrence of knock.

Remove Artifacts from a Single-Channel EEG Based on VMD and SOBI.

With the development of portable EEG acquisition systems, the collected EEG has gradually changed from being multi-channel to few-channel or single-channel, thus the removal of single-channel EEG signal artifacts is extremely significant. For the artifact removal of single-channel EEG signals, the current mainstream method is generally a combination of the decomposition method and the blind source separation (BSS) method. Between them, a combination of empirical mode decomposition (EMD) and its derivative methods and ICA has been used in single-channel EEG artifact removal. However, EMD is prone to modal mixing and it has no relevant theoretical basis, thus it is not as good as variational modal decomposition (VMD) in terms of the decomposition effect. In the ICA algorithm, the implementation method based on high-order statistics is widely used, but it is not as effective as the implementation method based on second order statistics in processing EMG artifacts. Therefore, aiming at the main artifacts in single-channel EEG signals, including EOG and EMG artifacts, this paper proposed a method of artifact removal combining variational mode decomposition (VMD) and second order blind identification (SOBI). Semi-simulation experiments show that, compared with the existing EEMD-SOBI method, this method has a better removal effect on EOG and EMG artifacts, and can preserve useful information to the greatest extent.

Data driven approach to forecast the next day aggregate production of scattered small rooftop solar photovoltaic systems without meteorological parameters

Photovoltaic (PV) power has became an attractive research subject, despite the variability and uncertainty of the phenomenon, PV power forecasting is considered as a promising solution for successful PV power integration, and also an important decision making information for both, grid operators and energy traders. Forecasting the aggregated PV power in different spatiotemporal scales is very relevant for grid operators, but unfortunately, in the state of the art, few works deal with this subject. In the aim to forecast directly the next day aggregate photovoltaic power of scattered small rooftop installations based only on historical production data, we propose in this paper a hybrid nonlinear autoregressive regression model, composed from a combination of empirical mode decomposition (EMD), stepwise regression (SWR) and least square support vector regression (LsSVR) techniques. To address the lack of meteorological parameters, we propose a different data preprocessing strategy, this strategy will also allow capturing the diurnal component of the PV power time series in an efficient way. An in depth analysis of the proposed approach using publicly available database was conducted. We compared the results of the proposed approach with three other models, two nonlinear autoregressive models based on LsSVR (AR-LsSVR) and FFNN (AR-FFNN), and the third one is a persistent forecaster. Three accuracy metrics were adopted to compare the different models, the nMAE, nMBE and nMRSE. In general good results were obtained in clear and partially cloudy days, but there are few days characterized by sudden change in the time series pattern that the model cant handle. But still competitive results are obtained, the hybrid model gives an nMAE = 4.12% compared to 4.94%, 4.95% and 164.98% for AR-LsSVR, AR-FFNN and the persistent forecaster respectively. The projection of the obtained results on five recently developed models shows the effectiveness of the proposed approach.

Identification of Visual Imagery by Electroencephalography Based on Empirical Mode Decomposition and an Autoregressive Model.

The traditional imagery task for brain–computer interfaces (BCIs) consists of motor imagery (MI) in which subjects are instructed to imagine moving certain parts of their body. This kind of imagery task is difficult for subjects. In this study, we used a less studied yet more easily performed type of mental imagery—visual imagery (VI)—in which subjects are instructed to visualize a picture in their brain to implement a BCI. In this study, 18 subjects were recruited and instructed to observe one of two visual-cued pictures (one was static, while the other was moving) and then imagine the cued picture in each trial. Simultaneously, electroencephalography (EEG) signals were collected. Hilbert–Huang Transform (HHT), autoregressive (AR) models, and a combination of empirical mode decomposition (EMD) and AR were used to extract features, respectively. A support vector machine (SVM) was used to classify the two kinds of VI tasks. The average, highest, and lowest classification accuracies of HHT were 68.14 ± 3.06%, 78.33%, and 53.3%, respectively. The values of the AR model were 56.29 ± 2.73%, 71.67%, and 30%, respectively. The values obtained by the combination of the EMD and the AR model were 78.40 ± 2.07%, 87%, and 48.33%, respectively. The results indicate that multiple VI tasks were separable based on EEG and that the combination of EMD and an AR model used in VI feature extraction was better than an HHT or AR model alone. Our work may provide ideas for the construction of a new online VI-BCI.

Epileptic seizure detection in EEG using mutual information-based best individual feature selection

Epilepsy is a group of neurological disorders that affect normal brain activities and human behavior. Electroencephalogram based automatic epileptic seizure detection has significant applications in epilepsy treatment and medical diagnosis. In this study, a novel epileptic seizure detection method is proposed with a combination of empirical mode decomposition, mutual information-based best individual feature (MIBIF) selection algorithm and multi-layer perceptron neural network. Initially, fixed length EEG epochs are decomposed into amplitude and frequency-modulated components called intrinsic mode functions (IMFs). Three features named ellipse area of second-order difference plot, variance and fluctuation index are calculated from first few IMFs. The most significant features are then selected from the calculated features using the MIBIF algorithm to produce a final feature set. Later, the generated feature set is fed into the multi-layer perceptron neural network (MLPNN) classifier. Two well-known benchmark epileptic EEG datasets are used in this study for experimental evaluations. The result of proposed approach shows a significant performance improvement compared to the recent state-of-the-art methods.

Ensembled mechanical fault recognition system based on deep learning algorithm

Primary detection and removal of mechanical fault is vital for the recovery of mechanical and electrical equipment. The conventional mechanical fault recognition modules are not able obtain highly sensitive feature attributes for mechanical fault classification in the absence of prior knowledge. The fault diagnosis via data-driven methods have become a point of expansion with recent development in smart manufacturing and fault recognition techniques using the concept of deep learning. In this work, a combination of feature selection with Artificial Intelligence (AI) algorithm is presented for the mechanical fault recognition to deal with smart machine tools. This article proposes a CNN based fault recognition and classification framework that uses the combination of feature extraction, feature vector decomposition using Empirical Mode Decomposition (EMD) and deep neural network (DNN) for recognising the different fault states of the rotating machinery. The experimental outcomes obtained by the combination of EMD, feature selection module and Convolutional Neural Network (CNN) provides the detailed fault information by selecting the sensitive features from large number of faulty feature attributes. The proposed fault recognition and classification method performs better in terms of all the parameters yielding 99.01 % accuracy with respective cross-entropy loss of 0.325 and time complexity of 18 mins and 31 seconds. The comparative analysis is also done with other mainstream models and other state of the art methods, which reveals that the maximum improvement of 12.29 % is attained in terms of accuracy for the proposed fault recognition method. The presented method is robust in terms of reduction of network size, improvement of mechanical fault recognition, providing classification accuracy along with high fault diagnostic solution.

An ultrasonic signal processing method to improve defect depth estimation in composites based on empirical mode decomposition

In this paper, an ultrasonic signal processing method is proposed to improve depth evaluation of phased array ultrasonic non-destructive testing in composite structures. The proposed algorithm is based on an improved adaptive time–frequency analysis algorithm, and is a combination of empirical mode decomposition, correlation coefficient analysis, a fuzzy entropy algorithm and Hilbert transform. The ultrasonic signal is decomposed into intrinsic mode functions (IMFs) using an improved complete ensemble empirical mode decomposition with adaptive noises. Subsequently, the correlation coefficient and fuzzy entropy are used to select the optimal IMFs to reconstruct the signal. Then, Hilbert transform is executed to obtain the envelope of the reconstructed signal. Finally, the arrival time of the ultrasonic echo is estimated through the signal envelope, and then used to calculate the defect depth. The simulation and experimental results demonstrated that the proposed method has high evaluation accuracy in processing intense noisy signals or overlapped echoes. For simulated signals with different signal-to-noise ratios, the maximum estimation error of arrival time is 0.06 µs. Compared with the traditional gating method, the defect depth evaluation result is significantly improved. In particular, for near-surface defects, the maximum depth detection error is reduced from 0.13 mm to 0.06 mm.

Improved Hilbert–Huang transform with soft sifting stopping criterion and its application to fault diagnosis of wheelset bearings

Vibration signals from rotating machineries are usually of multi-component and modulated signals. Hilbert–Huang transform (HHT), hereby referring to the combination of empirical mode decomposition (EMD) and normalized Hilbert transform (NHT), is an effective method to extract useful information from the multi-component and modulated signals. However, sifting stopping criterion (SSC) that is crucial to the HHT performance has not been well explored for this sift-driven method in the past decades. This paper proposes the soft SSC, which can ease the mode-mixing problem in signal decomposition through the EMD and improve demodulation performance in signal demodulation. The soft SSC can adapt to input signals and determine the optimal iteration number of a sifting process by tracking this sifting process. Extensive simulations show that the soft SSC can enhance the performance of the HHT in signal decomposition, signal demodulation, and the estimation of the instantaneous amplitude and frequency over the existing state-of-the-art SSCs. Finally, the improved HHT with the soft SSC is demonstrated on the fault diagnosis of wheelset bearings.

Research on Feature Extracted Method for Flutter Test Based on EMD and CNN

Due to the inevitable deviations between the results of theoretical calculations and physical experiments, flutter tests and flutter signal analysis often play significant roles in designing the aeroelasticity of a new aircraft. The measured structural response from aeroelastic models in both wind tunnel tests and real fight flutter tests contain an abundance of structural information, but traditional methods tend to have limited ability to extract features of concern. Inspired by deep learning concepts, a novel feature extraction method for flutter signal analysis was established in this study by combining the convolutional neural network (CNN) with empirical mode decomposition (EMD). It is widely hypothesized that when flutter occurs, the measured structural signals are harmonic or divergent in the time domain, and that the flutter modal (1) is singular and (2) its energy increases significantly in the frequency domain. A measured-signal feature extraction and flutter criterion framework was constructed accordingly. The measured signals from a wind tunnel test were manually labeled “flutter” and “no-flutter” as the foundational dataset for the deep learning algorithm. After the normalized preprocessing, the intrinsic mode functions (IMFs) of the flutter test signals are obtained by the EMD method. The IMFs are then reshaped to make them the suitable size to be input to the CNN. The CNN parameters are optimized though the training dataset, and the trained model is validated through the test dataset (i.e., cross-validation). The accuracy rate of the proposed method reached 100% on the test dataset. The training model appears to effectively distinguish whether or not the structural response signal contains flutter. The combination of EMD and CNN provides effective feature extraction of time series signals in flutter test data. This research explores the connection between structural response signals and flutter from the perspective of artificial intelligence. The method allows for real-time, online prediction with low computational complexity.

Cardiac Severity Classification Using Pre Trained Neural Networks.

Electrocardiogram (ECG) is the most effective instrument for making decisions about various forms of heart disease. As a result, several researchers have focused on the ECG signal to extract the features of heartbeats with high precision and efficiency. This article offers a hybrid approach to classifying different cardiac conditions using the Feed Forward Back Propagation Neural Network (FFBPNN), by providing a pre-processed ECG signal as an excitation. The modified ECG signal is obtained through the combination of EMD (Empirical Mode Decomposition) and DWT (Discrete Wavelet Transform). In this proposed method, the input signal is first decomposed into the Intrinsic Mode Functions (IMF's) and the first three IMF's are combined to obtain a modified partially denoted ECG sample and then DWT is used to obtain an improved denoised signal. This pre-processed signal is classified using the Neural Network architecture. For the EMD approach, the ECG-based EMD-DWT signal provides improved classification accuracy of 67, 0762 percent, 90, 4305 percent for the DWT approach, and 95,0797 percent for the proposed technique. The methodology is applied to the MIT-BIH database and, in terms of classification accuracy, is found to be higher than the different methodologies.

A novel carbon price prediction model combines the secondary decomposition algorithm and the long short-term memory network

Carbon trading is regarded as an important measure to reduce carbon emissions. To provide more accurate carbon prediction results for policymakers and market participants, a hybrid carbon price prediction model combines empirical mode decomposition, variational mode decomposition, and long short-term memory network is proposed. The empirical analysis was conducted based on the actual data of all eight carbon market pilots in China. According to the results of empirical analysis, several main conclusions can be summarized. First, the prediction accuracy and robustness of the proposed model are optimal in comparison experiments. In the Beijing carbon market, the MAPE, RMSE, and R2 of the proposed model improved by 63.98%, 66.07%, and 12.24%, respectively, compared with the worst model. Second, the secondary decomposition can effectively improve the prediction accuracy. In the Beijing dataset, the combination of empirical mode decomposition and variational mode decomposition improved the MAPE, RMSE, and R2 values of the model by an average of 35.52%, 46.57%, and 8.94%. Third, the carbon market in Hubei province is relatively mature, while the carbon market in Tianjin is relatively low in maturity. The study can make a theoretical and practical contribution to the literature within this realm.

Remaining useful life prediction for the air turbine starter based on empirical mode decomposition and relevance vector machine

An air turbine starter (ATS) is used to start the aero-engine before an aircraft takes off, which plays a significant role in the reliable operation of the aero-engine and is critical to the flight security, so it is vital to monitor the health and predict the remaining useful life (RUL) for the ATS. This paper proposes a fusion framework based on the combination of empirical mode decomposition (EMD) and relevance vector machine (RVM). EMD is used to smooth out the non-stationary data by pattern decomposition, and the multiple intrinsic mode functions (IMF) which can effectively reflect the fault characteristics, are carefully selected from all IMFs by kurtosis index technique. RVM is used to train the selected smooth IMFs samples and establish a regression model for remaining useful life prediction. In addition, the subtraction clustering technique is introduced to reduce the samples scale and speed up the RVM’s training efficiency. The effectiveness of the proposed fusion framework is illustrated via an experiment of ATS, and the results show that the proposed method has satisfactory prediction performance.

Extraction Method of Fetal Phonocardiogram Based on Lifting wavelet analysis

Long-term monitoring of fetal health status is important for high-risk pregnancies. In order to extract the pure fetal phonocardiogram(fPCG) and increase the calculating accuracy of fetal heart rate (FHR), a combination of Empirical Mode Decomposition (EMD), Cepstrum, Lifting Wavelet (LWT) and Hilbert transform (HT) method was proposed. First, the heart sound signal was decomposed into finite intrinsic mode functions (IMF) by EMD, and then the signal de-noising was implemented by LWT. Second, the envelope of the signal was obtained by HHT. Finally, the fetal heart rate was obtained by cepstrum analysis. The simulation result shows that the fetal heart rate extracted by this integrated signal processing method is right, and it enhances the precision of fetal heart rate greatly. The wavelet de-noising technology can reduce the noise very well with small computation. It is concluded that this integrated signal method is capable of extracting feature from fPCG.

Microseismic Signal Denoising via Empirical Mode Decomposition, Compressed Sensing, and Soft-thresholding

Microseismic signal denoising is of great significance for P wave, S wave first arrival picking, source localization, and focal mechanism inversion. Therefore, an Empirical Mode Decomposition (EMD), Compressed Sensing (CS), and Soft-thresholding (ST) combined EMD_CS_ST denoising method is proposed. First, through EMD decomposition of the noise signal, a series of Intrinsic Mode Functions (IMF) from high frequency to low frequency are obtained. By calculating the correlation coefficient between each IMF and the original signal, the boundary component between the signal and the noise was identified, and the boundary component and its previous components were sparsely processed in the discrete wavelet transform domain to obtain the original sparse coefficient θ. Second, θ is filtered by ST to get the reconstruction coefficient θnew after denoising. Then, CS was used to recover and reconstruct θnew to get the denoised IMFnew component and then recombined with the remaining IMF components to get the signal after denoising. In the simulation experiment, the denoising process of EMD_CS_ST method is introduced in detail, and the denoising ability of EMD_CS_ST, DWT, EEMD, and VMD_DWT under 10 different noise levels is discussed. The signal-to-noise ratio, signal standard deviation, correlation coefficient, waveform diagram, and spectrogram before and after denoising are compared and analyzed. Moreover, the signals obtained from the underground cavern of the Shuangjiangkou hydropower station were denoised by the EMD_CS_ST method, and the signals before and after denoising were analyzed by time-frequency spectrum. These results show that the proposed method has better denoising ability.

Electrostatic Sensor for Determining the Characteristics of Particles Moving From Deposition to Suspension in Pneumatic Conveying

The minimum conveying velocity or the lowest point of pressure drop curve can reflect the characteristics of particles moving from deposition to suspension in pneumatic conveying. However, when the mass flow rate is low, the change of particles flow cannot be effectively reflected by the above methods. In this paper, based on a 4-arc electrode electrostatic sensor, with localised sensitivity, the detailed scale signals that represent the particle random motion are extracted by the combination of Empirical Mode Decomposition (EMD) and Hurst exponent. The differences in the particle random motion energy ratio (PRMER) of 4-channel electrode signals are used to characterize the transition of flow state. In the verification experiment by using a belt-style electrostatic velocity measured rig, the higher the velocity of rubber belt or the closer to the electrode, the higher the PRMERs of electrostatic signal. In the experiment of gas-solid two-phase flow rig, the PRMERs of 4-channel electrode signals are all increasing with the increase of superficial gas velocity, and the PRMERs of different electrodes are rather different at low superficial gas velocity ( ${V}_{g}$ ). When ${V}_{g}$ drops at the minimum pressure drop point ( ${P}_{{MPD}}$ ), the PRMERs of top/bottom and left/right electrodes begin to separate (e.g. the particle mass flow rates are 100 kg/h and 120 kg/h). Furthermore, when the solid mass flow rate is 80 kg/h, the proposed method can clearly characterize the transition of flow states in the pipeline, but the pressure drop phase diagram cannot.