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Keywords = short-term multiple load forecasting

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36 pages, 10238 KB  
Article
Evaluating the Reliability of Cross-Building Load Forecasting Under Distribution Shift and Sensor Missingness
by Yunkai Hao, Jian Yang and Zhigang Ji
Appl. Sci. 2026, 16(16), 7984; https://doi.org/10.3390/app16167984 - 11 Aug 2026
Cited by 1 | Viewed by 315
Abstract
Short-term building-electricity-load forecasting is important for energy management and smart-building operation. However, existing evaluations mainly focus on prediction accuracy and provide limited assessment of reliability under cross-building shifts and data quality variations. This study develops an empirical evaluation framework based on the HEEW [...] Read more.
Short-term building-electricity-load forecasting is important for energy management and smart-building operation. However, existing evaluations mainly focus on prediction accuracy and provide limited assessment of reliability under cross-building shifts and data quality variations. This study develops an empirical evaluation framework based on the HEEW dataset. A five-fold cross-building validation protocol was designed, including 55 main buildings and 27 additional buildings for extended sensitivity analysis. The prediction performance, sensor missingness robustness, prediction interval calibration, and model interpretation stability were evaluated. The results show that the LightGBM residual model outperforms the Lag-1 persistence baseline in cross-building forecasting. It reduces Normalized Mean Absolute Error (NMAE) by 11.3% in the unseen-building future-year scenario. Missingness experiments indicate that historical load features have a stronger influence on one-hour-ahead forecasting than weather features. A 50% missing rate in auxiliary load history increases NMAE by 96.71%, while weather feature missingness causes limited degradation. Conformal prediction maintains reasonable coverage for seen buildings but shows reduced coverage after transferring to unseen buildings. SHAP analysis further shows stable feature importance patterns across different scenarios. Overall, this study shows that the reliability of cross-building load forecasting should be evaluated from multiple angles, beyond point prediction accuracy alone. Full article
(This article belongs to the Section Energy Science and Technology)
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24 pages, 1382 KB  
Article
A Multi-Scale Convolutional Neural Network with Residual Blocks and LSTM for Multi-Step Forecasting of Electricity Load
by Yuhang Zhang, Yiting Zhao, Yujing Meng, Jingqi Li, Tianze Zhang and Ying Zhang
Computers 2026, 15(7), 457; https://doi.org/10.3390/computers15070457 - 18 Jul 2026
Viewed by 411
Abstract
Electricity load forecasting is essential for balancing energy supply and demand, reducing energy waste, and maintaining power grid stability. Accurate forecasts enable power utilities to optimize energy dispatch and mitigate the risk of supply shortages or outages. However, conventional forecasting methods often struggle [...] Read more.
Electricity load forecasting is essential for balancing energy supply and demand, reducing energy waste, and maintaining power grid stability. Accurate forecasts enable power utilities to optimize energy dispatch and mitigate the risk of supply shortages or outages. However, conventional forecasting methods often struggle to capture highly nonlinear local fluctuations in electricity consumption and long-term temporal dependencies. To address these challenges, this study proposes MSCNN-ResLSTM, a hybrid model for multi-step electricity load forecasting. The proposed model integrates Multi-Scale Convolutional Neural Networks (MSCNNs) to extract local time-series features at multiple temporal scales, residual blocks (ResBlocks) to enhance feature representation through residual connections, and Long Short-Term Memory (LSTM) networks to model long-range temporal dependencies. To comprehensively evaluate its effectiveness, a cross-paradigm experimental framework is established in which MSCNN-ResLSTM is compared with seven representative benchmark models from three methodological categories: traditional machine learning (Extreme Gradient Boosting-XGBoost), classical recurrent and convolutional neural networks (LSTM, Temporal Convolutional Network-TCN, CNN-LSTM, MSCNN-LSTM, and Direct LSTM (Seq2Seq)), and self-attention-based architectures (Transformer). Experimental results show that MSCNN-ResLSTM achieves higher forecasting accuracy and greater stability across the full 24-step prediction horizon, consistently outperforming all competing baselines while effectively suppressing recursive error propagation. Full article
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20 pages, 3094 KB  
Article
Distributionally Robust Coordinated Maintenance and Dispatch in Multi-Energy Systems with Electricity, Heat, and Hydrogen Carriers: A Wasserstein-Metric Framework
by Anurag Gautam, Pitshou Ntambu Bokoro, Gulshan Sharma and Rajesh Kumar
Energies 2026, 19(13), 3221; https://doi.org/10.3390/en19133221 - 7 Jul 2026
Cited by 1 | Viewed by 501
Abstract
The high energy demand driven by industrial development has transformed the power system from a single energy source to multiple energy systems (MESs). These systems, which involve thermal generators, combined heat-and-power (CHP) units, electrolyzers, fuel cells, etc., with realistic forecast uncertainty, are very [...] Read more.
The high energy demand driven by industrial development has transformed the power system from a single energy source to multiple energy systems (MESs). These systems, which involve thermal generators, combined heat-and-power (CHP) units, electrolyzers, fuel cells, etc., with realistic forecast uncertainty, are very operationally challenged. This paper proposes a Distributionally Robust Optimization (DRO) based on a Wasserstein-metric ambiguity set, which simultaneously optimizes the annual maintenance schedules and short-term operational dispatch across MESs. The ambiguity set is constructed using joint samples of forecast errors for the three carriers’ demand, allowing for a data-driven worst-case distribution approach that mitigates the excessive conservatism typically associated with conventional robust optimization (CRO). The penalties are explicitly enforced for load and renewable energy curtailments across each of the MESs with source-specific value-of-lost-load coefficients. The Wasserstein radius is improved by sensitivity analysis, obtaining a θ value of 0.20 as the cost reduction radius for a 40% RES penetration. Five RES penetration levels are implemented here on the IEEE 39-bus New England network, with CHP, electrolyzer, fuel cell, thermal storage, and hydrogen storage. The DRO reduces the total annual system cost by 56% compared to CRO, while reducing the unbalanced energy. Full article
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19 pages, 2157 KB  
Article
FTimeDD: A Time–Frequency Collaborative Model for Multi-Energy Load Forecasting
by Zi Lin, Ziyi Wang, Tengyue Guo and Min Xia
Energies 2026, 19(11), 2729; https://doi.org/10.3390/en19112729 - 5 Jun 2026
Viewed by 391
Abstract
With the global energy transition, Integrated Energy Systems (IESs) improve efficiency by coordinating multiple energy sources, including electricity, cooling, and heating. Accurate load forecasting is essential for reliable energy system operation. However, multi-energy loads show complex coupling, non-stationarity, and long-term dependencies. These characteristics [...] Read more.
With the global energy transition, Integrated Energy Systems (IESs) improve efficiency by coordinating multiple energy sources, including electricity, cooling, and heating. Accurate load forecasting is essential for reliable energy system operation. However, multi-energy loads show complex coupling, non-stationarity, and long-term dependencies. These characteristics pose significant challenges to forecasting tasks. Existing methods have improved short-term forecasting accuracy, but still struggle to jointly capture long-term trends and local fluctuations. To address these issues, this paper proposes FTimeDD, a time–frequency collaborative model for multi-energy load forecasting in IESs. It adopts a dual-path decoupling architecture. The time-domain path separates trend and fluctuation components, while the frequency-domain path extracts dominant periodic features. The two paths are then fused to predict electricity, cooling, and heating loads. Experiments on the ASU Integrated Energy System dataset show that FTimeDD performs well across different forecasting horizons. Compared with the strongest baseline for each metric and horizon, FTimeDD reduces MAE, RMSE, and MAPE by 3.85%, 2.48%, and 1.91% on average, respectively. The method improves forecasting accuracy under the adopted experimental setting while maintaining a compact model scale and low computational cost. Full article
(This article belongs to the Special Issue Artificial Intelligence for Energy Forecasting)
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21 pages, 1852 KB  
Article
An Explainable Meta-Learning Framework for Adaptive Model Selection in Short-Term Load Forecasting
by Abeer Masfer and Samia Dardouri
Electronics 2026, 15(10), 2060; https://doi.org/10.3390/electronics15102060 - 12 May 2026
Viewed by 601
Abstract
Accurate short-term load forecasting (STLF) is essential for the reliable and efficient operation of modern power systems, particularly with the increasing integration of renewable energy and the transition toward smart grids. However, most existing approaches rely on a single forecasting model, despite evidence [...] Read more.
Accurate short-term load forecasting (STLF) is essential for the reliable and efficient operation of modern power systems, particularly with the increasing integration of renewable energy and the transition toward smart grids. However, most existing approaches rely on a single forecasting model, despite evidence that model performance varies across datasets and forecasting horizons. To address this limitation, this paper proposes an explainable meta-learning framework for adaptive model selection in STLF. Unlike conventional methods that aim to identify a universally optimal model, the proposed approach learns to select the most suitable model based on dataset characteristics and forecasting conditions. The framework integrates cross-dataset evaluation, meta-feature extraction, and a Random Forest-based meta-learner to dynamically determine the best-performing model. The proposed approach is evaluated on three benchmark power systems—Panama, PJM, and Spanish datasets—under both single-step and multi-horizon forecasting settings. The results provide initial evidence of adaptability across multiple datasets. Specifically, LSTM achieves the best single-step performance on the Panama (MAPE = 2.88%) and PJM (MAPE = 7.71%) datasets, while XGBoost outperforms other models on the Spanish dataset (MAPE = 1.07%). Statistical analysis suggests meaningful performance differences, although these findings should be interpreted with caution due to the limited sample size. Furthermore, SHapley Additive exPlanations (SHAP) are employed to enhance interpretability, revealing that forecasting horizon, data variability, and dataset characteristics are the most influential factors in model selection. Overall, the proposed framework improves forecasting accuracy, robustness, and transparency, while promoting a shift from model-centric design to adaptive, data-driven model selection. The framework offers a structured and explainable approach with potential for practical deployment in smart grid applications. Full article
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20 pages, 6572 KB  
Article
A Complex-Valued Neural Network Approach to Time Series Forecasting in Smart Grid Energy Systems
by Igor Aizenberg, Lorenzo Becchi, Marco Bindi, Matteo Intravaia and Antonio Luchetta
Energies 2026, 19(9), 2247; https://doi.org/10.3390/en19092247 - 6 May 2026
Viewed by 542
Abstract
This work is devoted to the application of complex-valued neural networks based on the multilayer neural network with multi-valued neurons (MLMVN) for short-term electrical load forecasting in smart grid energy systems. Accurate forecasting is a critical component of energy management systems, as it [...] Read more.
This work is devoted to the application of complex-valued neural networks based on the multilayer neural network with multi-valued neurons (MLMVN) for short-term electrical load forecasting in smart grid energy systems. Accurate forecasting is a critical component of energy management systems, as it directly impacts the efficiency of control and optimization strategies in increasingly distributed and stochastic environments. The proposed approach leverages the intrinsic properties of complex numbers to model periodicity and nonlinear relationships typical of load time series. A compact feedforward architecture with two hidden layers is adopted and combined with multiple preprocessing strategies, including unit circle encoding, Fourier transform representations, and hybrid feature mappings incorporating temporal information such as the day of the week. The performance of the proposed models is evaluated on real-world prosumer data and compared against two benchmarks: a seasonal persistence model and a Long Short-Term Memory network. Results show that MLMVN-based approaches achieve comparable or improved performance in terms of RMSE and error reduction capability, despite their lower architectural complexity. Fourier-based preprocessing methods demonstrate strong effectiveness in capturing underlying temporal patterns. These findings suggest that complex-valued representations provide a promising alternative to traditional deep learning approaches, offering a favorable balance between accuracy, interpretability, and computational efficiency in Smart Grid forecasting applications. Full article
(This article belongs to the Special Issue Artificial Intelligence in Modern Power and Energy Systems)
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21 pages, 1311 KB  
Article
Interpretable Multi-Sensor Fusion for Short-Term Energy Consumption Forecasting
by Rakibul Hasan, Majdi Mansouri, Jura Arkhangelski and Mahamadou Abdou Tankari
Energies 2026, 19(9), 2230; https://doi.org/10.3390/en19092230 - 5 May 2026
Cited by 2 | Viewed by 676
Abstract
Accurate forecasting of energy consumption in sensor-rich environments remains challenging due to strong inter-sensor dependencies, temporal variability, and heterogeneous sensor behavior. This paper proposes a lightweight and interpretable multi-sensor fusion framework for short-term energy consumption forecasting. The heterogeneous sensor dataset is first preprocessed [...] Read more.
Accurate forecasting of energy consumption in sensor-rich environments remains challenging due to strong inter-sensor dependencies, temporal variability, and heterogeneous sensor behavior. This paper proposes a lightweight and interpretable multi-sensor fusion framework for short-term energy consumption forecasting. The heterogeneous sensor dataset is first preprocessed to handle missing values, outliers, and temporal misalignment, followed by synchronization of the multivariate signals on a common timeline to enable consistent learning. The proposed framework systematically investigates multiple strategies for exploiting information from synchronized multi-sensor data without performing explicit feature elimination or time-lag engineering. In particular, three fusion paradigms are considered: (i) Early Fusion, where all sensor measurements are jointly used as input features for a multivariate regression model; (ii) Late Fusion, where individual sensor predictors are trained independently and their outputs are combined using reliability-based weighting; and (iii) an attention-inspired fusion strategy, in which adaptive weights are assigned to sensor-level predictions based on their predictive reliability estimated from training errors and normalized via a softmax function. In addition, classical machine learning models including Random Forest (RF), Support Vector Regression (SVR), and Gradient Boosting (GB) are evaluated under the same experimental conditions to provide a consistent benchmark. Experimental results on a real-world building energy monitoring dataset consisting of nine heterogeneous sensors demonstrate that multi-sensor fusion approaches consistently improve forecasting performance compared to single-model baselines. Among the evaluated strategies, Late Fusion provides stable performance across strongly correlated loads, while the attention-inspired fusion strategy exhibits improved robustness when handling sensors with varying predictive reliability. To ensure robustness and reproducibility, results are reported using multiple chronological validation splits, with performance evaluated in terms of RMSE, MAE, and R2 along with statistical measures including standard deviation and confidence intervals. The proposed framework provides a practical balance between predictive accuracy, interpretability, and computational efficiency, making it suitable for smart building energy management and real-world deployment scenarios. Full article
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21 pages, 7514 KB  
Article
Multi-Scale Displacement Prediction and Failure Mechanism Identification for Hydrodynamically Triggered Landslides
by Jian Qi, Ning Sun, Zhong Zheng, Yunzi Wang, Zhengxing Yu, Shuliang Peng, Jing Jin and Changhao Lyu
Water 2026, 18(8), 917; https://doi.org/10.3390/w18080917 - 11 Apr 2026
Viewed by 546
Abstract
Hydrodynamically triggered landslides remain a major concern in reservoir regions, where the mechanisms controlling displacement evolution are still not fully understood and the multi-scale deformation responses induced by individual hydrodynamic factors remain difficult to quantify. To address these issues, this study establishes a [...] Read more.
Hydrodynamically triggered landslides remain a major concern in reservoir regions, where the mechanisms controlling displacement evolution are still not fully understood and the multi-scale deformation responses induced by individual hydrodynamic factors remain difficult to quantify. To address these issues, this study establishes a TSD-TET composite framework by integrating time-series signal decomposition with deep learning for multi-scale displacement prediction and the mechanism-oriented interpretation of hydrodynamically triggered landslides. The monitored displacement sequence is first decomposed into physically interpretable components, including trend, periodic, and random terms. Each component is subsequently predicted using deep temporal learning models to capture different deformation characteristics at multiple temporal scales. Meanwhile, key hydrodynamic driving factors, including rainfall, reservoir water level, and groundwater level, are decomposed within the same framework to examine their statistical associations with different displacement components. The proposed approach is applied to the Donglingxin landslide located in the Sanbanxi Hydropower Station reservoir area. Results show that the model achieves high prediction accuracy under both long-term forecasting horizons and limited-sample conditions, with a cumulative displacement coefficient of determination reaching R2 = 0.945. Mechanism analysis further indicates that trend deformation is mainly controlled by geological structure and gravitational loading, periodic deformation is strongly modulated by hydrological cycles associated with reservoir water level fluctuations, and random deformation is more likely to reflect short-term disturbances and transient hydrodynamic forcing. These findings provide new insights into the deformation mechanisms of hydrodynamically triggered landslides and offer a promising technical pathway for improving displacement prediction, monitoring, and early warning of reservoir-induced landslide hazards. Full article
(This article belongs to the Special Issue Landslide on Hydrological Response)
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24 pages, 3485 KB  
Article
A Hybrid Deep Learning Framework with CEEMDAN, Multi-Scale CNN, and Multi-Head Attention for Building Load Forecasting
by Limin Wang, Dezheng Wei, Jumin Zhao, Wei Gao and Dengao Li
Buildings 2026, 16(6), 1248; https://doi.org/10.3390/buildings16061248 - 21 Mar 2026
Cited by 3 | Viewed by 553
Abstract
Accurate building load forecasting is essential for smart grid and energy management, yet nonlinearity, non-stationarity, and multi-scale characteristics of load data challenge traditional methods. To address these issues, we propose a hybrid deep learning framework, CEEMDAN-MultiScale-CNN-BiLSTM-MultiAttention. First, Complete Ensemble Empirical Mode Decomposition with [...] Read more.
Accurate building load forecasting is essential for smart grid and energy management, yet nonlinearity, non-stationarity, and multi-scale characteristics of load data challenge traditional methods. To address these issues, we propose a hybrid deep learning framework, CEEMDAN-MultiScale-CNN-BiLSTM-MultiAttention. First, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) decomposes the load sequence into intrinsic mode functions (IMFs), mitigating mode mixing and complexity. Then, a MultiScale Convolutional Neural Network extracts multi-scale local features from each IMF. A Bidirectional Long Short-Term Memory network captures bidirectional temporal dependencies, and a Multi-Attention mechanism dynamically emphasizes critical time steps and feature channels, enhancing interpretability and prediction. The framework is validated on the Building Data Genome Project 2 dataset, achieving a Mean Absolute Percentage Error (MAPE) of 2.6464% and a coefficient of determination R2 of 0.8999, outperforming mainstream methods across multiple metrics. The main contributions are: (1) a hybrid framework integrating CEEMDAN, multi-scale feature extraction, and attention mechanisms to handle nonlinearity and non-stationarity; (2) a MultiScale-CNN to capture multi-scale temporal features and adapt to multi-frequency components; (3) a Multi-Attention mechanism to dynamically focus on key time steps and channels, improving accuracy and robustness. This work provides an effective solution for building load forecasting in complex energy systems. Full article
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26 pages, 3092 KB  
Article
A Cluster- and Temperature-Aware Auto-Ensemble Model for Airport Cooling Load Forecasting
by Xiao-Yu Xie, Yu-Wei Fan, Yi-Zhou Wang, Jie-Ru Li and Xin-Rong Zhang
Energies 2026, 19(5), 1375; https://doi.org/10.3390/en19051375 - 9 Mar 2026
Viewed by 607
Abstract
Accurate cooling load forecasting supports energy-efficient operation in large public buildings such as airports. Cooling load time series are often nonlinear and temporally dependent, with frequent operating condition changes and pronounced thermal inertia, which limits the reliability of single-model forecasting. This study proposes [...] Read more.
Accurate cooling load forecasting supports energy-efficient operation in large public buildings such as airports. Cooling load time series are often nonlinear and temporally dependent, with frequent operating condition changes and pronounced thermal inertia, which limits the reliability of single-model forecasting. This study proposes a cluster- and temperature-aware auto-ensemble model (CATS-Ens) for short- and long-term cooling load prediction. CATS-Ens learns condition-dependent model contributions within temperature-based operating intervals and distinct load regimes, enabling collaborative prediction across complementary experts and avoiding reliance on a single globally optimal predictor. The proposed model is evaluated on a real-world hourly cooling load dataset collected from an airport terminal. Results show that CATS-Ens achieves consistently better performance than representative baselines under multiple metrics, including MAE, RMSE, MAPE, sMAPE, and R2. Compared with the best individual baseline, CATS-Ens reduces MAE by 8.5%, RMSE by 8.4%, MAPE by 12.6%, and sMAPE by 7.1%, with an R2 of 0.967. The model maintains stable accuracy under varying operating conditions and alleviates false-positive predictions during zero-load and low-load periods, demonstrating its practical value for cooling load forecasting in complex building energy systems. Full article
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18 pages, 3739 KB  
Article
Smart Energy Monitoring for Sustainable Campuses: A Hybrid Anomaly Detection Approach Based on Prophet and Isolation Forest
by Ângelo Sousa, Pedro J. S. Cardoso and Jânio Monteiro
Sustainability 2026, 18(5), 2589; https://doi.org/10.3390/su18052589 - 6 Mar 2026
Cited by 2 | Viewed by 1229
Abstract
The transition towards sustainable educational campuses requires robust energy management strategies that integrate operational oversight with advanced analytics. This paper presents a campus-scale electricity monitoring system at the University of Algarve, designed to support the institution’s sustainability goals through continuous monitoring, data reliability, [...] Read more.
The transition towards sustainable educational campuses requires robust energy management strategies that integrate operational oversight with advanced analytics. This paper presents a campus-scale electricity monitoring system at the University of Algarve, designed to support the institution’s sustainability goals through continuous monitoring, data reliability, portability, and scalability to handle concurrent high-frequency campus-wide telemetry. The system consolidates heterogeneous meters into a unified platform, enabling precise tracking of energy consumption and photovoltaic generation. Beyond operational efficiency, the platform incorporates a data-driven analytical layer featuring short-term forecasting using Prophet, chosen for its computational scalability, and a hybrid anomaly detection scheme combining forecast residuals with Isolation Forest. These capabilities facilitate the early identification of waste and abnormal consumption patterns, directly contributing to energy conservation and carbon footprint reduction. Validated across multiple buildings, the system demonstrates both portability to different energy profiles and high data continuity, reducing the cognitive load on facility managers. By providing a reproducible blueprint for intelligent energy monitoring, this work supports institutions in their pursuit of energy efficiency and sustainable development, aligning operational practices with broader environmental objectives. Full article
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22 pages, 4299 KB  
Article
A Multi-Strategy Enhanced Whale Optimization Algorithm for Long Short-Term Memory—Application to Short-Term Power Load Forecasting for Microgrid Buildings
by Lili Qu, Qingfang Teng, Hao Mai and Jing Chen
Sensors 2026, 26(3), 1003; https://doi.org/10.3390/s26031003 - 3 Feb 2026
Cited by 1 | Viewed by 893
Abstract
High-accuracy short-term electric load forecasting is essential for ensuring the security of power systems and enhancing energy efficiency. Power load sequences are characterized by strong randomness, non-stationarity, and nonlinearity over time. To improve the precision and efficiency of short-term load forecasting in microgrids, [...] Read more.
High-accuracy short-term electric load forecasting is essential for ensuring the security of power systems and enhancing energy efficiency. Power load sequences are characterized by strong randomness, non-stationarity, and nonlinearity over time. To improve the precision and efficiency of short-term load forecasting in microgrids, a hybrid predictive model combining Complementary Ensemble Empirical Mode Decomposition (CEEMD) and a multi-strategy enhanced Whale Optimization Algorithm (WOA) with Long Short-Term Memory (LSTM) neural networks has been proposed. Initially, this study employs CEEMD to decompose the short-term electric load time series. Subsequently, a multi-strategy enhanced WOA with chaotic initialization and reverse learning is introduced to enhance the search capability of model parameters and avoid entrapment in local optima. Finally, considering the distinct characteristics of each component, the multi-strategy improved WOA is utilized to optimize the LSTM model, establishing individual predictive models for each component, and the predictions are then aggregated. The proposed method’s forecasting accuracy has been validated through multiple case studies using the UC San Diego microgrid data, demonstrating its reliability and providing a solid foundation for microgrid system planning and stable operation. Full article
(This article belongs to the Section Intelligent Sensors)
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18 pages, 10989 KB  
Article
Ensemble Entropy with Adaptive Deep Fusion for Short-Term Power Load Forecasting
by Yiling Wang, Yan Niu, Xuejun Li, Xianglong Dai, Xiaopeng Wang, Yong Jiang, Chenghu He and Li Zhou
Entropy 2026, 28(2), 158; https://doi.org/10.3390/e28020158 - 31 Jan 2026
Cited by 1 | Viewed by 633
Abstract
Accurate power load forecasting is crucial for ensuring the safety and economic operation of power systems. However, the complex, non-stationary, and heterogeneous nature of power load data presents significant challenges for traditional prediction methods, particularly in capturing instantaneous dynamics and effectively fusing multi-feature [...] Read more.
Accurate power load forecasting is crucial for ensuring the safety and economic operation of power systems. However, the complex, non-stationary, and heterogeneous nature of power load data presents significant challenges for traditional prediction methods, particularly in capturing instantaneous dynamics and effectively fusing multi-feature information. This paper proposes a novel framework—Ensemble Entropy with Adaptive Deep Fusion (EEADF)—for short-term multi-feature power load forecasting. The framework introduces an ensemble instantaneous entropy extraction module to compute and fuse multiple entropy types (approximate, sample, and permutation entropies) in real-time within sliding windows, creating a sensitive representation of system states. A task-adaptive hierarchical fusion mechanism is employed to balance computational efficiency and model expressivity. For time-series forecasting tasks with relatively structured patterns, feature concatenation fusion is used that directly combines LSTM sequence features with multimodal entropy features. For complex multimodal understanding tasks requiring nuanced cross-modal interactions, multi-head self-attention fusion is implemented that dynamically weights feature importance based on contextual relevance. A dual-branch deep learning model is constructed that processes both raw sequences (via LSTM) and extracted entropy features (via MLP) in parallel. Extensive experiments on a carefully designed simulated multimodal dataset demonstrate the framework’s robustness in recognizing diverse dynamic patterns, achieving MSE of 0.0125, MAE of 0.0794, and R2 of 0.9932. Validation on the real-world ETDataset for power load forecasting confirms that the proposed method significantly outperforms baseline models (LSTM, TCN, transformer, and informer) and traditional entropy methods across standard evaluation metrics (MSE, MAE, RMSE, MAPE, and R2). Ablation studies further verify the critical roles of both the entropy features and the fusion mechanism. Full article
(This article belongs to the Section Multidisciplinary Applications)
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28 pages, 6394 KB  
Article
Prediction of Blade Root Loads for Wind Turbine Based on RBMO-VMD and TCN-BiLSTM-Attention
by Yifan Liu and Jing Cheng
Mathematics 2026, 14(2), 218; https://doi.org/10.3390/math14020218 - 6 Jan 2026
Cited by 2 | Viewed by 675
Abstract
Addressing the challenges associated with wind turbine blade root loads—including nonlinearity, strong coupling effects, high computational complexity, and the limitations of conventional mathematical-physical modeling approaches. This paper proposes a wind turbine blade root load prediction model that integrates Variational Mode Decomposition (VMD) optimized [...] Read more.
Addressing the challenges associated with wind turbine blade root loads—including nonlinearity, strong coupling effects, high computational complexity, and the limitations of conventional mathematical-physical modeling approaches. This paper proposes a wind turbine blade root load prediction model that integrates Variational Mode Decomposition (VMD) optimized by the Red-billed Blue Magpie Algorithm (RBMO) and a combined Temporal Convolutional Network (TCN)—Bidirectional Long Short-Term Memory (BiLSTM)—Attention mechanism. First, the RBMO algorithm optimizes VMD parameters. VMD decomposes data into multiple sub-sequences, which are combined with environmental and operational parameters to form input components for the TCN-BiLSTM-Attention ensemble prediction model. Finally, the RBMO algorithm determines the optimal hyperparameter configuration for the combined model. Prediction outputs from each component are then aggregated and reconstructed to yield the final blade root load prediction. Predictions are compared against actual data and results from other forecasting models. Results demonstrate superior predictive performance for the proposed model, effectively enhancing the accuracy of blade root load prediction for wind turbines. Full article
(This article belongs to the Collection Applied Mathematics for Emerging Trends in Mechatronic Systems)
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25 pages, 7271 KB  
Article
A Three-Stage Hybrid Learning Framework for Sustainable Multi-Energy Load Forecasting in Park-Level Integrated Energy Systems
by Zhenlan Dou, Shuangzeng Tian, Fanyue Qian and Yongwen Yang
Sustainability 2025, 17(24), 11158; https://doi.org/10.3390/su172411158 - 12 Dec 2025
Cited by 2 | Viewed by 809
Abstract
Accurate multi-energy load forecasting is essential for the low-carbon, efficient, and resilient operation of park-level Integrated Energy Systems (PIESs), where cooling, heating, and electricity networks interact closely and increasingly incorporate renewable energy resources. However, forecasting in such systems remains challenging due to complex [...] Read more.
Accurate multi-energy load forecasting is essential for the low-carbon, efficient, and resilient operation of park-level Integrated Energy Systems (PIESs), where cooling, heating, and electricity networks interact closely and increasingly incorporate renewable energy resources. However, forecasting in such systems remains challenging due to complex cross-energy coupling, high-dimensional feature interactions, and pronounced nonlinearities under diverse meteorological and operational conditions. To address these challenges, this study develops a novel three-stage hybrid forecasting framework that integrates Recursive Feature Elimination with Cross-Validation (RFECV), a Multi-Task Long Short-Term Memory network (MTL-LSTM), and Random Forest (RF). In the first stage, RFECV performs adaptive and interpretable feature selection, ensuring robust model inputs and capturing meteorological drivers relevant to renewable energy dynamics. The second stage employs MTL-LSTM to jointly learn shared temporal dependencies and intrinsic coupling relationships among multiple energy loads. The final RF-based residual correction enhances local accuracy by capturing nonlinear residual patterns overlooked by deep learning. A real-world case study from an East China PIES verifies the superior predictive performance of the proposed framework, achieving mean absolute percentage errors of 4.65%, 2.79%, and 3.01% for cooling, heating, and electricity loads, respectively—substantially outperforming benchmark models. These results demonstrate that the proposed method offers a reliable, interpretable, and data-driven solution to support refined scheduling, renewable energy integration, and sustainable operational planning in modern multi-energy systems. Full article
(This article belongs to the Section Energy Sustainability)
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