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22 pages, 10487 KB  
Article
Sources, Bioconcentration, and Translocation of Heavy Metals in Haloxylon Ammodendron in the Eastern Junggar Coalfield, Xinjiang, China
by Ziqi Wang, Xuemin He, Zhao An, Xingwang Gao, Gang Wang and Mingqin Chen
Agronomy 2026, 16(4), 460; https://doi.org/10.3390/agronomy16040460 - 15 Feb 2026
Viewed by 332
Abstract
A study on the sources, bioconcentration, and translocation of heavy metals in Haloxylon ammodendron in the Eastern Junggar Coalfield, Xinjiang, China, was conducted and evaluated. The quantities of Pb, Cd, and Cr were 1.2, 22.5, and 1.9 times higher than the baseline values [...] Read more.
A study on the sources, bioconcentration, and translocation of heavy metals in Haloxylon ammodendron in the Eastern Junggar Coalfield, Xinjiang, China, was conducted and evaluated. The quantities of Pb, Cd, and Cr were 1.2, 22.5, and 1.9 times higher than the baseline values of Xinjiang soils, respectively. The mean concentrations of these heavy metals in the rhizosphere soil of Haloxylon ammodendron were 48.81, 17.74, 93.25, 3.32, 29.05, and 26.95 mg/kg. The exceedance rates for Cd, Cr, and Pb in bare soil were 100%, 99.03%, and 75.73%, respectively, indicating significant accumulation of heavy metals, with Cd demonstrating the highest enrichment degree. Most sampling sites showed moderate pollution according to the Pollution Load Index (PLI). Meanwhile, the Pollution Index (PN) indicated elevated pollution levels at all the sampling sites, with Cr identified as the first contaminant. The absolute principal component score–multiple linear regression (APCS-MLR) model revealed three principal sources of heavy metal pollutants in soil: 44.2% from natural processes and mining activities, 22.7% from industrial coal combustion and sewage, and 33.1% of undetermined origins. The bioconcentration factors (BCFs) and translocation factors (TFs) revealed Haloxylon ammodendron to have clear accumulation and translocation abilities with respect to these heavy metals. The fuzzy membership function showed that the overall assessment score for Haloxylon ammodendron was 9.1325, indicating the substantial remediation potential of Haloxylon ammodendron for heavy metal pollutants, especially for Cd. Furthermore, Haloxylon ammodendron demonstrated substantial Pb and Cr accumulation and remediation ability. Haloxylon ammodendron exhibited remarkable heavy metal accumulation and translocation abilities, making it a suitable tool for phytoremediation in the study area. The findings of this study will prove useful in promoting and implementing sustainable mining practices and safeguarding regional ecological security and may contribute to advancing local ecological conservation and social economic development. Full article
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33 pages, 1844 KB  
Article
A Prototypical Fuzzy Similarity-Based Classification Framework for Ultrasonic Defect Detection in Concrete
by Matteo Cacciola, Giovanni Angiulli, Pietro Burrascano, Filippo Laganà and Mario Versaci
Eng 2026, 7(2), 88; https://doi.org/10.3390/eng7020088 - 14 Feb 2026
Viewed by 224
Abstract
In this study, we present an extension of the Takagi–Sugeno fuzzy inference system (TS-FIS) framework based on prototypical fuzzy similarity (PFS) for defect detection in concrete. The key novelty lies in integrating the PFS mechanism into the TS-FIS+ANFIS architecture, thus enabling a hybrid [...] Read more.
In this study, we present an extension of the Takagi–Sugeno fuzzy inference system (TS-FIS) framework based on prototypical fuzzy similarity (PFS) for defect detection in concrete. The key novelty lies in integrating the PFS mechanism into the TS-FIS+ANFIS architecture, thus enabling a hybrid rule–activation mechanism, bringing together fuzzy interpretability with data-driven similarity learning. To describe the ultrasonic concrete defect scenario, a high-fidelity finite element method (FEM) model that combines solid mechanics with fluid acoustics has been developed. From this numerical model, a synthetic dataset of about 36.8 million samples has been generated. The performance of the proposed TS-FIS+ANFIS+PFS classification system has been compared with that of a conventional FIS+ANFIS model, its particle-swarm-optimized (PSO) version and a Decision Tree (DT) classifier. The proposed model achieved the best performance, with a classification accuracy of 85.4% and an inference time of approximately 0.2 ms per sample. In contrast, the conventional, the PSO and the DT classifiers yielded accuracies of 60.5%, 62.0%, and 76.0%, respectively. These results confirm that PFS improves sensitivity and alleviates the computational effort, representing a potential candidate toward the realization of a defect abacus for concrete, an atlas conceived as a systematic collection of defect configurations associated with specific ultrasonic responses. Full article
(This article belongs to the Special Issue Artificial Intelligence for Engineering Applications, 2nd Edition)
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25 pages, 461 KB  
Article
Fuzzy Improved Distributions for Exceedance Counts in Order Statistic Intervals
by Gulser Oz and Ismihan Bayramoglu
Mathematics 2026, 14(4), 627; https://doi.org/10.3390/math14040627 - 11 Feb 2026
Viewed by 150
Abstract
We study exceedance counts for order statistic intervals when boundary uncertainty is modeled through a fuzzy improved distribution function. In an ordinary setting, whether an observation falls below a threshold is decided by a crisp comparison, which can be unstable when specifications are [...] Read more.
We study exceedance counts for order statistic intervals when boundary uncertainty is modeled through a fuzzy improved distribution function. In an ordinary setting, whether an observation falls below a threshold is decided by a crisp comparison, which can be unstable when specifications are vague, subject to tolerance bands, or expressed linguistically. We replace the crisp rule by a graded membership function and use the fuzzy improved cumulative distribution function Fμ. From an initial independent and identically distributed sample, with ordinary cumulative distribution function F, we form the random interval between the r-th and s-th order statistics, and we count how many of m independent newcomers fall inside this interval. Newcomers follow either the ordinary model (Q=F) or the fuzzy improved model (Q=Fμ). We derive exact finite-sample formulas, moments, and a distribution-free representation based on a probability integral transform, which yields the large-m limit law of the newcomer proportion. Numerical illustrations for exponential and uniform distributions show how fuzzification reshapes the distribution and can materially change predictive dispersion of exceedance counts. Full article
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30 pages, 9131 KB  
Article
Multi-Objective Optimization Design of High-Power Permanent Magnet Synchronous Motor Based on Surrogate Model
by Zhihao Zhu, Xiang Li, Yingzhi Lin, Hao Wu, Junhui Chen, Niannian Zhang, Thomas Wu, Bo Lin and Suyan Wang
Sustainability 2026, 18(3), 1705; https://doi.org/10.3390/su18031705 - 6 Feb 2026
Viewed by 349
Abstract
Energy scarcity has evolved into one of the most pressing challenges confronting the global community today. Fuel-driven loaders suffer from drawbacks such as high fuel consumption, low energy conversion efficiency, and heavy pollution, which not only aggravate atmospheric environmental pollution but also exacerbate [...] Read more.
Energy scarcity has evolved into one of the most pressing challenges confronting the global community today. Fuel-driven loaders suffer from drawbacks such as high fuel consumption, low energy conversion efficiency, and heavy pollution, which not only aggravate atmospheric environmental pollution but also exacerbate the global energy crisis, directly undermining sustainable development goals. In contrast, permanent magnet synchronous motors (PMSMs) have become the preferred choice for the electrification of loaders owing to their exceptional torque density, strong overload capacity, and high reliability. However, during the optimal design of high-power interior permanent magnet synchronous motors (IPMSMs), traditional methods encounter issues with inadequate optimization efficiency and excessive computational expenses, thus hindering the large-scale deployment of power systems for eco-friendly loaders. Therefore, this paper takes a 125 kW, 3000 rpm IPMSM as the research object and proposes a multi-objective optimization strategy integrating a high-precision surrogate model with modern intelligent algorithms. This approach not only enhances motor performance but also cuts down computational overhead, which holds considerable significance for reducing industrial carbon emissions and driving the sustainable development of the manufacturing industry. Taking the key performance of IPMSM as the optimization objective and the related structural parameters as the optimization variables, the multi-performance characteristic index, interaction effect and comprehensive sensitivity of the variables are calculated and analyzed by fuzzy Taguchi experiment, and the hierarchical dimension reduction in the variables is completed. The Multicriteria Optimal-Latin Hypercube Sampling (MO-LHS) method is adopted to construct the sample data space, and a back-propagation neural network (BPNN) surrogate model is used to predict and fit the motor performance. The second-generation non-dominated sorting genetic algorithm (NSGA-II) is employed for iterative optimization, and the optimized motor dimension parameters are obtained through the Pareto optimal solution. Finally, through finite element analysis (FEA) and experiments, the rated torques obtained are 417.6 N·m and 425.1 N·m, respectively, with an error not exceeding 1.8%. This verifies the correctness and effectiveness of the proposed multi-objective optimization method based on the surrogate model. Full article
(This article belongs to the Section Energy Sustainability)
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35 pages, 3963 KB  
Article
Systemic Risk Transmission in Commodity Markets
by Irina Georgescu
Risks 2026, 14(2), 27; https://doi.org/10.3390/risks14020027 - 1 Feb 2026
Viewed by 323
Abstract
This paper investigates tail-risk transmission and asymmetric dependence in commodity markets using an asymmetric fuzzy vine copula framework applied to gold, crude oil, natural gas, and silver from 1 January 2015 to 1 January 2025, extracted from Yahoo Finance. Bootstrap-based trapezoidal fuzzy numbers [...] Read more.
This paper investigates tail-risk transmission and asymmetric dependence in commodity markets using an asymmetric fuzzy vine copula framework applied to gold, crude oil, natural gas, and silver from 1 January 2015 to 1 January 2025, extracted from Yahoo Finance. Bootstrap-based trapezoidal fuzzy numbers are used to estimate fuzzy tail dependence, VaR, and CoVaR, capturing both sampling variability and parameter uncertainty. Results show generally weak and symmetric dependence among commodities, except for strong lower-tail dominance between crude oil and natural gas, indicating downside contagion within the energy sector. Adding the SKEW index as a market-implied tail-risk proxy has negligible effects on dependence and spillovers, revealing that equity-market tail-risk sentiment does not influence commodity markets. Systemic risk remains localized within energy and precious-metal linkages, underscoring the need for sector-specific monitoring. Full article
(This article belongs to the Special Issue Fundamentals and Risk Factors in Commodity Markets)
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55 pages, 2886 KB  
Article
Hybrid AI and LLM-Enabled Agent-Based Real-Time Decision Support Architecture for Industrial Batch Processes: A Clean-in-Place Case Study
by Apolinar González-Potes, Diego Martínez-Castro, Carlos M. Paredes, Alberto Ochoa-Brust, Luis J. Mena, Rafael Martínez-Peláez, Vanessa G. Félix and Ramón A. Félix-Cuadras
AI 2026, 7(2), 51; https://doi.org/10.3390/ai7020051 - 1 Feb 2026
Viewed by 853
Abstract
A hybrid AI and LLM-enabled architecture is presented for real-time decision support in industrial batch processes, where supervision still relies heavily on human operators and ad hoc SCADA logic. Unlike algorithmic contributions proposing novel AI methods, this work addresses the practical integration and [...] Read more.
A hybrid AI and LLM-enabled architecture is presented for real-time decision support in industrial batch processes, where supervision still relies heavily on human operators and ad hoc SCADA logic. Unlike algorithmic contributions proposing novel AI methods, this work addresses the practical integration and deployment challenges arising when applying existing AI techniques to safety-critical industrial environments with legacy PLC/SCADA infrastructure and real-time constraints. The framework combines deterministic rule-based agents, fuzzy and statistical enrichment, and large language models (LLMs) to support monitoring, diagnostic interpretation, preventive maintenance planning, and operator interaction with minimal manual intervention. High-frequency sensor streams are collected into rolling buffers per active process instance; deterministic agents compute enriched variables, discrete supervisory states, and rule-based alarms, while an LLM-driven analytics agent answers free-form operator queries over the same enriched datasets through a conversational interface. The architecture is instantiated and deployed in the Clean-in-Place (CIP) system of an industrial beverage plant and evaluated following a case study design aimed at demonstrating architectural feasibility and diagnostic behavior under realistic operating regimes rather than statistical generalization. Three representative multi-stage CIP executions—purposively selected from 24 runs monitored during a six-month deployment—span nominal baseline, preventive-warning, and diagnostic-alert conditions. The study quantifies stage-specification compliance, state-to-specification consistency, and temporal stability of supervisory states, and performs spot-check audits of numerical consistency between language-based summaries and enriched logs. Results in the evaluated CIP deployment show high time within specification in sanitizing stages (100% compliance across the evaluated runs), coherent and mostly stable supervisory states in variable alkaline conditions (state-specification consistency Γs0.98), and data-grounded conversational diagnostics in real time (median numerical error below 3% in audited samples), without altering the existing CIP control logic. These findings suggest that the architecture can be transferred to other industrial cleaning and batch operations by reconfiguring process-specific rules and ontologies, though empirical validation in other process types remains future work. The contribution lies in demonstrating how to bridge the gap between AI theory and industrial practice through careful system architecture, data transformation pipelines, and integration patterns that enable reliable AI-enhanced decision support in production environments, offering a practical path toward AI-assisted process supervision with explainable conversational interfaces that support preventive maintenance decision-making and equipment health monitoring. Full article
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23 pages, 1858 KB  
Article
State Estimation-Based Disturbance Rejection Control for Third-Order Fuzzy Parabolic PDE Systems with Hybrid Attacks
by Karthika Poornachandran, Elakkiya Venkatachalam, Oh-Min Kwon, Aravinth Narayanan and Sakthivel Rathinasamy
Mathematics 2026, 14(3), 444; https://doi.org/10.3390/math14030444 - 27 Jan 2026
Viewed by 284
Abstract
In this work, we develop a disturbance suppression-oriented fuzzy sliding mode secured sampled-data controller for third-order parabolic partial differential equations that ought to cope with nonlinearities, hybrid cyber attacks, and modeled disturbances. This endeavor is mainly driven by formulating an observer model with [...] Read more.
In this work, we develop a disturbance suppression-oriented fuzzy sliding mode secured sampled-data controller for third-order parabolic partial differential equations that ought to cope with nonlinearities, hybrid cyber attacks, and modeled disturbances. This endeavor is mainly driven by formulating an observer model with a T–S fuzzy mode of execution that retrieves the latent state variables of the perceived system. Progressing onward, the disturbance observers are formulated to estimate the modeled disturbances emerging from the exogenous systems. In due course, the information received from the system and disturbance estimators, coupled with the sliding surface, is compiled to fabricate the developed controller. Furthermore, in the realm of security, hybrid cyber attacks are scrutinized through the use of stochastic variables that abide by the Bernoulli distributed white sequence, which combat their unpredictability. Proceeding further in this framework, a set of linear matrix inequality conditions is established that relies on the Lyapunov stability theory. Precisely, the refined looped Lyapunov–Krasovskii functional paradigm, which reflects in the sampling period that is intricately split into non-uniform intervals by leveraging a fractional-order parameter, is deployed. In line with this pursuit, a strictly (Φ1,Φ2,Φ3)ϱ dissipative framework is crafted with the intent to curb norm-bounded disturbances. A simulation-backed numerical example is unveiled in the closing segment to underscore the potency and efficacy of the developed control design technique. Full article
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23 pages, 813 KB  
Article
Digital Transformation and High-Quality Development in China’s Leading Agribusiness Firms: A TOE-Based Configurational Analysis
by Xi Zhou, Jingyi Hu, Wen Liu and Yuchuan Fan
Agriculture 2026, 16(3), 304; https://doi.org/10.3390/agriculture16030304 - 25 Jan 2026
Viewed by 375
Abstract
Leading agribusiness firms are pivotal to modernizing agricultural supply chains, yet evidence on how digital transformation translates into high-quality development remains fragmented. Using a 2024 sample of 30 Chinese national agribusiness leaders and the technology–organization–environment (TOE) framework, we integrate grey relational analysis with [...] Read more.
Leading agribusiness firms are pivotal to modernizing agricultural supply chains, yet evidence on how digital transformation translates into high-quality development remains fragmented. Using a 2024 sample of 30 Chinese national agribusiness leaders and the technology–organization–environment (TOE) framework, we integrate grey relational analysis with DEMATEL to quantify interdependencies among conditions, and combine fuzzy-set QCA with necessary condition analysis to identify both configurational pathways and binding constraints. The results of the analysis indicate that high-quality development rarely stems from a single driver; it emerges from complementary bundles linking digital technologies and R&D investment with organizational readiness (e.g., talent and governance) under supportive external conditions (e.g., policy incentives and market pressure). The findings provide a configurational explanation of digital upgrading in agribusiness and inform differentiated digital strategies for managers and policymakers. Full article
(This article belongs to the Section Agricultural Economics, Policies and Rural Management)
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22 pages, 10592 KB  
Article
Dominant Role of Horizontal Swelling Pressure in Progressive Failure of Expansive Soil Slopes: An Integrated FAHP and 3D Numerical Analysis
by Chao Zheng, Shiguang Xu, Lixiong Deng, Jiawei Zhang, Zhihao Lu and Xian Li
Appl. Sci. 2026, 16(2), 1110; https://doi.org/10.3390/app16021110 - 21 Jan 2026
Viewed by 152
Abstract
Directional swelling pressure is a critical yet often overlooked factor governing the instability of expansive soil slopes. Most existing studies simplify swelling behavior as a uniform or purely vertical stress, thereby underestimating the distinct contribution of horizontal swelling pressure. In this study, an [...] Read more.
Directional swelling pressure is a critical yet often overlooked factor governing the instability of expansive soil slopes. Most existing studies simplify swelling behavior as a uniform or purely vertical stress, thereby underestimating the distinct contribution of horizontal swelling pressure. In this study, an integrated framework combining the Fuzzy Analytic Hierarchy Process (FAHP), multivariate regression analysis based on 35 expansive soil samples, and three-dimensional strength-reduction numerical modeling was developed to systematically evaluate the mechanistic roles of vertical and horizontal swelling pressures in slope deformation. The FAHP and regression analyses indicate that water content is the dominant factor controlling both the free swell ratio and swelling pressure, leading to predictive relationships that link swelling behavior to fundamental physical indices. These empirical correlations were subsequently incorporated into a three-dimensional numerical model of a representative Neogene expansive soil slope. The simulation results demonstrate that neglecting swelling pressure results in substantial discrepancies between predicted and observed displacements. Vertical swelling pressure induces moderate surface uplift but exerts a limited influence on overall failure patterns. In contrast, horizontal swelling pressure markedly amplifies downslope displacement—by more than four times under saturated conditions—reduces the factor of safety by 24.7%, and promotes the progressive development of a continuous slip surface. These findings clearly demonstrate that horizontal swelling pressure is the dominant driver of progressive failure in expansive soil slopes. This study provides new mechanistic insights into swelling-induced deformation and offers a quantitative framework for incorporating directional swelling stresses into slope stability assessment, design optimization, and mitigation strategies for geotechnical structures in expansive soil regions. Full article
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35 pages, 1361 KB  
Article
A Fuzzy-SNA Computational Framework for Quantifying Intimate Relationship Stability and Social Network Threats
by Ning Wang and Xiangzhi Kong
Symmetry 2026, 18(1), 201; https://doi.org/10.3390/sym18010201 - 21 Jan 2026
Viewed by 232
Abstract
Intimate relationship stability is fundamental to human wellbeing, yet its quantitative assessment faces dual challenges: the inherent subjectivity of psychological constructs and the complexity of social ecosystems. Symmetry, as a fundamental structural feature of social interaction, plays a pivotal role in shaping relational [...] Read more.
Intimate relationship stability is fundamental to human wellbeing, yet its quantitative assessment faces dual challenges: the inherent subjectivity of psychological constructs and the complexity of social ecosystems. Symmetry, as a fundamental structural feature of social interaction, plays a pivotal role in shaping relational dynamics. To address these limitations, this study proposes an innovative computational framework that integrates Fuzzy Set Theory with Social Network Analysis (SNA). The framework consists of two complementary components: (1) a psychologically grounded fuzzy assessment model that employs differentiated membership functions to transform discrete subjective ratings into continuous and interpretable relationship quality indices and (2) an enhanced Fuzzy C-Means (FCM) threat detection model that utilizes Weighted Mahalanobis Distance to accurately identify and cluster potential interference sources within social networks. Empirical validation using a simulated dataset—comprising typical characteristic samples from 10 couples—demonstrates that the proposed framework not only generates interpretable relationship diagnostics by correcting biases associated with traditional averaging methods, but also achieves high precision in threat identification. The results indicate that stable relationships exhibit greater symmetry in partner interactions, whereas threatened nodes display structural and behavioural asymmetry. This study establishes a rigorous mathematical paradigm—“Subjective Fuzzification → Multidimensional Feature Engineering → Intelligent Clustering”—for relationship science, thereby advancing the field from descriptive analysis toward data-driven, quantitative evaluation and laying a foundation for systematic assessment of relational health. Full article
(This article belongs to the Section Mathematics)
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18 pages, 966 KB  
Article
Anomaly Detection Based on Hybrid Kernelized Fuzzy Density
by Kaitian Luo, Shenhong Lei, Chaoqing Li and Yi Li
Symmetry 2026, 18(1), 192; https://doi.org/10.3390/sym18010192 - 20 Jan 2026
Viewed by 189
Abstract
Unsupervised anomaly detection has been extensively studied. However, most existing methods are designed for either numerical or nominal data, which struggle to detect anomalies effectively in real-world mixed-type datasets. Fuzzy information granulation is a key concept in granular computing, which offers a potent [...] Read more.
Unsupervised anomaly detection has been extensively studied. However, most existing methods are designed for either numerical or nominal data, which struggle to detect anomalies effectively in real-world mixed-type datasets. Fuzzy information granulation is a key concept in granular computing, which offers a potent framework for managing uncertainty in mixed-type data and provides a viable pathway for unsupervised anomaly detection. Nevertheless, conventional fuzzy information granulation-based detection methods often model only simple, linear fuzzy relations between samples. This limitation prevents them from capturing the complex, nonlinear structures inherent in the data, leading to a degradation in detection performance. To address these shortcomings, we propose a Hybrid Kernelized Fuzzy Density-based anomaly detector (HKFD). HKFD pioneers a hybrid kernelized fuzzy relation by integrating a hybrid distance metric with kernel methods. This new relation allows us to define a hybrid kernelized fuzzy density for each sample within every feature subspace, effectively capturing the local data dispersion. Crucially, we introduce an information-theoretic weighting mechanism. By calculating the fuzzy information entropy of each feature’s distribution, HKFD automatically assigns higher weights to more informative feature subspaces that contribute more to identifying anomalies. The final anomaly factor is then calculated by the weighted fusion of these densities. Comprehensive experiments on 20 datasets demonstrate that HKFD significantly outperforms state-of-the-art methods, achieving superior anomaly detection performance. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Sets and Fuzzy Systems)
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25 pages, 10707 KB  
Article
Stochastic–Fuzzy Assessment Framework for Firefighting Functionality of Urban Water Distribution Networks Against Post-Earthquake Fires
by Xiang He, Hong Huang, Fengjiao Xu, Chao Zhang and Tingxin Qin
Sustainability 2026, 18(2), 949; https://doi.org/10.3390/su18020949 - 16 Jan 2026
Viewed by 367
Abstract
Post-earthquake fires often cause more severe losses than the earthquakes themselves, highlighting the critical role of water distribution networks (WDNs) in mitigating fire risks. This study proposed an improved assessment framework for the post-earthquake firefighting functionality of WDNs. This framework integrates a WDN [...] Read more.
Post-earthquake fires often cause more severe losses than the earthquakes themselves, highlighting the critical role of water distribution networks (WDNs) in mitigating fire risks. This study proposed an improved assessment framework for the post-earthquake firefighting functionality of WDNs. This framework integrates a WDN firefighting simulation model into a cloud model-based assessment method. By combining seismic damage and firefighting scenarios, the simulation model derives sample values of the functional indexes through Monte Carlo simulations. These indexes integrate the spatiotemporal characteristics of the firefighting flow and pressure deficiencies to assess a WDN’s capability to control fire and address fire hazards across three dimensions: average, severe, and prolonged severe deficiencies. The cloud model-based assessment method integrates the sample values of functional indexes with expert opinions, enabling qualitative and quantitative assessments under stochastic–fuzzy conditions. An illustrative study validated the efficacy of this method. The flow- and pressure-based indexes elucidated functionality degradation owing to excessive firefighting flow and the diminished supply capacity of a WDN, respectively. The spatiotemporal characteristics of severe flow and pressure deficiencies demonstrated the capability of firefighting resources to manage concurrent fires while ensuring a sustained water supply to fire sites. This method addressed the limitations of traditional quantitative and qualitative assessment approaches, resulting in more reliable outcomes. Full article
(This article belongs to the Section Hazards and Sustainability)
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26 pages, 6946 KB  
Article
Distributionally Robust Optimization for Integrated Energy System with Tiered Carbon Trading: Synergizing CCUS with Hydrogen Blending Combustion
by Mingyao Huang, Meiheriayi Mutailipu, Peng Wang, Jun Huang, Fusheng Xue and Xiaofeng Li
Processes 2026, 14(2), 328; https://doi.org/10.3390/pr14020328 - 16 Jan 2026
Viewed by 245
Abstract
In this study, an Integrated Energy System (IES) with hydrogen refinement within a tiered carbon trading mechanism (TCTM) is presented to improve energy efficiency and support decarbonization. To address uncertainties in the IES, a distributionally robust optimization (DRO) approach, employing a fuzzy set [...] Read more.
In this study, an Integrated Energy System (IES) with hydrogen refinement within a tiered carbon trading mechanism (TCTM) is presented to improve energy efficiency and support decarbonization. To address uncertainties in the IES, a distributionally robust optimization (DRO) approach, employing a fuzzy set framework with Kernel Density Estimation (KDE) to construct error distributions and specify output ranges for renewable energy (RE), is proposed. Latin hypercube sampling (LHS) and K-means clustering are, respectively, applied to generate original and representative scenarios. Subsequently, case studies are performed to evaluate advantages of the presented model. The results indicate that hydrogen refinement within the TCTM framework has substantial benefits for the IES. Specifically, the proposed scenario integrates hydrogen blending combustion (HBC) with synthetic methane, demonstrating significant economic and carbon benefits, with cost reductions of 7.3%, 7.1%, and 4.3% and carbon emission reductions of 6%, 3%, and 2.4% compared to scenarios with no hydrogen utilization, HBC only, and synthetic methane only, respectively. In contrast, to exclude carbon trading and include fixed-price trading, the TCTM achieves a 3.5% and 1.1% reduction in carbon emissions, respectively. Finally, a comprehensive sensitivity analysis is performed, examining factors such as the ratio of hydrogen blending, price, and growth rate of carbon trading. Full article
(This article belongs to the Section Energy Systems)
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22 pages, 1343 KB  
Article
Stability Improvement of PMSG-Based Wind Energy System Using the Passivity-Based Non-Fragile Retarded Sampled Data Controller
by Thirumoorthy Ramasamy, Thiruvenkadam Srinivasan and In-Ho Ra
Mathematics 2026, 14(2), 293; https://doi.org/10.3390/math14020293 - 13 Jan 2026
Viewed by 228
Abstract
This work presents the design of passivity based non-fragile retarded sampled data control (NFRSDC) for the wind energy system using permanent magnet synchronous generator. At first, the proposed system is characterized in terms of non-linear dynamical equations, which is later expressed in terms [...] Read more.
This work presents the design of passivity based non-fragile retarded sampled data control (NFRSDC) for the wind energy system using permanent magnet synchronous generator. At first, the proposed system is characterized in terms of non-linear dynamical equations, which is later expressed in terms of linear sub-systems via fuzzy membership functions using the Takagi–Sugeno fuzzy approach. After that, a more applicative NFRSDC is proposed along with the delay involved during signal transmission as well as randomly occurring controller gain perturbations (ROCGPs). Here, the ROCGPs are modeled accordingly using stochastic variable which obeys the certain Bernoulli distribution sequences. Folowing that, an appropriate Lyapunov–Krasovskii functionals are constructed to obtain the sufficient conditions in the form of linear matrix inequalities. These obtained conditions are then used to ensure the global asymptotic stability of the given system with the exogenous disturbances. Finally, numerical simulations are performed using MATLAB/Simulink and the obtained results have clearly demonstrated the efficacy of the proposed controller. Full article
(This article belongs to the Special Issue Applied Mathematics and Intelligent Control in Electrical Engineering)
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10 pages, 1944 KB  
Proceeding Paper
An Optimized ANFIS Model for Predicting Water Hardness and TDS in Ion-Exchange Wastewater Treatment Systems
by Jaloliddin Eshbobaev, Adham Norkobilov, Komil Usmanov, Zafar Turakulov, Azizbek Kamolov, Sarvar Rejabov and Sitora Farkhadova
Eng. Proc. 2025, 117(1), 18; https://doi.org/10.3390/engproc2025117018 - 7 Jan 2026
Cited by 1 | Viewed by 273
Abstract
Industrial wastewater treatment processes often exhibit highly nonlinear, dynamic behavior, making accurate prediction and control difficult when using conventional modeling approaches. This study presents an enhanced Adaptive Neuro-Fuzzy Inference System (ANFIS) framework for modeling the ion-exchange purification process based on 200 experimentally collected [...] Read more.
Industrial wastewater treatment processes often exhibit highly nonlinear, dynamic behavior, making accurate prediction and control difficult when using conventional modeling approaches. This study presents an enhanced Adaptive Neuro-Fuzzy Inference System (ANFIS) framework for modeling the ion-exchange purification process based on 200 experimentally collected data samples obtained from a laboratory-scale treatment system. The initial ANFIS structure was generated using subtractive clustering to automatically derive the rule base, while hybrid learning combining backpropagation and least-squares estimation was applied to train the model. The training results demonstrated stable convergence across 100, 200, and 300 epochs, with progressive improvements in model accuracy. To further enhance performance, several meta-heuristic optimization methods, including Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and the Adam optimizer, were integrated within a Python 3.13-based environment to refine model parameters. Ensemble learning and an extended Boosting++ strategy was subsequently employed to reduce variance, correct residual errors, and strengthen generalization capability. The optimized ANFIS model achieved strong predictive accuracy across both training and unseen test datasets. The performance metrics for the full dataset yielded RMSE (Root Mean Square Error) = 1.3369, MAE (Mean Absolute Error) = 0.9989, and R2 = 0.9313, while correlation analysis showed consistently high R-values for training (0.96745), validation (0.95206), test (0.95754), and overall data (0.96507). The results demonstrate that the combination of subtractive clustering, hybrid learning, meta-heuristic optimization, and ensemble boosting produces a highly reliable soft-computing model capable of effectively capturing the nonlinear dynamics of ion-exchange wastewater treatment. The proposed approach provides a robust foundation for intelligent monitoring and control strategies in industrial purification systems. Full article
(This article belongs to the Proceedings of The 4th International Electronic Conference on Processes)
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