Low-frequency Intrinsic Mode Functions Research Articles

Multi-step forecasting of dissolved oxygen in River Ganga based on CEEMDAN-AdaBoost-BiLSTM-LSTM model

Accurate prediction of Dissolved Oxygen (DO) is an integral part of water resource management. This study proposes a novel approach combining Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) with AdaBoost and deep learning for multi-step forecasting of DO. CEEMDAN generates Intrinsic Mode Functions (IMFs) with different frequencies, capturing non-linear and non-stationary characteristics of the data. The high-frequency and medium-frequency IMFs, characterized by complex patterns and frequent changes over time, are predicted using Adaboost with Bidirectional Long Short-Term Memory (BiLSTM) as the base estimator. The low-frequency IMFs, characterized by relatively simple patterns, are predicted using standalone Long Short-Term Memory (LSTM). The proposed CEEMDAN-AdaBoost-BiLSTM-LSTM model is tested on data from ten stations of river Ganga. We compare the results with six models without decomposition and four models utilizing decomposition. Experimental results show that using a tailored prediction technique based on each IMF’s distinctive features leads to more accurate forecasts. CEEMDAN-AdaBoost-BiLSTM-LSTM outperforms CEEMDAN-BiLSTM with an average improvement of 25.458% for RMSE and 37.390% for MAE. Compared with CEEMDAN-AdaBoost-BiLSTM, an average improvement of 20.779% for RMSE and 28.921% for MAE is observed. Diebold-Mariano test and t-test suggest a statistically significant difference in performance between the proposed and compared models.

EMD-based noise reduction study of steel cored conveyor belt containing slag signal

This paper proposes a noise reduction technique that combines empirical mode decomposition (EMD) and wavelet thresholding to eliminate the noise interference caused by metal slag in the steel cord conveyor belt damage signal. Initially, the original signal undergoes decomposition by EMD into high- and low-frequency intrinsic mode function (IMF) components based on metal slag signal feature analysis. The wavelet threshold de-noising method is then applied to filter out the high-frequency noise while preserving the low-frequency IMF components. The IMF components containing slag noise are discarded, and the filtered signal and the low-frequency IMF components are used for signal reconstruction to obtain an optimal noise reduction effect. The study demonstrates that this method is more effective in suppressing metal slag noise, environmental noise, and other noise interferences than traditional EMD decomposition noise reduction and wavelet threshold noise reduction methods. This research provides a valuable reference for noise reduction in steel cord conveyor belt detection data.

Application of EMD combined with wavelet algorithm for filtering slag noise in steel cord conveyor belt

This study proposes a noise reduction technique that combines empirical mode decomposition (EMD) with wavelet thresholding to remove noise interference generated by metal slag in the damage signal of steel cord conveyor belts. The initial step involves decomposing the original signal into high-frequency and low-frequency intrinsic mode function (IMF) components using empirical mode decomposition (EMD), guided by the metal slag signal characteristics analysis. The high-frequency noise is filtered away while the low-frequency IMF components are kept intact through the wavelet threshold de-noising technique. The slag noise-containing IMF components are deleted, and the filtered signal and the low-frequency IMF components are utilized for signal reconstruction to provide the optimum noise reduction result. The study demonstrates that this method is more effective in suppressing metal slag noise, environmental noise, and other noise interferences than traditional EMD decomposition noise reduction and wavelet threshold noise reduction methods. This research provides a valuable reference for noise reduction in steel cord conveyor belt detection data.

Accurate Prediction of Workloads and Resources With Multi-Head Attention and Hybrid LSTM for Cloud Data Centers

Currently, cloud computing service providers face big challenges in predicting large-scale workload and resource usage time series. Due to the difficulty in capturing nonlinear features, traditional forecasting methods usually fail to achieve high prediction performance for resource usage and workload sequences. Besides, there is much noise in original time series of resources and workloads. If these time series are not de-noised by smoothing algorithms, the prediction results can fail to meet the providers' requirements. To do so, this work proposes a hybrid prediction model named VAMBiG that integrates <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</u> ariational mode decomposition, an <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</u> daptive Savitzky-Golay (SG) filter, a <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</u> ulti-head attention mechanism, <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Bi</u> directional and <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</u> rid versions of Long and Short Term Memory (LSTM) networks. VAMBiG adopts a signal decomposition method named variational mode decomposition to decompose complex and non-linear original time series into low-frequency intrinsic mode functions. Then, it adopts an adaptive SG filter as a data pre-processing tool to eliminate noise and extreme points in such functions. Afterwards, it adopts bidirectional and grid LSTM networks to capture bidirectional features and dimension ones, respectively. Finally, it adopts a multi-head attention mechanism to explore importance of different data dimensions. VAMBiG aims to predict resource usage and workloads in highly variable traces in clouds. Extensive experimental results demonstrate that it achieves higher-accuracy prediction than several advanced prediction approaches with datasets from Google and Alibaba cluster traces.

Experimental mode decomposition investigation on 3-stage axial flow compressor stall phenomena using aeroacoustics measurements

Safely operating compressors is quite critical. Rotating stall is highly undesirable and affects negatively the performance and stability of aero-engine compressors. It is important to identify a precursor of such rotating stalling phenomena observed on the compressor. In this work, we conduct experimental measurements on a 3-stage axial flow compressor by using 8 acoustic pressure sensors. Emphasis is being placed on applying different mode decomposition methods such as Proper Orthogonal Decomposition (POD) and Empirical Mode Decomposition (EMD) on these acoustics data to shed lights on the stall phenomena. Comparison is then made between these methods and conventional means like continuous wavelet (CWA), and PSD (Power Spectrum Density) analyses to achieve a timely detection of stall inception and the energy distribution before and after stall occurred. It is found from POD that the dominant acoustic modes contributing to more than 90% of the total fluctuation energy are changed from 3 to 4, when the stall occurred. The EMD investigation shows that the compressor stall is associated with a few low-frequency IMFs (intrinsic mode function). Time evolutions of such IMFs are observed to grow from negligible amplitude disturbances into limit cycles. Additionally, applying CWA reveals that the stall cell is originated from the first stage and then propagates circumferentially and axially to the second and third stage. Finally, PSD analysis shows that the stall frequency related to the spike-type stall cell exists only on the first stage. This is different from the blade passing frequency as observed on all stages of the compressor. In summary, the present work offers alternative acoustic measurements to examine the dynamic instability of a compressor stall with advanced signal-processing techniques applied.

Faulty Feeder Detection Under High Impedance Faults for Resonant Grounding Distribution Systems

The problem of high impedance fault (HIF) detection in resonant grounding distribution systems has not been well solved. In practical applications, the existing detection methods either have complex calculation processes and low accuracy or have a weak ability to adapt to complex fault conditions, which limits the adaptability of the existing methods. Based on a theoretical analysis, a novel faulty feeder detection method based on the inner product transformation of extreme values is proposed in this paper. First, to eliminate the interference of high-frequency components, the low-frequency characteristic modes of zero-sequence current of each feeder are extracted by the variational mode decomposition (VMD) algorithm. On this basis, the low-frequency intrinsic mode functions (IMFs) are processed by the first-order difference to obtain the current waveform after the difference. Second, the zero crossing point of the differential current waveform is obtained, and then the extreme value point of the original zero-sequence current is calibrated, including the maximum and minimum. Third, at the extreme value point, the comprehensive inner product values (CIPV) of each feeder are calculated. Then, when the values are positive, it is judged as a bus fault, when the value has at least one negative value, it is judged as a feeder fault, and the feeder with the minimum value is judged as a faulty feeder. A large number of simulations and field tests show that this method has better fault detection accuracy in practical applications and is suitable for strong noise interference and asynchronous sampling.

Nonlinear frequency analysis of COVID-19 spread in Tokyo using empirical mode decomposition

Empirical mode decomposition (EMD) was adopted to decompose daily COVID-19 infections in Tokyo from February 28, 2020, to July 12, 2021. Daily COVID-19 infections were nonlinearly decomposed into several monochromatic waves, intrinsic mode functions (IMFs), corresponding to their periodic meanings from high frequency to low frequency. High-frequency IMFs represent variabilities of random factors and variations in the number of daily PCR and antigen inspections, which can be nonlinearly denoised using EMD. Compared with a moving average and Fourier transform, EMD provides better performance in denoising and analyzing COVID-19 spread. After variabilities of daily inspections were weekly denoised by EMD, one low-frequency IMF reveals that the average period of external influences (public health and social measures) to stop COVID-19 spread was 19 days, corresponding to the measures response duration based on the incubation period. By monitoring this nonlinear wave, public health and social measures for stopping COVID-19 spread can be evaluated and visualized quantitatively in the instantaneous frequency domain. Moreover, another low-frequency IMF revealed that the period of the COVID-19 outbreak and retreat was 57 days on average. This nonlinear wave can be used as a reference for setting the timeframe for state of emergency declarations. Thus, decomposing daily infections in the instantaneous frequency domain using EMD represents a useful tool to improve public health and social measures for stopping COVID-19 spread.

Motion Artifacts Suppression From EEG Signals Using an Adaptive Signal Denoising Method

Motion artifacts are one of the most challenging non-physiological noise sources present in the biomedical signal, which can hinder the true performance of EEG-based neuro-engineering applications. Therefore, motion artifact removal from EEG signals can be potentially the utmost protuberant research topic. To solve this issue, a hybrid signal denoising framework which comprises modified empirical mode decomposition (EMD) and an optimized Laplacian of Gaussian (LoG) filter is proposed for the suppression of motion artifacts from EEG signals. The modified-EMD decomposes the single-channel noisy EEG signal into a set of the optimal number of intrinsic mode functions (IMFs). Furthermore, the optimized LoG filter has been applied to the motion artifact intermixed EEG signal which is considered as low-frequency noise likely to present at low-frequency IMFs. This filter performs smoothing of the signal and removes background noises or artifacts from the EEG signal. The denoised signal is reconstructed by adding filtered output signal and high-frequency IMFs. The robustness of the proposed method is demonstrated through simulated and real EEG data with artifacts. The experimental values of the different sets of performance assessment metrics reveal that the proposed algorithm outperforms the existing state-of-the-art EEG signal denoising algorithms for the suppression of motion artifacts from EEG signals.

Time‐dependent intrinsic correlation analysis of crude oil and the US dollar based on CEEMDAN

AbstractIn this article, we analyze the dynamic linkage between crude oil price and the US dollar at multi‐scale frequencies using time‐dependent intrinsic correlation analysis based on the complete ensemble empirical mode decomposition with adaptive noise. After applying a refined method to extract the trend, we reveal that the overall correlation and the long‐term trend correlation exhibit very similar patterns. The correlation coefficients between crude oil and the US dollar are negative at most of the time; however, the coefficients become positive in certain periods, such as 2013–2014 and 2017–2018. Furthermore, the negative correlations in high frequency intrinsic mode functions (IMFs), with a shorter time horizon, are weaker and display time‐varying characteristics, whereas the correlation in low frequency IMFs, with a longer time horizon, are stronger and more static. The findings of this article may have important implications for investors to construct optimal portfolio diversification.

Research on UAV image denoising effect based on improved Wavelet Threshold of BEMD

Aiming at the noise generated by external or internal factors reduces the sharpness of unmanned aerial vehicle (UAV) images, an improved bi-dimensional empirical mode decomposition (BEMD) de-noising algorithm is proposed to solve the problem. Firstly, an intrinsic mode function (IMF) is obtained after BEMD decomposition of noisy image, and then the high frequency apply particle swarm optimization (PSO) after wavelet decomposition to the high-frequency IMF to obtain the optimal threshold filtering. As for the low frequency, it is filtered by the exponential attenuation threshold algorithm of wavelet semi-soft threshold. Finally, the filtered both high-frequency and low-frequency IMF are reconstructed after inverse wavelet transformation. This algorithm is applied to the processing of UAV images, and compared with the traditional UAV image denoising method and the advanced UAV image denoising method. Simulation results demonstrate that the proposed denoising method outperforms other de-noising methods in terms of peak signal-to-noise ratio and mean square error.

Two-Level W-ESMD Denoising for Dynamic Deflection Measurement of Railway Bridges by Microwave Interferometry

Aiming to reduce the influences of noise for dynamic deflection measurements of railway bridges by microwave interferometry, this paper proposes a two-level wavelet-based extreme-point symmetric mode decomposition (ESMD) denoising algorithm on the basis of the characteristics of different noise frequency scales. First, the ESMD method is adopted to decompose the obtained dynamic deflection signal into a series of intrinsic mode functions (IMFs) from high to low frequency. Second, the first-level denoising is performed to eliminate the influences of high frequency noise by integrating the heursure threshold rule, soft thresholding, and different decomposition scales for high or low frequency IMFs, respectively. Third, the reconstructed first-level denoised signal is further decomposed into a series of IMFs, from high to low frequency, by the ESMD method. Last, the second-level denoising is performed to eliminate the influences of low frequency noise and some residual high frequency noise. For the low frequency noise, by using the heursure threshold rule, soft thresholding and a lower decomposition scale, and for some residual high frequency noise by using minimax threshold rule, hard thresholding and a moderate decomposition scale, the results on both simulated and real dynamic deflection signals show that the proposed two-level denoising algorithm is superior to wavelet threshold denoising and conventional empirical mode decomposition-based denoising techniques.

Noise Reduction Method of Underwater Acoustic Signals Based on Uniform Phase Empirical Mode Decomposition, Amplitude-Aware Permutation Entropy, and Pearson Correlation Coefficient.

Noise reduction of underwater acoustic signals is of great significance in the fields of military and ocean exploration. Based on the adaptive decomposition characteristic of uniform phase empirical mode decomposition (UPEMD), a noise reduction method for underwater acoustic signals is proposed, which combines amplitude-aware permutation entropy (AAPE) and Pearson correlation coefficient (PCC). UPEMD is a recently proposed improved empirical mode decomposition (EMD) algorithm that alleviates the mode splitting and residual noise effects of EMD. AAPE is a tool to quantify the information content of nonlinear time series. Unlike permutation entropy (PE), AAPE can reflect the amplitude information on time series. Firstly, the original signal is decomposed into a series of intrinsic mode functions (IMFs) by UPEMD. The AAPE of each IMF is calculated. The modes are separated into high-frequency IMFs and low-frequency IMFs, and all low-frequency IMFs are determined as useful IMFs (UIMFs). Then, the PCC between the high-frequency IMF with the smallest AAPE and the original signal is calculated. If PCC is greater than the threshold, the IMF is also determined as a UIMF. Finally, all UIMFs are reconstructed and the denoised signal is obtained. Chaotic signals with different signal-to-noise ratios (SNRs) are used for denoising experiments. Compared with EMD and extreme-point symmetric mode decomposition (ESMD), the proposed method has higher SNR and smaller root mean square error (RMSE). The proposed method is applied to noise reduction of real underwater acoustic signals. The results show that the method can further eliminate noise and the chaotic attractors are smoother and clearer.

Denoising of Lightning Electric Field Signals Based on EMD-Wavelet Method

In this paper, a new lightning electric field (LEF) signals denoising approach combined with empirical mode decomposition (EMD) and wavelet transform (WT) is proposed. Unlike the conventional EMD or WT denoising approaches, we use EMD to decompose the LEF signal firstly, the continuous mean square error(CMSE) criteria are used to determine a turning point in the original signal energy, then the Birge-Massart threshold wavelet denoising method is employed to denoise the high frequency component which contains lots of noise. Finally, the clean high frequency component and the remaining low frequency intrinsic mode function, and the residual of the EMD operation are employed to synthesize a cleaner LEF signal. The method is illustrated on real data, and the performance of the proposed method is evaluated in terms of several standard metrics. The results show that the proposed method is able to reduce noise from the noisy LEF signals more accurately and effectively in comparison to EMD filtering and Wavelet filtering methods.

Research of Penetration Overload Signals Processing Method Based on EEMD and WT

Hard Target Penetration is a very complex dynamic problem, and penetration signals contain axial de-acceleration signals, vibration signals and other weakly noise signals. It is difficult to obtain penetration feature signals through some methods filtering unwanted vibration signals and noise signals. As such, we propose a joint filtering method based on EEMD (Ensemble Empirical Mode Decomposition) and WT (Wavelet Transform) to solve this problem. This method consists of four main steps: (a) penetration signals decomposing via EEMD method, this gets the IMF (Intrinsic Mode Function) components, (b)then we calculate the Whole BURG power spectrum of the original signals and each component, after that compare the power spectrum of each component with the original signals, this draws the original signals EEMD decomposition scale, (c) the high-frequency components of IMF filtering based on the WT threshold, (d) signals reconstruct by using low-frequency IMF components which reflect signals characteristic and high-frequency IMF components through wavelet filtered. Experiment show that proposed method can effectively determine the penetration signals decomposition scale, eliminate vibration and noise signals of penetration process, avoid the losing of the high-frequency components when using a single wavelet filtering method. The result of the proposed method can get better SNR than WT, the velocity and depth are in good agreement with the results of experiment.

Trend extraction of rail corrugation measured dynamically based on the relevant low-frequency principal components reconstruction

Rail corrugation dynamic measurement techniques are critical to guarantee transport security and guide rail maintenance. During the inspection process, low-frequency trends caused by rail fluctuation are usually superimposed on rail corrugation and seriously affect the assessment of rail maintenance quality. In order to extract and remove the nonlinear and non-stationary trends from original mixed signals, a hybrid model based ensemble empirical mode decomposition (EEMD) and modified principal component analysis (MPCA) is proposed in this paper. Compared with the existing de-trending methods based on EMD, this method first considers low-frequency intrinsic mode functions (IMFs) thought to be underlying trend components that maybe contain some unrelated components, such as white noise and low-frequency signal itself, and proposes to use PCA to accurately extract the pure trends from the IMFs containing multiple components. On the other hand, due to the energy contribution ratio between trends and mixed signals is prior unknown, and the principal components (PCs) decomposed by PCA are arranged in order of energy reduction without considering frequency distribution, the proposed method modifies traditional PCA and just selects relevant low-frequency PCs to reconstruct the trends based on the zero-crossing numbers (ZCN) of each PC. Extensive tests are presented to illustrate the effectiveness of the proposed method. The results show the proposed EEMD-PCA-ZCN is an effective tool for trend extraction of rail corrugation measured dynamically.

Capacity Optimization and Operational Strategy of the Wind-Energy Storage Hybrid Systems for Energy Dispatching

Wind power output fluctuation brings a lot of negative influences on utility grid as a result of increasing penetration level of wind power. A supercapacitor-battery hybrid storage system is proposed to balance the wind power and planned export power of the wind farm. Firstly, using empirical mode decomposition(EMD), the difference between planned export power and the original wind power(unbalanced power, UP) is analyzed to obtain the intrinsic mode functions(IMFs). Secondly, a mathematic method is then developed to confirm a so-called gap frequency to decompose the unbalanced power into high and low frequency components based on the concept of minimum overlap energy. Unbalanced power smoothing is then achieved by dispatching the powers of supercapatiors and batteries to compensate the high- and low-frequency IMFs according to the characteristics of supercapacitor and batteries respectively. Finally, based on a set of data acquired from an existing wind farm, a hybrid storage system(HSS) is designed aiming at minimizing the capital cost and also can make wind power approach the planned export power of the wind farm in a great extent, numerical analysis verifies the efficiency of the developed method.

Edge detection, color quantization, segmentation, texture removal, and noise reduction of color image using quaternion iterative filtering

Empirical mode decomposition (EMD) is a simple, local, adaptive, and efficient method for nonlinear and nonstationary signal analysis. However, for dealing with multidimensional signals, EMD and its variants such as bidimensional EMD (BEMD) and multidimensional EMD (MEMD) are very slow due to the needs of a large amount of envelope interpolations. Recently, a method called iterative filtering has been proposed. This filtering-based method is not as precise as EMD but its processing speed is very fast and can achieve comparable results as EMD does in many image and signal processing applications. We combine quaternion algebra and iterative filtering to achieve the edge detection, color quantization, segmentation, texture removal, and noise reduction task of color images. We can obtain similar results by using quaternion combined with EMD; however, as mentioned before, EMD is slow and cumbersome. Therefore, we propose to use quaternion iterative filtering as an alternative method for quaternion EMD (QEMD). The edge of color images can be detected by using intrinsic mode functions (IMFs) and the color quantization results can be obtained from residual image. The noise reduction algorithm of our method can be used to deal with Gaussian, salt-and-pepper, speckle noise, etc. The peak signal-to-noise ratio results are satisfactory and the processing speed is also very fast. Since textures in a color image are high-frequency components, we also can use quaternion iterative filtering to decompose a color image into many high- and low-frequency IMFs and remove textures by eliminating high-frequency IMFs.

The Rolling Bearing Fault Diagnosis Research Based on Improved Hilbert-Huang Transformation

For empirical mode decomposition (EMD) of Hilbert-Huang transform (HHT) exists the problem of mode mixing. An analysis method based on ensemble empirical mode decomposition (EEMD) is proposed to apply to fault diagnosis of rolling bearing. This paper puts forward, after signal pretreatment, applying EEMD method to acquire the intrinsic mode function (IMF) of fault signal. Then according to correlation coefficient for IMFs and the signal before decomposing by EEMD method, some redundant low frequency IMFs produced in the process of decomposition can be eliminated, then the effective IMF components are selected to perform a local Hilbert marginal spectrum analysis, then fault characteristics are extracted. Through the vibration analysis of inner-race fault bearing it shows that this method can be effectively applied to extract fault characteristics of rolling bearing.

A new short-term load forecasting method of power system based on EEMD and SS-PSO

Aiming to the disadvantages of short-term load forecasting with empirical mode decomposition (EMD) such as mode mixing and many high-frequency random components, a new short-term load forecasting model based on ensemble empirical mode decomposition (EEMD) and sub-section particle swarm optimization (SS-PSO) is proposed in this paper. Firstly, the load sequence is decomposed into a limited number of intrinsic mode function (IMF) components and one remainder by EEMD, which can avoid the mode mixing problem of traditional EMD. Then, through calculating and observing the spectrum of decomposed series, some low-frequency IMFs are extracted and reconstructed. Other IMFs can be forecasted with appropriate forecasting models. Since IMF1 is main random component of the load sequence, the linear combination model is adopted to forecast IMF1. Because the weights of the linear combination model are very important to obtain high forecasting accuracy, SS-PSO is proposed and used to optimize the linear combination weights. In addition, the factors such as temperature and weekday are taken into consideration for short-term load forecasting. Simulation results show that accuracy of the load forecasting model proposed in the paper is higher than that of BP neural network, RBF neural network, support vector machine, EMD and their combinations.

Random Noise Reduction Based on Ensemble Empirical Mode Decomposition and Wavelet Threshold Filtering

This paper presents a random noise reduction method based on ensemble empirical mode decomposition (EEMD) and wavelet threshold filtering. Firstly, we have conducted spectrum analysis and analyzed the frequency band range of effective signals and noise. Secondly, we make use of EEMD method on seismic signals to obtain intrinsic mode functions (IMFs) of each trace. Then, wavelet threshold noise reduction method is used on the high frequency IMFs of each trace to obtain new high frequency IMFs. Finally, reconstruct the desired signal by adding the new high frequency IMFs on the low frequency IMFs and the trend item together. When applying our method on synthetic seismic record and field data we can get good results.