Empirical Mode Decomposition Research Articles

Bearing faults classification using novel log energy-based empirical mode decomposition and machine Mel-frequency cepstral coefficients

The accurate diagnosis of faults in bearing components is crucial for the safe and efficient operation of electrical and power drives. These machines generate sound and vibration signals that indicate their operational state. While vibration signals are often utilized for fault diagnosis, they require costly transducers. On the other hand, sound signal transducers are more affordable, but their lower signal-to-noise ratio complicates the differentiation between healthy and faulty bearings. This paper addresses these challenges by introducing a machine sound-based bearing fault diagnosis system. The proposed method employs a novel Log Energy-based Empirical Mode Decomposition and Reconstruction for advanced sound preprocessing. Feature extraction is performed using Machine Mel-frequency Cepstral Coefficients, with feature selection facilitated by a Genetic Algorithm. Classification is achieved through Support Vector Machines. The system demonstrated a high classification accuracy of 99.26% on the SUBF v2.0 dataset, outperforming other diagnostic methods, even in noisy conditions. This approach is particularly suited for industrial applications, offering a reliable solution for preventing downtime and ensuring the reliability of equipment.

Analyzing spatio-temporal dynamics of dissolved oxygen for the River Thames using superstatistical methods and machine learning

By employing superstatistical methods and machine learning, we analyze time series data of water quality indicators for the River Thames (UK). The indicators analyzed include dissolved oxygen, temperature, electrical conductivity, pH, ammonium, turbidity, and rainfall, with a specific focus on the dynamics of dissolved oxygen. After detrending, the probability density functions of dissolved oxygen fluctuations exhibit heavy tails that are effectively modeled using q-Gaussian distributions. Our findings indicate that the multiplicative Empirical Mode Decomposition method stands out as the most effective detrending technique, yielding the highest log-likelihood in nearly all fittings. We also observe that the optimally fitted width parameter of the q-Gaussian shows a negative correlation with the distance to the sea, highlighting the influence of geographical factors on water quality dynamics. In the context of same-time prediction of dissolved oxygen, regression analysis incorporating various water quality indicators and temporal features identify the Light Gradient Boosting Machine as the best model. SHapley Additive exPlanations reveal that temperature, pH, and time of year play crucial roles in the predictions. Furthermore, we use the Transformer, a state-of-the-art machine learning model, to forecast dissolved oxygen concentrations. For long-term forecasting, the Informer model consistently delivers superior performance, achieving the lowest Mean Absolute Error (0.15) and Symmetric Mean Absolute Percentage Error (21.96%) with the 192 historical time steps that we used. This performance is attributed to the Informer’s ProbSparse self-attention mechanism, which allows it to capture long-range dependencies in time-series data more effectively than other machine learning models. It effectively recognizes the half-life cycle of dissolved oxygen, with particular attention to critical periods such as morning to early afternoon, late evening to early morning, and key intervals between the 16th and 26th quarter-hours of the previous half-day. Our findings provide valuable insights for policymakers involved in ecological health assessments, aiding in accurate predictions of river water quality and the maintenance of healthy aquatic ecosystems.

Short-term wind power prediction method based on multivariate signal decomposition and RIME optimization algorithm

Accurate characterization of the dynamics of wind power systems under highly unstable conditions is essential for short-term wind power forecasting. Multivariate factors, such as wind speed, wind direction and climatic factors at different heights, as well as the relationships between them, need to be fully considered. To this end, after the Pearson correlation coefficient is used to identify the main influencing variables, the empirical modal decomposition (MEMD) method is utilized to decompose the data in order to capture the deep coupling relationship and the spatio-temporal pattern of change among the variables. Combined with a bidirectional long and short-term memory network (BiLSTM) optimized through the RIME algorithm, a short-term wind power prediction model was constructed. Data analysis of two wind farms in Xinjiang and Gansu, China, shows that the model has higher prediction accuracy compared to the baseline model. The effectiveness of RIME and MEMD is verified through component ablation experiments and comparison experiments with other optimization algorithms and signal decomposition algorithms. To cope with large-scale data, dimensionality reduction of IMF features using Elastic Net (EN) is explored to reduce computational requirements and maintain good prediction performance. The method provides strong support for power system scheduling and efficient utilization of renewable energy.

Short-term air quality prediction using point and interval deep learning systems coupled with multi-factor decomposition and data-driven tree compression

Clean air, as a symbol of high-quality air quality, is the most basic requirement for people to maintain health. Moreover, in keeping humans fit, accurate short-term air quality prediction is vital. The decomposition algorithm can better capture the local features and temporal changes of the data. However, it increases the computation time, resource consumption, and complexity of the model. On the other hand, existing forecasting systems overlook instability and uncertainty. To solve the above problems, a deterministic and uncertainty AOA-DBGRU-MDN deep learning systems is proposed, which combines arithmetic optimization algorithm (AOA), double-layer bi-directional GRUs (DBGRU), and mixture density network (MDN). The above systems consider meteorological factors and air pollutants comprehensively. It involves feature selection using maximum information coefficient (MIC), decomposition using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm, classification, and compression of decomposed components using entropy-Huffman tree compression. Firstly, the information measurement process reduces the number of components significantly. Following the incorporation of multi-factor data, the optimal DBGRU model is then obtained using AOA. Finally, the training errors are fitted using MDN to obtain interval prediction results. The experiments demonstrate that (1) Using the CEEMDAN algorithm can improve the prediction accuracy; (2) Classifying and reconstructing the data based on entropy-Huffman tree compression can not only decrease the model's training volume and improve training efficiency but also boost the model's prediction accuracy; (3) The AOA-DBGRU-MDN system performs probabilistic prediction to obtain an effective and intuitive prediction interval to improve the point prediction of air quality prediction.

A hybrid intelligent diagnostic approach for spool jamming faults of hydraulic directional valves

Directional valves are critical functional components in hydraulic systems for diverting the flow of hydraulic oil and controlling oil pressure. Faults of the valves could lead to failure and even serious accidents in hydraulic systems. Fault diagnostic accuracy is directly influenced by the effectiveness of signal processing. Due to the harsh operating environment of hydraulic systems, the condition monitoring signal acquired from the systems contains a large amount of redundant information and environmental noise. This makes the training processes of fault diagnostic approaches time-consuming and inefficient. In this paper, a new hybrid intelligent approach to spool jamming fault diagnostics for hydraulic directional valves is presented. The approach is designed based on the combined strengths of wavelet packet decomposition (WPD), empirical mode decomposition (EMD), variable mode decomposition (VMD), and the multi-layer perceptron (MLP) to improve the efficiency and accuracy of the fault diagnostic process. Five evaluation indices, including processing time (PT), local average accuracy (LAA), stability of accuracy (SA), weighted average of the neuron number (WANN), and robustness of WANN (ROB), are applied to benchmark the approach using ablation experiments. The experimental results show that the hybrid approach has a strong capability to extract fault-related features from the signal and perform fault diagnostics with high accuracy, efficiency, and robustness.

Cardiac Time Intervals under Motion Using Bimodal Chest E-Tattoos and Multistage Processing.

We present a thin, soft, and chest conformable bimodal sensor, known as the chest e-tattoo, coupled with an advanced signal processing framework to accurately identify various cardiac events, and thereby extract cardiac time intervals even during body motion. We built a wireless electronic tattoo that features synchronous electrocardiography (ECG) and seismocardiography (SCG). The SCG measures chest vibrations due to heartbeat, providing information on cardiovascular health that is complementary to the ECG. However, the efficacy of the SCG is compromised by motion-induced artifacts. The slim and stretchy design of the e-tattoo allows it to be strategically placed near the xiphoid process, facilitating high-quality monitoring of the ECG and SCG for increased signal quality. Nine participants were measured during walking and cycling. We propose a multistage signal processing framework, integrating an adaptive Normalized Least Mean Squares (NLMS) filter, ensemble averaging, and Empirical Mode Decomposition (EMD), together named the FAD framework, to accurately extract cardiac time intervals (CTIs).

A Novel Hybrid Model (EMD-TI-LSTM) for Enhanced Financial Forecasting with Machine Learning

Financial forecasting involves predicting the future financial states and performance of companies and investors. Recent technological advancements have demonstrated that machine learning-based models can outperform traditional financial forecasting techniques. In particular, hybrid approaches that integrate diverse methods to leverage their strengths have yielded superior results in financial prediction. This study introduces a novel hybrid model, entitled EMD-TI-LSTM, consisting of empirical mode decomposition (EMD), technical indicators (TI), and long short-term memory (LSTM). The proposed model delivered more accurate predictions than those generated by the conventional LSTM approach on the same well-known financial datasets, achieving average enhancements of 39.56%, 36.86%, and 39.90% based on the MAPE, RMSE, and MAE metrics, respectively. Furthermore, the results show that the proposed model has a lower average MAPE rate of 42.91% compared to its state-of-the-art counterparts. These findings highlight the potential of hybrid models and mathematical innovations to advance the field of financial forecasting.

AEEFCSR: an adaptive ensemble empirical feed-forward cascade stochastic resonance system for weak signal detection

Abstract A novel adaptive ensemble empirical feed-forward cascade stochastic resonance (AEEFCSR) method is proposed in this study for the challenges of detecting target signals from intense background noise. At first, we create an unsaturated piecewise self-adaptive variable-stable potential function to overcome the limitations of traditional potential functions. Subsequently, based on the foundation of a feed-forward cascaded stochastic resonance method, a novel weighted function and system architecture is created, which effectively addresses the issue of low-frequency noise enrichment through ensemble empirical mode decomposition. Lastly, inspired by the spider wasp algorithm and nutcracker optimization algorithm, the spider wasp nutcracker optimization algorithm is proposed to optimize the system parameters and overcome the problem of relying on manual experience. In this paper, to evaluate its performance, the output signal-to-noise ratio (SNR), spectral sub-peak difference, and time-domain recovery capability are used as evaluation metrics. The AEEFCSR method is demonstrated through theoretical analysis. To further illustrate the performance of the AEEFCSR method, Validate the adoption of multiple engineering datasets. The results show that compared with the compared algorithms, the output SNR of the AEEFCSR method is at least 6.2801 dB higher, the spectral subpeak difference is more than 0.25 higher, and the time-domain recovery effect is more excellent. In summary, the AEEFCSR method has great potential for weak signal detection in complex environments.

Prediction of SO2, NOx and PM in the sintering process based on deep learning

The accurate prediction of SO2, NOx and PM emissions in the iron ore sintering process could adjust the desulfurization and denitrification operation in time. The study presented an integrated prediction model for SO2, NOx and PM in sintering flue gas. Gradient boosting decision tree, recurrent neural network, gated recurrent unit were chosen as sub-models to predict SO2, NOx and PM by comparing different regression prediction models, which were then combined to form an integrated prediction model (MMEP). The box plots, empirical mode decomposition algorithm, Pearson correlation coefficient and maximum information coefficient to select independent variables for the predictive model. The MMEP model had an overall accuracy greater than 0.82, as verified by production data, which could provide guidance for on-site sintering production.

Analysis of Global and Key PM2.5 Dynamic Mode Decomposition Based on the Koopman Method

Understanding the spatiotemporal dynamics of atmospheric PM2.5 concentration is highly challenging due to its evolution processes have complex and nonlinear patterns. Traditional mode decomposition methods struggle to accurately capture the mode features of PM2.5 concentrations. In this study, we utilized the global linearization capabilities of the Koopman method to analyze the hourly and daily spatiotemporal processes of PM2.5 concentration in the Beijing–Tianjin–Hebei (BTH) region from 2019 to 2021. This approach decomposes the data into the superposition of different spatial modes, revealing their hierarchical spatiotemporal structure and reconstructing the dynamic processes. The results show that PM2.5 concentrations exhibit high-frequency cycles of 12 and 24 h, as well as low-frequency cycles of 124 and 353 days, while also revealing spatiotemporal modes of growth, recession, and oscillation. The superposition of these modes enables the reconstruction of spatiotemporal dynamics with a mean absolute percentage error (MAPE) of only 0.6%. Unlike empirical mode decomposition (EMD), Koopman mode decomposition (KMD) method avoids mode aliasing and provides a clearer identification of global and key modes compared to wavelet analysis. These findings underscore the effectiveness of KMD method in analyzing and reconstructing the spatiotemporal dynamics of PM2.5 concentration, offering new insights into the understanding and reconstruction of other complex spatiotemporal phenomena.

Intelligent crude oil price probability forecasting: Deep learning models and industry applications

The crude oil price has been subject to periodic fluctuations because of seasonal changes in industrial demand and supply, weather, natural disasters and global political unrest. An accurate forecast of crude oil prices is of utmost importance for decision makers and industry players in the energy sector. Despite this, the volatility of crude oil prices contributes to the uncertainty of the energy industry, which was particularly challenging following the recent global spread of the COVID-19 epidemic and the Russia–Ukraine conflict. This paper proposes a hybrid deep learning (DL) modelling framework to deal with the volatility of crude oil prices, applying ensemble empirical mode decomposition (EEMD), convolutional neural network (CNN) and bidirectional long short-term memory (BiLSTM) integrated with quantile regression (QR); named EEMD-CNN-BiLSTM-QR. Two real-world datasets on crude oil prices from the West Texas Intermediate and Brent Crude Oil markets were employed to validate the EEMD-CNN-BiLSTM-QR hybrid modelling framework. Given that the probability density forecast can capture uncertainty, an in-depth analysis was carried out and prediction accuracy calculated. The findings of this study demonstrate that the proposed EEMD-CNN-BiLSTM-QR DL modelling framework, which uses the probability density forecast method, is superior to other tested models in terms of its ability to forecast crude oil prices. The novelty of this study stems mainly from its use of QR, which allows for the description of the conditional distribution of predicted variables and the extraction of more uncertain information for probability density forecasts.

Short-term air quality prediction based on EMD-transformer-BiLSTM

Actual acquired air quality time series data are highly volatile and nonstationary, and accurately predicting nonlinear time series data containing complex noise is an ongoing challenge. This paper proposes an air quality prediction method based on empirical mode decomposition (EMD), a transformer and a bidirectional long short-term memory neural network (BiLSTM), which is good at addressing the ultrashort-term prediction of nonlinear time-series data and shows good performance for application to the air quality dataset of Patna, India (6:00 am on October 3, 2015–0:00 pm on July 1, 2020). The AQI sequence is first decomposed into intrinsic mode functions (IMFs) via EMD and subsequently predicted separately via the improved transformer algorithm based on BiLSTM, where linear prediction is performed for IMFs with simple trends. Finally, the predicted values of each IMF are integrated using BiLSTM to obtain the predicted AQI values. This paper predicts the AQI in Patna with a time window of 5 h, and the RMSE, MAE and MAPE are as low as 5.6853, 2.8230 and 2.23%, respectively. Moreover, the scalability of the proposed model is validated on air quality datasets from several other cities, and the results prove that the proposed hybrid model has high performance and broad application prospects in real-time air quality prediction.

A Data-Driven Approach for Forecasting Current Direction With a Hybrid Model of Empirical Mode Decomposition and Warped Gaussian Process

Abstract Ocean current forecasting is essential for tidal renewable energy generation and operation. However, forecasting the current direction at multiple points along the water depth are still lacking of comprehensive studies. In this study, a data-driven approach was developed to attain short-term prediction in the current direction with reasonable uncertainty quantification. The developed approach employed empirical mode decomposition (EMD) and the warped Gaussian process (WGP) in the forecasting process. The ocean current data, which were measured by a seabed-mounted acoustic Doppler current profiler in the Haitian Strait, were used to illustrate the developed approach. The measured current direction data were preprocessed with the average shifting method to obtain the principal and random components for the improvement of the forecasting accuracy. The random components were decomposed into intrinsic mode functions (IMFs) and residuals. The principal components, IMFs, and residuals of the current direction were then forecasted by the WGP approach. The forecasting performance of the developed approach was investigated through comparisons with those of single standard GP, single WGP, and EMD + GP models. The effects of the kernel function and training input on the forecasting efficiency and precision were investigated. The extrapolation performances of the proposed model for a 1-step prediction and multistep-ahead prediction were also examined.

Multi-Source Image Fusion Based on BEMD and Region Sharpness Guidance Region Overlapping Algorithm

Multi-focal image and multi-modal image fusion technology can fully take advantage of different sensors or different times, retaining the image feature information and improving the image quality. A multi-source image fusion algorithm based on bidimensional empirical mode decomposition (BEMD) and a region sharpness-guided region overlapping algorithm are studied in this article. Firstly, source images are decomposed into multi-layer bidimensional intrinsic mode functions (BIMFs) and residuals from high-frequency layer to low-frequency layer by BEMD. Gaussian bidimensional intrinsic mode functions (GBIMFs) are obtained by applying Gaussian filtering operated on BIMF and calculating the sharpness value of segmented regions using an improved weighted operator based on the Tenengrad function, which is the key to comparison selection and fusion. Then, the GBIMFs and residuals selected by sharpness comparison strategy are fused by the region overlapping method, and the stacked layers are weighted to construct the final fusion image. Finally, based on qualitative evaluation and quantitative evaluation indicators, the proposed algorithm is compared with six typical image fusion algorithms. The comparison results show that the proposed algorithm can effectively capture the feature information of images in different states and reduce the redundant information.

An improved denoising method for [formula omitted]-OTDR signal based on the combination of temporal local GMCC and ICEEMDAN-WT

A noise reduction method based on the combination of improved complete ensemble empirical mode decomposition with adaptive noise and temporal local generalized maximum cross-correlation entropy and wavelet threshold (ICEEMDAN-TLGMCC-WT) is proposed to improve the noise rejection ratio (NRR) of phase-sensitive optical time-domain reflectometer (φ-OTDR) system signals. Firstly, the principle of the proposed ICEEMDAN-TLGMCC-WT denoising method is introduced. On this basis, experiments are carried out to verify the feasibility of the noise reduction algorithm for non-stationary signals. and the results demonstrate that the vibration event can be detected with an improved average NRR of 72.18 dB and a root mean square error (RMSE) 0.017 within 5 km sensing distance by employing the ICEEMDAN-TLGMCC-WT denoising method, which confirm the effectiveness of proposed scheme for the performance improvement of φ-OTDR system.

Performance Analysis of Cooperative Spectrum Sensing using Empirical Mode Decomposition and Artificial Neural Network in Wireless Regional Area Network

Background: Radio spectrum is natural and the most precious means in wireless communication systems. Optimal spectrum utilization is a key concern for today's cutting-edge wireless communication networks. The impending problem of the lack of available spectrum has prompted the development of a new idea called “Cognitive Radio” (CR). Cooperative spectrum sensing (CSS) is utilized to improve the detection performance of the system. Several fusion algorithms of decision-making are proposed for sensing the licensed user, but they do not work well under low signal-to-noise ratio (SNR). Objectives: To address the issue of poor detection performance under low SNR, Empirical mode decomposition (EMD) and artificial neural network (ANN) based CSS under Rayleigh multipath fading channel in IEEE 802.22 wireless regional area network (WRAN) is proposed in this paper. Method: In this work, we propose the use of ANN as a fusion center. First, the received signal's energy is calculated using EMD. The computed energy, SNR, and false alarm probability are combined to form a data set of 2048 samples. They are utilized to train Levenberg- Marquardt back propagation training algorithm-based feed-forward neural network (FFNN). Using this trained network, CSS in WRAN is simulated under Rayleigh multipath fading. Results: Simulation results show that the proposed CSS method based on EMD-ANN outperforms the standard fast Fourier transform (FFT) and EMD detection-based cooperative spectrum sensing with a hard "OR" fusion at low SNR. With Pf =0.01, 100% detection accuracy with proposed techniques is obtained at SNR= -22dB. Conclusion: The findings show that the suggested approach outperforms EMD and FFT based energy detection scheme-based traditional CSS in low SNR environments.

A Hybrid Forecasting Model for Electricity Demand in Sustainable Power Systems Based on Support Vector Machine

Renewable energy sources, such as wind and solar power, are increasingly contributing to electricity systems. Participants in the energy market need to understand the future electricity demand in order to plan their purchasing and selling strategies. To forecast the electricity demand, this study proposes a hybrid forecasting model. The method uses Kalman filtering to eliminate noise from the electricity demand series. After decomposing the electricity demand using an empirical model, a support vector machine optimized by a genetic algorithm is employed for prediction. The performance of the proposed forecasting model was evaluated using actual electricity demand data from the Australian energy market. The simulation results indicate that the proposed model has the best forecasting capability, with a mean absolute percentage error of 0.25%. Accuracy improved by 74% compared to the Support Vector Machine (SVM) electricity demand forecasting model, by 73% when compared to the SVM with empirical mode decomposition, and by 51% when compared to the SVM with Kalman filtering for noise reduction. Additionally, compared to existing forecasting methods, this study’s accuracy surpasses LSTM by 63%, Transformer by 47%, and LSTM-Adaboost by 36%. The simulation of and comparison with existing forecasting methods validate the effectiveness of the proposed hybrid forecasting model, demonstrating its superior predictive capabilities.

A sensitive wavelength-enhanced reconstruction algorithm for track quality assessment based on measured data and vehicle dynamics

High-speed railways are extensively utilized worldwide. However, with prolonged operation, track irregularities increasingly pose significant challenges, adversely affecting the safety and stability of train operations. This paper proposes a sensitive wavelength-enhanced reconstruction algorithm based on the cmplete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method to address this issue. This method evaluates the influence of reconstructed track irregularities on vehicle dynamic response, considering sensitive wavelengths and amplification factors. The algorithm effectively enhances these sensitive wavelengths while maintaining the integrity of the input signal, utilizing measured track irregularities. After applying the algorithm, the maximum vertical body acceleration rises by 206.09%. The study validates a coupled train model and analyzes the mapping relationship between single-wave irregularities and vertical body acceleration. Compared to random irregularities, the maximum vertical acceleration can amplify up to 122.80% under various operating conditions. The periodic sensitive wavelengths of track irregularities significantly impact the train’s dynamic response.

Multiscale tail risk integration between safe-haven assets and Africa’s emerging equity market

This study examines the multiscale tail risk integration between safe-haven assets and top equity markets in Africa (South Africa, Kenya, Egypt, Ghana, Nigeria, Botswana, Zambia, and Morocco) as well as portfolio implications. We further investigate the role of global economic factors in these relationships by employing Conditional Autoregressive Value at Risk and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise-based TVP-VAR with data spanning from January 2010 to September 2024. Our findings show that while the equity market in South Africa is a net transmitter of tail risk spillovers, the rest of the equity markets are net receivers. They also reveal that while gold and silver transmit significant shocks to the other assets, Bitcoin receives considerable shocks from the other assets. We conclude that global economic factors and spillovers from safe-haven assets significantly affect the tail risk exposures of Africa’s equity markets. Our findings have significant implications for investment decision-making.

ER-GET: Emotion Recognition Based on Global ECG Trajectory.

In recent years, the recognition of human emotions based on electrocardiogram (ECG) signals has been considered a novel area of study among researchers. Despite the challenge of extracting latent emotion information from ECG signals, existing methods are able to recognize emotions by calculating the heart rate variability (HRV) features. However, such local features have drawbacks, as they do not provide a comprehensive description of ECG signals, leading to suboptimal recognition performance. For the first time, we propose a new strategy to extract hidden emotional information from the global ECG trajectory for emotion recognition. Specifically, a period of ECG signals is decomposed into sub-signals of different frequency bands through ensemble empirical mode decomposition (EEMD), and a series of multi-sequence trajectory graphs is constructed by orthogonally combining these sub-signals to extract latent emotional information. Additionally, to better utilize these graph features, a network has been designed that includes self-supervised graph representation learning and ensemble learning for classification. This approach surpasses recent notable works, achieving outstanding results, with an accuracy of 95.08% in arousal and 95.90% in valence detection. Additionally, this global feature is compared and discussed in relation to HRV features, with the intention of providing inspiration for subsequent research.