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Keywords = improved time-frequency entropy

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28 pages, 9757 KB  
Article
Time-Frequency Feature Extraction and Modal Component Reconstruction for Structural Dynamic Monitoring Using MTM-eNTFT
by Ling’ai Li, Junwei Wang and Chi Zhang
Entropy 2026, 28(9), 1001; https://doi.org/10.3390/e28091001 - 7 Sep 2026
Viewed by 222
Abstract
Field-measured structural responses are often noisy, multicomponent, nonstationary, and finite in length, complicating dominant-frequency identification, component extraction, and time-frequency characterization. This study develops an MTM-assisted Normal Time-Frequency Transform procedure with multiscale permutation entropy (MPE)-guided endpoint extension, termed MTM-eNTFT, to improve target-frequency-band determination and [...] Read more.
Field-measured structural responses are often noisy, multicomponent, nonstationary, and finite in length, complicating dominant-frequency identification, component extraction, and time-frequency characterization. This study develops an MTM-assisted Normal Time-Frequency Transform procedure with multiscale permutation entropy (MPE)-guided endpoint extension, termed MTM-eNTFT, to improve target-frequency-band determination and mitigate boundary-related reconstruction errors. Multitaper spectral estimation is used to determine stable target-frequency regions, while MPE-guided endpoint extension is used before band-limited NTFT reconstruction. Under the investigated simulation conditions, MTM-eNTFT provides more accurate component reconstruction, better noise suppression, and smaller boundary-related reconstruction errors than conventional NTFT, CEEMDAN, VMD, and SET. The reconstructed signal yields an RMSE below 0.08, a Pearson correlation coefficient over 0.98, and an SNR improvement of about 19 dB relative to the noisy input. The method is also applied to a selected continuous 15-min X-direction acceleration record acquired at a roof-corner sensor of a 68-storey building in Hong Kong during a high-wind event. Two dominant frequency components centered at approximately 0.208 and 0.965 Hz are extracted. Their energy increases between approximately 130 and 460 s, possibly indicating a temporary increase in the measured dynamic response. The results indicate the applicability of MTM-eNTFT to component extraction and time-frequency characterization of noisy finite-length structural-response records. Full article
(This article belongs to the Section Multidisciplinary Applications)
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34 pages, 21458 KB  
Article
Adaptive Flight Maneuver Boundary Localization via Spectral Entropy-Weighted Multi-Channel Spectrogram Fusion
by Shansong Song, Wei Han, Bing Wan, Xiangyi Liu, Xichao Su, Chao Li and Yunyang Cao
Entropy 2026, 28(8), 922; https://doi.org/10.3390/e28080922 - 17 Aug 2026
Viewed by 214
Abstract
To address ambiguous maneuver boundaries, background interference, and uneven multi-sensor quality in long-duration flight parameter recordings, this paper proposes an adaptive flight maneuver boundary localization algorithm that integrates spectral entropy-weighted multi-channel spectrogram fusion with attitude-constrained structural correction. Multi-channel Short-Time Fourier Transform (STFT) spectrograms [...] Read more.
To address ambiguous maneuver boundaries, background interference, and uneven multi-sensor quality in long-duration flight parameter recordings, this paper proposes an adaptive flight maneuver boundary localization algorithm that integrates spectral entropy-weighted multi-channel spectrogram fusion with attitude-constrained structural correction. Multi-channel Short-Time Fourier Transform (STFT) spectrograms are first constructed from flight parameter time series. Spectral entropy (SE) is introduced to quantify the uncertainty of each channel’s time–frequency energy distribution and is combined with the maneuver activation ratio (MAR) and the linear contrast ratio (LCR) to form objective credibility weights, thereby suppressing channels dominated by aerodynamic turbulence and high frequency structural vibration. Normal overload soft gating and logarithmic noise floor subtraction are then applied to obtain an enhanced fused spectrogram, from which candidate intervals are extracted by low band energy thresholding. Finally, roll and pitch angle steady-state priors refine the event structure through local boundary refinement, cross-segment expansion/chain merging, and semantic post-processing, recovering continuous maneuvers fragmented by instantaneous energy valleys. On the held-out test sorties (SE_018–SE_020; 61 annotated intervals), the proposed algorithm achieves Precision, Recall, and F1-scores of 0.967. On the full primary corpus of 20 sorties (461 intervals), used for ablation and sensitivity analyses, the corresponding figures are Precision 0.934, Recall 0.959, and F1 0.946, with start and end boundary mean absolute errors of 1.484 s and 1.471 s. Under the same IoU protocol, consistent superiority is observed against learning-based baselines, and an independent external set of 10 sorties yields F1 = 0.938. The results indicate that entropy-constrained multi-sensor time–frequency fusion mainly improves maneuver/background separability, whereas attitude-constrained structural correction restores the integrity of long continuous maneuvers. Full article
(This article belongs to the Section Signal and Data Analysis)
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31 pages, 4731 KB  
Article
Multi-Horizon Probabilistic Wind Power Forecasting for Mountainous Wind Farms Based on Entropy-Weighted Fusion and Permutation Entropy-Guided Decomposition
by Chunhui Liu, Bilin Shao, Dawen Nie, Ning Tian, Hongbin Dai, Huibin Zeng, Wei Zhao, Xue Zhao, Xinyu Liu and Caiyun Qin
Entropy 2026, 28(8), 902; https://doi.org/10.3390/e28080902 - 10 Aug 2026
Viewed by 351
Abstract
Wind power integration into mountainous power grids amplifies probabilistic forecasting challenges arising from strong non-stationarity, multi-source meteorological redundancy and frequent curtailment events. To address the limitations of existing approaches, this paper proposes a multi-horizon probabilistic forecasting framework integrating multi-perspective entropy-weighted fusion, permutation-entropy-guided decomposition, [...] Read more.
Wind power integration into mountainous power grids amplifies probabilistic forecasting challenges arising from strong non-stationarity, multi-source meteorological redundancy and frequent curtailment events. To address the limitations of existing approaches, this paper proposes a multi-horizon probabilistic forecasting framework integrating multi-perspective entropy-weighted fusion, permutation-entropy-guided decomposition, and residual-anchored probability modelling. First, an Entropy-Weighted Multi-criteria Permutation Feature Importance (EW-MPFI) module fuses KSG mutual information, Tree-SHAP, and elastic-net permutation importance through entropy-based weighted aggregation, distilling 23-dimensional meteorological inputs into eight informative features while suppressing single-criterion bias. Then, a three-stage decomposition strategy applies ICEEMDAN primary decomposition, permutation-entropy and sample-entropy guided band reconstruction, and SSA secondary refinement on high-frequency components, achieving complexity-aligned multi-scale separation. Finally, a decomposition-aware patch-based Transformer backbone (DPC-Former) generates three-quantile point forecasts, upon which an NGBoost residual layer models the conditional distribution via natural-gradient optimization in the information-geometric parameter space. Case studies on a 130 MW mountainous wind farm in Sichuan, China, covering 8736 15-min samples with 566 curtailment samples (6.48% of the dataset), show that, under the partition-wise offline batch-evaluation protocol, the proposed framework achieves an NMAE of 5.21%, an NCRPS of 3.74%, and a PICP80 of 0.84 across forecasting horizons from 15 min to 4 h. Ablation analysis attributes NMAE improvements of 25.36% and 24.57% to the decomposition and feature-selection modules, respectively, while 50-seed ensembling further reduces NCRPS, NMAE, and NRMSE by 7.40%, 7.00%, and 13.70% relative to single-seed training. A fixed-checkpoint test-block diagnostic further shows limited sensitivity at approximately weekly and three-day decomposition cadences, but a material degradation at a one-day cadence. The reported metrics should therefore be interpreted as offline best-case results rather than as performance under strictly causal real-time deployment. Full article
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32 pages, 11212 KB  
Article
Bayesian Convolutional Neural Networks for Uncertainty-Aware Classification of Infrasound Events
by Hao Yin, Kai Zhang, Yu Lu, Yunfen Chang, Yunhui Wu, Fan Yang, Xuexu Li, Jiaoheng Xu and Xinliang Pang
Sensors 2026, 26(15), 4955; https://doi.org/10.3390/s26154955 - 5 Aug 2026
Viewed by 405
Abstract
Accurate classification of infrasound signals is essential for nuclear-test verification, natural-hazard warning, and geophysical monitoring. Conventional convolutional neural networks (CNN) applied to this task tend to overfit small, class-imbalanced datasets and cannot quantify predictive uncertainty. To address these limitations, we introduce a Bayesian [...] Read more.
Accurate classification of infrasound signals is essential for nuclear-test verification, natural-hazard warning, and geophysical monitoring. Conventional convolutional neural networks (CNN) applied to this task tend to overfit small, class-imbalanced datasets and cannot quantify predictive uncertainty. To address these limitations, we introduce a Bayesian CNN framework that treats network weights as probability distributions and performs inference by variational approximation. LeNet-5, AlexNet, and 4Conv3Fc network serve as baselines and are converted into Bayes LeNet-5, Bayes AlexNet, and Bayes 4Conv3Fc. The short-time Fourier transform (STFT) provides time–frequency spectrograms as model input. On a highly imbalanced dataset comprising nuclear tests, chemical explosions, volcanic eruptions, rocket launches, earthquakes, and lightning, Bayes 4Conv3Fc reaches an overall accuracy of 99.14% without any data augmentation. Relative to the deterministic baselines, precision, recall, and F1-score increase by up to 6.91, 7.12, and 7.20 percentage points, respectively, and Cohen’s Kappa coefficient by up to 8.86 percentage points. Against class-weighted cross-entropy, a standard imbalance-handling baseline, the Bayesian models yield consistently lower Brier scores, indicating that the gains stem from principled uncertainty modelling rather than loss re-weighting alone.. This study quantifies both epistemic and aleatoric uncertainty in an infrasound signal classification model, and the calibration analysis validates that these uncertainty estimates are reliable, providing a basis for evaluating prediction reliability and diagnosing potential failure modes, thereby contributing to improved model interpretability. Coupled with an event-level data partitioning strategy, the evaluation faithfully reflects the model’s generalization to unseen events and offers a promising direction toward uncertainty-aware infrasound monitoring. Full article
(This article belongs to the Section Physical Sensors)
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36 pages, 3798 KB  
Article
IMVMD-MADNet: A Hybrid Framework for Multi-Scale Prediction of Chiller Energy Consumption
by Ronghao Cheng, Xiaoqin Wen and Yinghao Li
Appl. Sci. 2026, 16(15), 7716; https://doi.org/10.3390/app16157716 - 3 Aug 2026
Viewed by 329
Abstract
Accurate prediction of chiller energy consumption is crucial for the efficient operation and intelligent management of heating, ventilation, and air conditioning (HVAC) systems in large buildings. However, such prediction remains challenging due to the multi-scale temporal coupling and nonstationary dynamics of chiller systems. [...] Read more.
Accurate prediction of chiller energy consumption is crucial for the efficient operation and intelligent management of heating, ventilation, and air conditioning (HVAC) systems in large buildings. However, such prediction remains challenging due to the multi-scale temporal coupling and nonstationary dynamics of chiller systems. Therefore, an IMVMD-MADNet hybrid framework integrating Improved Multivariate Variational Mode Decomposition (IMVMD) and a Multi-scale Aggregation Decomposition Network (MADNet) is proposed for chiller energy consumption prediction. To avoid information leakage and capture multi-scale features, a rolling local decomposition strategy with adaptive mode selection is employed. First, IMVMD performs stepwise decomposition within a sliding window, and the optimal number of modes is determined using envelope entropy. Then, sample entropy is used to reconstruct the multivariate modes into high-, medium-, and low-frequency components. Subsequently, a dual-branch MADNet combining wavelet-domain time-frequency modeling (WDP) and time-domain causal dependency modeling (TDP) predicts each component, and the results are aggregated to generate the final prediction. Bayesian optimization is employed to optimize the key hyperparameters. One year of real industrial chiller data from a plant in Huizhou, China, is used to evaluate the proposed model against 11 forecasting models. Results show that the dual-branch architecture outperforms single-branch models. The proposed model achieves the best performance across all forecasting horizons, with its advantage becoming more pronounced as the forecasting horizon increases, demonstrating stable predictive performance under the same-plant setting. Full article
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32 pages, 5046 KB  
Article
Scalable Machine Learning on IoT Edge Devices Through Adaptive Coreset Selection with Differentiable Greedy Sampling
by Fatema A. Albalooshi and M. R. Qader
Technologies 2026, 14(8), 476; https://doi.org/10.3390/technologies14080476 - 2 Aug 2026
Viewed by 378
Abstract
The rapid growth of Internet of Things (IoT) devices generates high-dimensional, high-velocity data streams that demand real-time machine learning (ML) inference under strict hardware constraints. We propose the Adaptivecoreset Selection Engine (ACS-Engine), a unified framework for adaptive, differentiable, and resource-aware coreset selection on [...] Read more.
The rapid growth of Internet of Things (IoT) devices generates high-dimensional, high-velocity data streams that demand real-time machine learning (ML) inference under strict hardware constraints. We propose the Adaptivecoreset Selection Engine (ACS-Engine), a unified framework for adaptive, differentiable, and resource-aware coreset selection on streaming IoT data. ACS-Engine introduces three tightly integrated innovations: (i) Differentiable Greedy Sampling (DGS), which relaxes discrete subset selection via Gumbel-Softmax reparameterization to enable end-to-end gradient-based optimization; (ii) Entropy-Aware Regularization (EAR), which promotes coreset diversity and provides implicit concept drift detection through a self-calibrating entropy threshold; and (iii) Resource-Aware Memory Management (RAMM), which dynamically adjusts the target coreset size based on real-time hardware telemetry—available memory, CPU utilization, remaining energy, and sampling frequency. Evaluated on eight real-world IoT datasets spanning three heterogeneous edge platforms, ACS-Engine achieves 15× memory reduction and a 20% energy efficiency improvement while retaining 98% of full-dataset accuracy, with a per-sample latency of 2 ms that satisfies real-time edge deployment requirements. Full article
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20 pages, 5986 KB  
Article
Spatio-Temporal Characteristics of Extreme Precipitation and Flood Risk Assessment: A Case Study of the Yangtze River Delta Region in China
by Chong Li, Yibao Wang and Mengqi Zhang
Water 2026, 18(15), 1853; https://doi.org/10.3390/w18151853 - 30 Jul 2026
Viewed by 417
Abstract
This study aims to deepen the understanding of the spatiotemporal evolution of the Extreme Precipitation Index in the YRD, evaluating the comprehensive flood disaster risk across the region. Existing studies have rarely incorporated the frequency, duration, and intensity of extreme precipitation events as [...] Read more.
This study aims to deepen the understanding of the spatiotemporal evolution of the Extreme Precipitation Index in the YRD, evaluating the comprehensive flood disaster risk across the region. Existing studies have rarely incorporated the frequency, duration, and intensity of extreme precipitation events as indicators of the hazard of causative factors into comprehensive flood risk assessments. Using daily precipitation records from 107 national meteorological stations spanning 1960–2024, this study employs four extreme precipitation indices recommended by the ETCCDI (PREPTOT, CWD, R95p, and Rx1day) to examine the spatiotemporal characteristics of extreme precipitation in the YRD, one of China’s most densely populated and economically significant regions. Furthermore, a comprehensive flood risk assessment framework encompassing the hazard of causative factors, the sensitivity of disaster-forming environments, the vulnerability of disaster-affected entities, and disaster prevention capabilities is constructed. Based on this framework, an integrated Analytic Hierarchy Process–Entropy Weight method is adopted to evaluate Flood Risks in the YRD. The results showed that: (1) during the period 1960—2024, only the Extreme Precipitation Index (R95p) exhibited a significant upward trend, increasing at a rate of 1.7 mm/10a, whereas PREPTOT, CWD, and Rx1day showed slight declining trends. Nevertheless, all four indices displayed pronounced oscillatory characteristics, characterized by recurring “decrease—increase” cycles over time. (2) In terms of spatial distribution, PREPTOT and R95p exhibited a clear south-to-north gradient pattern, while CWD and Rx1day demonstrated a multicentric distribution. This pattern highlights the combined influence of typhoon landfall frequency and topographic conditions on extreme precipitation across the southern YRD. (3) The Flood Risks in the YRD exhibited a distinct spatial pattern characterized by higher risk levels in the east than in the west and in the south than in the north. Areas classified as moderate-to-high risk accounted for 48.6% of the total study area, with high-risk zones primarily concentrated in the Shanghai—Hangzhou—Ningbo corridor. These findings suggest that Flood Risks in the YRD are not driven by a single factor; rather, they result from the complex interactions among extreme precipitation, topographic and geomorphological conditions, levels of social exposure, and regional buffering capacities. Consequently, under the increasingly frequent occurrence of extreme precipitation events, flood management strategies that rely predominantly on static engineering measures are becoming insufficient. Greater emphasis should therefore be placed on enhancing the resilience of urban lifeline infrastructure, improving high-resolution forecasting and early-warning capabilities for extreme precipitation, and establishing dynamic warning-release mechanisms based on risk thresholds. Such measures are essential for effectively mitigating regional flood risks. Full article
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32 pages, 12384 KB  
Article
An Entropy-Weighted Multi-Factor Ambiguity Subset Selection Algorithm for Partial Ambiguity Resolution in Multi-GNSS and Multi-Frequency Precise Point Positioning
by Mingduan Zhou, Lu Qin, Likun Cui, Qiao Song, Shiqi Lin, Peng Yan, Shufa Li, Qianlong Xie, Yuhan Qin, Zihan Zhou and Guanxiu Wu
Sensors 2026, 26(14), 4388; https://doi.org/10.3390/s26144388 - 10 Jul 2026
Viewed by 553
Abstract
Reliable ambiguity subset selection is essential for partial ambiguity resolution (PAR) in multi-GNSS and multi-frequency precise point positioning (PPP), as the increasing number of satellite–frequency ambiguities expands the ambiguity search space and reduces ambiguity-fixing reliability in high-dimensional scenarios. To address this issue, this [...] Read more.
Reliable ambiguity subset selection is essential for partial ambiguity resolution (PAR) in multi-GNSS and multi-frequency precise point positioning (PPP), as the increasing number of satellite–frequency ambiguities expands the ambiguity search space and reduces ambiguity-fixing reliability in high-dimensional scenarios. To address this issue, this study proposes a multi-factor ranking and screening partial ambiguity resolution (MPAR) algorithm, an entropy-weighted multi-factor ambiguity subset selection algorithm designed for multi-GNSS and multi-frequency undifferenced and uncombined precise point positioning (UDUC PPP). The proposed MPAR algorithm evaluates candidate ambiguities using three quality indicators: signal-to-noise ratio, ambiguity variance, and carrier-phase residual. Min–max normalization is used to eliminate scale differences among the indicators, while entropy-based adaptive weighting is introduced to dynamically determine their relative contributions. Based on the integrated ranking results, ambiguities are divided into easy-to-fix and hard-to-fix subsets, with the hard-to-fix subset further refined through iterative screening before integer fixing. The proposed algorithm was validated using 24 h BDS-3/GPS/Galileo observations collected from 11 globally distributed MGEX stations on day 350 of 2025 under five-, four-, and three-frequency configurations. Its performance was compared with the baseline full ambiguity resolution strategy (FAR), which fixes all candidate ambiguities without subsequent iterative exclusion after an initial fixing failure, as well as elevation-angle-factor-based partial ambiguity resolution (ELE) and variance-factor-based partial ambiguity resolution (VAR). The MPAR algorithm achieved ambiguity-fixing rates of 98.9%, 98.7%, and 99.2% under the three configurations, respectively, exhibiting performance comparable to ELE while outperforming VAR and FAR. Compared with VAR, MPAR increased the average proportions of wide-lane and narrow-lane ambiguity residuals within ±0.1 cycle by 13.6% and 46.4%, respectively. Under the five-frequency configuration, MPAR achieved the best overall performance, with horizontal and vertical convergence times of 9.1 and 8.1 min, respectively. These results demonstrate that the proposed entropy-weighted multi-factor subset selection algorithm improves ambiguity estimation quality and enhances the reliability and convergence performance of high-dimensional multi-GNSS and multi-frequency PPP. Full article
(This article belongs to the Special Issue Advances in GNSS Signal Processing and Navigation—Second Edition)
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29 pages, 9555 KB  
Article
OFOTD-FRMSST for LFM Signal Representation and Parameter Estimation Under Impulsive Noise
by Shan Zhang, Yong Guo and Lidong Yang
Fractal Fract. 2026, 10(7), 436; https://doi.org/10.3390/fractalfract10070436 - 26 Jun 2026
Viewed by 242
Abstract
Due to the memory and non-local characteristics of fractional calculus, fractional-order tracking differentiator (FOTD) performs excellently in suppressing impulse noise. However, the parameters of FOTD need to be manually adjusted according to the scene requirements, and cannot automatically maintain optimal performance in scenarios [...] Read more.
Due to the memory and non-local characteristics of fractional calculus, fractional-order tracking differentiator (FOTD) performs excellently in suppressing impulse noise. However, the parameters of FOTD need to be manually adjusted according to the scene requirements, and cannot automatically maintain optimal performance in scenarios where the signal and noise intensities change dynamically. To address this issue, this paper proposes a multi-parameter optimization-driven FOTD (OFOTD) based on envelope entropy, enhancing the adaptability of FOTD in complex scenarios. Furthermore, a fractional multisynchrosqueezing transform (FRMSST) is developed, and OFOTD-FRMSST is established to accurately represent the signal under impulsive noise. Finally, OFOTD-FRMSST is applied to parameter estimation of linear frequency modulation (LFM) signal, demonstrating its superiority in accuracy, noise robustness, and practicality. Experimental results demonstrate that, from both time domain and time-frequency plane, OFOTD achieves enhanced noise suppression performance through adaptive parameter optimization. Furthermore, in comparison with existing methods, OFOTD-FRMSST yields a more accurate signal representation under impulsive noise, thereby improving accuracy and noise robustness of parameter estimation. Full article
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31 pages, 6039 KB  
Article
A Tri-Band Frequency-Aware Heterogeneous Expert Collaboration Framework for Short-Term Wind Speed Forecasting
by Ziyuan Qiao, Weiyi Yang, Manqi Yang, Hongqing Wang and Xiaodong Ji
Sustainability 2026, 18(11), 5659; https://doi.org/10.3390/su18115659 - 3 Jun 2026
Viewed by 286
Abstract
Short-term wind speed forecasting plays a critical role in enabling the reliable integration of renewable energy and supporting the sustainable operation of power systems. However, traditional dual-frequency decomposition methods oversimplify wind speed dynamics by separating them into only high-frequency disturbances and low-frequency trends, [...] Read more.
Short-term wind speed forecasting plays a critical role in enabling the reliable integration of renewable energy and supporting the sustainable operation of power systems. However, traditional dual-frequency decomposition methods oversimplify wind speed dynamics by separating them into only high-frequency disturbances and low-frequency trends, making it difficult to capture intermediate-frequency transitional dynamics. Additionally, single models struggle to adapt to multi-scale temporal features, limiting forecasting performance. To address these issues, this paper proposes a tri-band frequency-aware heterogeneous expert collaboration framework. First, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is employed for signal denoising, followed by Particle Swarm Optimization-Time Varying Filtering-based Empirical Mode Decomposition (PSO-TVF-EMD) for multi-scale signal disentanglement. Then, Permutation Entropy (PE) is used to construct a tri-band structure consisting of high-, intermediate-, and low-frequency components. A frequency-aware expert routing mechanism assigns Bayesian Optimization Long Short-Term Memory (BO-LSTM), an improved Markov model, and Auto-Regressive Integrated Moving Average (ARIMA) to the corresponding frequency bands. Finally, a reliability-aware cooperative aggregation strategy integrates predictions from multiple experts. Experimental results show that representative baseline models, including BO-LSTM, Markov, ARIMA, Gated Recurrent Unit (GRU) and Convolutional Neural Network Long Short-Term Memory (CNN-LSTM), achieve MAE values ranging from 0.308 to 0.429, while the proposed framework reduces the Mean Absolute Error (MAE) to 0.193 and Root Mean Square Error (RMSE) to 0.274, with a Mean Absolute Percentage Error (MAPE) of 7.35% and R2 of 0.927. Compared with the dual-frequency decomposition scheme (MAE = 0.266), the proposed tri-band framework achieves an average improvement of approximately 28.1%. The results suggest that explicitly modeling intermediate-frequency dynamics and aligning model inductive biases with multi-scale signal characteristics can effectively enhance short-term wind speed forecasting performance. Full article
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21 pages, 798 KB  
Article
Optimizing EMG-Based Transtibial Movement Classification for Real-Time Prosthetic Control: A Feature Engineering and Multi-Window Voting Study
by Carlos Gabriel Mireles-Preciado, Diana Carolina Toledo-Pérez, Roberto Augusto Gómez-Loenzo, Marcos Aviles and Juvenal Rodríguez-Reséndiz
Algorithms 2026, 19(5), 351; https://doi.org/10.3390/a19050351 - 1 May 2026
Viewed by 511
Abstract
Objective: This study investigates the optimization of surface EMG (sEMG) classification for seven transtibial movements using short analysis windows (64 ms) suitable for real-time control of below-knee prostheses. Methods: We systematically evaluated feature engineering strategies, dimensionality reduction techniques, and classification approaches using linear [...] Read more.
Objective: This study investigates the optimization of surface EMG (sEMG) classification for seven transtibial movements using short analysis windows (64 ms) suitable for real-time control of below-knee prostheses. Methods: We systematically evaluated feature engineering strategies, dimensionality reduction techniques, and classification approaches using linear Support Vector Machines on four-channel sEMG data from the transtibial region. We compared amplitude-based versus derivative-based time-domain features, integrated frequency-domain features, and implemented multi-window majority voting with 50% overlap. Results: Evaluated across nine subjects (four male, five female), the optimized system achieves a population-level accuracy of 70.16%±7.09% with multi-window majority voting (per-subject range: 60.71–78.57%), with voting consistently improving accuracy over single-window classification by +7.06% on average. We demonstrate that PCA provides zero benefit for linear classifiers when all features are retained. Documented failed approaches include adaptive windowing and spectral entropy features. Conclusion: Careful feature engineering combining time-domain (MAV2, RMS, VAR, MAX, LOG, IEMG) and frequency-domain features (MPF, MF, band powers) with multi-window voting substantially recovers accuracy losses from aggressive window reduction while maintaining sub-100 ms latency suitable for prosthetic control. This work provides a validated methodology across multiple subjects for optimizing EMG classification latency–accuracy trade-offs, demonstrates that PCA is unnecessary for linear classifiers with well-engineered features, and documents negative results to guide future prosthetic control research. Full article
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21 pages, 3045 KB  
Article
Distribution Network Fault Diagnosis with Noise-Assisted Multivariate Empirical Mode Decomposition and a Modified Multiple Branch Convolutional Neural Network
by Fei Xiao, Xiaoya Shang, Qinxue Li, Yiyi Zhan, Rui Li, Qian Ai and Yi Zhang
Energies 2026, 19(9), 2187; https://doi.org/10.3390/en19092187 - 30 Apr 2026
Viewed by 443
Abstract
A novel method based on noise-assisted multivariate empirical mode decomposition (NA-MEMD) combined with a modified multiple branch convolutional neural network (MMBCNN) is designed to detect fault events in distribution networks and to classify various faults in a distribution system. Given the presence of [...] Read more.
A novel method based on noise-assisted multivariate empirical mode decomposition (NA-MEMD) combined with a modified multiple branch convolutional neural network (MMBCNN) is designed to detect fault events in distribution networks and to classify various faults in a distribution system. Given the presence of noise components in transient voltage signals, a moving time window technique integrated with the NA-MEMD method is employed to process high-frequency sampling and long-term series signals. This method is also utilized to reliably identify noise components in modal components through permutation entropy. On this basis, the Clarke transform is employed to convert transient voltage signals into the d–q axis, and three-phase voltage waveforms are transformed into a ring image. Moreover, an MMBCNN is developed to accurately detect and classify distribution network faults, and a modified pooling function is introduced to improve feature extraction ability and model convergence performance. Finally, the accuracy and effectiveness of the proposed algorithm are estimated and analyzed using measurement and fault simulation data from distribution networks. Full article
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17 pages, 10447 KB  
Article
A Refined Prediction Model for Regional Zenith Troposphere Combining ICEEMDAN and BiLSTM-XGBoost
by Chao Chen, Yinghao Zhao, Wenyuan Zhang, Yulong Ge, Jiajia Yuan and Chao Hu
Remote Sens. 2026, 18(9), 1381; https://doi.org/10.3390/rs18091381 - 30 Apr 2026
Viewed by 573
Abstract
To address the degradation of zenith tropospheric delay (ZTD) prediction accuracy caused by time-varying noise and error accumulation in multi-step forecasting, this study proposes an integrated prediction model, named IBX, which combines improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), bidirectional [...] Read more.
To address the degradation of zenith tropospheric delay (ZTD) prediction accuracy caused by time-varying noise and error accumulation in multi-step forecasting, this study proposes an integrated prediction model, named IBX, which combines improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), bidirectional long short-term memory (BiLSTM), and extreme gradient boosting (XGBoost). In the proposed framework, ICEEMDAN is first used to decompose the original ZTD series into components at different temporal scales. A three-criterion reconstruction strategy based on the Pearson correlation coefficient, dominant period, and sample entropy is then applied to obtain high-, medium-, and low-frequency subsequences with clearer physical meanings. BiLSTM and XGBoost are used to predict the reconstructed components, and their outputs are fused through a root mean square error (RMS)-based weighting strategy to improve forecasting robustness. Hourly ZTD data from 27 global navigation satellite system (GNSS) stations in China from 2011 to 2020 were used for model validation under 1–12 h rolling forecasting horizons. The results show that IBX achieves the best overall performance among the tested models. Its mean RMS and mean absolute error (MAE) over the 1–12 h horizons are 14.17 mm and 10.24 mm, respectively, which are 22.5% and 21.4% lower than those of the baseline BiLSTM model. Spatial and climate-region-based analyses further indicate that ZTD prediction accuracy is strongly affected by altitude, regional moisture conditions, and climate type. The proposed IBX model shows stable error suppression across heterogeneous station environments, especially in the temperate monsoon region and low-altitude regions with complex water vapor variability. These results demonstrate that IBX provides a reliable and physically interpretable approach for short- to medium-term ZTD forecasting and real-time atmospheric delay correction. Full article
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22 pages, 3980 KB  
Article
A Contrastive Multi-Modal Time-Frequency Swin Transformer Network for Semi-Supervised Mechanical Equipment Fault Diagnosis
by Na Wu, Hao Song, Jianwei Yang, Tong Ji and Lingli Cui
Appl. Sci. 2026, 16(9), 4333; https://doi.org/10.3390/app16094333 - 29 Apr 2026
Viewed by 579
Abstract
Traditional deep learning networks in fault diagnosis tasks struggle to effectively utilize unlabeled data, and their diagnostic performance is constrained by the limited availability of labeled samples. To address this issue, this paper proposes a semi-supervised method based on multi-modal time-frequency fusion and [...] Read more.
Traditional deep learning networks in fault diagnosis tasks struggle to effectively utilize unlabeled data, and their diagnostic performance is constrained by the limited availability of labeled samples. To address this issue, this paper proposes a semi-supervised method based on multi-modal time-frequency fusion and an improved Swin Transformer, termed the Contrastive Multi-modal Time-Frequency Swin Transformer for Semi-Supervised Fault Diagnosis (CMTFST-SFD). First, a multi-scale shift window attention fusion module is designed as the backbone network, performing parallel computations with a 7 × 7 fine-grained window and a 14 × 14 coarse-grained window. Subsequently, a three-channel time-frequency encoder and a multi-frequency fusion convolution module are constructed to extract diverse frequency characteristics. Finally, by integrating a joint contrastive-cross-entropy loss function, the network backbone is trained in the first stage using a combination of unlabeled and labeled data, followed by training the classification head solely with labeled data in the second stage, thereby fully leveraging all available data for comprehensive model training. The proposed method is evaluated on two bearing fault datasets under three different labeling rates, consistently achieving a recognition rate exceeding 97%. Compared to other advanced techniques, the proposed method demonstrates superior recognition rates and enhanced clustering performance. Full article
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23 pages, 2091 KB  
Article
A Photovoltaic Power Prediction Method Based on Wavelet Convolutional Neural Networks and Improved Transformer
by Yibo Zhou, Zihang Liu, Zhen Cheng, Hanglin Mi, Zhaoyang Qin and Kangyangyong Cao
Energies 2026, 19(9), 2040; https://doi.org/10.3390/en19092040 - 23 Apr 2026
Cited by 1 | Viewed by 593
Abstract
The output power of photovoltaic (PV) systems is influenced by various environmental factors, exhibiting strong nonlinearity and non-stationarity, which poses significant challenges for accurate forecasting. To address these issues, this paper proposes a short-term PV power forecasting method based on wavelet convolutional neural [...] Read more.
The output power of photovoltaic (PV) systems is influenced by various environmental factors, exhibiting strong nonlinearity and non-stationarity, which poses significant challenges for accurate forecasting. To address these issues, this paper proposes a short-term PV power forecasting method based on wavelet convolutional neural networks and an improved Transformer. First, the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is employed to decompose the original PV power sequence into several intrinsic mode functions (IMFs). Fuzzy entropy is then utilized to evaluate the complexity of each component, and subsequences with similar entropy values are reconstructed to reduce the non-stationarity of the original series. Subsequently, Pearson correlation coefficients and the maximal information coefficient (MIC) are applied to capture both linear and nonlinear relationships between each reconstructed component and meteorological features, enabling the selection of strongly correlated variables. On this basis, a wavelet convolutional network (WTConv) is introduced to perform multi-scale decomposition and frequency-band feature extraction on the reconstructed components by integrating wavelet transform with convolution operations, effectively expanding the receptive field and extracting deep-seated features of the sequences. Finally, an improved iTransformer model is adopted for time-series modeling, leveraging its inverted encoding structure and self-attention mechanism to fully capture long-term dependencies among multivariate variables. The proposed model is validated using actual power data from a PV plant in Ningxia, China, across four seasons. Comprehensive experiments, including ablation studies, comparative analyses, loss function convergence evaluation, and Diebold–Mariano significance tests, are conducted to thoroughly assess the model’s effectiveness and superiority. Experimental results demonstrate that the proposed model achieves excellent prediction accuracy and stability in spring, summer, autumn, and winter, showing strong potential for engineering applications. Full article
(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
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