Into 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.

Research on a Sound Source Localization Method for UAV Detection Based on Improved Empirical Mode Decomposition.

To address the challenge of accurately locating unmanned aerial vehicles (UAVs) in situations where radar tracking is not feasible and visual observation is difficult, this paper proposes an innovative acoustic source localization method based on improved Empirical Mode Decomposition (EMD) within an adaptive frequency window. In this study, the collected flight signals of UAVs undergo smoothing filtering. Additionally, Robust Empirical Mode Decomposition (REMD) is applied to decompose the signals into Intrinsic Mode Function (IMF) components for spectrum analysis. We introduce a sliding frequency window with adjustable bandwidth, which is automatically determined using a Grey Wolf Optimizer (GWO) with a sliding index. This window is used to lock and extract specific frequencies from the IMFs. Based on predefined criteria, the extracted IMF components are reconstructed, and trigger signal times are analyzed and recorded from these reconstructed IMFs. The time differences between sensor receptions are then calculated. Furthermore, this study introduces the Chan-Taylor localization algorithm based on weighted least squares. This advanced algorithm takes sensor time delay parameters as input and solves a set of nonlinear equations to determine the target's location. Simulations and real-world signal tests are used to validate the robustness and performance of the proposed method. The results indicate that the localization error remains below 5% within a 15 m × 15 m measurement area. This provides an efficient and real-time method for detecting the location of small UAVs.

Identification of power grids low-frequency oscillations through a combined MEEMD-Prony method

Currently, the primary focus of power systems is to enhance precision and resilience against interference in identifying low-frequency oscillation modes. This research proposes a new method combined with ensemble empirical mode decomposition (MEEMD) to improve the sensitivity of traditional Prony to noise in parameter analysis of low-frequency oscillation signals. The method decomposes the measurement signal into intrinsic mode functions (IMF) using MEEMD, introduces permutation entropy to detect randomness, and reconstructs the remaining IMF components. The reconstructed signal was analyzed using the Prony method to extract the characteristic parameters associated with the low-frequency oscillation frequency. Simulations using numerical signals and the EPRI-36 node system confirm the method effectively suppresses modal mixing, mitigates noise interference, and accurately identifies low-frequency oscillation parameters. This approach offers advantages over traditional methods, including enhanced resistance to noise and increased accuracy.

EXPLORING CEEMDAN DECOMPOSITION FOR IMPROVED FINANCIAL MARKET FORECASTING: A CASE STUDY ON DOW JONES INDEX

This study presents an innovative financial time series analysis approach by integrating Complete Ensemble Empirical Mode Decomposition (CEEMDAN) with the Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX) model. The primary contribution of the research lies in significantly enhancing the predictive accuracy and understanding of the dynamics governing major stock indices. CEEMDAN adaptively decomposes complex financial time series into intrinsic mode functions (IMFs), a technique that has yet to be extensively utilized in this domain. IMFs are combined with ARIMAX's predictive proficiency, which accounts for the influence of historical trends and external factors. Our study showcases an R² of 0,93, aligning with some of the high-performing models in the literature. However, the unique strength of our model lies in its lag-free predicting of the DJIA, effectively mirroring its volatility and major movements with high fidelity, making it highly practical for financial applications.

PM2.5 concentration forecasting: Development of integrated multivariate variational mode decomposition with kernel Ridge regression and weighted mean of vectors optimization

The accurate prediction of the PM2.5 air quality parameter within industrial and urban settings is the most pressing issue examined by the researchers because it has high health implications. However, accurately forecasting PM2.5 levels is crucial. The traditional machine learning (ML) models are incapable, as the indices fluctuate daily. To successfully manage this problem, a new ML framework is proposed that incorporates various techniques, such as LGBM feature selection (light gradient-boosting machine), MVMD (multivariate variational mode decomposition), KRidge (kernel Ridge regression), and INFO (weighted mean of vectors). The proposed framework is used to estimate PM2.5 pollution at specific stations in China for a one-time prediction. The LGBM feature selection technique is the first step of the pre-processing, which performs to select the most important variables. Next, the MVMD splits the initial signal into intrinsic mode functions (IMFs), accommodating the signal's non-stationary multivariate. Following that, the KRidge approach is applied to each sub-component using the best input feature, and the resulting predictions are summed up to get the PM2.5 levels. To assess the validity of the proposed MVMD-KRidge-INFO model, the categories of gaussian-process-regression (GPR), locally-weighted-linear-regression (LWLR), and multivariate adaptive regression splines (MARS) are analyzed in individual and hybrid moldes. As observed from the research results, MVMD-KRidge-INFO performs optimally at forecasting PM2.5 levels at Huairou and Shunyi, as evidenced by R, RMSE, MAPE, IA, MdAE, and U95% metrics.

Study of the River Discharge Alteration

This article aims to analyze the alteration in water discharge due to the building of one of the largest dams in Romania. Modifications in the hydrological patterns of the studied river were emphasized by a complex technique that includes decomposition models of the series into trends, seasonal indices, and random components, as well as into Intrinsic Mode Functions (IMFs). The Mann–Kendall trend test indicates the existence of different positive slopes for the subseries S1 and S2 (before and after the inception of the Siriu dam, respectively) built from the raw series, S. The stationarity hypothesis was rejected for all series. The multifractal analysis shows two different patterns of the data series. After decomposing the subseries S1 and S2, it resulted that the seasonality indices are not the same. Moreover, the seasonal variations decreased after building the dam. Empirical Mode Decomposition (EMD) unveils different short- and long-term patterns of the series before and after building the dam, concluding that there is a significant alteration in the river discharge after the dam’s inception.

Fault Diagnosis of Imbalance and Misalignment in Rotor-Bearing Systems Using Deep Learning

Abstract Rotor-bearing systems are important components of rotating machinery and transmission systems, and imbalance and misalignment are inevitable in such systems. At present, the main challenges faced by state-of-the-art fault diagnosis methods involve the extraction of fault features under strong background noise and the classification of different fault modes. In this paper, a fault diagnosis method based on an improved deep residual shrinkage network (IDRSN) is proposed with the aim of achieving end-to-end fault diagnosis of a rotor-bearing system. First, a method called wavelet threshold denoising and variational mode decomposition (WTD-VMD) is proposed, which can process original noisy signals into intrinsic mode functions (IMFs) with a salient feature. These one-dimensional IMFs are then transformed into two-dimensional images using a Gramian angular field (GAF) to give datasets for the deep residual shrinkage network (DRSN), which can achieve high levels of accuracy under strong background noise. Finally, a comprehensive test platform for a rotor-bearing system is built to verify the effectiveness of the proposed method in the field. The true test accuracy of the model at a 95% confidence interval is found to range from 84.09% to 86.51%. The proposed model exhibits good robustness when dealing with noisy samples and gives the best classification results for fault diagnosis under misalignment, with a test accuracy of 100%. It also achieves a higher testing accuracy compared to fault diagnosis methods based on convolutional neural networks and deep residual networks without improvement. In summary, IDRSN has significant value for deep learning engineering applications involving the fault diagnosis of rotor-bearing systems.

Remaining Useful Life Prediction of Lithium‐Ion Batteries Based on a Combination of Ensemble Empirical Mode Decomposition and Deep Belief Network–Long Short‐Term Memory

The prediction of remaining useful life (RUL) for lithium‐ion batteries is a critical component of electric vehicle battery management systems. However, during the aging process, batteries exhibit an overall declining trend in capacity curves, coupled with capacity regeneration and localized fluctuations. Directly modeling this degradation trend based on the original capacity curve proves challenging, leading to reduced accuracy in RUL prediction. This article introduces a hybrid method to enhance the precision of battery RUL prediction. Utilizing the ensemble empirical mode decomposition technique, the battery's capacity degradation sequence is decomposed into intrinsic mode functions (IMFs) with varying degrees of fluctuations, along with a residue that characterizes the battery's overall declining trend. Subsequently, deep belief networks and long short‐term memory networks are established to predict the residue and IMFs separately. The combined results from these models yield the final battery RUL prediction. Finally, the effectiveness of this approach is validated on the NASA battery dataset, with diverse training periods and prediction time steps. Experimental results demonstrate that the root mean square error of predictions for all four batteries remains below 2%.

A novel hybrid model based on modal decomposition and error correction for building energy consumption prediction

Accurate energy consumption prediction is pivotal in supporting efficient grid scheduling and enhancing renewable energy penetration. This paper proposes a novel hybrid prediction model called CEEMDAN-SE-EC-BiLSTM. The proposed model utilizes Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) to decompose the original energy consumption data into Intrinsic Mode Functions (IMFs). Afterwards, Sample Entropy (SE) is employed to evaluate the complexity of the IMFs. The complexed IMFs are then transformed into simpler IMFs using a second decomposition. All IMFs are predicted using Bidirectional Long Short-Term Memory (BiLSTM) to attain the initial predicted sequence. To further refine the prediction, an Error Correction (EC) technique is introduced. This involves subtracting the initial predicted sequence from the original sequence to obtain the error sequence, which is then decomposed using CEEMDAN. Subsequently, the decomposed error sequence is predicted using BiLSTM to generate the error prediction sequence. Finally, the predicted results and the error prediction are combined to obtain the final energy forecast sequence. To verify the superior performance of the proposed method, the model is tested on five selected buildings and benchmarked against seven prediction models. The experimental results indicate that the proposed hybrid prediction model achieves the highest accuracy in building energy prediction.

A multi-factor combination prediction model of carbon emissions based on improved CEEMDAN.

As the global greenhouse effect intensifies, carbon emissions are gradually becoming a hot topic of discussion. Accurate carbon emissions prediction is an important foundation to realize carbon neutrality and peak carbon dioxide emissions. To accurately predict carbon emissions, a multi-factor combination prediction model based on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), bidirectional long short-term memory optimized by lemurs optimizer (LOBiLSTM) and least squares support vector machine optimized by lemurs optimizer (LOLSSVM), named ICEEMDAN-LOBiLSTM-LOLSSVM, is proposed. Firstly, the influencing factors of carbon emissions are selected by Spearman correlation coefficient, and carbon emissions are decomposed into intrinsic mode functions (IMFs) by ICEEMDAN. Secondly, the influencing factors and IMFs are input into LOBiLSTM and LOLSSVM respectively for prediction. Then, the point prediction results are obtained by weighting the prediction results of LOBiLSTM and LOLSSVM. Finally, probability density function of point prediction error is calculated by kernel density estimation, and the interval prediction results are calculated according to different confidence intervals. Carbon emissions of China and Germany are selected to verify the superiority of ICEEMDAN-LOBiLSTM-LOLSSVM. The experiment shows that RMSE, MAE, MAPE, and R2 of the proposed model are 0.4468, 0.3612, 0.0120, and 0.9839 respectively for China, which is the best among the nine models, as well as for Germany.

Hidden Markov Models based intelligent health assessment and fault diagnosis of rolling element bearings.

Hidden Markov Models (HMMs) have become an immensely popular tool for health assessment and fault diagnosis of rolling element bearings. The advantages of an HMM include its simplicity, robustness, and interpretability, while the generalization capability of the model still needs to be enhanced. The Dempster-Shafer theory of evidence can be used to conduct a comprehensive evaluation, and Stacking provides a novel training strategy. Therefore, the HMM-based fusion method and ensemble learning method are proposed to increase the credibility of quantitative analysis and optimize classifiers respectively. Firstly, vibration signals captured from bearings are decomposed into intrinsic mode functions (IMFs) using ensemble empirical mode decomposition (EEMD), and then the Hilbert envelope spectra of main components are obtained; Secondly, multi-domain features are extracted as model input from preprocessed signals; Finally, HMM-based intelligent health assessment framework and fault diagnosis framework are established. In this work, the life cycle health assessment modeling is performed using a few training samples, the bearing degradation state is quantitatively evaluated, normal and abnormal samples are effectively distinguished, and the accuracy of fault diagnosis is significantly improved.

New theoretical insights in the decomposition and time-frequency representation of nonstationary signals: The IMFogram algorithm

The analysis of the time–frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative time–frequency representations of a signal each with its advantages and limitations. In this work, following the success of nonlinear methods for the decomposition of signals into intrinsic mode functions (IMFs), we first provide more theoretical insights into the so–called Iterative Filtering decomposition algorithm, proving an energy conservation result for the derived decompositions. Furthermore, we present a new time–frequency representation method based on the IMF decomposition of a signal, which is called IMFogram. We prove theoretical results regarding this method, including its convergence to the spectrogram representation for a certain class of signals, and we present a few examples of applications, comparing results with some of the most well-known approaches available in the literature.

A vibration signal processing method based on SE-PSO-VMD for ultrasonic machining

Ultrasonic Machining (USM) has broad applicability in numerous industrial fields. Accurate capture of ultrasonic vibration signals is pivotal to the functioning of USM, making them areas of significant research interest. However, the nonlinear and non-stationary nature of the USM vibration signal makes it unsuitable for analysis with conventional methods such as Fast Fourier Transform. Despite current methodologies like Discrete Wavelet Transformation (DWT) yielding valuable insights, they involve manual parameter selection and could lead to sub-optimal results. This paper presents a novel method, using Variational Mode Decomposition (VMD) to automatically decompose USM vibration signals into intrinsic mode functions (IMFs). This method is complemented by Particle Swarm Optimization (PSO) algorithm to optimize the number of IMFs and penalty factor, with Sample Entropy (SE) serving as a fitness function. The innovative SE-PSO-VMD method is validated in ultrasonic metal welding and demonstrates a notable ability in predicting the pull force of welding materials with a high coefficient of determination R2 value of 0.78.

Time-series prediction of settlement deformation in shallow buried tunnels based on EMD-SSA-GRNN model

Tunnel settlement deformation monitoring is a complex task and can result in nonlinear dynamic changes. To overcome the disturbances caused by historical data and the difficulty in selecting input parameters during deformation prediction, a decomposition, reconstruction and optimization method for tunnel settlement deformation prediction is proposed. First, empirical mode decomposition (EMD) is used to decompose the in-situ monitoring data and reduce the interactions among information at different scales in sequences. Then, the monitoring data are decomposed into intrinsic mode functions (IMFs). Secondly, the smoothing factor of the generalized regression neural network (GRNN) is optimized by using the sparse search algorithm (SSA). An EMD-SSA-GRNN deformation prediction model is developed using the optimized GRNN algorithm and is used to predict the changes in the decomposed IMFs. Finally, using the measured deformation data from a shallowly buried tunnel along the Kaizhou-Yunyang Highway in Chongqing, China, the reliability and accuracy of different models are analysed. The results show that tunnel settlement deformation exhibited a trend and a slow change in the early stage, a rapid change in the middle stage and a slow change in the late stage, and the rate of change was significantly influenced by the excavation time and the upper and lower geological layers. The prediction accuracy of the EMD-SSA-GRNN model after EMD improved from 19.2 to 59.4% relative to that of the SSA-GRNN and single GRNN models. Moreover, we find that the three error evaluation indicators of the EMD-SSA-GRNN model are lower than those of the other models and that the results of the proposed model and are more strongly correlated with measured data.

BILSTM-SimAM: An improved algorithm for short-term electric load forecasting based on multi-feature.

With the growing number of user-side resources connected to the distribution system, an occasional imbalance between the distribution side and the user side arises, making short-term power load forecasting technology crucial for addressing this issue. To strengthen the capability of load multi-feature extraction and improve the accuracy of electric load forecasting, we have constructed a novel BILSTM-SimAM network model. First, the entirely non-recursive Variational Mode Decomposition (VMD) signal processing technique is applied to decompose the raw data into Intrinsic Mode Functions (IMF) with significant regularity. This effectively reduces noise in the load sequence and preserves high-frequency data features, making the data more suitable for subsequent feature extraction. Second, a convolutional neural network (CNN) mode incorporates Dropout function to prevent model overfitting, this improves recognition accuracy and accelerates convergence. Finally, the model combines a Bidirectional Long Short-Term Memory (BILSTM) network with a simple parameter-free attention mechanism (SimAM). This combination allows for the extraction of multi-feature from the load data while emphasizing the feature information of key historical time points, further enhancing the model's prediction accuracy. The results indicate that the R2 of the BILSTM-SimAM algorithm model reaches 97.8%, surpassing mainstream models such as Transformer, MLP, and Prophet by 2.0%, 2.7%, and 3.6%, respectively. Additionally, the remaining error metrics also show a reduction, confirming the validity and feasibility of the method proposed.

A Multistep Prediction Model for the Vibration Trends of Hydroelectric Generator Units Based on Variational Mode Decomposition and Stochastic Configuration Networks.

Accurately predicting the changes in turbine vibration trends is a key part of the operational condition maintenance of hydropower units, which is of great significance for improving both the operational condition and operational efficiency of hydropower plants. In this paper, we propose a multistep prediction model for the vibration trend of a hydropower unit. This model is based on the theoretical principles of signal processing and machine learning, incorporating variational mode decomposition (VMD), stochastic configuration networks (SCNs), and the recursive strategy. Firstly, in view of the severe fluctuations of the vibration signal of the unit, this paper decomposes the unit vibration data into intrinsic mode function (IMF) components of different frequencies by VMD, which effectively alleviates the instability of the vibration trend. Secondly, an SCN model is used to predict different IMF components. Then, the predicted values of all the IMF components are superimposed to form the prediction results. Finally, according to the recursive strategy, a multistep prediction model of the HGU's vibration trends is constructed by adding new input variables to the prediction results. This model is applied to the prediction of vibration data from different components of a unit, and the experimental results show that the proposed multistep prediction model can accurately predict the vibration trend of the unit. The proposed multistep prediction model of the vibration trends of hydropower units is of great significance in guiding power plants to adjust their control strategies to reach optimal operating efficiency.

Short-term wave power forecasting with hybrid multivariate variational mode decomposition model integrated with cascaded feedforward neural networks

Wave power is an emerging renewable energy technology that has not reached its full potential. For wave power plants, a reliable forecast system is crucial to managing intermittency. We propose a novel robust short-term wave power (Pw) forecasting method, MVMD-CFNN, based on a multivariate variational mode decomposition hybridized with cascaded feedforward neural networks. By using cross-correlation, we were able to determine the significant input predictor lags. To overcome the non-linearity and non-stationarity issues, the proposed MVMD method is then used to demarcate the significant lags into intrinsic mode functions (IMFs). To forecast the short-term PW, the MVMD-CFNN model incorporated the IMFs into cascaded feedforward neural networks. Validation and benchmarking of the MVMD-CFNN model at two stations in Queensland, Australia has been conducted against standalone cascaded feedforward neural networks, boosted regression trees, extreme learning machines, and hybrid models, MVMD-BRT and MVMD-ELM. According to the results, the MVMD-CFNN predicts PW accurately against the benchmark models. The outcomes of this research can contribute to the application and implementation of clean energy worldwide for sustainable energy generation.

Multimodal coupling and HRV assessment characterize autonomic functional changes in congestive heart failure patients with sinus rhythm or severe arrhythmia

Autonomic nervous system (ANS) dysfunction is a significant characteristic of patients with congestive heart failure (CHF). Respiratory sinus arrhythmia (RSA) serves as an index of parasympathetic nervous system (PNS) function usually quantified by the high-frequency power of heart rate variability (HRV). However, the high breathing rate of CHF patients results in deviations when estimating RSA by HRV. Multimodal coupling analysis (MMCA) is a novel method of quantifying RSA which decomposes the R-R signal adaptively into intrinsic mode functions (IMFs) followed by identification of the RSA-related IMF. MMCA also calculates the phase synchronization between RSA-related IMF and respiratory signals to exclude the influences that are unrelated to RSA. In this study, we introduced HRV and MMCA-derived parameters to quantify ANS function for CHF patients, along with their comparisons in the clinical efficacy evaluation. Thirty-seven CHF patients were recruited, including 17 with sinus rhythm (SRHF) and 20 with severe arrhythmia (ARHF). Our results showed that all parameters for SRHF patients increased after treatment except for LF/HF. Only LF/HF, α2, and MMCA-derived RSA showed significant differences after treatment for ARHF patients, wherein the MMCA-derived RSA significantly decreased regardless of the left ventricular ejection fraction. The PNS function and ANS balance were recovered in all the CHF patients after treatment. Metrics including MeanRR, SDRR, LF, HF, TPower, SD1, SD2, and MMCA-derived RSA showed more significant improvements in SRHF patients whose New York Heart Association functional class improved after treatment. These metrics can be used to guide prognosis and therapeutic efficacy monitoring.

Hybrid Time-Series Prediction Method Based on Entropy Fusion Feature

High-precision time sequence forecasting is a complicated cyber-physical system (CPS) task. Due to the diversity of data scales and types, the classic time-series prediction model meets the challenge to deliver accurate prediction results for many forms of time-series data. This work proposes a hybrid model with long short-term memory (LSTM) and embedded empirical mode decomposition (EEMD) based on the entropy fusion feature. First, we apply EEMD in entropy fusion feature long short-term memory (ELSTM) to lessen pattern confusion and edge effects in traditional empirical mode decomposition (EMD). The sequence is then divided into intrinsic mode functions (IMF) by using EEMD. Then, feature vectors are constructed between IMFs and their respective information entropy for feature merging. LSTM is used to build a full connection network for each entropy fusion feature IMF subsequence for prediction and each type of IMF subsequence as the feature dimension to obtain its prediction results. Finally, the output results of all IMF subsequences are reconstructed to obtain the final prediction result. Compared with the LSTM method, the performance of the proposed method has been improved 64.33% on the evaluation metric MAPE. The proposed model has also delivered the best prediction outcomes across four different time-series datasets. The experimental results conclusively show that the proposed method outperforms other models compared.

Enhancing wind speed forecasting accuracy using a GWO-nested CEEMDAN-CNN-BiLSTM model

This study introduces an advanced artificial model, grey wolf optimization (GWO)-nested complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)-convolutional neural network (CNN)-bidirectional long short-term memory (BiLSTM), for wind speed forecasting. Initially, CEEMDAN with two nested layers decomposes the time series into intrinsic mode functions (IMFs) to enhance accuracy. Subsequently, CNN extracts features from IMFs, and BiLSTM captures temporal dependencies for precise predictions. GWO further enhances the model by selecting optimal hyperparameters based on decomposition results. Test results on diverse wind speed datasets demonstrate the model’s superiority, with a mean absolute percentage error (MAPE) of approximately 3%.