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Search Results (13,047)

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Keywords = numerical integration

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29 pages, 20314 KB  
Article
Modeling and Evaluating Integrated Pollution Control Measures in Rivers: A Case Study of the Lianjiang River Basin
by Jinxi Zheng, Yongyou Hu, Wenqin Xu, Shewei Yang, Xiangzhuan Zeng, Youshun Guo, Zhenjiang Yu and Jianhua Cheng
Toxics 2026, 14(3), 216; https://doi.org/10.3390/toxics14030216 (registering DOI) - 1 Mar 2026
Abstract
With rapid industrialization and urbanization, water pollution in urban rivers has become increasingly severe, posing significant threats to regional ecological environments and water security. The Puning section of the Lianjiang River in Guangdong Province, China, suffers from complex pollution originating from multiple sources, [...] Read more.
With rapid industrialization and urbanization, water pollution in urban rivers has become increasingly severe, posing significant threats to regional ecological environments and water security. The Puning section of the Lianjiang River in Guangdong Province, China, suffers from complex pollution originating from multiple sources, including domestic sewage, industrial wastewater, and agricultural non-point source pollution. This underscores an urgent need for integrated river pollution control in the region. In this study, a coupled hydrodynamic-water quality model was established to systematically analyze and simulate water quality conditions in the Puning section. A total of 22 pollution control scenarios were proposed and evaluated. The results indicated that most monitoring sections in the Puning segment failed to meet the Class V surface water quality standards, with notably high concentrations of chemical oxygen demand (COD), ammonia nitrogen (NH3-N), and total phosphorus (TP). Numerical simulations revealed that the multi-source interception scenario—simultaneously intercepting inflows at Tiande Bridge (Baikeng Lake), Dayangmei (Liusha Zhonghe), and Liudoupu (Liusha Zhonghe)—performed best in reducing pollutant concentrations. Specifically, this scenario achieved reductions exceeding 90% in NH3-N and TP concentrations. Furthermore, the study demonstrates that for basins with complex pollution sources, integrated management strategies—including the construction of wastewater treatment facilities, control of point and non-point sources, and ecological restoration measures—can effectively improve water quality and optimize the water environmental capacity. These findings provide theoretical and technical support for water environment management in the Lianjiang River Basin and offer valuable insights for water quality management in similar regions. Full article
23 pages, 1010 KB  
Article
A Formal Optimization-Oriented Design Framework for Predictive Extrusion-Based 3D Bioprinting
by Antreas Kantaros, Theodore Ganetsos and Michail Papoutsidakis
Biomimetics 2026, 11(3), 165; https://doi.org/10.3390/biomimetics11030165 (registering DOI) - 1 Mar 2026
Abstract
Extrusion-based three-dimensional (3D) bioprinting has enabled the fabrication of complex, cell-laden constructs; however, process parameter selection remains largely empirical and system-specific. As biofabrication workflows scale in complexity and translational ambition, trial-and-error optimization increasingly limits reproducibility, transferability, and informed decision-making. In this work, a [...] Read more.
Extrusion-based three-dimensional (3D) bioprinting has enabled the fabrication of complex, cell-laden constructs; however, process parameter selection remains largely empirical and system-specific. As biofabrication workflows scale in complexity and translational ambition, trial-and-error optimization increasingly limits reproducibility, transferability, and informed decision-making. In this work, a formal, optimization-oriented design framework is proposed to structure extrusion-based bioprinting as a constrained, multivariable design problem. Rather than introducing a system-specific predictive model, the framework organizes process parameters, material descriptors, scaffold architecture, and biological feasibility into a unified formulation based on objective functions and admissible constraints. Symbolic coupling relationships are employed to make parameter dependencies, trade-offs, and constraint interactions explicit without imposing restrictive assumptions on material behavior or biological response. A demonstrative computational case study is presented to illustrate how qualitative predictive reasoning emerges through constraint-driven design space analysis and multi-objective considerations. The framework reveals how feasible operating regions are shaped by competing biological, mechanical, and manufacturing limitations, emphasizing robustness-aware parameter selection over isolated optimization. The proposed approach is intended as a transferable methodological foundation that supports structured reasoning, experimental planning, and future integration with numerical models, data-driven tools, and closed-loop biofabrication systems. Full article
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30 pages, 591 KB  
Article
Computing Rate–Distortion Functions of Continuous Memoryless Sources via Discrete Algorithms: An Integrated Scheme with Convergence Guarantee and Algorithmic Acceleration
by Lingyi Chen, Haoran Tang, Hao Wu, Huihui Wu, Shitong Wu and Wenyi Zhang
Entropy 2026, 28(3), 280; https://doi.org/10.3390/e28030280 (registering DOI) - 1 Mar 2026
Abstract
Numerical computation of the rate–distortion (RD) function is a key problem in RD theory. Thus far, efficient algorithms have been well studied for discrete sources, but for continuous sources, there is still lack of a rigorously developed solution. In this article, an integrated [...] Read more.
Numerical computation of the rate–distortion (RD) function is a key problem in RD theory. Thus far, efficient algorithms have been well studied for discrete sources, but for continuous sources, there is still lack of a rigorously developed solution. In this article, an integrated approach is conducted that bridges RD problems of continuous memoryless sources and discrete numerical algorithms. First, we analyze and establish the theoretical convergence guarantee when progressively approaching the continuous RD problem via a sequence of discrete problems. Next, discrete algorithms including the Blahut–Arimoto (BA) and constrained BA algorithms are reviewed, and estimates of their required amount of arithmetic operations to attain ε-accuracy in solving the continuous RD problem are derived. Finally, acceleration techniques that exploit structures of special distortion measures (i.e., squared-error and absolute-error) are developed. Full article
25 pages, 4935 KB  
Article
An Interpretable Nonlinear Intelligent Bias Correction Method for FY-4A/GIIRS Hyperspectral Infrared Brightness Temperatures
by Gen Wang, Bing Xu, Song Ye, Xiefei Zhi, Tiening Zhang, Youpeng Yang, Yang Liu, Feng Xie, Qiao Liu and Haili Zhang
Remote Sens. 2026, 18(5), 748; https://doi.org/10.3390/rs18050748 (registering DOI) - 1 Mar 2026
Abstract
The hyperspectral infrared observations of the Geostationary Interferometric Infrared Sounder (GIIRS) on the Fengyun-4A (FY-4A) satellite are an important data source for numerical weather prediction (NWP) assimilation. However, there are systematic differences between observed and simulated brightness temperatures (i.e., the observation increments contain [...] Read more.
The hyperspectral infrared observations of the Geostationary Interferometric Infrared Sounder (GIIRS) on the Fengyun-4A (FY-4A) satellite are an important data source for numerical weather prediction (NWP) assimilation. However, there are systematic differences between observed and simulated brightness temperatures (i.e., the observation increments contain predictable systematic bias components). To address the issue that traditional linear methods struggle to capture the nonlinear relationships between biases and forecast predictors, this study proposes an intelligent bias correction method that integrates ensemble learning and explainable artificial intelligence. First, the entropy reduction method is used to select 69 mid-wave channels. Then, Random Forest, XGBoost, LightGBM, Decision Tree, and Extra Tree are used as base learners to construct a weighted average ensemble model. Training and validation are conducted using high-frequency clear-sky observation data from FY-4A/GIIRS during Typhoon Lekima. The results show that: (1) the ensemble learning correction method outperforms single models and traditional offline methods, with root mean square errors of brightness temperature bias of less than 0.9209 K for the training set and 1.4447 K for the test set; (2) Shapley Additive Explanations (SHAP)-based interpretability analysis reveals the contribution and nonlinear influence mechanisms of factors such as longitude, atmospheric thickness, surface temperature, and total precipitable water on bias correction. This study provides an intelligent bias correction framework with both high precision and explainability, offering a reference for the bias correction and assimilation applications of hyperspectral satellite observations like GIIRS. Full article
(This article belongs to the Special Issue Improving Meteorological Forecasting Models Using Remote Sensing Data)
30 pages, 8388 KB  
Article
Full-Process Multiphysics Simulation and Experimental Study on the Fatigue Performance Enhancement of Butt-Welded Joints of QSTE700TM Through Ultrasonic Impact Treatment
by Huan Xue, Xiaojian Peng, Yanming Chen, Wenqian Zhang, Saiqing Xu, Kaixian Li and Jianwen Li
Appl. Sci. 2026, 16(5), 2397; https://doi.org/10.3390/app16052397 (registering DOI) - 28 Feb 2026
Abstract
Ultrasonic Impact Treatment (UIT), a prevalent surface-strengthening technology for welded structures, combines mechanical shock and ultrasonic vibration to induce plastic deformation and beneficial residual compressive stress at weld toes, effectively enhancing welded joint fatigue performance. This study adopts a full-process numerical simulation approach, [...] Read more.
Ultrasonic Impact Treatment (UIT), a prevalent surface-strengthening technology for welded structures, combines mechanical shock and ultrasonic vibration to induce plastic deformation and beneficial residual compressive stress at weld toes, effectively enhancing welded joint fatigue performance. This study adopts a full-process numerical simulation approach, integrating the finite element software ABAQUS and FE-SAFE fatigue-life prediction platform to investigate QSTE700TM high-strength automotive steel butt joints. Considering welding-induced initial residual stress, ABAQUS simulates the welding and subsequent UIT processes; explicit dynamic analysis reveals residual stress evolution, with pre- and post-UIT stress-distribution comparisons. The post-UIT residual stress field is input into a static tensile model to obtain load-stress distributions, which are then imported into FE-SAFE with S-N curves for fatigue-life prediction. Simulation results align well with experimental data: UIT improves the fatigue limit of welded specimens by 31.3% and unwelded ones by 42.9%. Additionally, optical and scanning electron microscopes observe fatigue fracture morphologies to further clarify UIT’s fatigue-enhancement mechanism. Full article
18 pages, 2332 KB  
Article
Parameter Optimization and Engineering Effect of Cut-and-Fill Mining Technology
by Xiaolei Lv, Zhiqiang Wang, Baowei Meng, Weiping Shi, Yaohua Yv and Changxiang Wang
Appl. Sci. 2026, 16(5), 2391; https://doi.org/10.3390/app16052391 (registering DOI) - 28 Feb 2026
Abstract
To address the limitations of existing subsidence control technologies in coal mining, this study systematically investigates the fundamental principles of cut-and-fill mining, the stability mechanism of the filling body, and the influence law of key parameters on mining engineering effects, through a comprehensive [...] Read more.
To address the limitations of existing subsidence control technologies in coal mining, this study systematically investigates the fundamental principles of cut-and-fill mining, the stability mechanism of the filling body, and the influence law of key parameters on mining engineering effects, through a comprehensive research framework integrating theoretical analysis, similar material simulation and numerical simulation. Firstly, the mechanical characteristics of horizontal and diagonal shear failure of gangue pillars are revealed via theoretical derivation. It is clarified that the diagonal stability of the gangue pillar can be guaranteed when its aspect ratio is ≤0.5, and the lateral constraint of metal mesh can effectively enhance its horizontal stability. Secondly, based on a physical model with a size similarity ratio of 1:100, the overburden failure characteristics are obtained: only local cracks appear in the immediate roof and the basic roof presents gentle subsidence after cut-and-fill mining, which directly verifies the effective control effect of this technology on mining-induced overburden movement and surface subsidence. On this basis, multiple sets of orthogonal tests are designed using FLAC3D software (5.0) to analyze the effects of roof cutting width, filling width and coal seam thickness on roof displacement and filling area stress. Combined with grey correlation analysis, it is determined that coal seam thickness is the most critical factor affecting the mining effect, with the correlation coefficients for roof displacement and filling area stress reaching 0.79 and 0.93, respectively. The research shows that the parameter combination of 10 m roof cutting width + 10 m filling width (Group 10-10-X) can achieve the optimal balance between subsidence control efficiency and filling engineering benefit; for working faces with higher requirements for surface subsidence control, the combination of 5 m roof cutting width + 10 m filling width is recommended. The research results clarify the action mechanism of cut-and-fill mining, optimize the key engineering parameters, and provide a solid theoretical basis and technical support for the engineering popularization of this technology and high-precision surface subsidence control. Full article
(This article belongs to the Special Issue Advanced Technologies in Intelligent and Sustainable Coal Mining)
36 pages, 5398 KB  
Article
Experimental and Numerical Investigation of Liquid Nitrogen Die Cooling for Increased Efficiency in Porthole Aluminum Extrusion Dies
by Evangelos Giarmas, Ioannis Theodoridis, Panagiotis Tounis, Tommaso Pinter and Dimitrios Tzetzis
Appl. Sci. 2026, 16(5), 2385; https://doi.org/10.3390/app16052385 (registering DOI) - 28 Feb 2026
Abstract
Die design plays a critical role in achieving high-quality aluminum extrusion products with optimal efficiency. Porthole dies are widely employed to produce hollow profiles for diverse industrial applications, yet their design parameters significantly influence surface quality, geometry, and productivity. In this study, a [...] Read more.
Die design plays a critical role in achieving high-quality aluminum extrusion products with optimal efficiency. Porthole dies are widely employed to produce hollow profiles for diverse industrial applications, yet their design parameters significantly influence surface quality, geometry, and productivity. In this study, a two-hole porthole die was investigated using both numerical and experimental approaches. The 6060 aluminum alloy (produced in the foundry of Alumil SA, Kilkis, Greece) was selected as the material of focus. Finite Element Analysis was conducted with HyperXtrude™ 2022 software, while experimental trials were performed on a 35 MN extrusion press. To further enhance productivity, a liquid nitrogen cooling system was integrated into the process. The combined numerical and experimental results demonstrated that the redesigned die and the integration of liquid nitrogen cooling significantly improved process performance. Productivity increased by 8.76%, with ram speed rising from 6.8 mm/s to 9.5 mm/s while maintaining dimensional accuracy and stable extrusion conditions. Full article
(This article belongs to the Special Issue Advanced Finite Element Method and Its Applications, Second Edition)
16 pages, 5246 KB  
Article
Towards a Population-Based Approach for Dynamic Monitoring of Underground Structures: A Numerical Study on Metro Tunnel Models
by Giulia Delo, Camilla Corbani and Cecilia Surace
Infrastructures 2026, 11(3), 79; https://doi.org/10.3390/infrastructures11030079 (registering DOI) - 28 Feb 2026
Abstract
Underground structures are becoming increasingly vital components of modern transportation networks and urban systems, making their structural integrity a critical factor for safety and operational reliability. However, despite considerable progress in Structural Health Monitoring (SHM), the application of data-driven and vibration-based strategies to [...] Read more.
Underground structures are becoming increasingly vital components of modern transportation networks and urban systems, making their structural integrity a critical factor for safety and operational reliability. However, despite considerable progress in Structural Health Monitoring (SHM), the application of data-driven and vibration-based strategies to underground infrastructures remains an open and under-explored field, often because of limited data availability. Population-Based Structural Health Monitoring (PBSHM) offers a promising pathway to overcome this challenge by leveraging transfer learning to share diagnostic knowledge among similar structures. This study investigates the feasibility of extending the PBSHM paradigm to underground infrastructures, with a particular focus on a metro tunnel application. Through dynamic finite element simulations, relevant vibration features are identified, and damage detection strategies based on transmissibilities and cross-correlation functions are evaluated. The numerical results show that transmissibility-based indicators enable accurate damage localisation along the tunnel lining, even under noisy conditions. In contrast, cross-correlation features exhibit more limited performance in some configurations. Building on this evidence, the transmissibility-based damage indicator is subsequently embedded within the PBSHM framework and used as a transferable feature between tunnel models, achieving reliable damage detection in a second tunnel with heterogeneous characteristics, with F1 scores exceeding 80% for all considered damage severities and above 94% for the most critical case, thereby highlighting the potential of knowledge transfer for large-scale underground networks. Full article
16 pages, 4677 KB  
Article
Immunohistochemical, Biochemical and Genetic Evaluation of the Effects of Ginseng Administration on Blood–Brain Barrier in Rats Exposed to 2100 MHz and 2450 MHz Electromagnetic Radiation
by İrem Postacı Karaman, Özlem Coşkun, Nurgül Şenol, Uğur Şahin and Selçuk Çömlekçi
Appl. Sci. 2026, 16(5), 2376; https://doi.org/10.3390/app16052376 (registering DOI) - 28 Feb 2026
Abstract
Numerous studies have demonstrated that the brain and blood–brain barrier, which are sensitive targets for cell phone and microwave radiation, are damaged after exposure. Additionally, ginseng has been shown to play a role in preserving the integrity of the blood–brain barrier. In this [...] Read more.
Numerous studies have demonstrated that the brain and blood–brain barrier, which are sensitive targets for cell phone and microwave radiation, are damaged after exposure. Additionally, ginseng has been shown to play a role in preserving the integrity of the blood–brain barrier. In this study, we investigated the immunohistochemical, genetic and biochemical effects of electromagnetic field (EMF) on the blood–brain barrier (BBB) and the protective role of ginseng on these effects. The animals were randomly allocated into seven groups (eight in each group): group I: control, group II: sham, group III: ginseng, group IV: 2100 MHz EMF, group V: 2100 MHz EMF + ginseng, group VI: 2450 MHz EMF, group VII: 2450 MHz EMF + ginseng. EMF groups exposed to EMF, 1 h day−1 for 30 days. Ginseng was administered 150 mg/kg/day for 30 days. As a result, it was determined immunohistochemically that EMF caused apoptosis in brain tissue. It was observed that cyclooxygenase-2 (COX-2) gene decreased and B-cell lymphoma/leukemia-2 gene (BCL-2)-associated X (BAX) protein increased in EMF groups, as well as apoptosis formation. On the other hand, it was concluded that ginseng decreased the harmful effects by increasing the expression of the COX-2 gene and decreasing the BAX protein in this process leading to apoptosis. Full article
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28 pages, 5203 KB  
Article
Energy Performance of a Gravity Flow Rack with Energy Recovery: Modelling and Validation
by Paweł Zając
Energies 2026, 19(5), 1217; https://doi.org/10.3390/en19051217 (registering DOI) - 28 Feb 2026
Abstract
This paper presents a patented design of a gravity flow rack with an energy recovery system, intended for pallet storage in first-in–first-out (FIFO) and last-in–first-out (LIFO) modes. Compared with conventional flow racks, the proposed solution integrates control of load-unit motion dynamics with energy [...] Read more.
This paper presents a patented design of a gravity flow rack with an energy recovery system, intended for pallet storage in first-in–first-out (FIFO) and last-in–first-out (LIFO) modes. Compared with conventional flow racks, the proposed solution integrates control of load-unit motion dynamics with energy recovery, thereby reducing losses and stabilising pallet flow. A Rack Energy Performance Index (REPI) is proposed to enable quantitative assessment of the energy consumption of storage racks in intralogistics applications. The research methodology comprised: (i) development of the mechanical architecture and pallet guidance principles; (ii) numerical modelling in the MSC Adams environment at Technology Readiness Level 3 (TRL-3); and (iii) validation using a full-scale prototype installed in a logistics centre. Operational tests confirmed stable operation, the required throughput, and the capability for energy compensation and recovery during storage cycles. The results indicate that energy-recovering racks can support the design of energetically passive warehouses. Full article
29 pages, 1732 KB  
Article
Fracture-Controlled Mechanisms of Sand Production in Deep Tight Sandstone: Insights from Coupled FDEM Modeling
by Bao Zhang, Junhui Wei, Xiaofei Bai, Rongjun Ye, Jianxin Shen, Shicai Huang, Changyin Dong and Fansheng Huang
Processes 2026, 14(5), 801; https://doi.org/10.3390/pr14050801 (registering DOI) - 28 Feb 2026
Abstract
Wellbore instability and sand production pose critical challenges in deep tight sandstone reservoirs, severely impairing wellbore integrity and reducing hydrocarbon recovery. This study introduces, for the first time, the combined finite–discrete element method (FDEM) to numerically simulate sand production under high in situ [...] Read more.
Wellbore instability and sand production pose critical challenges in deep tight sandstone reservoirs, severely impairing wellbore integrity and reducing hydrocarbon recovery. This study introduces, for the first time, the combined finite–discrete element method (FDEM) to numerically simulate sand production under high in situ stress. The FDEM By seamlessly integrates continuum and discontinuum representations within a unified framework, enabling the simulation of the complete failure sequence—from matrix damage and fracture growth to granular flow. High-resolution numerical simulations are conducted to compare intact and naturally fractured formations, with a focus on the governing role of pre-existing geological discontinuities. Results show that in intact sandstone, stress concentration drives helical crack growth leading to a symmetrical V-shaped breakout, with a critical borehole pressure (CBHP) of 60.05 MPa required to prevent instability. In fractured rock, however, pre-existing fractures act as dominant weakness planes that distort the stress field and induce earlier, asymmetric failure, raising the CBHP to 64.05 MPa. A strong negative linear correlation is observed between reservoir pressure depletion and CBHP: a pore-pressure reduction of 23.75 MPa decreases the CBHP by 4.8–5.0 MPa. Notably, natural fractures amplify the destabilizing effect of depletion, raising the required CBHP by 4.0 MPa at initial reservoir pressure (95 MPa) and by 5.0 MPa under full depletion. Consequently, although fractured formations require a higher CBHP (64.05 MPa vs. 60.05 MPa), their safe operating window is effectively narrower. These findings advance the mechanistic understanding of fracture-controlled sand production and provide a validated numerical framework for determining safe production pressures in deep, fractured sandstone reservoirs. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
28 pages, 1677 KB  
Article
A Proposal of Secure and Automated Over-the-Air Firmware Update Mechanism for IoT Devices Using Continuous Integration and Continuous Delivery
by Noprianto, Nobuo Funabiki, Htoo Htoo Sandi Kyaw, Komang Candra Brata and I Nyoman Darma Kotama
Sensors 2026, 26(5), 1535; https://doi.org/10.3390/s26051535 (registering DOI) - 28 Feb 2026
Abstract
The Internet of Things (IoT) technology has grown rapidly over the past decade, resulting in deployments of thousands of IoT devices around the world. Then, managing firmware updates for these numerous devices poses significant challenges. Firmware updates face issues such as version rollback [...] Read more.
The Internet of Things (IoT) technology has grown rapidly over the past decade, resulting in deployments of thousands of IoT devices around the world. Then, managing firmware updates for these numerous devices poses significant challenges. Firmware updates face issues such as version rollback, modified firmware files, and potential man-in-the-middle (MITM) attacks, highlighting the need for a secure over-the-air (OTA) firmware update mechanism. In this paper, we propose an automated OTA firmware update mechanism, integrated with continuous integration (CI) and continuous delivery (CD) to ensure trusted sources for firmware origins. It offers security, error handling during firmware updates, and monitoring of the update process. For evaluations, we implemented the proposal with the SEMAR IoT application server that has been implemented in our previous studies. Then, we verified the integrity and authentication, measured the performance and resource utilization, and performed benchmarking tests to assess the efficiency. The results demonstrate that the proposal is sufficiently reliable and efficient. Full article
23 pages, 933 KB  
Article
Optimization and H Performance Analysis for Load Frequency Control of Power System with Transmission Delay Under DoS Attacks
by Zilong Chen, Xianyong Zhang, Li Li and Wenyong Duan
Mathematics 2026, 14(5), 822; https://doi.org/10.3390/math14050822 (registering DOI) - 28 Feb 2026
Abstract
This paper addresses the stability and H performance of a single-area discrete-time power system with time-varying transmission delays under Denial-of-Service (DoS) attacks. First, the power system is modeled as a discrete-time delay system that integrates both DoS-induced delays and transmission delays, with [...] Read more.
This paper addresses the stability and H performance of a single-area discrete-time power system with time-varying transmission delays under Denial-of-Service (DoS) attacks. First, the power system is modeled as a discrete-time delay system that integrates both DoS-induced delays and transmission delays, with PI controllers incorporated for Load Frequency Control (LFC). Using advanced summation inequality techniques, a Lyapunov–Krasovskii Functional (LKF) is constructed to capture comprehensive system state information, enabling the derivation of less conservative stability criteria. The proposed stability criterion based on linear matrix inequalities (LMI) ensures asymptotic stability and meets the H performance index, while considering norm-bounded external load disturbances. Two convex optimization algorithms are designed to obtain optimal controller gains, either for a given H index or by searching within a specified index range. Numerical examples and MATLAB simulations validate the effectiveness of the method. The results demonstrate that the maximum allowable delay upper bounds (MADUBs) estimated by the proposed criterion are larger than those obtained by existing methods, with an increase of at least 1 s. This indicates a reduction in conservatism. Simulation trajectories of frequency deviation (Δf) and area control error (ACE) confirm that the system remains stable under DoS attacks, with responses converging to zero after transient oscillations. Full article
(This article belongs to the Special Issue Artificial Intelligence and Game Theory)
16 pages, 6411 KB  
Article
A Combined AHP-Entropy and Game Theory Weighting Approach for Aqueduct Safety Evaluation: A Case Study of the Kezi River Aqueduct
by Jianxin Wang, Chengming Feng, Jianing Zhu, Shihao Zhang and Rui Cheng
Appl. Sci. 2026, 16(5), 2360; https://doi.org/10.3390/app16052360 (registering DOI) - 28 Feb 2026
Abstract
This study applies a multi-criteria decision-making (MCDM) framework integrating the Analytic Hierarchy Process (AHP), entropy weight method, and game theory to evaluate the safety of aqueducts, using the Kezi River Aqueduct in Xinjiang, China, as a case study. Field water filling tests were [...] Read more.
This study applies a multi-criteria decision-making (MCDM) framework integrating the Analytic Hierarchy Process (AHP), entropy weight method, and game theory to evaluate the safety of aqueducts, using the Kezi River Aqueduct in Xinjiang, China, as a case study. Field water filling tests were conducted to simulate operational loads, monitoring strain, deflection, and settlement. Subjective weights were derived via an AHP model using a natural index scale, while objective weights were aggregated from existing expert studies via entropy weighting. Game theory was then employed to reconcile these into a final combined weight set across three primary criteria: safety, durability, and applicability. Results show that the aqueduct behaves elastically under load, with measured values well below code limits, confirming adequate bearing capacity. The combined model yielded a comprehensive safety score of 87.15, classifying the structure as ‘first class’ according to DB44/T2041-2017. Although numerous non-structural web cracks were observed, they were assessed as not compromising current structural integrity. Full article
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27 pages, 4682 KB  
Article
A Computational Approach to Preliminary Tunnel Design: Integrating Kirsch Equations and the Generalized Hoek–Brown Criterion
by Josip Vincek, Ivan Vujević, Vinko Škrlec and Karolina Herceg
Appl. Sci. 2026, 16(5), 2347; https://doi.org/10.3390/app16052347 (registering DOI) - 28 Feb 2026
Abstract
Reliable preliminary assessment of stress redistribution and rock mass stability is a critical step in tunnel design, providing guidance before detailed numerical modeling and support design are undertaken. This study presents RockStressCalc, a Python-based computational framework that integrates classical elastic stress–displacement analysis with [...] Read more.
Reliable preliminary assessment of stress redistribution and rock mass stability is a critical step in tunnel design, providing guidance before detailed numerical modeling and support design are undertaken. This study presents RockStressCalc, a Python-based computational framework that integrates classical elastic stress–displacement analysis with empirical rock mass strength evaluation for circular tunnels within a transparent analytical workflow. The tool combines Kirsch’s closed-form solution for stress redistribution around a circular opening under anisotropic in situ stress conditions with the generalized Hoek–Brown criterion to enable spatially resolved evaluation of elastic strength reserve. The framework assumes a homogeneous, isotropic, linear–elastic rock mass under plane strain conditions and introduces a Stability Factor as a stress-based indicator of proximity to initial yield. The analytical implementation is verified against finite-element simulations performed in Plaxis2D under equivalent elastic assumptions. The maximum stress difference at the excavation boundary remained below 10%, while displacement deviations were below approximately 4%. In addition, comparison between the analytical far-field Stability Factor and the numerical strength reduction multiplier demonstrated close agreement, confirming consistency between the analytical and finite-element formulations under uniform stress conditions. The results show that RockStressCalc provides a computationally efficient analytical baseline suitable for rapid parametric evaluation, sensitivity studies, educational use, and independent verification of numerical models in early-stage tunnel design. By emphasizing explicit coupling of stress redistribution and strength evaluation within a reproducible framework, rather than introducing new constitutive models, the proposed approach offers practical engineering value as a screening and benchmarking tool and provides a foundation for future probabilistic or extended tunnel stability analyses. Full article
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