Intrinsic Mode Functions Research Articles

Short-to-Medium-Term Wind Power Forecasting through Enhanced Transformer and Improved EMD Integration

Accurate wind power forecasting (WPF) is critical in optimizing grid operations and efficiently managing wind energy resources. Challenges arise from the inherent volatility and non-stationarity of wind data, particularly in short-to-medium-term WPF, which extends to longer forecast horizons. To address these challenges, this study introduces a novel model that integrates Improved Empirical Mode Decomposition (IEMD) with an enhanced Transformer called TransIEMD. TransIEMD begins by decomposing the wind speed into Intrinsic Mode Functions (IMFs) using IEMD, transforming the scalar wind speed into a vector form that enriches the input data to reveal hidden temporal dynamics. Each IMF is then processed with channel attention, embedding, and positional encoding to prepare inputs for an enhanced Transformer. The Direct Embedding Module (DEM) provides an alternative viewpoint on the input data. The distinctive perspectives of IEMD and DEM offer interaction through cross-attention within the encoder, significantly enhancing the ability to capture dynamic wind patterns. By combining cross-attention and self-attention within the encoder–decoder structure, TransIEMD demonstrates enhanced proficiency in detecting and leveraging long-range dependencies and dynamic wind patterns, improving the forecasting precision. Extensive evaluations on a publicly available dataset from the National Renewable Energy Laboratory (NREL) demonstrate that TransIEMD significantly improves the forecasting accuracy across multiple horizons of 4, 8, 16, and 24 h. Specifically, at the 24 h forecast horizon, TransIEMD achieves reductions in the normalized mean absolute error and root mean square error of 4.24% and 4.37%, respectively, compared to the traditional Transformer. These results confirm the efficacy of integrating IEMD with attention mechanisms to enhance the accuracy of WPF.

A hybrid machine learning forecasting model for photovoltaic power

The increasing use of photovoltaic (PV) power generation presents a significant opportunity for global energy transformation. However, accurately forecasting PV power remains a challenge. This study proposes a hybrid approach that combines variational mode decomposition (VMD), whale optimization algorithm (WOA), and long short-term memory neural network (LSTM) to forecast photovoltaic (PV) power accurately. The model decomposes the time series of PV power using VMD to address the non-stationary nature of the time series. The VMD parameters are optimized using WOA. Subsequently, and the PV power time series data is then decomposed using the optimized VMD parameters to obtain multiple intrinsic mode functions (IMFs) components and a residual component. These components are then reconstructed with meteorological parameters to obtain the reconstructed IMF components and residuals. Finally, multiple LSTM sub-models are built, with each of them taking the IMF components and residual from the previous reconstruction as inputs. The sub-models are optimized using the WOA method to determine their hyperparameters and then constructed with these optimized hyperparameters. The predicted values of each IMF and residual are output and added for sequence reconstruction to derive the final predicted value of PV power. The model's effectiveness was verified for one-hour-ahead forecasting at the 1.8 MW solar system in Yulara, central Australia. The test results show that the proposed model outperforms other benchmark models, with mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and R-squared value (R2) of 15.247 kW, 19.753 kW, 4.405 % and 0.997, respectively. Compared to the LSTM, MAE, RMSE, and MAPE decreased by 84.942 %, 86.746 %, and 82.611 %, respectively, while R2 increased by 23.438 %. The proposed model has better predictive performance for both stable power changes and large fluctuations, essential for effectively integrating renewable energy sources into the power grid.

Research on rotor fault diagnosis technology of three-phase asynchronous motor based on NA-MEMD mutual information and SVM

Aiming at the problem of mode aliasing in the adaptive decomposition of nonlinear and non-stationary current signals generated by three-phase asynchronous motor faults, and the fault features contained in signals collected by a single sensor can not be accurately and comprehensively extracted and characterized when early rotor bar breakage and air gap eccentricity faults occur, A fault diagnosis method for three-phase asynchronous motor based on noise assisted multivariate empirical mode decomposition (NA-MEMD) and mutual information is proposed. Firstly, the NA-MEMD algorithm is used to decompose the three-phase stator current signal of the asynchronous motor to obtain multi-scale intrinsic mode functions (IMFs). Then, the correlation algorithm is used to screen the IMFs containing useful information. Then, the filtered IMF components are reconstructed into new signals and their features are extracted, Finally, support vector machines (SVM) are used to identify the rotor broken bars and air gap eccentric faults of the three-phase asynchronous motor. The experimental results show that the NA-MEMD method has a higher recognition rate than the traditional empirical mode decomposition (EMD) and the ensemble empirical mode decomposition (EEMD) methods.

Research on Dual-Grating Spacing Calibration Method Based on Multiple Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise Combined with Hilbert Transform

The paper proposes a method for the calibration of spacing in dual-grating based on Multiple Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) combined with Hilbert Transform (HT), referred to as Multiple ICEEMDAN-HT. This method addresses the potential impact of nonlinear factors on phase extraction accuracy, consequently on ranging precision in the homodyne interference of the dual-grating. Building upon the ICEEMDAN algorithm, the signal undergoes iterative decomposition and reconstruction using the sample entropy criterion. The intrinsic mode functions (IMFs) obtained from multiple iterations are then reconstructed to obtain the complete signal. Through a simulation and comparison with other signal decomposition methods, the repeatability and completeness of signal reconstruction by Multiple ICEEMDAN are verified. Finally, an actual dual-grating ranging system is utilized to calibrate the spacing of the planar grating. Experimental results demonstrate that the calibration relative error of the Multiple ICEEMDAN-HT phase unwrapping method can be reduced to as low as 0.07%, effectively enhancing the signal robustness and spacing calibration precision.

A time-frequency-based interval decomposition ensemble method for forecasting gasoil prices under the trend of low-carbon development

Given that gasoil plays a crucial role in carbon emission reduction, in this paper we propose a time-frequency-based interval decomposition ensemble (TFIDE) learning approach to forecast gasoil prices and capture the nonlinear impact of the global trend of low-carbon development on gasoil prices. The proposed method integrates bivariate empirical mode decomposition (BEMD), an interval multilayer perceptron (IMLP) network and a threshold autoregressive interval (TARI) model. First, we use BEMD to decompose interval-valued weekly gasoil prices into a finite number of complex-valued intrinsic mode function (IMF) components and a residual component. Second, we apply the IMLP model to forecast the IMFs and the TARI model to predict the residual part with predictors of carbon reduction technology and carbon emission concerns. After that, we combine all the forecasting results to generate the final gasoil price interval forecasting results. Our empirical results show that our carbon reduction technology variable improves middle-frequency IMF forecasting and that carbon emission concerns have a nonlinear impact on long-term gasoil price intervals. Furthermore, the proposed TFIDE approach outperforms other competing methods under different accuracy measurements.

A novel technology based on Raman spectroscopy for effective differentiation of alanine chiral isomers

In this study, Raman time-domain spectroscopy (R-TDS) was used to record the spectra of β-alanine, D-alanine, L-alanine, and DL-alanine molecules in the Raman shift range of 250–2000 cm−1. Baseline correction and smoothing of the original spectra yielded considerably different scattering peaks for β-alanine than the other three alanine isomers. The positions and intensities of the peaks in the spectra of D-alanine, L-alanine and DL-alanine were very similar, enabling β-alanine to be easily distinguished from the aforementioned isomers based on the Raman spectra. The Raman spectral data of D-alanine, L-alanine and DL-alanine were subjected to variational mode decomposition (VMD), whereby each spectral line was decomposed into four intrinsic mode functions (IMFs). Finally, a grid search-support vector machine (GS-SVM) classification recognition model was established for Raman spectral analysis and classification analysis using the first four IMFs as datasets. VMD-GS-SVM classification had a 96.67 % discriminative accuracy for predicted samples of the three isomers of D-alanine, L-alanine and DL-alanine. The classification recognition accuracy gradually trended downward as the number of mode components increased. The results show that the fast identification model of alanine isomers based on R-TDS and VMD-GS-SVM is effective and feasible, providing an accurate and fast optical measurement solution for the development of novel drugs and quality monitoring of fine chemicals.

Assessing cardiovascular stress based on heart rate variability in female shift workers: a multiscale-multifractal analysis approach.

Sleep-wake cycle disruption caused by shift work may lead to cardiovascular stress, which is observed as an alteration in the behavior of heart rate variability (HRV). In particular, HRV exhibits complex patterns over different time scales that help to understand the regulatory mechanisms of the autonomic nervous system, and changes in the fractality of HRV may be associated with pathological conditions, including cardiovascular disease, diabetes, or even psychological stress. The main purpose of this study is to evaluate the multifractal-multiscale structure of HRV during sleep in healthy shift and non-shift workers to identify conditions of cardiovascular stress that may be associated with shift work. The whole-sleep HRV signal was analyzed from female participants: eleven healthy shift workers and seven non-shift workers. The HRV signal was decomposed into intrinsic mode functions (IMFs) using the empirical mode decomposition method, and then the IMFs were analyzed using the multiscale-multifractal detrended fluctuation analysis (MMF-DFA) method. The MMF-DFA was applied to estimate the self-similarity coefficients, α(q, τ), considering moment orders (q) between -5 and +5 and scales (τ) between 8 and 2,048 s. Additionally, to describe the multifractality at each τ in a simple way, a multifractal index, MFI(τ), was computed. Compared to non-shift workers, shift workers presented an increase in the scaling exponent, α(q, τ), at short scales (τ < 64 s) with q < 0 in the high-frequency component (IMF1, 0.15-0.4 Hz) and low-frequency components (IMF2-IMF3, 0.04-0.15 Hz), and with q> 0 in the very low frequencies (IMF4, < 0.04 Hz). In addition, at large scales (τ> 1,024 s), a decrease in α(q, τ) was observed in IMF3, suggesting an alteration in the multifractal dynamic. MFI(τ) showed an increase at small scales and a decrease at large scales in IMFs of shift workers. This study helps to recognize the multifractality of HRV during sleep, beyond simply looking at indices based on means and variances. This analysis helps to identify that shift workers show alterations in fractal properties, mainly on short scales. These findings suggest a disturbance in the autonomic nervous system induced by the cardiovascular stress of shift work.

Selection of the Discriming Feature Using the BEMD’s BIMF for Classification of Breast Cancer Mammography Image

Mammogram exam images are useful in identifying diseases, such as breast cancer, which is one of the deadliest cancers, affecting adult women around the world. Computational image analysis and machine learning techniques can help experts identify abnormalities in these images. In this work we present a new system to help diagnose and analyze breast mammogram images. To do this, the system a method the Selection of the Most Discriminant Attributes of the images preprocessed by BEMD “SMDA-BEMD”, this entails picking the most pertinent traits from the collection of variables that characterize the state under study. A reduction of attribute based on a transformation of the data also called an extraction of characteristics by extracting the Haralick attributes from the Co-occurrence Matrices Methods “GLCM” this reduction which consists of replacing the initial set of data by a new reduced set, constructed at from the initial set of features extracted by images decomposed using Bidimensional Empirical Multimodal Decomposition “BEMD”, for discrimination of breast mammogram images (healthy and pathology) using BEMD. This decomposition makes it possible to decompose an image into several Bidimensional Intrinsic Mode Functions “BIMFs” modes and a residue. The results obtained show that mammographic images can be represented in a relatively short space by selecting the most discriminating features based on a supervised method where they can be differentiated with high reliability between healthy mammographic images and pathologies, However, certain aspects and findings demonstrate how successful the suggested strategy is to detect the tumor. A BEMD technique is used as preprocessing on mammographic images. This suggested methodology makes it possible to obtain consistent results and establishes the discrimination threshold for mammography images (healthy and pathological), the classification rate is improved (98.6%) compared to existing cutting-edge techniques in the field. This approach is tested and validated on mammographic medical images from the Kenitra-Morocco reproductive health reference center (CRSRKM) which contains breast mammographic images of normal and pathological cases.

Bearing fault diagnosis of induction machines using VMD-DWT and composite multiscale weighted permutation entropy

PurposeBearings play a critical role in the reliable operation of induction machines, and their failure can lead to significant operational challenges and downtime. Detecting and diagnosing these defects is imperative to ensure the longevity of induction machines and preventing costly downtime. The purpose of this paper is to develop a novel approach for diagnosis of bearing faults in induction machine.Design/methodology/approachTo identify the different fault states of the bearing with accurately and efficiently in this paper, the original bearing vibration signal is first decomposed into several intrinsic mode functions (IMFs) using variational mode decomposition (VMD). The IMFs that contain more noise information are selected using the Pearson correlation coefficient. Subsequently, discrete wavelet transform (DWT) is used to filter the noisy IMFs. Second, the composite multiscale weighted permutation entropy (CMWPE) of each component is calculated to form the features vector. Finally, the features vector is reduced using the locality-sensitive discriminant analysis algorithm, to be fed into the support vector machine model for training and classification.FindingsThe obtained results showed the ability of the VMD_DWT algorithm to reduce the noise of raw vibration signals. It also demonstrated that the proposed method can effectively extract different fault features from vibration signals.Originality/valueThis study suggested a new VMD_DWT method to reduce the noise of the bearing vibration signal. The proposed approach for bearing fault diagnosis of induction machine based on VMD-DWT and CMWPE is highly effective. Its effectiveness has been verified using experimental data.

Spectral analysis of seismic data based on a combined generalized S transform

The S transform is widely used to delineate seismic spectral anomalies associated with hydrocarbons during reservoir characterization. To overcome the relatively poor time-frequency resolution due to the fixed varying pattern of the window used in the S transform, we present a combined generalized S transform (CGST) for the spectral analysis of seismic data. First, the CGST decomposes the signal into a series of intrinsic mode functions (IMFs) using a complete ensemble empirical mode decomposition (CEEMD). An objective function is defined to quantitatively determine the spectral energy concentration criteria for optimal parameter selection of the improved Gaussian windows. Then, the time-frequency spectra for all the IMFs within narrower frequency bands are calculated using the respective Gaussian windows with normalized energy and individual optimal controlling parameters. We applied the CGST to spectral analyses of both synthetic signals and seismic field data. The results indicate that the CGST exhibits good performance with a higher time-frequency resolution. Field examples illustrate that the CGST can be used to characterize the spectral behavior of thin beds and indicate low-frequency shadows associated with hydrocarbon reservoirs.

The HWAM-EMD-GRU Forecasting Model for Short-Term Passenger Flow in an Airport Light Rail Transit Line

Accurate forecasting of airport light rail transit line (ALRTL) outbound passenger flow is critical to the optimal operations of both light rail and airport systems. Considering the nonlinearity, non-stationarity, uncertainty, and periodicity of outbound passenger flow in the ALRTL, we propose a combined forecasting model that integrates the Holt and Winters additive model (HWAM), empirical mode decomposition (EMD) and gated recurrent unit (GRU). Firstly, the edge effect of EMD will greatly affect the performance of the forecasting model. To overcome this, we extend the passenger flow by HWAM. After that, the decomposition method, EMD, can be applied to passenger flow, and several intrinsic mode function (IMF) components can be extracted. After extracting all the IMFs, the remaining part is referred to as the residual (Res) component. Then, a correlation test is performed on all the components, followed by their aggregation. Finally, the GRU is used to predict each of the aggregated components, and the prediction of aggregated components requires reconstruction. To verify the performance of the HWAM-EMD-GRU, we conducted a comparative study on the hourly passenger flow data for Beijing Daxing International Airport Express and set the autoregressive integrated moving average model, HWAM, Prophet, and GRU as the baseline. Predictions of the HWAM-EMD-GRU combined model demonstrated higher accuracy than baseline models, with a root mean square error of 83.52 (Prophet is 110.21) and mean absolute percentage error of 8.32% (Prophet is 12.48 %). The experimental result shows that the HWAM-EMD-GRU forecasting model offers more accurate predictions.

Epileptic Seizure Detection from Decomposed EEG Signal through 1D and 2D Feature Representation and Convolutional Neural Network

Electroencephalogram (EEG) has emerged as the most favorable source for recognizing brain disorders like epileptic seizure (ES) using deep learning (DL) methods. This study investigated the well-performed EEG-based ES detection method by decomposing EEG signals. Specifically, empirical mode decomposition (EMD) decomposes EEG signals into six intrinsic mode functions (IMFs). Three distinct features, namely, fluctuation index, variance, and ellipse area of the second order difference plot (SODP), were extracted from each of the IMFs. The feature values from all EEG channels were arranged in two composite feature forms: a 1D (i.e., unidimensional) form and a 2D image-like form. For ES recognition, the convolutional neural network (CNN), the most prominent DL model for 2D input, was considered for the 2D feature form, and a 1D version of CNN was employed for the 1D feature form. The experiment was conducted on a benchmark CHB-MIT dataset as well as a dataset prepared from the EEG signals of ES patients from Prince Hospital Khulna (PHK), Bangladesh. The 2D feature-based CNN model outperformed the other 1D feature-based models, showing an accuracy of 99.78% for CHB-MIT and 95.26% for PHK. Furthermore, the cross-dataset evaluations also showed favorable outcomes. Therefore, the proposed method with 2D composite feature form can be a promising ES detection method.

Method for the P-wave arrival pickup of rock fracture acoustic emission signals under strong noise

This research aimed to investigate the accuracy of picking of P-wave arrival times in rock fracture acoustic emission signals. In order to simulate the mining scenario, Gaussian white noise and pulse noise were added to the data collected in the laboratory. Complete ensemble empirical mode decomposition with adaptive noise + Wavelet (CEEMDAN + Wavelet) was improved in this paper, where the Spearman rank correlation coefficient was adopted to effectively select intrinsic mode functions for denoising which retained the inherent characteristics of the rock fracture signal. The absolute amplitude and energy change rate of the envelope signal, calculated based on the Hilbert transform, were used as the input of the short term average/long term average (STA/LTA) normalization algorithm to pickup the P-wave arrival time. The reliability of this method was tested on 30 groups of recorded rock fracture laboratory data and 60 groups of added noise data. Taking the manual pickup results as the standard, the errors of CEEMDAN + Wavelet + STA/LTA + AIC (Akaike information criterion) method with the absolute amplitude of the signal as the input are all within 10 ms, and 86.67% of the results are within 5 ms. The method proposed in this paper effectively addressing the issue of false pickup caused by the sensitivity of AIC and traditional STA/LTA method for strong noise, and achieving relatively high accuracy and stability in processing low signal-to-noise ratio signals. This work contributes to monitor microscopic changes in rock bodies and is of great significance for the prediction and monitoring of geological disasters.

Accurate detection method of traveling wave shape based on EEMD and L1 norm regularization

Aiming at the problem of waveform distortion of the secondary traveling wave obtained from the primary traveling wave signal transmitted by the voltage traveling wave sensor, an accurate detection method of voltage traveling wave based on ensemble empirical mode decomposition (EEMD) and L1 norm least squares regularization is proposed in this paper. Firstly, the forward transfer function model of the specialized voltage traveling wave sensor is established, and the inversion model is derived to analyze the phase frequency and amplitude frequency characteristics of the secondary traveling wave after transmission. EEMD is used to decompose the secondary traveling wave into the intrinsic modal function (IMF) components of different frequency bands. The L1 norm least square regularization inversion algorithm was used to invert each IMF component. Finally, the IMF' components after inversion are synthesized to obtain the primary traveling wave. Simulation and experimental results demonstrate that the proposed method is not affected by noise, mode aliasing effect and regularization parameter accuracy, and the obtained waveform has high similarity to the simulated waveform, which enables precise identification of fault traveling wave.

Incipient Bearing Fault Extraction based on an Adaptive Multi-stage Noise Reduction Method

Considering the strong nonlinear and non-stationary characteristics of rolling bearing vibration signals, this paper proposes a multi-stage noise reduction method using adaptive variational mode decomposition and modulation signal bispectrum (AVMD-MSB) to extract the fault features of rolling bearings. Firstly, the AVMD is employed to adaptively select VMD parameters K and α and decompose the signal into a series of Intrinsic mode functions (IMFs), which allows an adaptive selection of the parameters of VMD. Then, all IMF components are reconstructed with weights according to the index of correlation kurtosis to avoid accidental omission of the IMFs containing important fault information. Finally, MSB is implemented to further suppress residual noises and interference components in the signal, precisely extract the bearing fault features. Numerical simulation and case study show that the AVMD-MSB is more advantageous in extracting fault characteristics from rolling bearing vibration signals compared with AVMD-Envelope and conventional VMD-MSB.

State-of-health estimation for lithium-ion batteries based on GWO–VMD-transformer neural network

State-of-health (SOH) estimation of lithium-ion batteries stands as a fundamental metric within the battery management system. It reflects the current level of battery aging and is important for early warning of battery failure to avoid unsafe battery behavior. Therefore, accurate SOH estimation can ensure safe and reliable battery operation. In this paper, the capacity data of the discharge phase are used as the input of the SOH estimation model, and a gray wolf optimization (GWO)–variable mode decomposition (VMD)-transformer-based SOH estimation method for lithium-ion batteries is proposed in a data-driven framework. First, the GWO algorithm is adopted to optimize VMD to decompose the original battery capacity degradation sequence into a series of intrinsic mode functions (IMFs). Then, the transformer is used to separately predict each of these IMFs. Finally, the predicted values of each IMF are integrated to obtain the final prediction of the battery capacity degradation sequence. The model undergoes testing across various datasets, and comparative evaluations are conducted against other data-driven prediction models. The experimental findings underscore the superior SOH estimation performance of the proposed method, along with its robustness when confronted with diverse types of lithium-ion batteries, spanning distinct operational conditions and different aging degrees.

Mid-to-long Term Wind Power Forecasting Based on ARIMA-BP Combined Model

Background: Increasing the accuracy of the output power forecasting for wind power is helpful to the improvement of the reliability of power dispatching. Objective: This study aimed to improve the forecasting accuracy of mid-to-long term wind power. Methods: A mid-to-long term wind power forecasting based on ARIMA-BP combined model was proposed. The Empirical Mode Decomposition (EMD) was used to decompose the historical wind power series and obtain the Intrinsic Mode Function (IMF) and residual components, thereby obtaining more regular components. Then, the optimum feature set was obtained based on the minimum Redundancy Maximum Relevance (mRAR) to improve the prediction accuracy for feature extraction. After that, the high-frequency components were predicted using the Back Propagation (BP) neural network model, while the low-frequency components were predicted using the Autoregressive Integrated Moving Average model (ARIMA). Finally, the predicted components obtained were superimposed to deduce the final mid- and long-term wind power prediction results. Results: An analysis was conducted according to the actual data from a typical wind farm. After comparison, it was found that, after empirical mode decomposition and feature extraction analysis, the error of the intelligent combination algorithm based on the ARIMA-BP combined model was smaller than that using only the BP neural network or only the ARIMA. Conclusion: By means of actual data analysis, the effectiveness of the method proposed by the study for mid- and long-term wind power prediction was verified.

Extraction of reflected waves from acoustic logging data using variation mode decomposition and curvelet transform

Remote reflection waves, essential for acquiring high-resolution images of geological structures beyond boreholes, often suffer contamination from strong direct mode waves propagating along the borehole. Consequently, the extraction of weak reflected waves becomes pivotal for optimizing migration image quality. This paper introduces a novel approach to extracting reflected waves by sequentially operating in the spatial frequency and curvelet domains. Using variation mode decomposition (VMD), single-channel spatial domain signals within the common offset gather are iteratively decomposed into high-wavenumber and low-wavenumber intrinsic mode functions (IMFs). The low-wavenumber IMF is then subtracted from the overall waveform to attenuate direct mode waves. Subsequently, the curvelet transform is employed to segregate upgoing and downgoing reflected waves within the filtered curvelet domain. As a result, direct mode waves are substantially suppressed, while the integrity of reflected waves is fully preserved. The efficacy of this approach is validated through processing synthetic and field data, underscoring its potential as a robust extraction technique.

A hybrid ICEEMDAN and OMEDA-based vibrodiagnosis method for the bearing of rolling stock

Purpose. To develop a hybrid method based on ICEEMDAN and OMEDA for high-fidelity detection of the diagnostic features of the technical condition of roller bearing. Methodology. Due to digital signal processing the search was made of the informative components on the broadband spectra, envelope spectra, squared envelope spectra. The usage of the methods of mathematical statistics for the selection of informative IMFs as a result of iterative calculate procedures. The introduction of blind deconvolution method with a proper objective function for the enhancement of impulse fault features. Findings. The use of traditional spectral methods provided an incomplete list of diagnostic features of bearing roller damage. The empirical mode decomposition (EMD) method and its minor versions provide the series of intrinsic mode functions (IMFs). On the broadband vibration spectra of the selected low-frequency IMFs, diagnostic features were not detected in a sufficient number. Further research focused on the development of a hybrid method that takes into account the demodulation procedure of the high-frequency components of those IMFs that were selected according to the complex evaluation index. The Fast Kurtogram technique determined an informative frequency band of 7.2–7.5 kHz for demodulation and construction of the squared envelope spectra, where harmonics of the roller spin frequency and some side bands with a width equal to the separator rotation frequency appeared. The use of OMEDA caused the reduction of residual noise on the squared envelope spectra and bilateral sidebands to appear around all harmonics of the roller spin frequency. Originality. For the first time, the whole list of the diagnostic features of roller faults of the axle-box bearing was identified using the developed hybrid method, which involves steps of noise reduction for enhancing a physical meaning of a proper frequency components, associated with faults. The usage of the optimal minimum entropy deconvolution adjusted method helped to eliminate noise and provide all diagnostic features of the technical condition on the squared envelope spectrum. Practical value. The results of the study help to control the quality of repair of the axle-box rolling bearings on the test rig at the workshop of the freight railway car depot.

Predicting carbon dioxide emissions in the United States of America using machine learning algorithms.

Carbon dioxide (CO2) emissions result from human activities like burning fossil fuels. CO2 is a greenhouse gas, contributing to global warming and climate change. Efforts to reduce CO2 emissions include transitioning to renewable energy. Monitoring and reducing CO2 emissions are crucial for mitigating climate change. Strategies include energy efficiency and renewable energy adoption. In the past few decades, several nations have experienced air pollution and environmental difficulties because of carbon dioxide (CO2) emissions. One of the most crucial methods for regulating and maximizing CO2 emission reductions is precise forecasting. Four machine learning algorithms with high forecasting precision and low data requirements were developed in this study to estimate CO2 emissions in the United States (US). Data from a dataset covering the years 1973/01 to 2022/07 that included information on different energy sources that had an impact on CO2 emissions were examined. Then, four algorithms performed the CO2 emissions forecast from the layer recurrent neural network with 10 nodes (L-RNN), a feed-forward neural network with 10 nodes (FFNN), a convolutional neural network with two layers with 10 and 5 filters (CNN1), and convolutional neural network with two layers and with 50 and 25 filters (CNN2) models. Each algorithm's forecast accuracy was assessed using eight indicators. The three preprocessing techniques used are (1) without any processing techniques, (2) processed using max-min normalization technique, and (3) processed using max-min normalization technique and decomposed by variation mode decomposition (VMD) technique with 7 intrinsic mode functions and 1000 iterations. The latter with L-RNN algorithm gave a high accuracy between the forecasting and actual values. The results of CO2 emissions from 2011/05 to 2022/07 have been forecasted, and the L-RNN algorithm had the highest forecast accuracy. The L-RNN model has the lowest value of 1.187028078, 135.5668592, and 11.64331822 for MAPE, MSE, and RMSE, respectively. The L-RNN model provides precise and timely forecasts that can help formulate plans to reduce carbon emissions and contribute to a more sustainable future. Moreover, the results of this investigation can improve our comprehension of the dynamics of carbon dioxide emissions, resulting in better-informed environmental policies and initiatives targeted at lowering carbon emissions.