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Keywords = maximal information coefficient (MIC) model

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25 pages, 3860 KB  
Article
Short-Term Wind Power Forecasting Using CEEMDAN-CNN-BiLSTM Based on MIC Feature Selection
by Zheng Jiajia, Linjun Zeng, Shuang Liang, Wen Xia, Nuersimanguli Abuduwasiti and Xianhua Zeng
Processes 2026, 14(9), 1456; https://doi.org/10.3390/pr14091456 - 30 Apr 2026
Viewed by 198
Abstract
To address the issue of insufficient accuracy in wind power forecasting arising from intermittency and volatility, this paper proposes a short-term wind power prediction model integrating MIC (Maximal Information Coefficient) feature selection with adaptive noise-complete set empirical mode decomposition, convolutional neural networks, and [...] Read more.
To address the issue of insufficient accuracy in wind power forecasting arising from intermittency and volatility, this paper proposes a short-term wind power prediction model integrating MIC (Maximal Information Coefficient) feature selection with adaptive noise-complete set empirical mode decomposition, convolutional neural networks, and a bidirectional long short-term memory network hybrid architecture. The main innovations of this work lie in the following: Firstly, MIC quantifies the strength of the nonlinear correlation between meteorological features and the MAE (Mean Absolute Error) in power generation, thereby enabling the identification of highly correlated features to reduce the input dimensionality. Secondly, CEEMDAN (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) performs adaptive modal decomposition on raw power sequences. Combining sample entropy with K-means clustering reconstructs IMFs (Intrinsic Mode Functions), while the introduction of VMD (Variational Mode Decomposition) for quadratic optimisation significantly improves the quality of signal decomposition, enabling a more refined separation of fluctuation characteristics across different time scales. Finally, the optimised meteorological features and reconstructed components are input into a CNN (Convolutional Neural Network)-BiLSTM (Bidirectional Long Short-Term Memory) module. Power regression prediction is achieved through the synergistic effect of spatial feature extraction and bidirectional temporal dependency modelling. Case study results demonstrate that compared to the TCN (Temporal Convolutional Network)-Transformer, the proposed method achieves a 0.4022 improvement in the coefficient of determination R2, a 13.2598 reduction in MAE, a 19.864 decrease in RMSE (Root Mean Square Error). At the same time, it maintains stable performance even when faced with unreliable data scenarios involving random missing features, demonstrating excellent generalisation ability. Furthermore, the model training time has been reduced to 77.6469 s, with a single prediction response time of just 0.0659 s. Full article
(This article belongs to the Section Energy Systems)
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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
Viewed by 297
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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26 pages, 2573 KB  
Article
Interpretable Data-Driven Crystal Diameter Prediction in CZ Silicon Single-Crystal Growth via MIC-Guided and GWO-Optimized TCN–LSTM
by Hao Pan, Pengju Zhang, Chen Xue and Ding Liu
Processes 2026, 14(7), 1153; https://doi.org/10.3390/pr14071153 - 3 Apr 2026
Viewed by 390
Abstract
This study proposes a data-driven framework with post hoc interpretability analysis for one-step-ahead crystal diameter prediction in the Czochralski (CZ) silicon single-crystal growth process. To address the strong multivariable coupling, nonlinear dynamics, variable-specific delays, and difficulty of online measurement in CZ growth, the [...] Read more.
This study proposes a data-driven framework with post hoc interpretability analysis for one-step-ahead crystal diameter prediction in the Czochralski (CZ) silicon single-crystal growth process. To address the strong multivariable coupling, nonlinear dynamics, variable-specific delays, and difficulty of online measurement in CZ growth, the maximal information coefficient (MIC) was first used to screen key auxiliary variables from industrial process data. The Grey Wolf Optimizer (GWO) was then employed for multi-variable delay estimation and feature alignment, and a hybrid temporal convolutional network (TCN)–long short-term memory (LSTM) model was constructed to combine local temporal feature extraction with long-term dependency learning. Four input configurations were designed according to whether lag alignment and diameter history were included, and the proposed TCN-LSTM was systematically compared with standalone TCN and LSTM models. The results show that both diameter history and delay alignment improve prediction performance. Under the current single-run evaluation protocol, the TCN-LSTM configurations yielded lower prediction errors than the corresponding TCN and LSTM models under the same input settings. Under the withlag-withY configuration, the TCN-LSTM model achieved MSE = 0.00259, RMSE = 0.05087, MAE = 0.03949, and R2 = 0.96982. After GWO-based hyperparameter optimization, the best TCN-LSTM configuration further improved to MSE = 0.00239, RMSE = 0.04894, MAE = 0.03651, and R2 = 0.97207. SHAP-based analysis was further used to provide a post hoc interpretation of the relative contributions of key process variables to diameter variation. Overall, the proposed framework provides a data-driven prediction approach and may support subsequent process analysis and optimization in industrial CZ growth. Full article
(This article belongs to the Section AI-Enabled Process Engineering)
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29 pages, 6240 KB  
Article
Explainable Prediction of Power Generation for Cascaded Hydropower Systems Under Complex Spatiotemporal Dependencies
by Zexin Li, Xiaodong Shen, Yuhang Huang and Yuchen Ren
Energies 2026, 19(6), 1540; https://doi.org/10.3390/en19061540 - 20 Mar 2026
Viewed by 319
Abstract
Hydropower plays a key regulating role in new-type power systems, and both forecasting accuracy and interpretability are critical for power dispatch. However, cascade hydropower forecasting is constrained by strong spatiotemporal coupling among multi-dimensional features, flow propagation delays, as well as the limited transparency [...] Read more.
Hydropower plays a key regulating role in new-type power systems, and both forecasting accuracy and interpretability are critical for power dispatch. However, cascade hydropower forecasting is constrained by strong spatiotemporal coupling among multi-dimensional features, flow propagation delays, as well as the limited transparency of deep learning models. To tackle these issues, this paper develops a hybrid framework integrating Maximal Information Coefficient (MIC), the Long- and Short-term Time-series Network (LSTNet), and the SHapley Additive exPlanations (SHAP) interpretability method. First, an MIC-based nonlinear screening mechanism is employed to remove redundant noise and construct a high-quality input space. Second, an LSTNet model is developed to deeply extract spatiotemporal coupling features among cascade stations and flow evolution patterns, achieving high-accuracy forecasting of both system-level and station-level outputs. Finally, SHAP is used for global and local interpretability analysis to perform physics-consistency verification with respect to the model’s decision-making rationale. Experimental results indicate that the proposed approach achieves low errors in total output forecasting, reducing error levels by approximately 57–88% compared with Recurrent Neural Network (RNN), Gated Recurrent Unit (GRU), and Informer. Moreover, SHAP feature-dependence analysis reveals a nonlinear response change of station D around 7.8 MW, providing evidence for the physical consistency of the model outputs and improving model interpretability. Full article
(This article belongs to the Section F5: Artificial Intelligence and Smart Energy)
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24 pages, 2125 KB  
Article
MIC-SSO: A Two-Stage Hybrid Feature Selection Approach for Tabular Data
by Wei-Chang Yeh, Yunzhi Jiang, Hsin-Jung Hsu and Chia-Ling Huang
Electronics 2026, 15(4), 856; https://doi.org/10.3390/electronics15040856 - 18 Feb 2026
Viewed by 453
Abstract
High-dimensional structured datasets are common in fields such as semiconductor manufacturing, healthcare, and finance, where redundant and irrelevant features often increase computational cost and reduce predictive accuracy. Feature selection mitigates these issues by identifying a compact, informative subset of features, enhancing model efficiency, [...] Read more.
High-dimensional structured datasets are common in fields such as semiconductor manufacturing, healthcare, and finance, where redundant and irrelevant features often increase computational cost and reduce predictive accuracy. Feature selection mitigates these issues by identifying a compact, informative subset of features, enhancing model efficiency, performance, and interpretability. This study proposes Maximal Information Coefficient–Simplified Swarm Optimization (MIC-SSO), a two-stage hybrid feature selection method that combines the MIC as a filter with SSO as a wrapper. In Stage 1, MIC ranks feature relevance and removes low-contribution features; in Stage 2, SSO searches for an optimal subset from the reduced feature space using a fitness function that integrates the Matthews Correlation Coefficient (MCC) and feature reduction rate to balance accuracy and compactness. Experiments on five public datasets compare MIC-SSO with multiple hybrid, heuristic, and literature-reported methods, with results showing superior predictive accuracy and feature compression. The method’s ability to outperform existing approaches in terms of predictive accuracy and feature compression underscores its broader significance, offering a powerful tool for data analysis in fields like healthcare, finance, and semiconductor manufacturing. Statistical tests further confirm significant improvements over competing approaches, demonstrating the method’s effectiveness in integrating the efficiency of filters with the precision of wrappers for high-dimensional tabular data analysis. Full article
(This article belongs to the Special Issue Feature Papers in Networks: 2025–2026 Edition)
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16 pages, 934 KB  
Article
Data-Driven Scheduling Optimization of Electricity Customer Service Based on Demand Analysis and Skill Matching
by Hao Qin, Zhipeng Xu, Yingqi Yi, Shunda Wu and Ying Xue
Energies 2026, 19(3), 808; https://doi.org/10.3390/en19030808 - 3 Feb 2026
Viewed by 477
Abstract
To address surging and uncertain electricity customer demands, this paper proposes a data-driven electricity customer service scheduling (ECSS) optimization model to improve customer service quality and alleviate agent scheduling pressure. The method begins by building a demand analysis model based on customer feature [...] Read more.
To address surging and uncertain electricity customer demands, this paper proposes a data-driven electricity customer service scheduling (ECSS) optimization model to improve customer service quality and alleviate agent scheduling pressure. The method begins by building a demand analysis model based on customer feature extraction using the maximal information coefficient (MIC). An agent workforce sizing model is then developed by integrating the AHP–fuzzy comprehensive evaluation and Z-score standardization, accounting for call-volume proportion, hourly call-handling capacity, and time-period length. Furthermore, a demand–skill matching method is introduced between customer calls and agent skills. A particle swarm optimization (PSO)-based intelligent scheduling algorithm is established, with queuing time, skill level, and handling time as key objectives and constraints. Case-study validation shows that the model improves operational efficiency by approximately 26.28% and reduces annual labor costs by about 6.13%, thereby enhancing customer satisfaction, service center efficiency, and scheduling system economy. Full article
(This article belongs to the Special Issue Application of Artificial Intelligence in Electrical Power Systems)
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22 pages, 5670 KB  
Article
An Attention-Based Multi-Feature Fusion Physics-Informed Neural Network for State-of-Health Estimation of Lithium-Ion Batteries
by Haiwei Wu, Jianwei Liu, Zhihao Wang and Xuexin Li
Energies 2025, 18(23), 6270; https://doi.org/10.3390/en18236270 - 28 Nov 2025
Cited by 3 | Viewed by 994
Abstract
This study proposes an Attention Mechanism–Multi-Feature Fusion Physics-Informed Neural Network (AM-MFF-PINN) for accurate and physically consistent estimation of the State of Health (SOH) of lithium-ion batteries in practical battery management systems (BMSs). The model integrates multi-domain features, including time-domain, frequency–domain, and wavelet–domain indicators, [...] Read more.
This study proposes an Attention Mechanism–Multi-Feature Fusion Physics-Informed Neural Network (AM-MFF-PINN) for accurate and physically consistent estimation of the State of Health (SOH) of lithium-ion batteries in practical battery management systems (BMSs). The model integrates multi-domain features, including time-domain, frequency–domain, and wavelet–domain indicators, to capture both macroscopic degradation trends and microscopic dynamical behaviors under varying operating conditions. A dual-correlation feature selection strategy that combines the Pearson correlation coefficient and the maximal information coefficient (MIC) is adopted to automatically retain the most degradation-sensitive variables, while a dynamic loss balancing mechanism adaptively coordinates data-fitting and physics-based constraints to ensure robust convergence. Experimental results on the Xi’an Jiaotong University (XJTU) and Tongji University (TJU) datasets demonstrate that AM-MFF-PINN achieves superior performance, with a mean absolute error (MAE) of approximately 0.002, a root mean square error (RMSE) of about 0.004, and a coefficient of determination (R2) of 0.99 for the XJTU dataset, and an MAE of 0.005, an RMSE of 0.006, and an R2 of 0.97 for the TJU dataset. These results indicate that the proposed method can provide reliable SOH estimates across different chemistries, temperatures, and charging protocols, using only standard charging data that are readily available in on-board and stationary BMSs. Therefore, AM-MFF-PINN offers a generalizable and practically deployable evaluation methodology to support early fault warning, predictive maintenance, and life-cycle optimization of lithium-ion batteries in electric vehicles and energy storage systems. Full article
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25 pages, 6753 KB  
Article
Short-Term Power Load Forecasting Under Multiple Weather Scenarios Based on Dual-Channel Feature Extraction (DCFE)
by Xiaojun Pu and Mingrui Zhang
Appl. Sci. 2025, 15(21), 11733; https://doi.org/10.3390/app152111733 - 3 Nov 2025
Cited by 2 | Viewed by 1090
Abstract
Grid security and system dispatch can be compromised by pronounced volatility in power load under extreme meteorological conditions. However, the dynamic and nonlinear interactions between power load and meteorological variables across diverse weather scenarios are not well captured by existing methods, resulting in [...] Read more.
Grid security and system dispatch can be compromised by pronounced volatility in power load under extreme meteorological conditions. However, the dynamic and nonlinear interactions between power load and meteorological variables across diverse weather scenarios are not well captured by existing methods, resulting in limited accuracy and robustness. To address this gap, a short-term power load forecasting model with a dual-channel architecture is proposed. Features are extracted in parallel via dual-channel feature extraction (DCFE): the first channel employs an improved Cascaded Multiscale 2D Convolutional Network (CMCNN) to model local fluctuations and global periodicity in the load time series. The second channel derives scenario-aware variable weights using the Maximal Information Coefficient (MIC); meteorological variables are then gated and weighted before being processed by a multi-layer self-attention network to learn global dependencies. Subsequently, dynamic feature-level fusion is achieved through cross-attention, strengthening key interactions between power load and meteorological factors. The fused representation is fed into an Attention-Enhanced Bidirectional Gated Recurrent Unit (AE-BiGRU) to precisely model temporal dependencies across multiple weather scenarios. Experiments on five years of power load and meteorological data from a region in Australia indicate that the proposed method outperforms the best baseline across multiple weather conditions: RMSE, MAE, MAPE, and sMAPE decrease on average by 32.44%, 31.42%, 30.73%, and 31.05%, respectively, while R2 increases by 0.034 on average, demonstrating strong adaptability and robustness. Full article
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20 pages, 4591 KB  
Article
Short-Term Forecasting Approach of Wind Power Relying on NWP-CEEMDAN-LSTM
by Ying Yang and Yanlei Zhao
Processes 2025, 13(10), 3276; https://doi.org/10.3390/pr13103276 - 14 Oct 2025
Cited by 1 | Viewed by 951
Abstract
Precise wind power forecasting has several benefits, such as optimized peak regulation in power systems, enhanced safety analysis, and improved energy efficiency. Considering the substantial influence of meteorological data, such as wind speed and temperature, on wind power generation, and to minimize the [...] Read more.
Precise wind power forecasting has several benefits, such as optimized peak regulation in power systems, enhanced safety analysis, and improved energy efficiency. Considering the substantial influence of meteorological data, such as wind speed and temperature, on wind power generation, and to minimize the impact of fluctuations and complexity of wind power data on the forecast results, this paper proposes a combined wind power forecasting method. This approach is based on the long short-term memory network (LSTM) model, using the maximal information coefficient (MIC) method to select numerical weather prediction (NWP) and combining the efficiency of complete EEMD with the adaptive noise (CEEMDAN) method for nonlinear signal decomposition. Results indicate that the accuracy of the forecast results is supported by NWP. Moreover, wind power data are decomposed by the CEEMDAN algorithm and converted into relatively regular sub-sequences with small fluctuations. The MIC algorithm effectively reduces the redundant information in NWP data, and the LSTM algorithm addresses the uncertainty of wind power data. Finally, the wind power of multiple wind farms is forecasted. Comparison of the forecast results of different methods revealed that the NWP-CEEMDAN-LSTM method proposed in this paper, which considers feature extraction using MIC, effectively tracks power fluctuations and improves forecast performance, thereby reducing the forecast error of wind power. Full article
(This article belongs to the Section Energy Systems)
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27 pages, 12909 KB  
Article
Sustainability-Oriented Furnace Temperature Prediction for Municipal Solid Waste Incineration Using IWOA-SAGRU
by Jinxiang Pian, Mayan Si, Ao Sun and Jian Tang
Sustainability 2025, 17(20), 8987; https://doi.org/10.3390/su17208987 - 10 Oct 2025
Cited by 1 | Viewed by 923
Abstract
Municipal solid waste incineration promotes sustainable development by reducing waste, recovering resources, and minimizing environmental impact, with furnace temperature control playing a key role in maximizing efficiency. Accurate real-time temperature prediction is crucial in developing countries to optimize incineration, re-duce emissions, and enhance [...] Read more.
Municipal solid waste incineration promotes sustainable development by reducing waste, recovering resources, and minimizing environmental impact, with furnace temperature control playing a key role in maximizing efficiency. Accurate real-time temperature prediction is crucial in developing countries to optimize incineration, re-duce emissions, and enhance energy recovery for global sustainability. To address this, we propose a method integrating an improved whale optimization algorithm (IWOA) with a self-attention gated recurrent unit (SAGRU). Using the maximal information coefficient (MIC) to identify key factors, we optimize SAGRU parameters with IWOA, enhancing prediction accuracy by capturing temporal dependencies. Experimental validation from an MSWI plant in China demonstrates that the proposed model significantly enhances prediction accuracy under complex conditions. When compared with the Elman and LSTM models, the error is reduced by 0.7146 and 0.4689, respectively, highlighting its strong potential for practical applications in waste incineration temperature control. Full article
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22 pages, 2691 KB  
Article
A Short-Term Load Forecasting Method for Typical High Energy-Consuming Industrial Parks Based on Multimodal Decomposition and Hybrid Neural Networks
by Jingyu Li, Yu Shi, Na Zhang and Yuanyu Chen
Appl. Sci. 2025, 15(17), 9578; https://doi.org/10.3390/app15179578 - 30 Aug 2025
Viewed by 1368
Abstract
High energy-consuming industrial parks are characterized by high base-load-to-peak-valley ratios, overlapping production cycles, and megawatt-scale step changes, which significantly complicate short-term load forecasting. To tackle these challenges, this study proposes a novel forecasting framework that combines hierarchical multimodal decomposition with a hybrid deep [...] Read more.
High energy-consuming industrial parks are characterized by high base-load-to-peak-valley ratios, overlapping production cycles, and megawatt-scale step changes, which significantly complicate short-term load forecasting. To tackle these challenges, this study proposes a novel forecasting framework that combines hierarchical multimodal decomposition with a hybrid deep learning architecture. First, Maximal Information Coefficient (MIC) analysis is applied to identify key input features and eliminate redundancy. The load series is then decomposed in two stages: seasonal-trend decomposition uses the Loess (STL) isolates trend and seasonal components, while variational mode decomposition (VMD) further disaggregates the residual into multi-scale modes. This hierarchical approach enhances signal clarity and preserves temporal structure. A parallel neural architecture is subsequently developed, integrating an Informer network to model long-term trends and a bidirectional gated recurrent unit (BiGRU) to capture short-term fluctuations. Case studies based on real-world load data from a typical industrial park in northeastern China demonstrate that the proposed model achieves significantly improved forecasting accuracy and robustness compared to benchmark methods. These results provide strong technical support for fine-grained load prediction and intelligent dispatch in high energy-consuming industrial scenarios. Full article
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24 pages, 3350 KB  
Article
Seasonal Patterns in Yield and Gas Emissions of Greenhouse Tomatoes Under Different Fertilization Levels with Irrigation–Aeration Coupling
by Yanan Sun, Huayu Zhong, Huanjie Cai, Jiatun Xu and Zhijun Li
Agronomy 2025, 15(9), 2026; https://doi.org/10.3390/agronomy15092026 - 23 Aug 2025
Viewed by 1831
Abstract
Optimizing aeration, fertilization, and irrigation is vital for improving greenhouse tomato production while mitigating soil greenhouse gas (GHG) emissions. This study investigated the combined effects of three aeration levels (A1: single Venturi, A2: double Venturi, CK: no aeration), two fertilization rates (F1: 180 [...] Read more.
Optimizing aeration, fertilization, and irrigation is vital for improving greenhouse tomato production while mitigating soil greenhouse gas (GHG) emissions. This study investigated the combined effects of three aeration levels (A1: single Venturi, A2: double Venturi, CK: no aeration), two fertilization rates (F1: 180 kg/ha, F2: 240 kg/ha), and two irrigation levels (I1: 0.8 Epan, I2: 1.0 Epan) on tomato yield, CO2, N2O, and CH4 emissions, net GHG emissions, net global warming potential (NGWP), and GHG intensity (GHGI) across Spring–Summer and Autumn–Winter seasons. Results showed that aeration and fertilization significantly increased CO2 and N2O emissions but reduced CH4 emissions. Warmer conditions in Spring–Summer elevated all GHG emissions and yield compared to Autumn–Winter seasons. Tomato yield, net GHG emissions, NGWP, and GHGI were 12.05%, 24.3%, 14.46%, and 2.37% higher, respectively, in Spring–Summer. Combining the Maximal Information Coefficient and TOPSIS models, the optimal practice was A1-F1-I1 in Spring–Summer and A2-F1-I1 in Autumn–Winter seasons. These results provide a theoretical basis for selecting climate-smart management strategies that enhance yield and environmental sustainability in greenhouse tomato systems. Full article
(This article belongs to the Special Issue Advances in Tillage Methods to Improve the Yield and Quality of Crops)
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24 pages, 6464 KB  
Article
A Hybrid Model for Carbon Price Forecasting Based on Secondary Decomposition and Weight Optimization
by Yongfa Chen, Yingjie Zhu, Jie Wang and Meng Li
Mathematics 2025, 13(14), 2323; https://doi.org/10.3390/math13142323 - 21 Jul 2025
Cited by 3 | Viewed by 2127
Abstract
Accurate carbon price forecasting is essential for market stability, risk management, and policy-making. To address the nonlinear, non-stationary, and multiscale nature of carbon prices, this paper proposes a forecasting framework integrating secondary decomposition, two-stage feature selection, and dynamic ensemble learning. Firstly, the original [...] Read more.
Accurate carbon price forecasting is essential for market stability, risk management, and policy-making. To address the nonlinear, non-stationary, and multiscale nature of carbon prices, this paper proposes a forecasting framework integrating secondary decomposition, two-stage feature selection, and dynamic ensemble learning. Firstly, the original price series is decomposed into intrinsic mode functions (IMFs), using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). The IMFs are then grouped into low- and high-frequency components based on multiscale entropy (MSE) and K-Means clustering. To further alleviate mode mixing in the high-frequency components, an improved variational mode decomposition (VMD) optimized by particle swarm optimization (PSO) is applied for secondary decomposition. Secondly, a two-stage feature-selection method is employed, in which the partial autocorrelation function (PACF) is used to select relevant lagged features, while the maximal information coefficient (MIC) is applied to identify key variables from both historical and external data. Finally, this paper introduces a dynamic integration module based on sliding windows and sequential least squares programming (SLSQP), which can not only adaptively adjust the weights of four base learners but can also effectively leverage the complementary advantages of each model and track the dynamic trends of carbon prices. The empirical results of the carbon markets in Hubei and Guangdong indicate that the proposed method outperforms the benchmark model in terms of prediction accuracy and robustness, and the method has been tested by Diebold Mariano (DM). The main contributions are the improved feature-extraction process and the innovative use of a sliding window-based SLSQP method for dynamic ensemble weight optimization. Full article
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17 pages, 3415 KB  
Article
A Hybrid Multi-Step Forecasting Approach for Methane Steam Reforming Process Using a Trans-GRU Network
by Qinwei Zhang, Xianyao Han, Jingwen Zhang and Pan Qin
Processes 2025, 13(7), 2313; https://doi.org/10.3390/pr13072313 - 21 Jul 2025
Cited by 2 | Viewed by 1137
Abstract
During the steam reforming of methane (SRM) process, elevated CH4 levels after the reaction often signify inadequate heat supply or incomplete reactions within the reformer, jeopardizing process stability. In this paper, a novel multi-step forecasting method using a Trans-GRU network was proposed [...] Read more.
During the steam reforming of methane (SRM) process, elevated CH4 levels after the reaction often signify inadequate heat supply or incomplete reactions within the reformer, jeopardizing process stability. In this paper, a novel multi-step forecasting method using a Trans-GRU network was proposed for predicting the methane content outlet of the SRM reformer. First, a novel feature selection based on the maximal information coefficient (MIC) was applied to identify critical input variables and determine their optimal input order. Additionally, the Trans-GRU network enables the simultaneous capture of multivariate correlations and the learning of global sequence representations. The experimental results based on time-series data from a real SRM process demonstrate that the proposed approach significantly improves the accuracy of multi-step methane content prediction. Compared to benchmark models, including the TCN, Transformer, GRU, and CNN-LSTM, the Trans-GRU consistently achieves the lowest root mean squared error (RMSE) and mean absolute error (MAE) values across all prediction steps (1–6). Specifically, at the one-step horizon, it yields an RMSE of 0.0120 and an MAE of 0.0094. This high performance remains robust across the 2–6-step predictions. The improved predictive capability supports the stable operation and predictive optimization strategies of the steam reforming process in hydrogen production. Full article
(This article belongs to the Section Chemical Processes and Systems)
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24 pages, 4579 KB  
Article
Prediction of Sluice Seepage Based on Impact Factor Screening and the IKOA-BiGRU Model
by Xiaoran Sun, Jianhe Peng, Chunlin Zhang and Sen Zheng
Water 2025, 17(13), 1850; https://doi.org/10.3390/w17131850 - 21 Jun 2025
Cited by 1 | Viewed by 820
Abstract
Sluices play a critical role in flood control, power generation, water supply, etc. With decades of service, sluice safety assurance becomes a structural engineering imperative. Previous investigations have revealed that failures of sluices are often associated with seepage damage. To gain further insight [...] Read more.
Sluices play a critical role in flood control, power generation, water supply, etc. With decades of service, sluice safety assurance becomes a structural engineering imperative. Previous investigations have revealed that failures of sluices are often associated with seepage damage. To gain further insight into sluice seepage and ensure the safety of sluice structures, proposing an effective prediction method for sluice seepage nevertheless remains a challenging fundamental and practical perspective. Therefore, in this paper, a novel prediction model for sluice seepage based on impact factor screening methods, the improved Kepler optimization algorithm (IKOA) and the bidirectional gated recurrent unit (BiGRU), is presented. Primarily, the maximal information coefficient and the correlation-based feature selection (MIC–CFS) are introduced to screen the impact factors of the model, aiming to reduce redundant information and the complexity of the model. Subsequently, the Kepler optimization algorithm (KOA) is enhanced using three strategies: chaotic mapping-based initialization, Runge–Kutta-based position updating, and the enhanced solution quality (ESQ) strategy to optimize the hyperparameters of the BiGRU network. On this basis, the prediction model is established, which is applied in the Bengbu sluice to verify its fitting and prediction performance. Eventually, comparison analyses with a traditional stepwise regression model, IKOA–LSTM, and IKOA–GRU, were conducted based on monitoring sequences of three monitoring points. The coefficients of determination of the proposed model were located in the range of 0.974 to 0.988. Correspondingly, the mean absolute error values of the proposed model were the lowest, ranging from 0.074 to 0.064. The results of six evaluation metrics confirm that the proposed model consistently exhibits superior interpretability and is able to serve as a promising tool for sluice seepage prediction. Full article
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