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Search Results (617)

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Keywords = Empirical Mode Decomposition (EMD)

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24 pages, 3072 KB  
Article
Design of an Integrated Online Testing System for Pressure-Core Characteristics Using an Improved EMD–Wavelet Denoising Algorithm
by Yingjie Liu, Liwen Nan, Qiaoling Gao, Jiawang Chen, Yuankun Chen, Qinghua Sheng, Lieyu Tian and Chenlu Xu
J. Mar. Sci. Eng. 2026, 14(11), 1011; https://doi.org/10.3390/jmse14111011 - 29 May 2026
Abstract
Natural gas hydrates are regarded as a vital strategic energy resource for the future owing to their high energy density and clean combustion characteristics. To facilitate research into the physical and mechanical properties of pressure-maintained hydrate samples, this paper presents an integrated multi-parameter [...] Read more.
Natural gas hydrates are regarded as a vital strategic energy resource for the future owing to their high energy density and clean combustion characteristics. To facilitate research into the physical and mechanical properties of pressure-maintained hydrate samples, this paper presents an integrated multi-parameter online analysis system capable of rapidly measuring the P-wave velocity, electrical resistivity, thermal conductivity, and shear strength of core samples under pressure-maintaining conditions. The system comprises hardware acquisition boards based on ZYNQ and ARM platforms, specialized measurement probes, and comprehensive data acquisition and analysis software. To mitigate the susceptibility of P-wave signals to noise interference, an improved denoising algorithm combining Empirical Mode Decomposition (EMD) and wavelet thresholding is proposed. By employing autocorrelation function analysis, the algorithm identifies the transition boundary between noise-dominated and signal-dominated Intrinsic Mode Functions (IMFs), subsequently applying wavelet soft-thresholding to the noise-dominant components. Experimental results demonstrate that the proposed algorithm achieves a superior signal-to-noise ratio (SNR) compared to traditional EMD methods, particularly under low SNR conditions. System validation indicates measurement accuracies of 3.2% for P-wave velocity at 20 °C, 1.76% for electrical resistivity at 25 °C, and within 7% for both thermal conductivity and shear strength. Furthermore, sea trials conducted aboard the “HAIYANG SHIYOU 708” drilling vessel confirm that the system operates stably and effectively fulfills the requirements for deep-sea core parameter characterization. Full article
(This article belongs to the Section Ocean Engineering)
22 pages, 1511 KB  
Article
Improving Ethereum Price Forecasting Through Hybrid Decomposition and LSTM–Attention Mechanisms
by Amina Ladhari and Heni Boubaker
J. Risk Financial Manag. 2026, 19(6), 377; https://doi.org/10.3390/jrfm19060377 - 24 May 2026
Viewed by 222
Abstract
This study investigates the predictive performance of decomposition-based deep learning models through a focused case study on Ethereum price forecasting. Using hourly Ethereum price data from 5 September 2020 to 13 July 2025, we develop hybrid forecasting frameworks that integrate three signal decomposition [...] Read more.
This study investigates the predictive performance of decomposition-based deep learning models through a focused case study on Ethereum price forecasting. Using hourly Ethereum price data from 5 September 2020 to 13 July 2025, we develop hybrid forecasting frameworks that integrate three signal decomposition techniques—Wavelet Decomposition (WD), Variational Mode Decomposition (VMD), and Empirical Mode Decomposition (EMD)—with a Long Short-Term Memory network enhanced by an attention mechanism (LSTM–Attention). The decomposition methods are first applied to extract multiple frequency components from the original time series, allowing the forecasting model to capture both short-term fluctuations and long-term dynamics inherent in this specific digital asset. Each decomposed component is then modeled using the LSTM–Attention architecture, and the forecasts are aggregated to produce the final prediction. The predictive performance of the proposed models is evaluated using MAE, MSE, RMSE, and MAPE, and the results are compared with benchmark models including ARIMA-GARCH and standard LSTM–Attention. Forecast accuracy is assessed through out-of-sample one-step-ahead predictions, and robustness is ensured by averaging results across 10 independent runs. The empirical results demonstrate that incorporating decomposition techniques substantially improves forecasting accuracy. Among the tested models, the EMD–LSTM–Attention framework achieves the best performance, producing the lowest forecasting errors. While focused on the Ethereum market, these findings highlight the effectiveness of combining signal decomposition and attention-based deep learning architectures to enhance predictive performance in high-volatility cryptocurrency environments. Full article
(This article belongs to the Special Issue Machine Learning, Economic Forecasting, and Financial Markets)
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33 pages, 6410 KB  
Article
Wavelet-Fourier Network Combined with Advanced Preprocessing Techniques for Univariate Daily Rainfall Prediction
by Md. Jobayer Parvez Ratul, Usmi Akter, Tajrian Mollick, Eshrat Jahan Mumu, Nondita Deb Nath, Syeda Wasifa Adila, Wafa Saleh Alkhuraiji, Padam Jee Omar and Mohamed Zhran
Water 2026, 18(11), 1264; https://doi.org/10.3390/w18111264 - 23 May 2026
Viewed by 263
Abstract
Rainfall prediction is essential for the enhanced understanding of several issues related to water resources and agriculture, such as flood and drought alerts and flood management. Neural network models are frequently used due to their capability of effectively handling large datasets and addressing [...] Read more.
Rainfall prediction is essential for the enhanced understanding of several issues related to water resources and agriculture, such as flood and drought alerts and flood management. Neural network models are frequently used due to their capability of effectively handling large datasets and addressing the non-stationarity of rainfall data series, resulting in better accuracy and affordable solutions. However, further study is necessary to comprehend the dynamic nature and extreme events of rainfall. Therefore, we implemented a novel wavelet Fourier-enhanced network (W-FENet) that included a Fourier enhancement module (FEMEX) and an improved U-Net mechanism to strengthen the predictive accuracy of daily rainfall. The adopted U-Net structure facilitated efficient multiscale feature extraction and preservation of temporal rainfall information through encoder–decoder connections and residual learning. The results of the developed models for one-day-ahead rainfall prediction were evaluated against two traditional neural network models, i.e., artificial neural networks and long short-term memory networks. Mongla, being a coastal station and having a highly non-linear rainfall pattern, operated by the Bangladesh Meteorological Department, was selected as the study area. Four preprocessing techniques were incorporated to enhance the robustness of the models: empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), variational mode decomposition (VMD), and successive variational mode decomposition (SVMD). The SVMD-enhanced W-FENet model (abbreviated as W5) demonstrated significant improvements over existing literature with RMSE = 2.226 mm, MAE = 1.131 mm, PCC = 0.988, NSE = 0.974, and WI = 0.993 at the testing phase. Full article
(This article belongs to the Special Issue Climate Change and Hydrological Processes, 3rd Edition)
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25 pages, 3450 KB  
Article
A Causal EWT-LSTM Framework for Anomaly Detection and Localized Reconstruction of Indoor Temperature Time Series in District Heating Buildings
by Enze Zhou, Minjia Du, Yaning Liu, Yan Wu and Wenxiao Xu
Buildings 2026, 16(11), 2072; https://doi.org/10.3390/buildings16112072 - 23 May 2026
Viewed by 144
Abstract
Indoor temperature time series in district-heating buildings are often contaminated by anomalies embedded in nonstationary, multiscale thermal dynamics. This study proposes a hybrid Empirical Wavelet Transform and Long Short-Term Memory (EWT-LSTM) framework for adaptive anomaly detection and localized reconstruction. Evaluated on 15 min [...] Read more.
Indoor temperature time series in district-heating buildings are often contaminated by anomalies embedded in nonstationary, multiscale thermal dynamics. This study proposes a hybrid Empirical Wavelet Transform and Long Short-Term Memory (EWT-LSTM) framework for adaptive anomaly detection and localized reconstruction. Evaluated on 15 min interval data from 45 residential units over a 112-day heating season, the framework operates via a highest-frequency branch for anomaly detection and a full-modal branch for signal repair. Quantitative results show that the EWT Highest-Frequency LSTM (EWT(HF)-LSTM) achieved the best anomaly discrimination among decomposition variants with an average F1-score of 0.531. For anomaly repair, the full EWT-LSTM produced the highest fidelity with a localized Root Mean Square Error (RMSEa) of 0.818 °C. Furthermore, thermal comfort validation demonstrated that EWT-LSTM successfully prevented the severe comfort degradation of up to −82% in Exceeded Degree-Hours caused by unstable Empirical Mode Decomposition (EMD)-based reconstructions. These concrete results confirm that the proposed framework effectively provides clean, physically coherent temperature data for downstream district heating operations. Full article
(This article belongs to the Section Building Energy, Physics, Environment, and Systems)
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31 pages, 2002 KB  
Article
Coordinated Optimal Configuration for Hybrid Energy Storage System Involving Differentiated Requirements from Supply-Side and Demand-Side in Microgrid
by Jiyuan Zhang, Yang Liu and Huaqiang Li
Energies 2026, 19(10), 2410; https://doi.org/10.3390/en19102410 - 17 May 2026
Viewed by 141
Abstract
To address the challenges of power fluctuations caused by the integration of distributed generation (DG) and the difficulty in simultaneously managing peak-valley load regulation due to diverse user energy demands in a microgrid system, this paper presents a coordinated optimal configuration method for [...] Read more.
To address the challenges of power fluctuations caused by the integration of distributed generation (DG) and the difficulty in simultaneously managing peak-valley load regulation due to diverse user energy demands in a microgrid system, this paper presents a coordinated optimal configuration method for serving a hybrid energy storage system (HESS), which explicitly considers the differentiated requirements from both the supply-side and the demand-side. In the presented method, an improved empirical mode decomposition (EMD) method is first presented to decompose the DG power into high-frequency, medium-frequency, and low-frequency bands. Based on the complementary technical and economic characteristics of different energy storage types, a coordinated regulation strategy for HESS in the multiple time-frequency domains is developed. Second, a coordinated optimal configuration model for HESS is further established. This model integrates key performance indicators, including maximum fluctuation and renewable energy utilization rate on the supply-side and the peak-valley difference reduction rate on the demand-side. Finally, a distributed optimization algorithm based on an improved alternating direction method of multipliers (ADMM) is developed to solve the coordinated configuration model. The experimental results demonstrate that the presented method can effectively smooth the DG power fluctuations and reduce the load peak-valley difference. The renewable energy utilization rate reaches 100%, and the peak-valley difference reduction rate reaches approximately 80%. The presented method successfully achieves the coordinated optimal configuration of HESS on both the supply and demand sides, providing a theoretical underlying infrastructure for the configuration of energy storage in the microgrid system with high penetration of renewable energy. Full article
(This article belongs to the Special Issue Optimization and Control of Smart Energy Systems)
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12 pages, 565 KB  
Article
An Integrative System Based on Signal Processing and Tuned Regression Gaussian Process by Grey Wolf Optimization Algorithm for Bitcoin Price Forecasting
by Salim Lahmiri and Stelios Bekiros
Mathematics 2026, 14(10), 1615; https://doi.org/10.3390/math14101615 - 9 May 2026
Viewed by 321
Abstract
We propose various hybrid predictive systems to forecast the Bitcoin next-day price. In particular, we combine the decomposition methods based on signal processing techniques including maximum overlap discrete wavelet transform (MODWT), empirical wavelet transform (EWT), empirical mode decomposition (EMD), and variational mode decomposition [...] Read more.
We propose various hybrid predictive systems to forecast the Bitcoin next-day price. In particular, we combine the decomposition methods based on signal processing techniques including maximum overlap discrete wavelet transform (MODWT), empirical wavelet transform (EWT), empirical mode decomposition (EMD), and variational mode decomposition (VMD) for feature extraction from original price series. Then, the extracted features are fed to the machine learning models for training and forecasting. We implemented five machine learning models, including regression Gaussian process (RGP), support vector regression (SVR), k-nearest neighbors algorithm (kNN), regression trees (RT), and feedforward neural networks (FFNN). The grey wolf optimization (GWO) algorithm is employed for hyperparameter optimization of the machine learning models. The root mean squared error (RMSE) is used for the evaluation and comparison of 20 hybrid predictive systems. The simulation results show that the RGP-GWO-VMD hybrid predictive system achieved the lowest forecasting error. In addition, RGP-GWO yielded on average the lowest forecasting error across all of the machine learning systems. Furthermore, among signal decomposition methods, the lowest forecasting error is generally achieved under the EWT. Hence, we presented the best results in forecasting Bitcoin prices from 20 hybrid prediction systems to serve as the baseline for future work and to guide traders, investors, and portfolio managers. Full article
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26 pages, 5171 KB  
Article
A Deep Forest and Histogram Feature Fusion Framework for sEMG-Based Hand Gesture Recognition with Enhanced Signal Representation
by Huibin Li, Xiaorong Guan, Sijing Wang and Zhihua Yuan
Electronics 2026, 15(9), 1935; https://doi.org/10.3390/electronics15091935 - 2 May 2026
Viewed by 349
Abstract
A novel hand gesture recognition framework based on surface electromyography (sEMG) is proposed for soldier operational scenarios under small-sample conditions. The framework integrates Empirical Mode Decomposition (EMD) for signal reconstruction, histogram-based features, and the Deep Forest (DF) classifier. Evaluations are conducted under two [...] Read more.
A novel hand gesture recognition framework based on surface electromyography (sEMG) is proposed for soldier operational scenarios under small-sample conditions. The framework integrates Empirical Mode Decomposition (EMD) for signal reconstruction, histogram-based features, and the Deep Forest (DF) classifier. Evaluations are conducted under two protocols: subject-wise evaluation and mixed-subject nested 8-fold cross-validation. Under subject-wise evaluation, the proposed EMD-HIST-DF method achieves 99.94% accuracy with 0.00027 ms per sample. Under mixed-subject nested 8-fold cross-validation, 98.41% accuracy is maintained with 0.00053 ms per sample. Ablation studies confirm the significant contribution of EMD-based signal enhancement in the mixed-subject setting (approximately 10.6 percentage points, p < 0.001). Parameter sensitivity analysis guides optimal parameter selection, and statistical tests confirm significant performance gains over baseline methods. Confusion matrices illustrate high per-class accuracy with minimal inter-class confusion. The framework shows potential as a promising solution for accurate, efficient, and sample-sparing gesture recognition in resource-constrained environments such as supernumerary robotic limb control. Full article
(This article belongs to the Section Circuit and Signal Processing)
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21 pages, 3651 KB  
Article
A Novel Mechanism Analysis Method for the Robotic Grinding of a TC4 Workpiece Using Acoustic Emission Based on an Improved CCEEMD Algorithm
by Xiangye Zhu, Qi Liu, Liang Liang, Xiaohu Xu and Sijie Yan
Machines 2026, 14(5), 501; https://doi.org/10.3390/machines14050501 - 30 Apr 2026
Viewed by 247
Abstract
The instantaneous contact zone in robotic abrasive belt grinding involves highly coupled thermo-mechanical interactions between abrasive grains and the workpiece material. Acoustic Emission (AE) signals generated during this process are inherently nonlinear and nonstationary, posing challenges for accurate process monitoring and mechanistic understanding. [...] Read more.
The instantaneous contact zone in robotic abrasive belt grinding involves highly coupled thermo-mechanical interactions between abrasive grains and the workpiece material. Acoustic Emission (AE) signals generated during this process are inherently nonlinear and nonstationary, posing challenges for accurate process monitoring and mechanistic understanding. To address this, this study introduces an innovative AE signal processing framework designed to elucidate the robotic grinding mechanism for Ti-6Al-4V (TC4) titanium alloy. An improved Completely Complementary Ensemble Empirical Mode Decomposition (CCEEMD) algorithm, building upon Empirical Mode Decomposition (EMD), is developed to precisely extract intrinsic mode functions (IMFs) from raw AE data. Subsequently, a novel denoising algorithm utilizing noise statistical characteristics effectively removes invalid noise from the robotic machining system. Validation through robotic grinding experiments on TC4 workpieces successfully established quantifiable relationships between extracted AE features and the underlying grinding mechanism. Significantly, implementing this methodology contributed to extending the effective service life of a structured abrasive belt by approximately 20% while increasing machining efficiency by approximately 12%. This work presents a novel methodology combining improved CCEEMD and statistical denoising for AE analysis in robotic grinding, providing a robust link between AE signatures and material removal mechanisms, ultimately enabling quantitative process optimization. Full article
(This article belongs to the Special Issue Intelligent Design and Manufacturing of Mechanical Equipment)
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23 pages, 4383 KB  
Article
Motion Characteristics and Defect Diagnosis of Metallic Particles in GIS/GIL
by Long He, Chen Cao, Yongming Zhu, Baojun Ma, Huan Lei and Yan Hu
Energies 2026, 19(9), 2138; https://doi.org/10.3390/en19092138 - 29 Apr 2026
Viewed by 399
Abstract
The operational reliability of gas-insulated switchgear/gas-insulated transmission lines (GIS/GIL) is critically threatened by internal metallic particles, which serve as primary triggers for insulation degradation. Conventional partial discharge (PD) detection methods often lack sensitivity during the early stages of particle movement. To overcome these [...] Read more.
The operational reliability of gas-insulated switchgear/gas-insulated transmission lines (GIS/GIL) is critically threatened by internal metallic particles, which serve as primary triggers for insulation degradation. Conventional partial discharge (PD) detection methods often lack sensitivity during the early stages of particle movement. To overcome these limitations, this study aims to develop a novel non-intrusive defect diagnosis methodology based on the analysis of mechanical vibration signals. The coupled particle motion model integrating the electrostatic field, particle tracking, and multibody dynamics has been established. This model reveals the dynamic law that metallic particles migrate toward the conductor and undergo charge polarity reversal after collision, with a maximum speed of 2.7 m/s. Meanwhile, the peak vibration acceleration excited by the collision is calculated as 0.02 m/s2. Accordingly, the high-voltage experimental platform with the full-scale prototype is built to simulate the actual operating conditions of the power grid. With the particle defects set inside the prototype, vibration signals are collected by using an accelerometer, and the measured peak vibration acceleration is 0.017 m/s2. Finally, a defect diagnosis method based on the Hilbert–Huang Transform (HHT) and correlation coefficient analysis is proposed. This method uses Empirical Mode Decomposition (EMD) to extract the IMF4 component of the signal in the vicinity of the 1000 Hz frequency band. When particle defects occur, the correlation coefficient between the IMF4 component and the original signal exceeds 0.7668. This vibration-based monitoring technique provides an alternative for the condition-based maintenance of GIS/GIL, offering significant engineering value for enhancing the safety and reliability of power transmission infrastructure. Full article
(This article belongs to the Special Issue Advanced Control and Monitoring of High Voltage Power Systems)
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24 pages, 1530 KB  
Article
SS-RIME: A Scale-Stabilized Approach to EEG Cognitive Workload Classification
by Kais Khaldi, Afrah Alanazi, Inam Alanazi, Sahar Almenwer and Anis Mohamed
Sensors 2026, 26(9), 2679; https://doi.org/10.3390/s26092679 - 25 Apr 2026
Viewed by 839
Abstract
Accurate and interpretable assessment of cognitive workload from EEG remains a central challenge in neuroergonomics and real-time human–machine interaction. To address the limitations of existing Empirical Mode Decomposition (EMD) and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) approaches, particularly their instability, [...] Read more.
Accurate and interpretable assessment of cognitive workload from EEG remains a central challenge in neuroergonomics and real-time human–machine interaction. To address the limitations of existing Empirical Mode Decomposition (EMD) and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) approaches, particularly their instability, limited neuroscientific grounding, and sensitivity to amplitude fluctuations, this paper introduces Scale-Stabilized Relative Intrinsic Mode Energy (SS-RIME), a theoretically motivated and physiologically informed feature extraction framework. SS-RIME integrates instantaneous frequency stabilization to enforce a consistent oscillatory hierarchy across subjects, delta (1–4 Hz) and theta (4–7.5 Hz) spectral weighting based on established frontal-midline activity, and cross-IMF energy normalization to reduce amplitude-driven variability. Applied to 64-channel EEG recorded during N-back tasks, the proposed framework achieved high performance, outperforming both classical machine-learning baselines and deep learning models such as EEGNet, DeepConvNet, and ShallowConvNet. SS-RIME yielded accuracies of 99.12±0.41% (0 vs. 2-back), 97.84±0.63% (0 vs. 3-back), and 92.31±1.12% (2 vs. 3-back), demonstrating strong cross-subject generalization. Theta-dominant IMFs over frontal midline regions emerged as the most discriminative components, supporting the neuroscientific validity of the stabilized and spectrally weighted Hilbert–Huang representation. With an inference time below 20 ms per epoch, SS-RIME is computationally efficient and suitable for real-time neuroergonomics applications, providing a robust, explainable, and physiologically grounded solution for EEG-based cognitive workload decoding while addressing key methodological gaps in prior EMD/CEEMDAN and deep learning approaches. Full article
(This article belongs to the Section Intelligent Sensors)
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19 pages, 6501 KB  
Article
Study on Near-Field Spectral Characteristics and Vibration Control of Multi-Hole Blasting Based on VMD
by Dasong Zhang, Hongyan Xu, Hui Chen, Jinggang Zhang, Sifan Wei, Yuanxiang Mu and Fei Gao
Appl. Sci. 2026, 16(8), 3665; https://doi.org/10.3390/app16083665 - 9 Apr 2026
Viewed by 338
Abstract
To explore the spectral characteristics of near-field vibration signals from multi-hole millisecond-delay blasting in open-pit mines and the modulation effect of delay time on blasting energy distribution, field blasting vibration tests with multi-gradient delays were conducted taking an open-pit coal mine in Xinjiang [...] Read more.
To explore the spectral characteristics of near-field vibration signals from multi-hole millisecond-delay blasting in open-pit mines and the modulation effect of delay time on blasting energy distribution, field blasting vibration tests with multi-gradient delays were conducted taking an open-pit coal mine in Xinjiang as the engineering background. Particle Swarm Optimization (PSO) optimized Variational Mode Decomposition (VMD) and Hilbert-Huang Transform (HHT) were introduced for the refined processing and frequency band energy ratio analysis of the measured signals, and field vibration control tests were subsequently carried out. The results show that compared with the traditional Empirical Mode Decomposition (EMD), the PSO-optimized VMD can effectively overcome the mode aliasing phenomenon. By extracting the high-frequency Intrinsic Mode Function (IMF7) that characterizes the instantaneous detonation impulse, the actual delay time was successfully inverted to be 10.47 ms. The inter-hole delay time significantly affects the time-frequency distribution of vibration energy. Under the 25 ms delay condition, the energy ratio of the high-frequency band is the highest, and the low-frequency energy accumulation degree is the lowest, which is most conducive to shortening the vibration duration and accelerating energy attenuation. Control tests further confirmed that adopting a 17 ms delay in the near-slope area can effectively control the peak particle velocity (PPV) in the near field, while adopting a 23 ms delay in the middle and far areas can further reduce the low-frequency energy concentration. The research results demonstrate a dynamic matching strategy for millisecond delays based on spatial distance differences, which has important guiding significance for realizing safe and efficient blasting vibration control in open-pit mines. Full article
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23 pages, 557 KB  
Article
A Multi-Stage Decomposition and Hybrid Statistical Framework for Time Series Forecasting
by Swera Zeb Abbasi, Mahmoud M. Abdelwahab, Imam Hussain, Moiz Qureshi, Moeeba Rind, Paulo Canas Rodrigues, Ijaz Hussain and Mohamed A. Abdelkawy
Axioms 2026, 15(4), 273; https://doi.org/10.3390/axioms15040273 - 9 Apr 2026
Viewed by 613
Abstract
Modeling and forecasting nonstationary and nonlinear economic time series remain fundamentally challenging due to structural breaks, volatility clustering, and noise contamination that distort the intrinsic stochastic structure. To address these limitations, this study proposes a novel three-stage hybrid statistical framework that systematically integrates [...] Read more.
Modeling and forecasting nonstationary and nonlinear economic time series remain fundamentally challenging due to structural breaks, volatility clustering, and noise contamination that distort the intrinsic stochastic structure. To address these limitations, this study proposes a novel three-stage hybrid statistical framework that systematically integrates multi-level signal decomposition with structured parametric modeling to enhance predictive accuracy. The proposed hybrid architectures—EMD–EEMD–ARIMA, EMD–EEMD–GMDH, and EMD–EEMD–ETS—employ a hierarchical decomposition–reconstruction strategy before forecasting. In the first stage, Empirical Mode Decomposition (EMD) decomposes the observed series into intrinsic mode functions (IMFs) and a residual component. In the second stage, Ensemble Empirical Mode Decomposition (EEMD) is applied to further refine the extracted components, mitigating mode mixing and improving signal separability. In the final stage, each reconstructed component is modeled using ARIMA, Exponential Smoothing State Space (ETS), and Group Method of Data Handling (GMDH) frameworks, and the individual forecasts are aggregated to obtain the final prediction. Empirical evaluation based on a recursive one-step-ahead forecasting scheme demonstrates consistent numerical improvements across all standard accuracy measures. In particular, the proposed EMD–EEMD–ARIMA model achieves the lowest forecasting error, reducing the root-mean-square error (RMSE) by approximately 6–7% relative to the best-performing single-stage model and by about 3–4% relative to the two-stage EMD-based hybrids. Similar improvements are observed in mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), indicating enhanced stability and robustness of the three-stage architecture. The results provide strong numerical evidence that multi-level decomposition combined with structured statistical modeling yields superior predictive performance for complex nonlinear and nonstationary time series. The proposed framework offers a mathematically coherent, computationally tractable, and systematically structured hybrid modeling strategy that effectively integrates noise-assisted decomposition with parametric and data-driven forecasting techniques. Full article
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26 pages, 2531 KB  
Article
Underwater Acoustic Source DOA Estimation for Non-Uniform Circular Arrays Based on EMD and PWLS Correction
by Chuang Han, Boyuan Zheng and Tao Shen
Symmetry 2026, 18(4), 627; https://doi.org/10.3390/sym18040627 - 9 Apr 2026
Viewed by 440
Abstract
Uniform circular arrays (UCAs) are widely used in underwater source localization due to their omnidirectional coverage. However, random sensor position errors caused by installation inaccuracies and environmental disturbances convert UCAs into non-uniform circular arrays (NCAs), severely degrading the performance of high-resolution direction of [...] Read more.
Uniform circular arrays (UCAs) are widely used in underwater source localization due to their omnidirectional coverage. However, random sensor position errors caused by installation inaccuracies and environmental disturbances convert UCAs into non-uniform circular arrays (NCAs), severely degrading the performance of high-resolution direction of arrival (DOA) estimation algorithms. To address this issue, this paper proposes a robust DOA estimation method that integrates empirical mode decomposition (EMD) denoising with prior-weighted iterative least squares (PWLS) correction. The method first applies EMD to adaptively denoise received signals by selecting intrinsic mode functions based on a combined energy-correlation criterion. An initial DOA estimate is then obtained using the MUSIC algorithm. Finally, a PWLS correction algorithm leverages prior knowledge of deviated sensors to iteratively fit the circle center and gradually pull sensor positions toward the ideal circumference, using a differentiated relaxation mechanism to suppress outliers while preserving geometric features. Systematic Monte Carlo simulations compare five correction algorithms under multi-frequency and wideband signals. The results show that both multi-frequency and wideband signals reduce estimation errors to below 0.1°, with the proposed PWLS achieving the best accuracy under multi-frequency signals, while all algorithms approach zero error under wideband signals. The PWLS algorithm converges in about 10 iterations with high computational efficiency, providing a reliable solution for practical underwater NCA applications. Full article
(This article belongs to the Section Engineering and Materials)
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26 pages, 2184 KB  
Article
Performance Analysis of Advanced Feature Extraction Methods for Manufacturing Defect Detection via Vibration Sensors in CNC Milling Machines
by Gürkan Bilgin
Sensors 2026, 26(7), 2195; https://doi.org/10.3390/s26072195 - 2 Apr 2026
Viewed by 732
Abstract
This study investigates the effectiveness of various feature extraction methods applied to vibration signals for the automatic detection of production defects in CNC (Computerised Numerical Control) milling machines. A dataset consisting of real-world data collected from CNC machines equipped with accelerometers was used. [...] Read more.
This study investigates the effectiveness of various feature extraction methods applied to vibration signals for the automatic detection of production defects in CNC (Computerised Numerical Control) milling machines. A dataset consisting of real-world data collected from CNC machines equipped with accelerometers was used. The objective of the study is to compare three main groups of techniques: time-domain analysis (TDA), frequency-domain analysis (FDA), and time–frequency-domain analysis (TFA). The findings indicate that basic TDA features lack the necessary sensitivity to accurately distinguish between Good Processing (GP) and Bad Processing (BP) states. Frequency-domain methods, such as the Fast Fourier Transform (FFT), median frequency calculation, and the Welch periodogram, provide better insights but still have limitations. The most effective results are obtained with TFA methods, particularly Empirical Mode Decomposition (EMD) and the Hilbert–Huang Transform (HHT), which reveal deeper signal characteristics. Following the feature optimisation studies, it was determined that a combination of four features—FMED, IMF2, IMF5 and WPT26—yielded the optimal performance, with an accuracy of 91.48%. The incorporation of a fifth feature resulted in information saturation within the model and did not improve performance. This study makes a novel contribution to literature by conducting an in-depth investigation into the most effective feature extraction and selection techniques for achieving robust discrimination between GP and BP productions using vibration signals in CNC milling processes. Conclusively, TFA features, supported by advanced signal processing, offer a strong basis for reliable, automated defect detection in CNC milling operations. Full article
(This article belongs to the Special Issue Sensor-Based Fault Diagnosis and Prognosis)
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22 pages, 5107 KB  
Article
Adaptive Filtering Method for Low-SNR Rock Mass Fracture Microseismic Signals in Deep-Buried Tunnels Considering Noise Intrusion Characteristics
by Tao Lin, Weiwei Tao, Yakang Xu and Wenjing Niu
Geosciences 2026, 16(4), 143; https://doi.org/10.3390/geosciences16040143 - 1 Apr 2026
Viewed by 411
Abstract
Aiming at the problems of microseismic signals from rock mass fracture in deep-buried tunnels with low signal-to-noise ratio (SNR) suffering from coupled interference of multi-source noise, and traditional filtering methods having fixed parameters and poor processing effects on spectral aliasing, this study proposes [...] Read more.
Aiming at the problems of microseismic signals from rock mass fracture in deep-buried tunnels with low signal-to-noise ratio (SNR) suffering from coupled interference of multi-source noise, and traditional filtering methods having fixed parameters and poor processing effects on spectral aliasing, this study proposes a ternary coupled adaptive filtering method integrating the Sparrow Search Algorithm, Variational Mode Decomposition and Wavelet Threshold Denoising (SSA-VMD-DWT). First, the noise intrusion characteristics of low-SNR microseismic signals in deep-buried tunnels were analyzed, and the filtering difficulties of white noise, low-frequency noise, high-frequency noise and non-stationary noise were clarified. Subsequently, a parameter optimization framework with the Sparrow Search Algorithm (SSA) as the core was constructed to optimize the key parameters, including the penalty factor α and modal number K of Variational Mode Decomposition (VMD), as well as the wavelet basis and decomposition layers of Wavelet Threshold Denoising (DWT), respectively. A dual-index threshold decision function based on kurtosis and correlation coefficient, and a wavelet packet entropy weighted reconstruction algorithm were designed to realize the collaborative adaptive adjustment of decomposition depth and threshold rules. Finally, the performance of the algorithm was verified through simulation signal experiments and an engineering case of a deep-buried tunnel in Southwest China. The results show that for the simulated signal with a low SNR of 2 dB, the SNR is increased to 12.43 dB, and the root mean square error is reduced to 2.36 × 10−7 after denoising by this algorithm, which is significantly superior to the Empirical Mode Decomposition (EMD) and traditional DWT methods. In the engineering case, the information entropy of the filtered signal is the lowest among all methods, which can effectively suppress multi-band noise and retain the core characteristics of microseismic signals from rock mass fracture, solving the problems of spectral aliasing, detail loss and empirical parameter setting of traditional methods. This method provides a new technical paradigm for the processing of low-quality microseismic signals in deep tunnel engineering and can improve the accuracy of monitoring and early warning for rock mass dynamic disasters. Full article
(This article belongs to the Special Issue New Trends in Numerical Methods in Rock Mechanics)
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