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Keywords = dynamics of numerics

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30 pages, 1266 KB  
Article
Strain-Based Monitoring Methodology and Numerical Validation for the Evaluation of Transverse Connection Condition in Precast Multi-Girder Bridges
by Wenhao Zheng, Han Wei, Jiehua Jiang and Wanheng Li
Sensors 2026, 26(13), 4043; https://doi.org/10.3390/s26134043 (registering DOI) - 25 Jun 2026
Abstract
Precast multi-girder bridges are widely utilized in highway infrastructure but are susceptible to transverse connection deterioration, which can lead to single-girder load-bearing failures. Existing structural health monitoring methods based on the correlation of total dynamic strain responses often fail to identify early-stage damage [...] Read more.
Precast multi-girder bridges are widely utilized in highway infrastructure but are susceptible to transverse connection deterioration, which can lead to single-girder load-bearing failures. Existing structural health monitoring methods based on the correlation of total dynamic strain responses often fail to identify early-stage damage due to the static masking effect, where dominant, in-phase quasi-static components overshadow subtle, damage-sensitive dynamic features. To overcome this limitation, this paper proposes a novel condition indicator based on the correlation of high-frequency dynamic strain increments. An online streaming processing pipeline is developed, incorporating automated single-vehicle crossing event extraction, frequency-targeted signal decoupling, and indicator smoothing. Theoretical derivations on a dual-beam model demonstrate that the proposed indicator is a structural-intrinsic metric, exhibiting high sensitivity to joint stiffness while remaining robust against variations in vehicle weight and speed. Numerical simulations on an 8-slab finite element bridge model under stochastic traffic flow further verify the effectiveness of the framework. Results indicate that the proposed indicator can localize both progressive degradation and sudden brittle failures. Additionally, the method maintains reliability down to a signal-to-noise ratio of 30dB and robustness to hyper-parameter selection. While the current framework is established based purely on numerical validation and has not yet been tested using real bridge strain data, it shows numerical feasibility and provides a solid theoretical and algorithmic foundation for the automated condition evaluation of precast multi-girder bridges, supporting future field validation for both long-term maintenance and emergency response. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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23 pages, 2886 KB  
Article
Experimental and Mathematical Modeling of Unsteady Flow Around Darrieus H-Rotor of Vertical-Axis Wind Turbines
by Serhii Tarasov, Dmytro Redchyts, Koldo Portal-Porras, Unai Fernandez-Gamiz, Ihor Kostyukov, Andrii Tarasov, Svitlana Moiseienko, Volodymyr Zaika and Jesus María Blanco Ilzarbe
Fluids 2026, 11(7), 163; https://doi.org/10.3390/fluids11070163 (registering DOI) - 25 Jun 2026
Abstract
Small-scale vertical-axis wind turbines (VAWTs) are increasingly essential for the “blue economy,” providing autonomous power to remote coastal communities, offshore platforms, and marine industries. However, the design of efficient Darrieus-type rotors is complicated by complex unsteady aerodynamics, particularly the phenomenon of dynamic stall. [...] Read more.
Small-scale vertical-axis wind turbines (VAWTs) are increasingly essential for the “blue economy,” providing autonomous power to remote coastal communities, offshore platforms, and marine industries. However, the design of efficient Darrieus-type rotors is complicated by complex unsteady aerodynamics, particularly the phenomenon of dynamic stall. This study aims to establish and validate a cost-effective yet accurate mathematical modeling approach for simulating unsteady turbulent flow around a Darrieus H-rotor to support practical engineering applications. The research methodology integrates computational fluid dynamics (CFD) with physical experiments in a hydrodynamic channel. The numerical model utilizes the unsteady Reynolds-averaged Navier–Stokes (URANS) equations closed with the Strain-Adaptive Linear Spalart–Allmaras (SALSA) turbulence model, chosen for its efficiency in capturing flow separation. The system of initial equations was being devised relatively to an arbitrary curvilinear coordinate system. The pressure and velocity fields have been coordinated using the artificial compressibility method adapted to calculate non-stationary problems. Experimental verification was conducted in the GT-400 hydrodynamic tube using a three-bladed H-rotor model, where flow structures were visualized via the colored jet method at tip speed ratios λ ranging from 2 to 5 and Reynolds number 1470. The findings reveal that dynamic stall occurs over a significant portion of the blade trajectory, characterized by vortex generation at the leading edge and subsequent advection along the chord. Qualitative comparison demonstrates a high degree of correlation between the calculated vortex dynamics and physical flow spectra. These results confirm that the URANS-SALSA approach provides a rational compromise between computational cost and physical accuracy. Full article
(This article belongs to the Section Mathematical and Computational Fluid Mechanics)
14 pages, 1491 KB  
Article
An Effective Numerical Scheme for Fractional Integro-Differential Equation Systems Using Hermite Wavelets
by Arzu Turan Dincel and Sadiye Nergis Tural Polat
Fractal Fract. 2026, 10(7), 431; https://doi.org/10.3390/fractalfract10070431 (registering DOI) - 25 Jun 2026
Abstract
Numerous mathematical models, such as elasticity, nuclear reactor dynamics, and heat conduction in memory materials, use systems of fractional integro-differential equations, or FIDEs. In this research, the numerical solution of linear and nonlinear systems of FIDEs is obtained by means of an operational [...] Read more.
Numerous mathematical models, such as elasticity, nuclear reactor dynamics, and heat conduction in memory materials, use systems of fractional integro-differential equations, or FIDEs. In this research, the numerical solution of linear and nonlinear systems of FIDEs is obtained by means of an operational matrix approach based on Hermite wavelets. Using the operational matrix of the Hermite wavelets, the FIDE is transformed into an algebraic equation, and the solution of that algebraic equation is obtained. Three numerical examples are provided to show the accuracy and consistency of the suggested technique. Full article
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32 pages, 2491 KB  
Article
A Spectral-fPINN Framework for Fractional Optimal Control Problems
by Yonis Gulzar and Ishtiaq Ali
Computation 2026, 14(7), 146; https://doi.org/10.3390/computation14070146 (registering DOI) - 25 Jun 2026
Abstract
Fractional optimal control problems provide an effective mathematical framework for modeling dynamical systems with memory, hereditary behavior, and anomalous diffusion effects. However, the nonlocal nature of Caputo fractional operators and the reduced regularity of fractional solutions pose significant challenges for the development of [...] Read more.
Fractional optimal control problems provide an effective mathematical framework for modeling dynamical systems with memory, hereditary behavior, and anomalous diffusion effects. However, the nonlocal nature of Caputo fractional operators and the reduced regularity of fractional solutions pose significant challenges for the development of accurate and efficient computational methods. In this paper, we develop a spectral-fractional Physics-Informed Neural Network (Spectral-fPINN) framework for solving fractional optimal control problems governed by Caputo fractional differential equations. The proposed methodology combines normalized shifted Legendre spectral approximations, fractional operational matrix formulations, and physics-informed optimization within a unified computational framework. Unlike conventional PINN and fPINN approaches, which directly approximate the unknown solution variables, the proposed framework predicts the spectral coefficient vectors associated with the shifted Legendre basis functions, yielding a low-dimensional global representation with improved approximation efficiency. Caputo fractional derivatives are evaluated through spectral operational matrices, while the resulting optimization problem is discretized using Gauss–Legendre quadrature and solved through gradient-based optimization. In addition, a theoretical analysis of the proposed Spectral-fPINN framework is presented, including approximation, consistency, stability, and convergence results, together with error estimates and residual control properties. Several benchmark linear and nonlinear fractional optimal control problems are investigated to validate the proposed methodology. The numerical results demonstrate excellent agreement with exact solutions, very small residual errors, and rapid spectral coefficient decay, confirming the high-order accuracy and robustness of the proposed approach. Overall, the proposed Spectral-fPINN framework provides an accurate, stable, and computationally efficient methodology for solving a broad class of fractional optimal control problems. Full article
(This article belongs to the Special Issue Nonlinear System Modelling and Control—2nd Edition)
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19 pages, 2702 KB  
Article
Experimental and CFD Investigation of Bubble Dynamics in Geldart Group B Fluidized Beds: A Comparative 2D and 3D Analysis
by Zhu Yang, Germán Mazza, Maarten Vanierschot, Renaud Ansart and Yimin Deng
Appl. Sci. 2026, 16(13), 6372; https://doi.org/10.3390/app16136372 (registering DOI) - 25 Jun 2026
Abstract
Gas–solid bubbling fluidized beds involving Geldart Group B particles are fundamental to numerous industrial thermochemical processes, where bubble dynamics dictate the efficiency of heat and mass transfer. However, accurately predicting these complex hydrodynamic behaviors remains a challenge due to the non-linear coupling of [...] Read more.
Gas–solid bubbling fluidized beds involving Geldart Group B particles are fundamental to numerous industrial thermochemical processes, where bubble dynamics dictate the efficiency of heat and mass transfer. However, accurately predicting these complex hydrodynamic behaviors remains a challenge due to the non-linear coupling of phase interactions. This study presents a comprehensive validation of 2D and 3D Eulerian–Eulerian Two-Fluid Models (TFM) against an extensive experimental dataset. A ‘core-flow’ consistency principle is adopted, demonstrating that the 3D cylindrical simulation provides a physically equivalent representation of the central bubbling dynamics in the rectangular experimental bed. A key innovation of this work is a novel post-processing framework that bridges raw CFD datasets and quantitative bubbling metrics. Unlike traditional threshold-based segmentation or localized probe measurements, which are often limited by spatial resolution and noise sensitivity, the integrated use of Autodesk 3DS Max for volumetric reconstruction and customized MATLAB (R2024a) algorithms allows for the seamless processing of heterogeneous 2D and 3D data. This methodology significantly enhances the capability to track complex bubble coalescence and breakup events while improving batch-processing efficiency, providing a high-fidelity alternative for analyzing gas–-solid flow patterns in complex geometries. The results show that both experimental data and 2D simulations align with Werther’s correlation, yielding Mean Relative Errors (MRE) of 8.2% and 10.5%, respectively. In contrast, the 3D simulation tracks Darton’s prediction closely with a lower MRE of 7.4%, demonstrating superior concordance in volumetric bubble growth. The core innovation lies in the definition of a clear dimensional choice framework: 2D simulations are computationally sufficient and accurate for predicting macro-scale bubble heights and frequencies under pseudo-2D or narrow-bed constraints. However, 3D simulations are strictly necessary when evaluating unconstrained radial expansion, core-flow dynamics, and precise volumetric bubble diameters (dv) where full multi-directional degrees of freedom dictate hydrodynamics. Full article
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20 pages, 11698 KB  
Article
Annual Cycle of the Mesozooplankton in Oligotrophic Waters off Tenerife (Canary Islands, Spain)
by Marco Anglano, Genuario Belmonte, Enrique Isla, Juan Usó-Canós and Sergio Rossi
Water 2026, 18(13), 1553; https://doi.org/10.3390/w18131553 (registering DOI) - 25 Jun 2026
Abstract
Mesozooplankton were studied monthly (September 2023–August 2024, 12 months) at two coastal stations, at 35 and 90 m water depth, off Punta Blanca, SW Tenerife, Canary archipelago. Sample collection involved 250 and 500 μm bongo nets. This research focused on improving the description [...] Read more.
Mesozooplankton were studied monthly (September 2023–August 2024, 12 months) at two coastal stations, at 35 and 90 m water depth, off Punta Blanca, SW Tenerife, Canary archipelago. Sample collection involved 250 and 500 μm bongo nets. This research focused on improving the description of plankton biodiversity and dynamics of the Canary archipelago (Macaronesia area), including its role in the transport of particulate carbon. A total of 156 taxa were identified. Copepoda dominated with 85 taxa, including 72 Calanoida species. They were numerically followed by Appendicularia, Chaetognatha, and Hydrozoa. Mesh sizes varied in collection efficiency, but with a similar pattern during the annual cycle: abundance peaks in early autumn (October–November) and late winter–spring (February–April). The 35 m depth station showed 57 to 3809 ind. m−3 (250 μm mesh size) and 10 to 1577 ind. m−3 (500 μm). The 90 m depth station showed 22 to 402 ind. m−3 (250 μm) and 11 to 170 ind. m−3 (500 μm). The present study enhances our understanding of Macaronesia’s mesozooplankton dynamics related to environmental variability, which is crucial for energy transfer assessments in pelagic food webs. It reports new species for the study area, Labidocera acutifrons (Dana, 1849–1852) and Undinula vulgaris (Dana, 1849–1852), highlighting the need for consistent zooplankton monitoring to properly inform conservation and sustainable management actions in the region. Full article
(This article belongs to the Section Biodiversity and Functionality of Aquatic Ecosystems)
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13 pages, 2083 KB  
Article
On-Chip Mid-Infrared Wavefront Sensing Based on Vectorial Photocurrent Manipulation
by Tao Ye, Xiaofei He, Jun Ning, Xueling Guo, Xianda Zhang, Ziao Li, Wei Lu, Xiaoshuang Chen and Jing Zhou
Sensors 2026, 26(13), 4022; https://doi.org/10.3390/s26134022 (registering DOI) - 24 Jun 2026
Abstract
Wavefront sensing (WFS) is fundamental to adaptive optics, astronomical observation, biological microscopy, and free-space optical communications. However, conventional approaches—including Shack–Hartmann sensors, shearing interferometers, and transport of intensity equation-based methods—are inherently limited by trade-offs among spatial sampling density, angular dynamic range, and device compactness [...] Read more.
Wavefront sensing (WFS) is fundamental to adaptive optics, astronomical observation, biological microscopy, and free-space optical communications. However, conventional approaches—including Shack–Hartmann sensors, shearing interferometers, and transport of intensity equation-based methods—are inherently limited by trade-offs among spatial sampling density, angular dynamic range, and device compactness and have rarely been extended to the mid-infrared range. Here, we propose an on-chip mid-infrared wavefront sensing scheme operating based on vectorial photocurrent manipulation and analyze the properties of the proposed device through finite-element simulations. The proposed device comprises a hexagonal array of antenna-integrated graphene pixels, each equipped with three contacts and a microlens. Based on the antenna-induced vectorial photocurrent manipulation, angle-dependent absorption is translated into photocurrent signals, potentially enabling unambiguous recovery of both the elevation and azimuth angles of the incident light over an effective angular dynamic range of ±28°. The hexagonal layout provides a high spatial sampling density of 11,547 mm−2. Southwell algorithm-based wavefront reconstruction and numerical simulations yield faithful recovery of parabolic, conical, and quadrangular pyramidal wavefronts. In addition, simulation results indicate that this approach can enable high-fidelity reconstruction of both the phase and intensity distributions of an object based on angular-spectrum diffraction theory. Overall, this work theoretically demonstrates a new route toward high-density wavefront measurement and complex light field imaging in the mid-infrared range without a conventional imaging lens. Full article
(This article belongs to the Section Optical Sensors)
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24 pages, 1939 KB  
Article
The Wheat Nitro-Proteome: Protein Nitration Profiles During Drought and Rehydration
by Marta Gietler, Justyna Fidler-Jarkowska and Małgorzata Nykiel
Plants 2026, 15(13), 1951; https://doi.org/10.3390/plants15131951 (registering DOI) - 24 Jun 2026
Abstract
Protein nitration within the nitro-proteome is a dynamic component of drought and recovery responses in wheat (Triticum aestivum L.), yet its role in stress adaptation remains unclear. Young wheat seedlings demonstrate a degree of drought resistance, characterized by physiological and morphological adaptations, [...] Read more.
Protein nitration within the nitro-proteome is a dynamic component of drought and recovery responses in wheat (Triticum aestivum L.), yet its role in stress adaptation remains unclear. Young wheat seedlings demonstrate a degree of drought resistance, characterized by physiological and morphological adaptations, during the initial growth phases. However, this tolerance begins to diminish significantly in 5-day-old seedlings. The mechanisms behind this phenomenon are unclear. Our results indicate that it may be related to protein nitration. This study compared the physiological and nitrosative responses of 4-day-old drought-tolerant and 6-day-old sensitive wheat seedlings subjected to drought followed by rehydration. In tolerant seedlings, in contrast to sensitive ones, the water saturation deficit after rehydration returned to the control levels, confirming their drought tolerance. Moreover, NO2 accumulation in the recovery group was significantly higher in sensitive seedlings than in the control group. Results indicate that drought resistance correlates with protein nitration during the recovery phase. Nitro-proteomic analysis revealed that in tolerant seedlings, protein nitration is limited. The most significant differences are observed in the recovery group, with predominant downregulation of protein nitration in tolerant seedlings and significant upregulation of numerous proteins in sensitive seedlings. Upregulated nitration of vital proteins involved in energy production, photosynthesis (such as the Rubisco large subunit), ATP synthases, and cytosolic malate dehydrogenase may lead to disturbances in energy metabolism and thus prevent an effective response to changing environmental conditions. These findings suggest that regulation of protein nitration during recovery may contribute to drought resilience in wheat and could represent a potential target for improving stress tolerance. Full article
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28 pages, 3794 KB  
Article
Mining Weighted Temporal Association Rules in Dynamic Complex Systems via Non-Attributed Graph Sequence with Fuzzy Structure
by Fang Li, Yiman Zhao and Xiao Wang
Systems 2026, 14(7), 735; https://doi.org/10.3390/systems14070735 (registering DOI) - 24 Jun 2026
Abstract
Non-attributed graph sequence offers a powerful formalism for modeling the structural dynamics of complex systems—such as social networks, urban infrastructures, and document transmission pathways—where vertex interactions evolve over time without explicit attribute information. Mining association rules from such sequences to uncover recurring topological [...] Read more.
Non-attributed graph sequence offers a powerful formalism for modeling the structural dynamics of complex systems—such as social networks, urban infrastructures, and document transmission pathways—where vertex interactions evolve over time without explicit attribute information. Mining association rules from such sequences to uncover recurring topological patterns have attracted growing interest. Yet two fundamental challenges remain: (1) how to effectively encode edge-level temporal dynamics in non-attributed settings, and (2) how to perform efficient and semantically meaningful temporal association rule mining under structural uncertainty. To address these within a systems-oriented framework, we propose two novel algorithms: the weighted temporal association rule mining algorithm and the fuzzy weighted temporal association rule mining algorithm. The first algorithm introduces time-dependent numerical weights to quantify the strength and persistence of vertex connectivity, integrating them into support and confidence measures to capture both the intensity and evolution of interactions. The second algorithm extends this by incorporating fuzzy set theory, modeling ambiguous or context-sensitive relationships (e.g., indistinct links or weakly correlated vertices) and generating fuzzy-weighted rules that enhance interpretability for real-world system analysis. Evaluated through five comprehensive experiments across diverse datasets and scales using standard metrics (support, confidence, rule count, running time), our methods produce more selective rule sets and achieve lower computational times compared to the classical Apriori algorithm. The proposed approaches thus establish a robust, data-driven foundation for analyzing temporal evolution and structural uncertainty in dynamic complex systems—providing a generalizable methodology applicable beyond domain-specific constraints. Full article
(This article belongs to the Section Systems Theory and Methodology)
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20 pages, 670 KB  
Article
Fractional-Order SEIRS-V Dynamics of Worm Propagation in Wireless Sensor Networks: Semi-Analytical and Numerical Study with Stability and Uniqueness Insights
by Mahmoud M. Mokhtar and H. M. Hamouda
Fractal Fract. 2026, 10(7), 427; https://doi.org/10.3390/fractalfract10070427 (registering DOI) - 24 Jun 2026
Abstract
This study introduces a Caputo fractional-order version of the SEIRS-V model to investigate the spreading dynamics of worms within wireless sensor networks. Traditional integer-order worm propagation models describe the instantaneous evolution of network states; however, they do not adequately account for memory and [...] Read more.
This study introduces a Caputo fractional-order version of the SEIRS-V model to investigate the spreading dynamics of worms within wireless sensor networks. Traditional integer-order worm propagation models describe the instantaneous evolution of network states; however, they do not adequately account for memory and hereditary characteristics that may influence the transmission dynamics. Consequently, their ability to represent realistic network behavior can be limited in systems where past states affect current propagation patterns. The framework divides sensor nodes into susceptible, exposed, infectious, recovered, and vaccinated classes, while explicitly incorporating worm transmission rates, temporary loss of immunity, and the impact of preventive security measures under limited resource conditions. A detailed theoretical examination is performed, covering the existence, boundedness, and uniqueness of solutions of the fractional-order system. The coupled nonlinear fractional system is solved semi-analytically by means of the Fractional Reduced Differential Transform (FRDT) technique. To confirm accuracy and robustness, the identical system is also discretized and solved using the finite difference scheme (FDS). Unlike previous studies on worm propagation models in wireless sensor networks, which are mainly limited to equilibrium point analysis and qualitative investigations without deriving explicit solutions, the present work develops an approximate semi-analytical solution for the fractional-order SEIRS-V system using the FRDTM. Comparisons between the two solution sets demonstrate excellent agreement and high precision. Numerical outcomes are presented through a series of 2D graphical profiles that illustrate the time-dependent behavior of each compartment and reveal the sensitivity of worm propagation and suppression to variations in the fractional order and key model parameters. The integrated theoretical and computational findings underscore the strong protective role of vaccination in mitigating worm outbreaks and offer valuable guidelines for strengthening cybersecurity measures in wireless sensor networks. Full article
(This article belongs to the Section Numerical and Computational Methods)
20 pages, 7715 KB  
Article
Spatiotemporal Assessment of Environmental Change and Palm Tree Dynamics in Al-Ahsa Oasis Using Multi-Temporal Landsat Data and Machine Learning Approaches
by Yasir Ahmed Solangi, Rakan Alyamani, Farheen Solangi and Kashif Ali Solangi
Land 2026, 15(7), 1124; https://doi.org/10.3390/land15071124 (registering DOI) - 24 Jun 2026
Abstract
The Al-Ahsa Oasis region is an important agricultural area; however, continuous spatial–temporal monitoring is essential to assess and mitigate the impacts of climate change and land use change. The current study examines environmental and land cover changes in the Al-Ahsa Oasis region from [...] Read more.
The Al-Ahsa Oasis region is an important agricultural area; however, continuous spatial–temporal monitoring is essential to assess and mitigate the impacts of climate change and land use change. The current study examines environmental and land cover changes in the Al-Ahsa Oasis region from 1990 to 2025 by utilizing spectral indices derived from multiple satellites. Multi-temporal Landsat imagery (Landsat 5, 8, and 9) was processed in Google Earth Engine (GEE) to derive key biophysical indicators, including the Normalized Difference Vegetation Index (NDVI), land surface temperature (LST), and bare soil index (BSI). Supervised classification techniques were employed to generate LULC maps for each time step, enabling the assessment of spatiotemporal land cover dynamics. In addition, a random forest (RF) machine learning algorithm was applied to accurately quantify and map the distribution of palm trees across the study area. The results showed that NDVI values fluctuated between −0.19 and 0.75 during the period from 1990 to 2025. Higher vegetation density was observed in central and eastern areas, with maximum values of −0.44–0.75 in 2025. The higher LST was observed in 2025, with a range of 34.7 to 54.6 °C, and the lower LST was observed in 1990 with a range 28.7 to 48.34 °C. BSI values decreased from −0.40 to 0.46 between 1990 and 2025 to a more variable range of −0.27 to 0.36, indicating reduced soil exposure. The classification of LULC numerical data shows a rapid rise in urban development of 67.19% and a 25% decrease in vegetation area. Furthermore, the results of the RF model indicate that palm tree area increased by 16.23% from 1990 to 2025, with overall accuracy of 98.15, and kappa coefficient of 0.962. This research highlights that urban expansion impacts environmental indicators such as LST, while the increasing trend of NDVI could support the palm trees expansion. This study finds valuable information for policymakers and land use planners to develop sustainable urban growth strategies, protect agricultural lands, and enhance oasis ecosystem resilience. Combined remote-sensing-based monitoring into regional planning frameworks can inform decision making for balancing urban development, environmental protection, and long-term agricultural sustainability in the Al-Ahsa Oasis. Full article
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26 pages, 5368 KB  
Article
Investigation of Seismic Responses in Large-Span Spatial Structures Using the Dynamic Substructure Approach
by Shuyu Wang, Zeqiang Wang, Mingjie Liu, Yifeng Zhao, Yan Lu and Yang Hu
Buildings 2026, 16(13), 2505; https://doi.org/10.3390/buildings16132505 (registering DOI) - 24 Jun 2026
Abstract
The feasibility of employing the dynamic substructure approach for seismic response analysis of complex structures has been widely recognized. However, the analytical accuracy of this method is affected by several factors, including the element type, the structural configuration, and the analysis method. To [...] Read more.
The feasibility of employing the dynamic substructure approach for seismic response analysis of complex structures has been widely recognized. However, the analytical accuracy of this method is affected by several factors, including the element type, the structural configuration, and the analysis method. To address these issues, four types of reticulated shell structures were designed and analyzed using the mode superposition response spectrum method (MSRSM) and the time history analysis method (THAM). The displacements of the key nodes and all member stresses were extracted to compare the simplified finite element models with the original models. The relative errors of nodal displacements calculated by the models with reduced degree of freedom (DOF) were within 1.62%. For the member stresses of the single-layer reticulated shells, the relative errors of the simplified models were within 14.35%. In the simplified models of double-layer reticulated shells, several members exhibited a relative error greater than 30%; however, these members were mainly located near the substructure boundaries and accounted for less than 0.62% of the entire structure. Three strategies are proposed to mitigate the influence of the member stress errors on the structural analysis conclusions for double-layer reticulated shell structures. In addition, the dynamic substructure method was extended to the coupled system of large-span spatial structures and point-supported glass facades. The seismic response results confirmed that this method effectively reduces computational costs while maintaining satisfactory accuracy, indicating that it is a useful tool for simplifying large-span spatial structures in extensive numerical analyses. Full article
(This article belongs to the Section Building Structures)
60 pages, 5241 KB  
Article
Multi-Strategy Improved Graduate Student Evolutionary Algorithm for Numerical Optimization and Art Image Segmentation
by Yuxin Zhu, Zuowen Bao and Shan Yang
Symmetry 2026, 18(7), 1074; https://doi.org/10.3390/sym18071074 (registering DOI) - 24 Jun 2026
Abstract
The Graduate Student Evolutionary Algorithm (GSEA) has demonstrated promising optimization capability in several engineering tasks; however, its performance may deteriorate when dealing with high-dimensional and complex multimodal problems due to insufficient adaptive search behavior, weak diversity preservation, and stagnation during later optimization stages. [...] Read more.
The Graduate Student Evolutionary Algorithm (GSEA) has demonstrated promising optimization capability in several engineering tasks; however, its performance may deteriorate when dealing with high-dimensional and complex multimodal problems due to insufficient adaptive search behavior, weak diversity preservation, and stagnation during later optimization stages. To alleviate these limitations, this paper proposes a Multi-Strategy Improved Graduate Student Evolutionary Algorithm (MIGSEA) for numerical optimization and artistic image multi-threshold segmentation. First, an adaptive mentor-guided learning mechanism is introduced to dynamically regulate the influence of mentors and peers throughout the optimization process, enabling a more effective transition from global exploration to local exploitation. Second, an elite–random cooperative learning strategy is designed to combine high-quality solution guidance with stochastic perturbation, thereby improving population diversity and enhancing the ability to escape local optima. Third, a stagnation-aware local refinement mechanism is developed to activate adaptive neighborhood search when the optimization process becomes trapped, which further accelerates convergence and improves solution precision. To verify the effectiveness of the proposed algorithm, MIGSEA is evaluated on the IEEE CEC2017 and CEC2020 benchmark suites and compared with 11 advanced metaheuristic algorithms under identical experimental conditions. Experimental results demonstrate that MIGSEA achieves competitive optimization accuracy, convergence speed, robustness, and statistical superiority in most benchmark functions. Furthermore, MIGSEA is applied to Otsu-based artistic image multi-threshold segmentation using multiple benchmark images with different threshold levels. Quantitative evaluation based on PSNR, FSIM, and SSIM, together with visual analysis, confirms that the proposed method can generate more accurate and visually consistent segmentation results than existing competitors. Overall, the proposed MIGSEA provides an effective and robust optimization framework for both benchmark optimization and practical image segmentation applications. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Optimization Algorithm and Its Applications)
18 pages, 3077 KB  
Article
Communication-Efficient Consensus for Networked Robotic Sensors: A Weighted Sliding Integration-Based Adaptive Dynamic Event-Triggered Approach
by Xing Gu, Ning Lin, Bo Li, Zhikang Zhou and Zhicheng Hou
Sensors 2026, 26(13), 4006; https://doi.org/10.3390/s26134006 (registering DOI) - 24 Jun 2026
Abstract
This paper addresses the consensus problem for networked robotic sensors characterized by general linear dynamics and strict communication bandwidth limitations. We propose a weighted sliding integration-based adaptive dynamic event-triggered control (WSI-ADETC) strategy. First, we design a bounded adaptive parameter using a nonlinear protocol [...] Read more.
This paper addresses the consensus problem for networked robotic sensors characterized by general linear dynamics and strict communication bandwidth limitations. We propose a weighted sliding integration-based adaptive dynamic event-triggered control (WSI-ADETC) strategy. First, we design a bounded adaptive parameter using a nonlinear protocol to enhance sensitivity to changes in consensus error. To further alleviate the communication burden on the sensing network, we propose a weighted sliding integration-based event-triggering mechanism to reduce the number of triggers compared to traditional adaptive dynamic event-triggered control (ADETC) approaches. Using Lyapunov analysis, we establish sufficient conditions for asymptotic consensus and demonstrate that the proposed controller effectively eliminates Zeno behavior. Numerical simulations demonstrate that the proposed WSI-ADETC strategy significantly reduces communication frequency while maintaining satisfactory consensus performance. Compared with recent adaptive dynamic event-triggered methods, the proposed method reduces the total triggering number by more than 53%, providing a communication efficient solution for resource-constrained robotic sensing networks. Full article
(This article belongs to the Section Intelligent Sensors)
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25 pages, 3053 KB  
Article
A Study on a Simplified Thermo-Mechanical Coupling Model Based on the Improved Local Linearization Method
by Weifan Zhang and Yizhong Wu
Mathematics 2026, 14(13), 2256; https://doi.org/10.3390/math14132256 (registering DOI) - 24 Jun 2026
Abstract
The Absolute Nodal Coordinate Formulation (ANCF) is extensively utilized in the field of flexible multibody dynamics because it offers a constant mass matrix and inherently eliminates Coriolis forces. However, ANCF requires the computation of complex nonlinear elastic internal forces and thermal deformation forces [...] Read more.
The Absolute Nodal Coordinate Formulation (ANCF) is extensively utilized in the field of flexible multibody dynamics because it offers a constant mass matrix and inherently eliminates Coriolis forces. However, ANCF requires the computation of complex nonlinear elastic internal forces and thermal deformation forces at each time step, which imposes a significant computational burden. To alleviate this burden, researchers have developed local linearization (LL) methods. The local linearization method constructs constant elastic and thermal stiffness matrices within a small range by means of Taylor expansion, effectively reducing the number of stiffness matrix updates. But the method suffers from error accumulation and relies on displacement-based update criteria that are inefficient for systems with large rigid-body motion. This paper proposes an improved local linearization (I-LL) method to address these issues. Two key enhancements are introduced: (1) the update criterion for the elastic and thermal stiffness matrices is modified from displacement-based to total strain-based, enabling more accurate and size-independent updates; (2) accurate elastic or thermal deformation force calculations are inserted within the local linearization iteration cycle to mitigate error accumulation. These two improvements reduce the number of calculations of the nonlinear internal forces and, at the same time, lessen the error accumulation in the simplified model. The accuracy and effectiveness of the I-LL algorithm are demonstrated through three numerical examples. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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