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Keywords = Stochastic Configuration Networks

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21 pages, 4860 KB  
Article
Data-Driven Probabilistic Analysis of Power System Faults Using Monte Carlo Simulation
by Franjo Pranjić and Peter Virtič
Technologies 2026, 14(1), 14; https://doi.org/10.3390/technologies14010014 - 24 Dec 2025
Viewed by 319
Abstract
This paper presents a data-driven probabilistic framework for analysing power system faults using Monte Carlo simulations. The study evaluates the operational reliability of multiple high-voltage switchgear topologies—including single-busbar systems, double-busbar systems, and ring-type configurations—by modelling the stochastic behaviour of disconnectors, circuit breakers, busbars, [...] Read more.
This paper presents a data-driven probabilistic framework for analysing power system faults using Monte Carlo simulations. The study evaluates the operational reliability of multiple high-voltage switchgear topologies—including single-busbar systems, double-busbar systems, and ring-type configurations—by modelling the stochastic behaviour of disconnectors, circuit breakers, busbars, and withdrawable switching elements with bypass arrangements. Realistic unavailability parameters derived from statistical reliability data are used to generate fault intervals for each device, enabling the simulation of millions of operational scenarios and capturing both full and partial outage events. The proposed methodology quantifies outage probabilities, identifies critical components, and reveals how devices count, switching logic, and system redundancy influence overall resilience. Results show significant reliability differences between topologies and highlight the importance of optimized substation design for fault tolerance. The developed probabilistic framework provides a transparent and computationally efficient tool to support planning, modernization, and predictive maintenance strategies in transmission and distribution networks. Findings contribute to improved fault diagnosis, enhanced grid stability, and increased reliability in both conventional and renewable-integrated power systems. Full article
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29 pages, 2653 KB  
Article
GreenMind: A Scalable DRL Framework for Predictive Dispatch and Load Balancing in Hybrid Renewable Energy Systems
by Ahmed Alwakeel and Mohammed Alwakeel
Systems 2026, 14(1), 12; https://doi.org/10.3390/systems14010012 - 22 Dec 2025
Viewed by 292
Abstract
The increasing deployment of hybrid renewable energy systems has introduced significant challenges in optimal energy dispatch and load balancing due to the intrinsic stochasticity and temporal variability of renewable sources, along with the multi-dimensional optimization requirements of simultaneously achieving economic efficiency, grid stability, [...] Read more.
The increasing deployment of hybrid renewable energy systems has introduced significant challenges in optimal energy dispatch and load balancing due to the intrinsic stochasticity and temporal variability of renewable sources, along with the multi-dimensional optimization requirements of simultaneously achieving economic efficiency, grid stability, and environmental sustainability. This paper presents GreenMind, a scalable Deep Reinforcement Learning framework designed to address these challenges through a hierarchical multi-agent architecture coupled with Long Short-Term Memory (LSTM) networks for predictive energy management. The framework employs specialized agents responsible for generation dispatch, storage management, load balancing, and grid interaction, achieving an average decision accuracy of 94.7% through coordinated decision-making enabled by hierarchical communication mechanisms. The integrated LSTM-based forecasting module delivers high predictive accuracy, achieving a 2.7% Mean Absolute Percentage Error for one-hour-ahead forecasting of solar generation, wind power, and load demand, enabling proactive rather than reactive control. A multi-objective reward formulation effectively balances economic, technical, and environmental objectives, resulting in 18.3% operational cost reduction, 23.7% improvement in energy efficiency, and 31.2% enhancement in load balancing accuracy compared to state-of-the-art baseline methods. Extensive validation using synthetic datasets representing diverse hybrid renewable energy configurations over long operational horizons confirms the practical viability of the framework, with 19.6% average cost reduction, 97.7% system availability, and 28.6% carbon emission reduction. The scalability analysis demonstrates near-linear computational growth, with performance degradation remaining below 9% for systems ranging from residential microgrids to utility-scale installations with 2000 controllable units. Overall, the results demonstrate that GreenMind provides a scalable, robust, and practically deployable solution for predictive energy dispatch and load balancing in hybrid renewable energy systems. Full article
(This article belongs to the Special Issue Technological Innovation Systems and Energy Transitions)
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24 pages, 11354 KB  
Article
AI-Integrated Framework for Designing Optimized Groundwater Level Observation Networks Based on Hybrid Machine Learning and Stochastic Simulation Frameworks
by Mohamed Haythem Msaddek, Yahya Moumni, Lahcen Zouhri, Bilel Abdelkarim and Adel Zghibi
Hydrology 2025, 12(12), 326; https://doi.org/10.3390/hydrology12120326 - 10 Dec 2025
Viewed by 416
Abstract
This study develops an integrated framework combining groundwater numerical modeling, probabilistic simulation, and machine learning to optimize the spatial design of an Optimized Groundwater Level Observation Network (OGLON) in the Mareth basin. A total of 565 existing monitoring wells were used to calibrate [...] Read more.
This study develops an integrated framework combining groundwater numerical modeling, probabilistic simulation, and machine learning to optimize the spatial design of an Optimized Groundwater Level Observation Network (OGLON) in the Mareth basin. A total of 565 existing monitoring wells were used to calibrate the groundwater flow model, complemented by stochastic groundwater simulations to train two AI-based approaches: the AI-Assisted Centroid Clustering (AIACC) algorithm and the Data-Driven Sparse Bayesian Learning (DDSBL) model. Three OGLON configurations were generated, AIACC (30 wells), DDSBL (30 wells), and Refined-DDSBL (30 wells), and benchmarked against the current monitoring network. Model performance indicates that the AIACC configuration reduces model error from 17,232 to 31.30, achieving an RMSE of 0.2145 m, significantly outperforming both the existing network (RMSE 0.5028 m) and the original DDSBL system (RMSE 0.6678 m). The Refined-DDSBL configuration provides the best overall accuracy, reducing model error from 21,355 to 1.32 and achieving the lowest RMSE (0.0153 m) and MAE (0.0091 m). Groundwater levels simulated under the proposed networks range between 3.8 m and 94.7 m, with the AIACC and Refined-DDSBL approaches offering improved spatial representation of key hydrogeological patterns compared to existing wells. Overall, results demonstrate a clear trade-off between computational efficiency (AIACC) and maximum predictive accuracy (Refined-DDSBL). Both AIACC and Refined-DDSBL significantly enhance spatial coverage and groundwater representation, confirming the effectiveness of integrating machine learning with groundwater modeling for cost-efficient and high-performance OGLON design. Full article
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30 pages, 609 KB  
Article
Operational Cost Minimization in AC Microgrids via Active and Reactive Power Control of BESS: A Case Study from Colombia
by Daniel Sanin-Villa, Luis Fernando Grisales-Noreña and Oscar Danilo Montoya
Appl. Syst. Innov. 2025, 8(6), 180; https://doi.org/10.3390/asi8060180 - 26 Nov 2025
Viewed by 485
Abstract
This work proposes an intelligent strategy for the coordinated management of active and reactive power in Battery Energy Storage Systems (BESSs) within AC microgrids operating under both grid-connected (GCM) and islanded (IM) modes to minimize daily operational costs. The problem is formulated as [...] Read more.
This work proposes an intelligent strategy for the coordinated management of active and reactive power in Battery Energy Storage Systems (BESSs) within AC microgrids operating under both grid-connected (GCM) and islanded (IM) modes to minimize daily operational costs. The problem is formulated as a mixed-variable optimization model that explicitly leverages the control capabilities of BESS power converters. To solve it, a Parallel Particle Swarm Optimization (PPSO) algorithm is employed, coupled with a Successive Approximation (SA) power flow solver. The proposed approach was benchmarked against parallel implementations of the Crow Search Algorithm (PCSA) and the JAYA algorithm (PJAYA), both in parallel, using a realistic 33-node AC microgrid test system based on real demand and photovoltaic generation profiles from Medellín, Colombia. The strategy was evaluated under both deterministic conditions (average daily profiles) and stochastic scenarios (100 daily profiles with uncertainty). The proposed framework is evaluated on a 33-bus AC microgrid that operates in both grid-connected and islanded modes, with a battery energy storage system dispatched at both active and reactive power levels subject to network, state-of-charge, and power-rating constraints. Three population-based optimization algorithms are used to coordinate BESS schedules, and their performance is compared based on daily operating cost, BESS cycling, and voltage profile quality. Quantitatively, the PPSO strategy achieved cost reductions of 2.39% in GCM and 1.62% in IM under deterministic conditions, with a standard deviation of only 0.0200% in GCM and 0.2962% in IM. In stochastic scenarios with 100 uncertainty profiles, PPSO maintained its robustness, reaching average reductions of 2.77% in GCM and 1.53% in IM. PPSO exhibited consistent robustness and efficient performance, reaching the highest average cost reductions with low variability and short execution times in both operating modes. These findings indicate that the method is well-suited for real-time implementation and contributes to improving economic outcomes and operational reliability in grid-connected and islanded microgrid configurations. The case study results show that the different strategies yield distinct trade-offs between economic performance and computational effort, while all solutions satisfy the technical limits of the microgrid. Full article
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20 pages, 5643 KB  
Article
An Improved Regularization Stochastic Configuration Network for Robust Wind Speed Prediction
by Fuguo Jin, Xinyu Chen, Yuanhao Yu and Kun Li
Energies 2025, 18(23), 6170; https://doi.org/10.3390/en18236170 - 25 Nov 2025
Viewed by 295
Abstract
To address the limitations of Stochastic Configured Networks (SCNs) in wind speed prediction, specifically insufficient regularization capability and a high risk of overfitting, this paper proposes a novel Regularized Stochastic Configured Network (RSCN). By integrating L1 and L2 regularization techniques from Elastic Net, [...] Read more.
To address the limitations of Stochastic Configured Networks (SCNs) in wind speed prediction, specifically insufficient regularization capability and a high risk of overfitting, this paper proposes a novel Regularized Stochastic Configured Network (RSCN). By integrating L1 and L2 regularization techniques from Elastic Net, RSCNs achieve feature sparsity while preserving prediction accuracy. Furthermore, a dynamic loss coefficient and a penalty term based on historical training loss are introduced to adaptively modulate the regularization strength during model training. Experimental results demonstrate that RSCNs achieve superior prediction performance and enhanced stability across four benchmark regression datasets and two real-world wind speed datasets. Compared with conventional SCNs and the swarm intelligence optimization-based variant HPO-SCNs, RSCNs significantly reduce the performance gap between training and test sets while maintaining high predictive accuracy. On average, improvements in R2, MAE, and RMSE exceed 50% reduction in error discrepancies. The proposed method offers an effective solution for wind power forecasting by effectively balancing generalization ability and computational efficiency, thereby holding practical significance for real-world applications. Full article
(This article belongs to the Section A3: Wind, Wave and Tidal Energy)
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15 pages, 1217 KB  
Article
Optimal Design of Integrated Energy Systems Based on Reliability Assessment
by Dong-Min Kim, In-Su Bae, Jae-Ho Rhee, Woo-Chang Song and Sunghyun Bae
Mathematics 2025, 13(23), 3734; https://doi.org/10.3390/math13233734 - 21 Nov 2025
Viewed by 474
Abstract
This paper presents an optimal-design methodology for small-scale Integrated Energy Systems (IESs) that couple electricity and heat in distributed networks. A hybrid reliability assessment integrates probabilistic state enumeration with scenario-based simulation. Mathematically, the design is cast as a stochastic, reliability-driven ranking: time-sequential Monte [...] Read more.
This paper presents an optimal-design methodology for small-scale Integrated Energy Systems (IESs) that couple electricity and heat in distributed networks. A hybrid reliability assessment integrates probabilistic state enumeration with scenario-based simulation. Mathematically, the design is cast as a stochastic, reliability-driven ranking: time-sequential Monte Carlo (MC) produces estimators of Loss of Load Probability (LOLP), Expected Energy Not Supplied (EENS), and Self-Sufficiency Rate (SSR), which are normalized and combined into a Composite Reliability Index (CRI) that orders candidate siting/sizing options. The case study is the D-campus microgrid with Photovoltaic (PV), Combined Heat and Power (CHP), Fuel Cell (FC), Battery Energy Storage Systems (BESSs), and Heat Energy Storage Systems (HESSs; also termed TESs), across multiple siting and sizing scenarios. Results show consistent reductions in LOLP and EENS and increases in SSR as distributed energy resource capacity increases and resources are placed near critical nodes, with the strongest gains observed in the best-performing configurations. The CRI also reveals trade-offs across intermediate scenarios. The operational concept of the campus Energy Management System (EMS), including full operating modes and scheduling logic, is developed to maintain a design focus on reliability-driven decision making. Probability-based formulations, reliability metrics, and the sequential MC setup underpin the proposed ranking framework. The proposed method supports Distributed Energy Resource (DER) sizing and siting decisions for reliable, autonomy-oriented IESs. Full article
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23 pages, 7453 KB  
Article
Hybrid Linear–Nonlinear Model with Adaptive Regularization for Accurate X-Ray Fluorescence Determination of Total Iron Ore Grade
by Lanhao Wang, Zhenyu Zhu, Lixia Li, Zhaopeng Li, Wei Dai and Hongyan Wang
Minerals 2025, 15(11), 1179; https://doi.org/10.3390/min15111179 - 8 Nov 2025
Viewed by 460
Abstract
In mineral processing and metallurgy, total iron grade serves as a critical indicator guiding the entire production chain from crushing to smelting, directly influencing the quality and yield of steel products. To address the limitations of conventional matrix effect correction methods in X-ray [...] Read more.
In mineral processing and metallurgy, total iron grade serves as a critical indicator guiding the entire production chain from crushing to smelting, directly influencing the quality and yield of steel products. To address the limitations of conventional matrix effect correction methods in X-ray fluorescence (XRF) analysis—such as low accuracy, high time consumption, and labor-intensive procedures—this study proposes a novel hybrid model (DSCN-LS) integrating least squares (LS) with dynamically regularized stochastic configuration networks (DSCNs) for total iron ore grade quantification. Through feature analysis, we decompose the grade modeling problem into a linear structural component and nonlinear residual terms. The linear component is resolved by means of LS, while the nonlinear terms are processed by the DSCN with a dynamic regularization strategy. This strategy implements node-specific weighted regularization: weak constraints preserve salient features in high-weight-norm nodes, while strong regularization suppresses redundant information in low-weight-norm nodes, collectively enhancing model generalizability and robustness. Notably, the model was trained and validated using datasets collected directly from industrial sites, ensuring that the results reflect real-world production scenarios. Industrial validation demonstrates that the proposed method achieves an average absolute error of 0.3092, a root mean square error of 0.5561, and a coefficient of determination (R2) of 99.91% in total iron grade estimation. All metrics surpass existing benchmarks, confirming significant improvements in accuracy and operational practicality for XRF detection under complex industrial conditions. Full article
(This article belongs to the Section Mineral Processing and Extractive Metallurgy)
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27 pages, 2346 KB  
Article
Optimizing Sustainable and Resilient Electric Vehicle Battery Recycling Network: Insights from Fourth-Party Logistics
by Mingqiang Yin, Zhaolin Zhang, Liyan Wang, Xiwang Guo, Xiaohu Qian and Muhammad Kamran
Sustainability 2025, 17(21), 9872; https://doi.org/10.3390/su17219872 - 5 Nov 2025
Viewed by 625
Abstract
With the increasing scarcity of critical resources, competition in the electric vehicle battery (EVB) recycling market has intensified, and the strategic establishment of efficient and resilient recycling networks is increasingly vital for maintaining raw material security. Although existing studies have explored electric vehicle [...] Read more.
With the increasing scarcity of critical resources, competition in the electric vehicle battery (EVB) recycling market has intensified, and the strategic establishment of efficient and resilient recycling networks is increasingly vital for maintaining raw material security. Although existing studies have explored electric vehicle battery recycling network design (EVBRND), the impact of facility disruption risks on network decisions is rarely analyzed. This study explores a novel resilient EVBRND problem under disruption risk from the perspective of fourth-party logistics. To cope with disruptions, capacity backups, multi-source allocation, multiple third-party logistics (3PL), multiple transportation routes and facility fortification strategies are systematically integrated. A two-stage stochastic programming model is developed to characterize the problem, which is subsequently reformulated into a mixed-integer linear programming model using a scenario-based approach. To overcome the computational complexity resulting from the enlarged scenario set and the additional binary variables introduced by 3PL selection, a scenario reduction and decomposition-based heuristic (SRDBH) algorithm is developed, which integrates Lagrangian relaxation, conditional relaxation, scenario reduction, and the adaptive subgradient method. The proposed model and algorithm are validated through a real-world case study. Computational results confirm that the SRDBH algorithm achieves superior performance compared with CPLEX. Furthermore, sensitivity analyses highlight the critical role of flexible risk-mitigation configurations in balancing cost minimization with the enhancement of network resilience. Full article
(This article belongs to the Section Waste and Recycling)
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20 pages, 909 KB  
Article
GRU-Based Stock Price Forecasting with the Itô-RMSProp Optimizers
by Mohamed Ilyas El Harrak, Karim El Moutaouakil, Nuino Ahmed, Eddakir Abdellatif and Vasile Palade
AppliedMath 2025, 5(4), 149; https://doi.org/10.3390/appliedmath5040149 - 2 Nov 2025
Viewed by 535
Abstract
This study introduces Itô-RMSProp, a novel extension of the RMSProp optimizer inspired by Itô stochastic calculus, which integrates adaptive Gaussian noise into the update rule to enhance exploration and mitigate overfitting during training. We embed this optimizer within Gated Recurrent Unit (GRU) networks [...] Read more.
This study introduces Itô-RMSProp, a novel extension of the RMSProp optimizer inspired by Itô stochastic calculus, which integrates adaptive Gaussian noise into the update rule to enhance exploration and mitigate overfitting during training. We embed this optimizer within Gated Recurrent Unit (GRU) networks for stock price forecasting, leveraging the GRU’s strength in modeling long-range temporal dependencies under nonstationary and noisy conditions. Extensive experiments on real-world financial datasets, including a detailed sensitivity analysis over a wide range of noise scaling parameters (ε), reveal that Itô-RMSProp-GRU consistently achieves superior convergence stability and predictive accuracy compared to classical RMSProp. Notably, the optimizer demonstrates remarkable robustness across all tested configurations, maintaining stable performance even under volatile market dynamics. These findings suggest that the synergy between stochastic differential equation frameworks and gated architectures provides a powerful paradigm for financial time series modeling. The paper also presents theoretical justifications and implementation details to facilitate reproducibility and future extensions. Full article
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24 pages, 4420 KB  
Article
AttSCNs: A Bayesian-Optimized Hybrid Model with Attention-Guided Stochastic Configuration Networks for Robust GPS Trajectory Prediction
by Xue-Bo Jin, Ye-Qing Wang, Jian-Lei Kong, Yu-Ting Bai and Ting-Li Su
Entropy 2025, 27(11), 1094; https://doi.org/10.3390/e27111094 - 23 Oct 2025
Viewed by 683
Abstract
Trajectory prediction in the Internet of Vehicles (IoV) is crucial for enhancing road safety and traffic efficiency; however, existing methods often fail to address the challenges of colored noise in GPS data and long-term dependency modeling. To overcome these limitations, this paper proposes [...] Read more.
Trajectory prediction in the Internet of Vehicles (IoV) is crucial for enhancing road safety and traffic efficiency; however, existing methods often fail to address the challenges of colored noise in GPS data and long-term dependency modeling. To overcome these limitations, this paper proposes AttSCNs, a probabilistic hybrid framework integrating stochastic configuration networks (SCNs) with an attention-based encoder to model trajectories while quantifying prediction uncertainty. The model leverages SCNs’ stochastic neurons for adaptive noise filtering, attention mechanisms for dependency learning, and Bayesian hyperparameter optimization to infer robust configurations as a posterior distribution. Experimental results on real-world GPS datasets (10,000+ urban/highway trajectories) demonstrate that AttSCNs significantly outperform conventional approaches, reducing RMSE by 36.51% compared to traditional SCNs and lowering MAE by 97.8% compared to Kalman filter baselines. Moreover, compared to the LSTM model, AttSCNs achieve a 52.5% reduction in RMSE and a 68.5% reduction in MAE, with real-time inference speed. These advancements position AttSCNs as a robust, noise-resistant solution for IoV applications, offering superior performance in autonomous driving and smart city systems. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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15 pages, 6914 KB  
Article
Deep Learning-Based Inverse Design of Stochastic-Topology Metamaterials for Radar Cross Section Reduction
by Chao Zhang, Chunrong Zou, Shaojun Guo, Yanwen Zhao and Tongsheng Shen
Materials 2025, 18(21), 4841; https://doi.org/10.3390/ma18214841 - 23 Oct 2025
Viewed by 765
Abstract
Electromagnetic (EM) metamaterials have a wide range of applications due to their unique properties, but their design is often based on specific topological structures, which come with certain limitations. Designing with stochastic topologies can provide more diverse EM properties. However, this requires experienced [...] Read more.
Electromagnetic (EM) metamaterials have a wide range of applications due to their unique properties, but their design is often based on specific topological structures, which come with certain limitations. Designing with stochastic topologies can provide more diverse EM properties. However, this requires experienced designers to search and optimise in a vast design space, which is time-consuming and requires substantial computational resources. In this paper, we employ a deep learning network agent model to replace time-consuming full-wave simulations and quickly establish the mapping relationship between the metamaterial structure and its electromagnetic response. The proposed framework integrates a Convolutional Block Attention Module-enhanced Variational Autoencoder (CBAM-VAE) with a Transformer-based predictor. Incorporating CBAM into the VAE architecture significantly enhances the model’s capacity to extract and reconstruct critical structural features of metamaterials. The Transformer predictor utilises an encoder-only configuration that leverages the sequential data characteristics, enabling accurate prediction of electromagnetic responses from latent variables while significantly enhancing computational efficiency. The dataset is randomly generated based on the filling rate of unit cells, requiring only a small fraction of samples compared to the full design space for training. We employ the trained model for the inverse design of metamaterials, enabling the rapid generation of two cells for 1-bit coding metamaterials. Compared to a similarly sized metallic plate, the designed coding metamaterial radar cross-section (RCS) reduces by over 10 dB from 6 to 18 GHz. Simulation and experimental measurement results validate the reliability of this design approach, providing a novel perspective for the design of EM metamaterials. Full article
(This article belongs to the Section Materials Simulation and Design)
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16 pages, 363 KB  
Article
Machine Learning-Enhanced Last-Mile Delivery Optimization: Integrating Deep Reinforcement Learning with Queueing Theory for Dynamic Vehicle Routing
by Tsai-Hsin Jiang and Yung-Chia Chang
Appl. Sci. 2025, 15(21), 11320; https://doi.org/10.3390/app152111320 - 22 Oct 2025
Viewed by 1546
Abstract
We present the ML-CALMO framework, which integrates machine learning with queueing theory for last-mile delivery optimization under dynamic conditions. The system combines Long Short-Term Memory (LSTM) demand forecasting, Convolutional Neural Network (CNN) traffic prediction, and Deep Q-Network (DQN)-based routing with theoretical stability guarantees. [...] Read more.
We present the ML-CALMO framework, which integrates machine learning with queueing theory for last-mile delivery optimization under dynamic conditions. The system combines Long Short-Term Memory (LSTM) demand forecasting, Convolutional Neural Network (CNN) traffic prediction, and Deep Q-Network (DQN)-based routing with theoretical stability guarantees. Evaluation on modern benchmarks, including the 2022 Multi-Depot Dynamic VRP with Stochastic Road Capacity (MDDVRPSRC) dataset and real-world compatible data from OSMnx-based spatial extraction, demonstrates measurable improvements: 18.5% reduction in delivery time and +8.9 pp (≈12.2% relative) gain in service efficiency compared to current state-of-the-art methods, with statistical significance (p < 0.01). Critical limitations include (1) computational requirements that necessitate mid-range GPU hardware, (2) performance degradation under rapid parameter changes (drift rate > 0.5/min), and (3) validation limited to simulation environments. The framework provides a foundation for integrating predictive machine learning with operational guarantees, though field deployment requires addressing identified scalability and robustness constraints. All code, data, and experimental configurations are publicly available for reproducibility. Full article
(This article belongs to the Section Transportation and Future Mobility)
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20 pages, 1106 KB  
Article
Prediction Model of Component Content Based on Improved Black-Winged Kite Algorithm-Optimized Stochastic Configuration Network
by Zhaohui Huang, Liangfang Liao, Chunfa Liao, Hui Zhang, Tao Qi, Rongxiu Lu and Xingrong Hu
Appl. Sci. 2025, 15(20), 10880; https://doi.org/10.3390/app152010880 - 10 Oct 2025
Viewed by 379
Abstract
Accurate prediction of component content in the rare-earth extraction and separation process is crucial for control system design, product quality control, and optimization of energy consumption. To improve prediction accuracy and modeling efficiency, this paper proposes a model for predicting component content based [...] Read more.
Accurate prediction of component content in the rare-earth extraction and separation process is crucial for control system design, product quality control, and optimization of energy consumption. To improve prediction accuracy and modeling efficiency, this paper proposes a model for predicting component content based on an Improved Black-winged Kite Algorithm-Optimized Stochastic Configuration Network (IBKA-SCN). First, we develop an Improved Black-winged Kite Algorithm (IBKA), incorporating good point set initialization and Lévy random-walk strategies to enhance global optimization capability. Theoretical convergence analysis is provided to ensure the stability and effectiveness of the algorithm. Second, to address the issue that constraint parameters and weight-scaling factors in Stochastic Configuration Network (SCN) rely on manual experience and struggle to balance accuracy and efficiency, IBKA is employed to adaptively search for the optimal hyperparameter combination. The applicability of IBKA-SCN is corroborated through four real-world regression tasks. Finally, the effectiveness of the proposed method is validated through an engineering case study on predicting component content. The results show that IBKA-SCN significantly outperforms existing mainstream methods in both prediction accuracy and modeling speed. Full article
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21 pages, 1577 KB  
Article
Copper Closed-Loop Supply Chain Network Design Based on a Two-Stage Stochastic Programming Model Considering Uncertain Market Prices
by Mou Shen, Ying Guo, Hui Gao and Hongtao Ren
Sustainability 2025, 17(20), 8977; https://doi.org/10.3390/su17208977 - 10 Oct 2025
Viewed by 855
Abstract
Copper is a critically important metal for economic security, and its supply chain is influenced by various factors, particularly market prices. This paper aims to uncover the impact of high uncertainty in copper prices on the copper supply chain (CSC) configuration and propose [...] Read more.
Copper is a critically important metal for economic security, and its supply chain is influenced by various factors, particularly market prices. This paper aims to uncover the impact of high uncertainty in copper prices on the copper supply chain (CSC) configuration and propose strategies for CSC construction. To achieve this goal, this study presents a closed-loop supply chain (CLSC) network, simulates copper market volatility using the geometric Brownian motion (GBM) model, and establishes a two-stage stochastic programming (TSSP) model. An empirical study was conducted using geographical and economic data of the CSC in the Chinese province of Hunan. The research results indicate that there is a threshold in copper prices that can lead to the construction of a reverse supply chain (RSC). However, significant fluctuations in copper prices introduce uncertainty into the supply chain network configuration. Therefore, policy measures to encourage copper scrap recycling should be implemented to maintain the safety of the CLSC during market instability. The proposed modelling framework for addressing fluctuation factors in supply chain design has been validated and can be promoted to other similar industries affected by markets. Full article
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21 pages, 2027 KB  
Article
Fast Network Reconfiguration Method with SOP Considering Random Output of Distributed Generation
by Zhongqiang Zhou, Yuan Wen, Yixin Xia, Xiaofang Liu, Yusong Huang, Jialong Tan and Jupeng Zeng
Processes 2025, 13(10), 3104; https://doi.org/10.3390/pr13103104 - 28 Sep 2025
Viewed by 462
Abstract
Power outages in non-faulted zones caused by system failures significantly reduce the reliability of distribution networks. To address this issue, this paper proposes a fault self-healing technique based on the integration of soft open points (SOPs) and network reconfiguration. A mathematical model for [...] Read more.
Power outages in non-faulted zones caused by system failures significantly reduce the reliability of distribution networks. To address this issue, this paper proposes a fault self-healing technique based on the integration of soft open points (SOPs) and network reconfiguration. A mathematical model for power restoration is developed. The model incorporates SOP operational constraints and the stochastic output of photovoltaic (PV) distributed generation. And this formulation enables the determination of the optimal network reconfiguration strategy and enhances the restoration capability. The study first analyzes the operational principles of SOPs and formulates corresponding constraints based on their voltage support and power flow regulation capabilities. The stochastic nature of PV power output is then modeled and integrated into the restoration model to enhance its practical applicability. This restoration model is further reformulated as a second-order cone programming (SOCP) problem to enable efficient computation of the optimal network configuration. The proposed method is simulated and validated in MATLAB R2019a. Results demonstrate that combining the SOP with the reconfiguration strategy achieves a 100% load restoration rate. This represents a significant improvement compared to traditional network reconfiguration methods. Furthermore, the second-order cone programming (SOCP) transformation ensures computational efficiency. The proposed approach effectively enhances both the fault recovery capability and operational reliability of distribution networks with high penetration of renewable energy. Full article
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