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Search Results (485)

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Keywords = Frequency Domain Decomposition

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19 pages, 6992 KB  
Article
A Fault Identification Method for Micro-Motors Using an Optimized CNN-Based JMD-GRM Approach
by Yufang Bai, Zhengyang Gu, Junsong Yu and Junli Chen
Micromachines 2026, 17(1), 123; https://doi.org/10.3390/mi17010123 - 19 Jan 2026
Abstract
Micro-motors are widely used in industrial applications, which require effective fault diagnosis to maintain safe equipment operation. However, fault signals from micro-motors often exhibit weak signal strength and ambiguous features. To address these challenges, this study proposes a novel fault diagnosis method. Initially, [...] Read more.
Micro-motors are widely used in industrial applications, which require effective fault diagnosis to maintain safe equipment operation. However, fault signals from micro-motors often exhibit weak signal strength and ambiguous features. To address these challenges, this study proposes a novel fault diagnosis method. Initially, the Jump plus AM-FM Mode Decomposition (JMD) technique was utilized to decompose the measured signals into amplitude-modulated–frequency-modulated (AM-FM) oscillation components and discontinuous (jump) components. The proposed process extracts valuable fault features and integrates them into a new time-domain signal, while also suppressing modal aliasing. Subsequently, a novel Global Relationship Matrix (GRM) is employed to transform one-dimensional signals into two-dimensional images, thereby enhancing the representation of fault features. These images are then input into an Optimized Convolutional Neural Network (OCNN) with an AdamW optimizer, which effectively reduces overfitting during training. Experimental results demonstrate that the proposed method achieves an average diagnostic accuracy rate of 99.0476% for multiple fault types, outperforming four comparative methods. This approach offers a reliable solution for quality inspection of micro-motors in a manufacturing environment. Full article
(This article belongs to the Section E:Engineering and Technology)
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29 pages, 7220 KB  
Article
Investigation into Response Characteristics and Fault Diagnosis Methods for Intermittent Faults in High-Density Integrated Circuits Induced by Bonding Wires
by Wenxiang Yang, Yong Zhang, Xianzhe Cheng, Xinyu Luo, Guanjun Liu, Jing Qiu and Kehong Lyu
Appl. Sci. 2026, 16(2), 949; https://doi.org/10.3390/app16020949 - 16 Jan 2026
Viewed by 144
Abstract
Focusing on the challenges posed by the strong randomness, weak manifestation, and difficulty in diagnosing intermittent faults (IFs) in high-density integrated circuits (HDICs)—often induced by bonding wire defects—this paper takes the GPIO interfaces of a typical DSP chip as the research object. It [...] Read more.
Focusing on the challenges posed by the strong randomness, weak manifestation, and difficulty in diagnosing intermittent faults (IFs) in high-density integrated circuits (HDICs)—often induced by bonding wire defects—this paper takes the GPIO interfaces of a typical DSP chip as the research object. It systematically analyzes the response characteristics of intermittent short-circuit and open-circuit faults and proposes a hybrid intelligent diagnosis method based on the Sparrow Search Algorithm-optimized Variational Mode Decomposition and Attention-based Support Vector Machine (SSA–VMD–Attention–SVM). A dedicated fault injection circuit is designed to accurately replicate IFs and acquire the power supply current response signals. The Sparrow Search Algorithm (SSA) is employed to adaptively optimize the parameters of Variational Mode Decomposition (VMD) for effective extraction of frequency-domain features from fault signals. A three-level attention mechanism is introduced to adaptively weight multi-domain features, thereby highlighting the key fault components. Finally, the Support Vector Machine (SVM) is utilized to achieve high-precision fault classification under small-sample conditions. Experimental results demonstrate that the proposed method achieves a diagnostic accuracy of 97.78% for intermittent short-circuit and open-circuit faults in the GPIO interfaces of the DSP chip, significantly outperforming traditional methods and exhibiting notable advantages in terms of diagnostic accuracy, robustness, and interpretability. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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32 pages, 51773 KB  
Article
SAR Radio Frequency Interference Suppression Based on Kurtosis-Guided Attention Network
by Jiajun Wu, Jiayuan Shen, Bing Han, Di Yin and Jiaxin Wan
Remote Sens. 2026, 18(2), 255; https://doi.org/10.3390/rs18020255 - 13 Jan 2026
Viewed by 120
Abstract
Radio-frequency interference (RFI) severely degrades the imaging quality of synthetic aperture radar (SAR), especially when the interference energy is strongly coupled with ground backscatter in both the time and frequency domains. Existing algorithms typically rely on energy contrast or component decomposition in transform [...] Read more.
Radio-frequency interference (RFI) severely degrades the imaging quality of synthetic aperture radar (SAR), especially when the interference energy is strongly coupled with ground backscatter in both the time and frequency domains. Existing algorithms typically rely on energy contrast or component decomposition in transform domains, which limits their ability to cleanly separate complex RFI from high-power echoes. Exploiting the fact that kurtosis is insensitive to ground clutter and background noise, this paper proposes an interference suppression network based on the temporal kurtosis guidance mechanism. Specifically, a statistical prior vector capturing the non-Gaussian characteristics of RFI is constructed using kurtosis in the time–frequency domain and is integrated into a multi-scale attention mechanism, allowing the network to more effectively concentrate on interfered regions. Meanwhile, a systematic framework is established for the quantitative assessment of phase fidelity in the reconstruction of complex-valued SAR echoes. On this basis, by exploiting the strong generalization capability and high processing efficiency of data-driven models, the proposed network achieves improved RFI separation and enhanced reconstruction accuracy of underlying scene features. Ablation experiments validated that the design of a kurtosis-guided module can reduce the mean square error (MSE) loss by 14.87% compared to the basic model. Furthermore, regarding the phase fidelity, the correlation coefficient between the suppressed signal and the original true signal reached 0.99. Finally, GF-3 satellite data are used to further demonstrate the effectiveness and practicality of the proposed method. Full article
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21 pages, 23946 KB  
Article
Infrared Image Denoising Algorithm Based on Wavelet Transform and Self-Attention Mechanism
by Hongmei Li, Yang Zhang, Luxia Yang and Hongrui Zhang
Sensors 2026, 26(2), 523; https://doi.org/10.3390/s26020523 - 13 Jan 2026
Viewed by 117
Abstract
Infrared images are often degraded by complex noise due to hardware and environmental factors, posing challenges for subsequent processing and target detection. To overcome the shortcomings of existing denoising methods in balancing noise removal and detail preservation, this paper proposes a Wavelet Transform [...] Read more.
Infrared images are often degraded by complex noise due to hardware and environmental factors, posing challenges for subsequent processing and target detection. To overcome the shortcomings of existing denoising methods in balancing noise removal and detail preservation, this paper proposes a Wavelet Transform Enhanced Infrared Denoising Model (WTEIDM). Firstly, a Wavelet Transform Self-Attention (WTSA) is designed, which combines the frequency-domain decomposition ability of the discrete wavelet transform (DWT) with the dynamic weighting mechanism of self-attention to achieve effective separation of noise and detail. Secondly, a Multi-Scale Gated Linear Unit (MSGLU) is devised to improve the ability to capture detail information and dynamically control features through dual-branch multi-scale depth-wise convolution and gating strategy. Finally, a Parallel Hybrid Attention Module (PHAM) is proposed to enhance cross-dimensional feature fusion effect through the parallel cross-interaction of spatial and channel attention. Extensive experiments are conducted on five infrared datasets under different noise levels (σ = 15, 25, and 50). The results demonstrate that the proposed WTEIDM outperforms several state-of-the-art denoising algorithms on both PSNR and SSIM metrics, confirming its superior generalization capability and robustness. Full article
(This article belongs to the Section Sensing and Imaging)
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19 pages, 3110 KB  
Article
Multi-Scale Decomposition and Autocorrelation Modeling for Classical and Machine Learning-Based Time Series Forecasting
by Khawla Al-Saeedi, Andrew Fish, Diwei Zhou, Katerina Tsakiri and Antonios Marsellos
Mathematics 2026, 14(2), 283; https://doi.org/10.3390/math14020283 - 13 Jan 2026
Viewed by 122
Abstract
Environmental time series, such as near-surface air temperature, exhibit strong multi-scale structure and persistent autocorrelation. Accurate forecasting therefore requires careful consideration of both temporal scale separation and serial dependence. In this study, we evaluate a unified framework that integrates Kolmogorov–Zurbenko (KZ) filtering with [...] Read more.
Environmental time series, such as near-surface air temperature, exhibit strong multi-scale structure and persistent autocorrelation. Accurate forecasting therefore requires careful consideration of both temporal scale separation and serial dependence. In this study, we evaluate a unified framework that integrates Kolmogorov–Zurbenko (KZ) filtering with two classes of models: (i) classical regression with Cochrane–Orcutt autocorrelation correction, and (ii) an autocorrelation-adjusted Long Short-Term Memory (LSTM) network that learns an embedded correlation coefficient (ρ). All models are assessed using standardized meteorological predictors of T2M under walk-forward validation. The LSTM trained on raw predictors shows moderate performance (RMSE = 0.73, R2=0.46, DW = 0.79), which improves after KZ filtering (RMSE = 0.59, R2=0.63, DW = 1.84). Classical regression applied to KZ-decomposed predictors and corrected using the Cochrane–Orcutt procedure achieves substantially higher accuracy (RMSE = 0.41, R2=0.89, DW 2.0), outperforming the LSTM in both predictive precision and residual behavior. Visual diagnostics further confirm tighter predicted–actual alignment and near-white residuals in the classical models, whereas the LSTM retains small systematic deviations even after filtering. Overall, the results demonstrate that addressing multi-scale structures and autocorrelation had a greater impact than increasing model complexity. Integrating spectral decomposition with autocorrelation correction thus produces more reliable, statistically valid forecasts, demonstrating that classical regression with KZ filtering can surpass LSTM models in both accuracy and interpretability. These findings emphasize the value of combining time series–aware pre-processing with both traditional and neural network approaches for environmental prediction. Full article
(This article belongs to the Section D1: Probability and Statistics)
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20 pages, 1581 KB  
Article
Multi-Feature Identification of Transformer Inrush Current Based on Adaptive Variational Mode Decomposition
by Pan Duan, Linchuan Yang and Hexing Zhang
Energies 2026, 19(2), 364; https://doi.org/10.3390/en19020364 - 12 Jan 2026
Viewed by 160
Abstract
To address the problem that transformer inrush currents under no-load and energization conditions can easily trigger misoperations of differential protection, this paper proposes a multi-feature identification method for transformer inrush current based on adaptive variational mode decomposition. Traditional methods typically rely on fixed [...] Read more.
To address the problem that transformer inrush currents under no-load and energization conditions can easily trigger misoperations of differential protection, this paper proposes a multi-feature identification method for transformer inrush current based on adaptive variational mode decomposition. Traditional methods typically rely on fixed physical features or single criteria, making them sensitive to operating condition variations and prone to misclassification or missed detection under complex disturbances, with limited generalization capability. The proposed method first performs adaptive VMD decomposition of current waveforms under different operating conditions. On this basis, time-domain, frequency-domain, and nonlinear features are extracted to comprehensively characterize the signal’s amplitude, spectral, and complexity information. Then, by combining the ReliefF algorithm with forward stepwise feature selection, the method reduces feature dimensionality while maintaining high discriminative power and low redundancy. Using the VMD-ReliefF-EEFO-SVM classification model, the approach achieves efficient and accurate discrimination between inrush currents and fault currents. Simulation results demonstrate that the proposed identification method adapts well to various operating conditions and exhibits strong robustness and versatility. Full article
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14 pages, 2392 KB  
Article
Anti-Interference Compensation of Grating Moiré Fringe Signals via Parameter Adaptive Optimized VMD Based on MSPSO
by Gang Wu, Ruihao Wei, Shuo Wang, Xiaoqiao Mu, Jing Wang, Guangwei Sun and Yusong Mu
Electronics 2026, 15(2), 258; https://doi.org/10.3390/electronics15020258 - 6 Jan 2026
Viewed by 123
Abstract
This paper proposes a grating Moiré fringe signal compensation method based on Variational Mode Decomposition (VMD) to address signal errors in grating encoders. VMD decomposes Moiré fringe signals into multiple amplitude-modulated and frequency-modulated components, and realizes noise compensation through parameter optimization and signal [...] Read more.
This paper proposes a grating Moiré fringe signal compensation method based on Variational Mode Decomposition (VMD) to address signal errors in grating encoders. VMD decomposes Moiré fringe signals into multiple amplitude-modulated and frequency-modulated components, and realizes noise compensation through parameter optimization and signal reconstruction. The Multi-Strategy Particle Swarm Optimization (MSPSO) enhances optimization performance via adaptive inertia weight adjustment and chaotic perturbation, solving the problems of mode mixing or over-decomposition caused by blind parameter selection in traditional VMD. A hardware-software co-design test system based on ZYNQ FPGA is developed, which optimally allocates tasks between the Processing System and Programmable Logic, resolving issues of large data volume and long computation time in traditional systems. The compensation scheme provides excellent signal processing performance. The experimental tests on random periodic signals, triangular waves and square waves with different duty cycles have demonstrated the robustness of this scheme. After compensation, the output signal exhibits excellent sinuosity and orthogonality, with harmonic components and noise in the frequency domain almost negligible. It provides a practical solution for high-precision measurement in ultra-precision machining, semiconductor manufacturing, and automated control. Full article
(This article belongs to the Section Circuit and Signal Processing)
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22 pages, 1478 KB  
Article
A Novel Multi-Scale and Adaptive Multi-Period Deep Learning with Compression-Fusion Attention for Cold Storage Load Prediction
by Hao Cai, Yi Zhang, Jinhong Zhang, Jie Chen, Jiafu Liu and Jingxuan Xu
Electronics 2026, 15(1), 160; https://doi.org/10.3390/electronics15010160 - 29 Dec 2025
Viewed by 159
Abstract
Accurate load forecasting is essential for energy-efficient scheduling in cold storage facilities, where cooling demand is shaped by strong periodicity, nonlinear temporal dynamics, and irregular operational disturbances. Traditional statistical and machine-learning models struggle with these multi-scale variations, and existing deep learning approaches often [...] Read more.
Accurate load forecasting is essential for energy-efficient scheduling in cold storage facilities, where cooling demand is shaped by strong periodicity, nonlinear temporal dynamics, and irregular operational disturbances. Traditional statistical and machine-learning models struggle with these multi-scale variations, and existing deep learning approaches often rely on fixed receptive fields or fail to extract adaptive periodic structures. This study introduces MA-CFAN, a multi-scale and adaptive multi-period forecasting framework that integrates temporal decomposition, dynamic frequency-period identification, and a newly designed Compression-Fusion Attention Block (CFABlock) for cross-period representation learning. The architecture leverages FFT-derived adaptive periods to capture seasonal-trend components and employs compression-fusion attention to enhance feature discrimination across temporal scales. Furthermore, this work provides the first systematic evaluation of state-of-the-art forecasting models, including Informer, Autoformer, iTransformer, TimesNet, DLinear, and TimeMixer, to the domain of cold storage load prediction. Experiments on real operational data from a logistics center in Jinan, China, demonstrate that MA-CFAN consistently outperforms all baselines, reducing average MSE and MAE by up to 19.3% and 14.8%, respectively. Full article
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16 pages, 1050 KB  
Review
Fractal Analysis of Auditory Evoked Potentials: Research Gaps and Potential AI Applications
by Svetlana Valjarevic, Jovana Paunovic Pantic, Jelena Cumic, Peter R. Corridon and Igor Pantic
Fractal Fract. 2026, 10(1), 20; https://doi.org/10.3390/fractalfract10010020 - 29 Dec 2025
Viewed by 471
Abstract
Auditory evoked potentials (AEPs) are electroencephalographic (EEG) responses to auditory stimuli and are frequently used to evaluate auditory processing and cognitive integrity. Interpretation of AEPs today predominantly relies on standard linear techniques such as time-domain averaging and frequency-domain spectral decomposition. These approaches may [...] Read more.
Auditory evoked potentials (AEPs) are electroencephalographic (EEG) responses to auditory stimuli and are frequently used to evaluate auditory processing and cognitive integrity. Interpretation of AEPs today predominantly relies on standard linear techniques such as time-domain averaging and frequency-domain spectral decomposition. These approaches may not always capture nonlinear, nonstationary, and scale-free characteristics of EEG signals; therefore, in contemporary neurophysiology research, there may be a need for the utilization of additional nonlinear frameworks. Fractal analysis may be a powerful tool for the quantification of subtle changes in EEG and AEP complexity, irregularity, and variability. This approach is often overlooked due to methodological and conceptual limitations but nevertheless holds significant potential in revealing alterations in geometrical and spatial complexity of AEPs under various physiological conditions. Here, we discuss potential applications and shortcomings of fractal AEP analysis, as well as its possible integration with supervised machine learning algorithms. We also focus on novel artificial intelligence-based concepts that could, in theory, utilize the power of fractal AEP and EEG analysis to improve the classification and prediction of neurophysiological processes and phenomena. Full article
(This article belongs to the Special Issue Fractals in Physiology and Medicine)
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22 pages, 1902 KB  
Article
Optimization of Energy Management Strategy for Hybrid Power System of Rubber-Tyred Gantry Cranes Based on Wavelet Packet Decomposition
by Hanwu Liu, Kaicheng Yang, Le Liu, Yaojie Zheng, Xiangyang Cao, Wencai Sun, Cheng Chang, Yuhang Ma and Yuxuan Zheng
Energies 2026, 19(1), 139; https://doi.org/10.3390/en19010139 - 26 Dec 2025
Viewed by 179
Abstract
To further enhance economic efficiency and optimize energy conservation and emission reduction performance, an optimized energy management strategy (EMS) tailored for the hybrid power system of rubber-tyred gantry cranes is proposed. Wavelet packet decomposition (WPD) was employed as the signal processing approach, and [...] Read more.
To further enhance economic efficiency and optimize energy conservation and emission reduction performance, an optimized energy management strategy (EMS) tailored for the hybrid power system of rubber-tyred gantry cranes is proposed. Wavelet packet decomposition (WPD) was employed as the signal processing approach, and this method was further integrated with EMS for hybrid power systems. Through a three-layer progressive architecture comprising WPD frequency–domain decoupling, fuzzy logic real-time adjustment, and PSO offline global optimization, a cooperative optimization mechanism has been established in this study between the frequency-domain characteristics of signals, the physical properties of energy storage components, and the real-time and long-term states of the system. Firstly, the modeling and simulation of the power system were conducted. Subsequently, an EMS based on WPD and limit protection was developed: the load power curve was decomposed into different frequency bands, and power allocation was implemented via the WPD algorithm. Meanwhile, the operating states of lithium batteries and supercapacitors were adjusted in combination with state of charge limits. Simulation results show that this strategy can achieved reasonable allocation of load power, effectively suppressed power fluctuations of the auxiliary power unit system, and enhanced the stability and economy of the hybrid power system. Afterward, a fuzzy controller was designed to re-allocate the power of the hybrid energy storage system (HESS), with energy efficiency and battery durability set as optimization indicators. Furthermore, particle swarm optimization algorithms were adopted to optimize the EMS. The simulation results indicate that the optimized EMS enabled more reasonable power allocation of the HESS, accompanied by better economic performance and control effects. The proposed EMS demonstrated unique system-level advantages in enhancing energy efficiency, extending battery lifespan, and reducing the whole-life cycle cost. Full article
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16 pages, 14666 KB  
Article
WSG-FEC: Gray-Box Frequency-Domain Explanation of CNN Models Based on Weakly Supervised Learning
by Ying Zhan, Xianfeng Li, Yue Zheng and Haoran Sun
Appl. Sci. 2026, 16(1), 231; https://doi.org/10.3390/app16010231 - 25 Dec 2025
Viewed by 173
Abstract
Convolutional neural networks (CNNs) have achieved remarkable progress in recent years, largely driven by advances in computational hardware. However, their increasingly complex architectures continue to pose significant challenges for interpretability. Existing explanation methods predominantly rely on spatial saliency representations and therefore fail to [...] Read more.
Convolutional neural networks (CNNs) have achieved remarkable progress in recent years, largely driven by advances in computational hardware. However, their increasingly complex architectures continue to pose significant challenges for interpretability. Existing explanation methods predominantly rely on spatial saliency representations and therefore fail to capture the intrinsic frequency-domain characteristics of image data. This work introduces WSG-FEC, a Weakly Supervised Gray-box Frequency-domain Explanation framework that integrates multilevel Haar wavelet decomposition with gradient-weighted class activation mapping (Grad-CAM) to generate frequency-aware explanations. By leveraging hierarchical wavelet structures, the proposed method produces frequential–spatial saliency maps that overcome the low-resolution limitations of white-box approaches and the high computational cost of black-box perturbation methods. Quantitative evaluations using insertion and deletion metrics demonstrate that WSG-FEC provides more detailed, efficient, and interpretable explanations, offering a novel perspective for understanding CNN decision mechanisms. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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20 pages, 2800 KB  
Article
A High-Ratio Renewable-Energy Power System Time–Frequency Domain-Cooperative Harmonic Detection Method Based on Enhanced Variational Modal Decomposition and the Prony Algorithm
by Yao Zhong, Guangrun Yang, Jiaqi Qi, Cheng Guo, Dongyan Chen and Qihao Jin
Symmetry 2026, 18(1), 13; https://doi.org/10.3390/sym18010013 - 20 Dec 2025
Viewed by 255
Abstract
Accurate identification of harmonic components is a prerequisite for addressing resonance risks in new energy power stations. Traditional Variational Modal decomposition (VMD) is susceptible to the influence of the modal decomposition order K and the penalty factor α when decomposing harmonic signals. This [...] Read more.
Accurate identification of harmonic components is a prerequisite for addressing resonance risks in new energy power stations. Traditional Variational Modal decomposition (VMD) is susceptible to the influence of the modal decomposition order K and the penalty factor α when decomposing harmonic signals. This paper proposes an adaptive parameter selection method for VMD based on an improved Triangular Topology Aggregation Optimization (TTAO) algorithm. Firstly, the pre-set parameters of variational modal decomposition—modal order K and penalty factor α—exhibit strong coupling. Conventional optimization algorithms cannot effectively coordinate adjustments to both parameters. This paper employs an enhanced TTAO algorithm, whose triangular topology unit structure and dual aggregation mechanism enable simultaneous adjustment of modal order K and penalty factor α, effectively resolving their coupled optimization challenge. Using minimum envelope entropy as the fitness function, the algorithm obtains an optimized parameter combination for VMD to decompose the signal. Subsequently, dominant modal components are selected based on Pearson’s correlation coefficients for reconstruction, with harmonic parameters precisely identified using the Prony algorithm. Simulation results demonstrate that under a 20 dB noise environment, the proposed method achieves a signal-to-noise ratio (SNR) of 25.6952 for steady-state harmonics, with a root mean square error (RMSE) of 0.4889. The mean errors for frequency and amplitude identification are 0.055% and 3.085%, respectively, significantly outperforming methods such as PSO-VMD and EMD. Moreover, the runtime of our model is markedly shorter than that of the PSO-VMD algorithm, effectively resolving the symmetric trade-off between recognition accuracy and runtime inherent in variational modal decomposition. Full article
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31 pages, 11484 KB  
Article
Towards Heart Rate Estimation in Complex Multi-Target Scenarios: A High-Precision FMCW Radar Scheme Integrating HDBS and VLW
by Xuefei Dong, Yunxue Liu, Jinwei Wang, Shie Wu, Chengyou Wang and Shiqing Tang
Sensors 2025, 25(24), 7629; https://doi.org/10.3390/s25247629 - 16 Dec 2025
Viewed by 406
Abstract
Non-contact heart rate estimation technology based on frequency-modulated continuous wave (FMCW) radar has garnered extensive attention in single-target scenarios, yet it remains underexplored in multi-target environments. Accurate discrimination of multiple targets and precise estimation of their heart rates constitute key challenges in the [...] Read more.
Non-contact heart rate estimation technology based on frequency-modulated continuous wave (FMCW) radar has garnered extensive attention in single-target scenarios, yet it remains underexplored in multi-target environments. Accurate discrimination of multiple targets and precise estimation of their heart rates constitute key challenges in the multi-target domain. To address these issues, we propose a novel scheme for multi-target heart rate estimation. First, a high-precision distance-bin selection (HDBS) method is proposed for target localization in the range domain. Next, multiple-input multiple-output (MIMO) array processing is combined with the Root-multiple signal classification (Root-MUSIC) algorithm for angular domain estimation, enabling accurate discrimination of multiple targets. Subsequently, we propose an efficient method for interference suppression and vital sign extraction that cascades variational mode decomposition (VMD), local mean decomposition (LMD), and wavelet thresholding (WT) termed as VLW, which enables high-quality heartbeat signal extraction. Finally, to achieve high-precision and super-resolution heart rate estimation with low computational burden, an improved fast iterative interpolated beamforming (FIIB) algorithm is proposed. Specifically, by leveraging the conjugate symmetry of real-valued signals, the improved FIIB algorithm reduces the execution time by approximately 60% compared to the standard version. In addition, the proposed scheme provides sufficient signal-to-noise ratio (SNR) gain through low-complexity accumulation in both distance and angle estimation. Six experimental scenarios are designed, incorporating densely arranged targets and front-back occlusion, and extensive experiments are conducted. Results show this scheme effectively discriminates multiple targets in all tested scenarios with a mean absolute error (MAE) below 2.6 beats per minute (bpm), demonstrating its viability as a robust multi-target heart rate estimation scheme in various engineering fields. Full article
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33 pages, 4409 KB  
Article
An Integrated Framework for Electricity Price Analysis and Forecasting Based on DROI Framework: Application to Spanish Power Markets
by Nuo Chen, Caishan Gao, Luqi Yuan, Jiani Heng and Jianwei Fan
Sustainability 2025, 17(24), 11210; https://doi.org/10.3390/su172411210 - 15 Dec 2025
Viewed by 251
Abstract
Against the backdrop of electricity market liberalization and deregulation, accurate electricity price forecasting is critical for optimizing power dispatch and promoting the low-carbon transition of energy structures. However, electricity prices exhibit inherent complexities such as seasonality, high volatility, and non-stationarity, which undermine the [...] Read more.
Against the backdrop of electricity market liberalization and deregulation, accurate electricity price forecasting is critical for optimizing power dispatch and promoting the low-carbon transition of energy structures. However, electricity prices exhibit inherent complexities such as seasonality, high volatility, and non-stationarity, which undermine the efficacy of traditional forecasting methodologies. To address these challenges, this study proposes a four-stage Decomposition-Reconstruction-Optimization-Integration (DROI) framework, coupled with an econometric breakpoint test, to evaluate forecasting performance across distinct time segments of Spanish electricity price data. The framework employs CEEMDAN for signal decomposition, decomposing complex price sequences into intrinsic mode functions to retain essential features while mitigating noise, followed by frequency-based data reconstruction; integrates the Improved Sparrow Search Algorithm (ISSA) to optimize initial model parameters, minimizing errors induced by subjective factors; and leverages Convolutional Neural Networks (CNN) for frequency-domain feature extraction, enhanced by an attention mechanism to weight channels and prioritize critical attributes, paired with Long Short-Term Memory (LSTMs) for temporal sequence forecasting. Experimental results validate the method’s robustness in both interval forecasting (IPCP = 100% and IPNAW is the smallest, Experiment 1.3) and point forecasting tasks (MAPE = 1.3758%, Experiment 1.1), outperforming naive approaches in processing stationary sequence clusters and demonstrating substantial economic utility to inform sustainable power system management. Full article
(This article belongs to the Special Issue Energy Price Forecasting and Sustainability on Energy Transition)
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19 pages, 8744 KB  
Article
An Adaptive Hyperfine Spectrum Extraction Algorithm for Optical Sensing Based on SG Filtering and VMD
by Yupeng Wu, Kai Ma, Ziyan Yun, Yueheng Zhang, Qiming Su, Xinxin Kong, Zhou Wu and Wenxi Zhang
Sensors 2025, 25(24), 7590; https://doi.org/10.3390/s25247590 - 14 Dec 2025
Viewed by 325
Abstract
In optical sensing, signal demodulation often degrades fine spectral data, particularly in spectroscopic measurements affected by Doppler noise, aliasing, and circuit noise. Existing algorithms often fall short in addressing these issues effectively, as they either necessitate complex parameter tuning and extensive expertise or [...] Read more.
In optical sensing, signal demodulation often degrades fine spectral data, particularly in spectroscopic measurements affected by Doppler noise, aliasing, and circuit noise. Existing algorithms often fall short in addressing these issues effectively, as they either necessitate complex parameter tuning and extensive expertise or are limited to handling simple spectral signals. To address these challenges, this study proposes an adaptive spectral extraction algorithm combining Variational Mode Decomposition (VMD) and Savitzky-Golay (SG) filtering. The algorithm optimizes parameters through an innovative adaptation strategy. By analyzing key parameters such as SG frame length, order, and VMD mode number, it leverages signal time-domain and frequency spectrum information to adaptively determine the optimal VMD modes and SG order, ensuring effective noise suppression and feature preservation. Validated through simulations and experiments, the method significantly enhances spectral signal quality by restoring absorption peaks and eliminating manual parameter adjustments. This work provides a robust solution for improving measurement accuracy and reliability in optical sensing instrumentation, particularly in applications involving complex spectral analysis. Full article
(This article belongs to the Special Issue Advances in Optical Sensing, Instrumentation and Systems: 2nd Edition)
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