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Keywords = non-stationary wind

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29 pages, 2377 KB  
Article
Multi-Scale Spectral Recurrent Network Based on Random Fourier Features for Wind Speed Forecasting
by Eder Arley Leon-Gomez, Víctor Elvira, Jorge Iván Montes-Monsalve, Andrés Marino Álvarez-Meza, Alvaro Orozco-Gutierrez and German Castellanos-Dominguez
Technologies 2026, 14(4), 238; https://doi.org/10.3390/technologies14040238 (registering DOI) - 18 Apr 2026
Abstract
Accurate wind speed forecasting is critical for reliable wind-power integration, yet it remains challenging due to the strongly non-stationary and inherently multi-scale nature of atmospheric processes. While deep learning models—such as LSTM, GRU, and Transformer architectures—achieve competitive short- and medium-term performance, they frequently [...] Read more.
Accurate wind speed forecasting is critical for reliable wind-power integration, yet it remains challenging due to the strongly non-stationary and inherently multi-scale nature of atmospheric processes. While deep learning models—such as LSTM, GRU, and Transformer architectures—achieve competitive short- and medium-term performance, they frequently suffer from spectral bias, hyperparameter sensitivity, and reduced generalization under heterogeneous operating regimes. To address these limitations, we propose a multi-scale spectral–recurrent framework, termed RFF-RNN, which integrates multi-band Random Fourier Feature (RFF) encodings with parameterizable recurrent backbones. A key innovation of our approach is the deliberate relaxation of strict shift-invariance constraints; by jointly optimizing spectral frequencies, phase biases, and bandwidth scales alongside the neural weights, the framework dynamically shapes a fully data-driven spectral embedding. To ensure robust adaptation, we employ a two-stage optimization strategy combining gradient-based inner-loop learning with outer-loop Bayesian hyperparameter tuning. Our extensive evaluations on a controlled synthetic benchmark and six geographically diverse real-world wind datasets (spanning the USA, China, and the Netherlands) demonstrate the superiority of the proposed framework. Statistical validation via the Friedman test confirms that RFF-enhanced models—particularly RFF-GRU and RFF-LSTM—systematically outperform standard recurrent networks and state-of-the-art Transformer architectures (Autoformer and FEDformer). The proposed approach yields significantly lower error metrics (MAE and RMSE) and higher explained variance (R2), while exhibiting remarkable resilience against error accumulation at extended forecasting horizons. Full article
(This article belongs to the Special Issue AI for Smart Engineering Systems)
44 pages, 8887 KB  
Article
CEEMDAN–SST-GraphPINN-TimesFM Model Integrating Operating-State Segmentation and Feature Selection for Interpretable Prediction of Gas Concentration in Coal Mines
by Linyu Yuan
Sensors 2026, 26(8), 2476; https://doi.org/10.3390/s26082476 - 17 Apr 2026
Abstract
Gas concentration series in coal mining faces are jointly affected by multiple coupled factors, including geological conditions, mining disturbances, ventilation organization, and gas drainage intensity, and therefore exhibit pronounced nonstationarity, strong fluctuations, spatiotemporal correlations across multiple monitoring points, and occasional abrupt spikes. To [...] Read more.
Gas concentration series in coal mining faces are jointly affected by multiple coupled factors, including geological conditions, mining disturbances, ventilation organization, and gas drainage intensity, and therefore exhibit pronounced nonstationarity, strong fluctuations, spatiotemporal correlations across multiple monitoring points, and occasional abrupt spikes. To address these challenges, this study proposes a gas concentration prediction and early-warning method that integrates CEEMDAN–SST with GraphPINN-TimesFM (Graph Physics-Informed Neural Network–Time Series Foundation Model). First, based on multi-source monitoring data such as wind speed, gas concentrations at multiple monitoring points, and equipment operating status, anomaly removal, operating-condition segmentation, and change-point detection are performed to construct stable operating-state labels. Feature selection is then conducted by combining optimal time-lag correlation, Shapley value contribution, and dynamic time warping. Second, WGAN-GP is employed to augment samples from minority operating conditions, while CEEMDAN–SST is used to decompose and reconstruct the target series so as to reduce the interference of nonstationary noise and enhance sequence predictability. On this basis, TimesFM is adopted as the backbone for long-sequence forecasting to capture long-term dependency features in gas concentration evolution. Furthermore, GraphPINN is introduced to embed the topological associations among monitoring points, airflow transmission delays, and convection–diffusion mechanisms into the training process, thereby enabling collaborative modeling that integrates data-driven learning with physical constraints. Finally, the predictive performance, early-warning capability, and interpretability of the proposed model are systematically evaluated through regression forecasting, warning discrimination, and Shapley-based interpretability analysis. The results demonstrate that the proposed method can effectively improve the accuracy, robustness, and physical consistency of gas concentration prediction under complex operating conditions, thereby providing a new technical pathway for gas over-limit early warning and safety regulation in coal mining faces. Full article
(This article belongs to the Section Environmental Sensing)
21 pages, 4785 KB  
Article
Fault Diagnosis of Wind Turbine Bearings Based on a Multi-Scale Residual Attention Graph Neural Network
by Yubo Liu, Xiaohui Zhang, Keliang Dong, Zhilei Xu, Fengjuan Zhang and Zhiwei Li
Electronics 2026, 15(7), 1422; https://doi.org/10.3390/electronics15071422 - 29 Mar 2026
Viewed by 295
Abstract
Fault diagnosis of rolling bearings in wind turbines is significantly challenged by strong noise, non-stationary signals, and multi-source interference. To address these issues, a Multi-Scale Attention Residual Graph Convolutional Network (MSAR-GCN) is proposed. First, a fully connected graph is constructed in the frequency [...] Read more.
Fault diagnosis of rolling bearings in wind turbines is significantly challenged by strong noise, non-stationary signals, and multi-source interference. To address these issues, a Multi-Scale Attention Residual Graph Convolutional Network (MSAR-GCN) is proposed. First, a fully connected graph is constructed in the frequency domain using a temporal segmentation strategy, which preserves full spectral resolution and captures cross-frequency coupling features via node embeddings. Second, a multi-scale residual module with a cross-layer pyramid structure is designed to extract features at varying granularities, integrated with a dynamic multi-head attention mechanism to adaptively emphasize damage-sensitive frequency bands. Additionally, a hierarchical feature distillation mechanism is employed to compress high-dimensional features, ensuring model lightweighting while retaining critical fault information. Experimental validations on CWRU and JNU datasets demonstrate that MSAR-GCN achieves 97.02% and 92.5% accuracy under −10 dB Gaussian noise, respectively, outperforming existing methods by over 4%. Specifically, the model exhibits exceptional robustness, maintaining 93.09% accuracy under severe non-Gaussian impulsive noise. With verified feature separability and high computational efficiency, the proposed method offers a promising solution for high-precision, real-time industrial fault diagnosis. Full article
(This article belongs to the Special Issue Advances in Condition Monitoring and Fault Diagnosis)
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32 pages, 4620 KB  
Article
Joint Resource Allocation for Maritime RIS–RSMA Communications Using Fractal-Aware Robust Deep Reinforcement Learning
by Da Liu, Kai Su, Nannan Yang and Jingbo Zhang
Fractal Fract. 2026, 10(4), 223; https://doi.org/10.3390/fractalfract10040223 - 27 Mar 2026
Viewed by 231
Abstract
Sea-surface reflections and wind–wave motion render maritime channels strongly time-varying and statistically non-stationary, while nearshore deployments face sparse infrastructure and co-channel multiuser interference. This study integrates reconfigurable intelligent surfaces (RISs) with rate-splitting multiple access (RSMA) for joint online resource allocation. A physics-inspired time-varying [...] Read more.
Sea-surface reflections and wind–wave motion render maritime channels strongly time-varying and statistically non-stationary, while nearshore deployments face sparse infrastructure and co-channel multiuser interference. This study integrates reconfigurable intelligent surfaces (RISs) with rate-splitting multiple access (RSMA) for joint online resource allocation. A physics-inspired time-varying channel model is established by embedding fractional Brownian motion-driven slow statistical drift and reflection-phase perturbations. With imperfect, delayed channel state information (CSI) and discrete RIS phase quantization, a proportional-fairness utility maximization problem is formulated to jointly optimize shore base-station precoding, RIS phase shifts, and RSMA common-rate allocation. To cope with strong non-convexity, high dimensionality, mixed continuous–discrete coupling, and partial observability, a fractal-aware recurrent robust Actor–Critic (FRRAC) algorithm is developed. FRRAC encodes short observation histories using a gated recurrent unit and incorporates a lightweight Hurst-proxy estimator to capture slow channel statistics for robust value evaluation and policy learning. Truncated quantile critics and mixed prioritized–uniform replay further improve value robustness, training stability, and sample efficiency. Simulation results show that FRRAC converges faster and more stably under both conventional and fractal non-stationary channel modeling, and outperforms representative baselines across the objective and multiple statistical metrics, validating its effectiveness for joint resource optimization in maritime RIS–RSMA systems. Full article
(This article belongs to the Section Optimization, Big Data, and AI/ML)
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21 pages, 19468 KB  
Article
Comparative Study of Four Hybrid Spatiotemporal Models for Daily PM2.5 Prediction in the Chengdu–Chongqing Region
by Bin Hu, Ling Zeng and Haiming Fan
Sustainability 2026, 18(6), 3126; https://doi.org/10.3390/su18063126 - 23 Mar 2026
Viewed by 279
Abstract
The Chengdu–Chongqing Twin-City Economic Circle (CC-TCEC), located in the Sichuan Basin, frequently experiences persistent winter PM2.5 pollution due to basin-constrained ventilation and strong meteorology–emission coupling. Using daily PM2.5 observations from 113 monitoring stations with a strict two-year training and one-year testing [...] Read more.
The Chengdu–Chongqing Twin-City Economic Circle (CC-TCEC), located in the Sichuan Basin, frequently experiences persistent winter PM2.5 pollution due to basin-constrained ventilation and strong meteorology–emission coupling. Using daily PM2.5 observations from 113 monitoring stations with a strict two-year training and one-year testing split, we develop hybrid spatiotemporal forecasting models that couple a graph neural network (GCN/GAT) for inter-station spatial dependence learning with a temporal backbone (LSTM/Transformer) for evolving concentration dynamics. We adopt a rolling one-day-ahead forecasting scheme using a 7-day look-back window. Across 12-month, 6-month, and 3-month evaluation windows, the meteorology-augmented Multi-GAT-Transformer shows a slight but consistent advantage over the other tested variants, suggesting potential benefits of attention-based spatial weighting and long-range temporal self-attention under nonstationary basin pollution regimes. Spatiotemporal mappings derived from the best-performing configuration suggest that elevated winter PM2.5 is mainly associated with low-lying areas such as the Chengdu Plain, industry clusters, and dense urban cores, with peaks that also coincide with the New Year and the pre-Lunar New Year period, suggesting a possible contribution from elevated traffic and production activity. These impacts are amplified by winter stagnation (low winds, high humidity, limited precipitation). From a policy perspective, the results support sustainability-oriented winter haze management by enabling early episode warning and hotspot prioritization. Full article
(This article belongs to the Section Air, Climate Change and Sustainability)
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22 pages, 309 KB  
Article
Integrated Aerodynamic–Structural Validation Framework for Wind-Induced Load Assessment
by Tomasz Lamparski and Maciej Dutkiewicz
Appl. Sci. 2026, 16(6), 2986; https://doi.org/10.3390/app16062986 - 20 Mar 2026
Viewed by 302
Abstract
Understanding wind–structure interaction (WSI) in low-rise buildings remains a significant challenge in wind and structural engineering, particularly under highly turbulent and non-stationary wind phenomena such as downbursts and tornado-like vortices. While Computational Fluid Dynamics (CFD) has become a widely adopted tool for predicting [...] Read more.
Understanding wind–structure interaction (WSI) in low-rise buildings remains a significant challenge in wind and structural engineering, particularly under highly turbulent and non-stationary wind phenomena such as downbursts and tornado-like vortices. While Computational Fluid Dynamics (CFD) has become a widely adopted tool for predicting wind-induced loads, validation efforts remain predominantly limited to aerodynamic quantities—such as pressure and velocity fields—with insufficient consideration of structural response. This study presents a structured review of contemporary research in wind engineering, encompassing field measurements, wind tunnel experiments, and CFD modeling approaches. Particular attention is paid to turbulence model selection, methodological limitations of conventional validation strategies, and the often-overlooked necessity of incorporating structural response assessment into the validation process. Based on a synthesis of existing research, the paper outlines a multi-level validation perspective in which aerodynamic and structural validation are treated as interconnected components rather than independent procedures. The review identifies a prevailing focus on aerodynamic coefficients and flow field agreement, often lacking systematic integration of structural-scale verification. The proposed perspective emphasizes the need for a transparent and reproducible link between CFD-derived aerodynamic loads and structural response assessment. By bridging computational wind engineering and structural mechanics, this study supports a more reliable evaluation of wind-induced effects on building components and contributes to the development of robust, wind-resilient design methodologies for low-rise structures. Full article
(This article belongs to the Section Civil Engineering)
34 pages, 7008 KB  
Article
Development of a TimesNet–NLinear Framework Based on Seasonal-Trend Decomposition Using LOESS for Short-Term Motion Response of Floating Offshore Wind Turbines
by Xinheng Zhang, Yao Cheng, Peng Dou, Yihan Xing, Renwei Ji, Pei Zhang, Puyi Yang, Xiaosen Xu and Shuaishuai Wang
J. Mar. Sci. Eng. 2026, 14(6), 571; https://doi.org/10.3390/jmse14060571 - 19 Mar 2026
Viewed by 349
Abstract
Floating offshore wind turbines (FOWTs) exhibit complex motions under marine environmental loads and frequently undergo coupled oscillations across multiple degrees of freedom (DOFs). Accurate short-term motion prediction of these responses is crucial for operational safety and maintenance. To overcome the limitations of traditional [...] Read more.
Floating offshore wind turbines (FOWTs) exhibit complex motions under marine environmental loads and frequently undergo coupled oscillations across multiple degrees of freedom (DOFs). Accurate short-term motion prediction of these responses is crucial for operational safety and maintenance. To overcome the limitations of traditional “black-box” models under complex aero-hydrodynamic loads, this study proposes STL–TimesNet–NLinear, a novel physics-informed deep learning framework. The framework utilizes STL decomposition to explicitly decouple motion signals: NLinear captures non-stationary low-frequency slow drifts, while TimesNet extracts multi-periodic wave-frequency responses. The model was evaluated across different platform typologies—a 5 MW semi-submersible and a larger-scale 15 MW Spar-type platform—under various typical operational and extreme environmental conditions. Model performance was evaluated using comparative and ablation experiments. At a prediction-ahead time (PAT) of 5 s, the proposed model achieves coefficients of determination (R2) exceeding 0.95. Even at longer PATs, the R2 remains above 0.90, consistently outperforming multiple benchmark models. Compared to traditional recurrent neural networks (e.g., LSTM), it decreases the Mean Absolute Error (MAE) for pitch motion under extreme sea states by 54.7% and increases the R2 to 0.9573. Furthermore, the inference latency is only 2.4 ms per step. These findings confirm that the proposed STL–TimesNet–NLinear model provides fast and accurate solutions for the short-term motion response prediction of FOWTs, demonstrating valuable potential applications for enhancing the safety planning of offshore wind turbine operation and maintenance. Full article
(This article belongs to the Special Issue Breakthrough Research in Marine Structures)
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19 pages, 6417 KB  
Article
Improved Football Team Training Algorithm Based on Modal Decomposition and BiLSTM Method for Short-Term Wind Power Forecasting
by Lingling Xie, Yanjing Luo, Chunhui Li, Long Li and Fengyuan Liu
Processes 2026, 14(6), 951; https://doi.org/10.3390/pr14060951 - 17 Mar 2026
Viewed by 346
Abstract
Reliable wind power forecasting is essential for maintaining the safe and stable operation of power systems with high renewable energy penetration. This study proposes a short-term wind power forecasting model based on decomposition–optimization–prediction, integrating complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN), [...] Read more.
Reliable wind power forecasting is essential for maintaining the safe and stable operation of power systems with high renewable energy penetration. This study proposes a short-term wind power forecasting model based on decomposition–optimization–prediction, integrating complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN), the improved football team training algorithm (IFTTA), and the bidirectional long short-term memory network model (BiLSTM). CEEMDAN is employed to decompose the non-stationary wind power sequence into relatively stable intrinsic mode functions (IMFs), thereby separating multi-scale fluctuation features. The IFTTA incorporates a dynamic probability allocation strategy and an adaptive parameter adjustment mechanism, which contributes to a better balance between global exploration and local exploitation. After optimizing the hyperparameters of BiLSTM using IFTTA, the prediction performance significantly improved. Validations were conducted on three datasets from Xinjiang, Ningxia, and Inner Mongolia, China, each containing 1440 samples (1152 for training and 288 for testing). Comparisons with the benchmark forecasting model demonstrate that the pro-posed model reduces the mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) by at least 25.29%, 29.62%, and 20.66%, respectively. Correspondingly, the coefficient of determination (R2) was improved by at least 0.0069. This model provides an effective solution for short-term wind power prediction in practical engineering. Full article
(This article belongs to the Special Issue Adaptive Control and Optimization in Power Grids)
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25 pages, 7057 KB  
Article
Vertical Wind Speed Extrapolation and Power Estimation via a Hybrid Physics-Data-Driven Approach
by Zongxuan Wu, Borui Lv, Bingcun Chen, Genliang Wang, Yinzhu Wan, Boya Zhao and Minyi He
Energies 2026, 19(5), 1302; https://doi.org/10.3390/en19051302 - 5 Mar 2026
Viewed by 305
Abstract
The scale mismatch between wind turbine hub heights and conventional meteorological masts introduces uncertainties in wind resource assessment. Vertical wind speed extrapolation serves as a critical technique to bridge this spatial gap. Current extrapolation paradigms struggle with two fundamental limitations. Physical models fail [...] Read more.
The scale mismatch between wind turbine hub heights and conventional meteorological masts introduces uncertainties in wind resource assessment. Vertical wind speed extrapolation serves as a critical technique to bridge this spatial gap. Current extrapolation paradigms struggle with two fundamental limitations. Physical models fail to capture non-stationary atmospheric stability, whereas purely data-driven methods depend heavily on unavailable hub-height ground truth. To bridge this gap, this paper proposes a Physically Guided Neural Network framework. By integrating physical boundary-layer principles with an adaptive residual correction mechanism, the model introduces an inductive bias that maps near-surface observations to dynamic wind shear evolutions. The network employs a “Near-Surface Learning and Hub-Height” Transfer strategy. This approach optimizes the model exclusively on multi-level observations from 10 to 70 m to eliminate the dependency on high-altitude target labels. Validation on a 100 MW wind farm dataset, utilizing a 70 m proxy variable evaluation, demonstrates that this framework reduces the wind speed extrapolation root mean square error by 56.48% compared to traditional power law models. Furthermore, downstream theoretical power estimation errors are reduced by 10.72%, effectively mitigating power curve lag phenomena. This hybrid approach establishes a robust and low-cost paradigm for refined wind energy assessment in engineering scenarios lacking tall meteorological monitoring. Full article
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22 pages, 4305 KB  
Article
Wind Noise Reduction Based on the Double Masking and Permutation-Invariant Training
by Kai-Wen Liang, Wenny Ramadha Putri, Wei-Hung Liu, Yen-Ting Lai, Bach-Tung Pham, Jian-Hong Wang, Ming-Hsiang Su, Kuo-Chen Li, Shih-Lun Chen, Zhao-Di Jiang, Jang-Zern Tsai, Yung-Hui Li, Jia-Ching Wang and Pao-Chi Chang
Electronics 2026, 15(5), 978; https://doi.org/10.3390/electronics15050978 - 27 Feb 2026
Viewed by 354
Abstract
Wind noise is a pervasive and non-stationary form of interference in outdoor audio recordings, posing a significant challenge for speech enhancement systems. To address this problem, this paper proposes a speech separation-based wind noise reduction framework termed Dual-mask permutation-invariant training (DMPIT). Building upon [...] Read more.
Wind noise is a pervasive and non-stationary form of interference in outdoor audio recordings, posing a significant challenge for speech enhancement systems. To address this problem, this paper proposes a speech separation-based wind noise reduction framework termed Dual-mask permutation-invariant training (DMPIT). Building upon the dual-masking concept, the key contribution of DMPIT lies in embedding the dual-mask structure within a permutation-invariant training (PIT) framework and reformulating the loss function to better align with speech-oriented noise reduction objectives. Specifically, two supervised masks are jointly optimized: a speech mask that directly estimates the target speech from the mixture and a noise mask that isolates the wind noise component. Assuming that the mixture consists solely of speech and wind noise, the training process computes the loss using both estimated components and the corresponding clean speech. Since wind noise is not a signal of interest, the estimated noise is subtracted from the mixture to obtain a residual speech signal, which is then used to refine the direct speech estimate. The final enhanced speech output is produced by fusing the direct and residual speech estimates through a weighted combination. The experimental results demonstrate that DMPIT consistently outperforms conventional single-mask and single-channel wind noise reduction methods in terms of speech quality and noise suppression. Full article
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19 pages, 7695 KB  
Article
High-Precision Ultrasonic Anemometry System Based on Polyvinylidene Fluoride Piezoelectric Film and Variational Mode Decomposition-Extended Kalman Filter Joint Optimization
by Haodong Niu, Yunbo Shi, Kuo Zhao, Jinzhou Liu, Qinglong Chen and Xiaohui Yang
Sensors 2026, 26(5), 1482; https://doi.org/10.3390/s26051482 - 26 Feb 2026
Viewed by 320
Abstract
Ultrasonic wind speed measurements performed in complex flow fields face challenges related to low signal-to-noise ratio (SNR) and non-stationary waveform distortion. In this study, we aim to address this issue by proposing a measurement system that employs a polyvinylidene fluoride (PVDF) piezoelectric film [...] Read more.
Ultrasonic wind speed measurements performed in complex flow fields face challenges related to low signal-to-noise ratio (SNR) and non-stationary waveform distortion. In this study, we aim to address this issue by proposing a measurement system that employs a polyvinylidene fluoride (PVDF) piezoelectric film ultrasonic transducer integrated with a microphone (MIC). In addition, a signal processing framework is proposed based on the joint optimization of variational mode decomposition (VMD) and an extended Kalman filter (EKF) and integrating cross-correlation interpolation. By leveraging the low Q-factor and wide bandwidth characteristics of the PVDF, the system achieved omnidirectional transmission and high-fidelity reception within a compact structural design. The experimental results demonstrated that the proposed VMD-reference signal-assisted EKF method enhanced the SNR by approximately 26% and reduced the wind speed measurement error by approximately 35% compared with the conventional EKF. The proposed system exhibited superior robustness and measurement linearity across a wide wind speed range of 0–60 m/s. The proposed scheme significantly enhances the accuracy and environmental adaptability of ultrasonic wind speed measurements and provides an essential theoretical basis and engineering reference for the development of precision instruments in fields such as meteorological monitoring and wind energy assessment. Full article
(This article belongs to the Special Issue Ultrasonic Sensors and Ultrasonic Signal Processing)
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17 pages, 2049 KB  
Article
Simulation of Nonstationary Fluctuating Wind Fields Using POD Decoupling and Spline Interpolation
by Junfeng Zhang, Yuhang Xia, Ningbo Liu, Zheng Liu and Jie Li
Buildings 2026, 16(4), 804; https://doi.org/10.3390/buildings16040804 - 15 Feb 2026
Viewed by 340
Abstract
Improving the simulation efficiency of the spectral representation method (SRM) for nonstationary fluctuating wind fields has attracted considerable attention. To this end, this study proposes a method based on proper orthogonal decomposition (POD) decoupling and Spline interpolation to enhance computational efficiency. This method [...] Read more.
Improving the simulation efficiency of the spectral representation method (SRM) for nonstationary fluctuating wind fields has attracted considerable attention. To this end, this study proposes a method based on proper orthogonal decomposition (POD) decoupling and Spline interpolation to enhance computational efficiency. This method selects a limited number of interpolation points in the time-frequency domain of the evolutionary power spectral density (EPSD) for Cholesky decomposition, utilizes the proper orthogonal decomposition (POD) technique to achieve time-frequency decoupling of the spectral matrix, and employs Spline interpolation but not the traditional Hermite-interpolation to reconstruct the complete time-frequency functions, thereby enabling the rapid synthesis of wind-velocity time histories via the FFT. Then, the wind field on a three-span frame lightning-rod structure is taken as an example to validate the reliability of the proposed method. The influences of the modal order and the number of time-frequency interpolation points on both simulation efficiency and error are investigated, and comparisons are given with the Hermite-interpolation-based method. The results indicate that the simulation efficiency is governed primarily by the modal order, and the method with Spline interpolation shows higher computational efficiency and accuracy because it can satisfy accuracy requirements at a lower modal order. Finally, a rational truncation criterion based on the cumulative energy ratio of at least 99.9% is suggested to determine the optimal modal order, thereby achieving a balance between accuracy and computational efficiency. Full article
(This article belongs to the Special Issue Dynamic Response Analysis of Structures Under Wind and Seismic Loads)
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29 pages, 4216 KB  
Article
Random Vibrations of Wind Turbines Mitigated by the Hourglass Transition Piece
by Alessandro Tombari, Marco Fabiani and Yucheng Peng
J. Mar. Sci. Eng. 2026, 14(4), 325; https://doi.org/10.3390/jmse14040325 - 7 Feb 2026
Viewed by 406
Abstract
Wind turbines are subjected to complex stochastic loadings generated by various environmental sources, including wind, waves, and earthquakes. Efficient mitigation of the resulting vibrations in the structural components, such as the tower and monopile, leads to more cost-effective designs and longer operational life [...] Read more.
Wind turbines are subjected to complex stochastic loadings generated by various environmental sources, including wind, waves, and earthquakes. Efficient mitigation of the resulting vibrations in the structural components, such as the tower and monopile, leads to more cost-effective designs and longer operational life by reducing fatigue accumulation. Conventional vibration control systems have primarily relied on tuned mass dampers. However, alternative and non-conflicting strategies that modify the connection between the tower and the foundation at the transition piece level have recently gained attention. This study investigates the hourglass transition piece (HGTP), a novel concept that utilises the Reduced Column Section approach. The hourglass geometry enables fine-tuning of the wind turbine’s fundamental period and introduces controlled rotational motion, both contributing to a reduction in structural stresses and improved dynamic performance. To assess the efficacy of the HGTP as a vibration control system, an analytical model of a simplified wind turbine is developed. The formulation employs frequency-dependent solutions of prismatic and tapered beam elements, assembled to capture the dynamic behaviour of the turbine equipped with the HGTP. Exact dynamic stiffness matrices are derived and assembled into a stochastic framework suitable for uniformly modulated non-stationary random processes. Modal and dynamic responses are evaluated for different reductions of the hourglass central section. A case study based on the IEA 15 MW Reference Wind Turbine demonstrates that the HGTP can mitigate stochastic mean peak bending moments induced by wind and earthquake excitations by up to 50%, confirming its potential as an effective vibration control solution. Full article
(This article belongs to the Special Issue New Era in Offshore Wind Energy)
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25 pages, 8031 KB  
Article
A Dual-Optimized Hybrid Deep Learning Framework with RIME-VMD and TCN-BiGRU-SA for Short-Term Wind Power Prediction
by Zhong Wang, Kefei Zhang, Xun Ai, Sheng Liu and Tianbao Zhang
Appl. Sci. 2026, 16(3), 1531; https://doi.org/10.3390/app16031531 - 3 Feb 2026
Viewed by 344
Abstract
Precise short-term forecasting of wind power generation is indispensable for ensuring the security and economic efficiency of power grid operations. Nevertheless, the inherent non-stationarity and stochastic nature of wind power series present significant challenges for prediction accuracy. To address these issues, this paper [...] Read more.
Precise short-term forecasting of wind power generation is indispensable for ensuring the security and economic efficiency of power grid operations. Nevertheless, the inherent non-stationarity and stochastic nature of wind power series present significant challenges for prediction accuracy. To address these issues, this paper proposes a dual-optimized hybrid deep learning framework combining Spearman correlation analysis, RIME-VMD, and TCN-BiGRU-SA. First, Spearman correlation analysis is employed to screen meteorological factors, eliminating redundant features and reducing model complexity. Second, an adaptive Variational Mode Decomposition (VMD) strategy, optimized by the RIME algorithm based on Minimum Envelope Entropy, decomposes the non-stationary wind power series into stable intrinsic mode functions (IMFs). Third, a hybrid predictor integrating Temporal Convolutional Network (TCN), Bidirectional Gated Recurrent Unit (BiGRU), and Self-Attention (SA) mechanisms is constructed to capture both local trends and long-term temporal dependencies. Furthermore, the RIME algorithm is utilized again to optimize the hyperparameters of the deep learning predictor to avoid local optima. The proposed framework is validated using full-year datasets from two distinct wind farms in Xinjiang and Gansu, China. Experimental results demonstrate that the proposed model achieves a Root Mean Square Error (RMSE) of 7.5340 MW on the primary dataset, significantly outperforming mainstream baseline models. The multi-dataset verification confirms the model’s superior prediction accuracy, robustness against seasonal variations, and strong generalization capability. Full article
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22 pages, 16609 KB  
Article
A Unified Transformer-Based Harmonic Detection Network for Distorted Power Systems
by Xin Zhou, Qiaoling Chen, Li Zhang, Qianggang Wang, Niancheng Zhou, Junzhen Peng and Yongshuai Zhao
Energies 2026, 19(3), 650; https://doi.org/10.3390/en19030650 - 27 Jan 2026
Cited by 1 | Viewed by 400
Abstract
With the large-scale integration of power electronic converters, non-linear loads, and renewable energy generation, voltage and current waveform distortion in modern power systems has become increasingly severe, making harmonic resonance amplification and non-stationary distortion more prominent. Accurate and robust harmonic-level prediction and detection [...] Read more.
With the large-scale integration of power electronic converters, non-linear loads, and renewable energy generation, voltage and current waveform distortion in modern power systems has become increasingly severe, making harmonic resonance amplification and non-stationary distortion more prominent. Accurate and robust harmonic-level prediction and detection have become essential foundations for power quality monitoring and operational protection. However, traditional harmonic analysis methods remain highly dependent on pre-designed time–frequency transformations and manual feature extraction. They are sensitive to noise interference and operational variations, often exhibiting performance degradation under complex operating conditions. To address these challenges, a Unified Physics-Transformer-based harmonic detection scheme is proposed to accurately forecast harmonic levels in offshore wind farms (OWFs). This framework utilizes real-world wind speed data from Bozcaada, Turkey, to drive a high-fidelity electromagnetic transient simulation, constructing a benchmark dataset without reliance on generative data expansion. The proposed model features a Feature Tokenizer to project continuous physical quantities (e.g., wind speed, active power) into high-dimensional latent spaces and employs a Multi-Head Self-Attention mechanism to explicitly capture the complex, non-linear couplings between meteorological inputs and electrical states. Crucially, a Multi-Task Learning (MTL) strategy is implemented to simultaneously regress the Total Harmonic Distortion (THD) and the characteristic 5th Harmonic (H5), effectively leveraging shared representations to improve generalization. Comparative experiments with Random Forest, LSTM, and GRU systematically evaluate the predictive performance using metrics such as root mean square error (RMSE) and mean absolute percentage error (MAPE). Results demonstrate that the Physics-Transformer significantly outperforms baseline methods in prediction accuracy, robustness to operational variations, and the ability to capture transient resonance events. This study provides a data-efficient, high-precision approach for harmonic forecasting, offering valuable insights for future renewable grid integration and stability analysis. Full article
(This article belongs to the Special Issue Technology for Analysis and Control of Power Quality)
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