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Modelling, Volume 7, Issue 3 (June 2026) – 45 articles

Cover Story (view full-size image): Magmatic–hydrothermal systems move heat through coupled conduction and buoyancy-driven fluid flow in porous rock, a behavior traditionally captured by grid-based simulators such as HYDROTHERM. Here we explore a mesh-free alternative: a physics-informed neural network (PINN), built on the NVIDIA PhysicsNeMo framework, which uses automatic differentiation and collocation to solve the governing equations directly. Applied to a magma-chamber configuration based on the Rio Pisco pluton in the Peruvian Coastal Batholith, the PINN reproduces the conductive temperature gradient, a directionally consistent flow field, and a cooling time comparable to a published HYDROTHERM reference. We then examine when this approach offers a practical complement to conventional solvers. View this paper
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24 pages, 4627 KB  
Article
A State Space Model-Driven Feature Disentanglement Network for Real-Time Detection of Morphologically Complex Insect Pests in Agricultural Fields
by Jiaren Sun, Yating Jiang, Shuai Teng, Zongchao Liu and Nuo Chen
Modelling 2026, 7(3), 122; https://doi.org/10.3390/modelling7030122 - 21 Jun 2026
Viewed by 280
Abstract
Accurate detection of field insect pests remains a significant challenge for precision agriculture due to the elongated and variable morphology of the target organisms, their frequent resemblance to complex background textures, and the long-tail distribution of species in natural datasets. While deep convolutional [...] Read more.
Accurate detection of field insect pests remains a significant challenge for precision agriculture due to the elongated and variable morphology of the target organisms, their frequent resemblance to complex background textures, and the long-tail distribution of species in natural datasets. While deep convolutional neural networks (CNNs) have advanced the field, they are often constrained by a limited effective receptive field and the entanglement of semantic and spatial features, which can lead to elevated false-positive rates and missed detections for low-contrast or rare targets. This paper introduces a novel detection framework that integrates state space modeling with multi-stream feature disentanglement to address these limitations. First, a visual state space module is employed as the backbone feature extractor, enabling the establishment of a global receptive field with linear computational complexity and thereby improving the perception of long-range morphological structures. Second, a Topological Feature Disentanglement Pyramid Network is proposed. This architecture explicitly separates feature representations into semantic and spatial streams and recombines them through graph convolutional interactions, which serves to suppress background interference and enhance localization precision. A meta-auxiliary detection head, active only during training, is introduced to amplify supervision signals for hard, low-contrast samples via adversarial gradient modulation. Furthermore, an implicit neural radiance field augmentation pipeline is used to generate physically consistent synthetic views of underrepresented pest classes, mitigating the negative effects of long-tail data distributions. Experimental evaluations on the public BAU-Insectv2 benchmark demonstrate that the proposed method achieves a mean average precision (mAP@0.5) of 81.8%, representing a 4.4-percentage-point improvement over a comparable baseline, while maintaining a compact parameter count of 2.33 M and an inference speed of 178.6 FPS. The framework exhibits particular efficacy in detecting elongated, minute, and rare pests, suggesting a promising technical approach for real-time, field-based pest surveillance in precision agriculture. Full article
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19 pages, 17175 KB  
Article
Numerical Analysis on Cracking Resistance of Wet Joint in Prefabricated Steel–UHPC Composite Bridge Decks
by Ming-Lei Ma, Cheng-Da Yu, Ji-Long Chai, Guo-Wen Xu, Biao Wu, Jing-Zhong Tong and Qing-Hua Li
Modelling 2026, 7(3), 121; https://doi.org/10.3390/modelling7030121 - 19 Jun 2026
Viewed by 289
Abstract
To address the deterioration issues of wet joints in prefabricated steel–UHPC composite bridge decks caused by inadequate interfacial performance, an orthotropic steel–UHPC composite bridge deck system under hogging moments was investigated. A numerical study on the cracking resistance of wet joints was conducted [...] Read more.
To address the deterioration issues of wet joints in prefabricated steel–UHPC composite bridge decks caused by inadequate interfacial performance, an orthotropic steel–UHPC composite bridge deck system under hogging moments was investigated. A numerical study on the cracking resistance of wet joints was conducted using a cohesive zone model based on the traction–separation law to characterize the interfacial mechanical behavior. The numerical model was validated against experimental results, showing good agreement in terms of crack development and structural response. Subsequently, a parametric analysis was carried out to evaluate the influence of different reinforcement details, UHPC thickness and stud spacing. The results indicated that the adopted cohesive model was capable of accurately simulating the cracking behavior at the wet joint interface. In addition, the cracking resistance of UHPC wet joints could be significantly improved by providing additional reinforcement and reducing the longitudinal stud spacing. Moreover, the results revealed that joint reinforcement primarily enhanced local crack control performance, while having a limited effect on the global load–deflection response of the structure. These findings provide a reliable basis for the design and optimization of wet joint configurations in prefabricated steel–UHPC composite bridge decks. Full article
(This article belongs to the Section Modelling in Engineering Structures)
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30 pages, 12985 KB  
Article
Crashworthiness Assessment Using Lumped Parameter Models for Reduced-Order Modelling in Railway Crashworthiness Analysis
by Rogério F. F. Lopes, Christian J. Silva, Rodrigo R. Menéres, Pedro J. S. C. P. Sousa, Pedro M. G. P. Moreira, João S. Silva and Rodrigo S. Andrade
Modelling 2026, 7(3), 120; https://doi.org/10.3390/modelling7030120 - 18 Jun 2026
Viewed by 312
Abstract
The design of a railway coach must meet strict certification requirements, especially in crashworthiness analysis under the European standard EN 15227. Performing this analysis with full-scale FEM models is highly demanding in terms of time, computational power and engineering resources, even with large [...] Read more.
The design of a railway coach must meet strict certification requirements, especially in crashworthiness analysis under the European standard EN 15227. Performing this analysis with full-scale FEM models is highly demanding in terms of time, computational power and engineering resources, even with large server clusters. To improve efficiency, it is useful to simplify regions of the structure that are less influenced by external loads. In this approach, less critical parts are replaced with flexible one-dimensional elements, reducing the number of degrees of freedom while preserving the vehicle’s main dynamic behaviour. By concentrating on a specific mid-span section, the model becomes more robust and easier to manage. Calibrated elements are introduced to accurately reproduce the mass and stiffness of the removed structural components. The methodology also integrates mass and stiffness elements to capture structural response over a broader frequency range. An iterative non-gradient calibration procedure is then applied to adjust the equivalent stiffness and mass distribution so that the simplified model reproduces the response of the full-scale reference model. The results show that this strategy is effective, achieving a 77.6% reduction in simulation time while maintaining reliable accuracy. However, the process is still labour-intensive, and its performance may decline under large deformation conditions. Full article
(This article belongs to the Special Issue Optimization in Engineering: Models and Algorithms)
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20 pages, 3382 KB  
Article
Theoretical Estimation of Sound Absorption Coefficients for Randomly Packed Spherical Granules Using Single-Clearance Model
by Shuichi Sakamoto, Kenta Saito, Yoshiaki Kojima, Ryuki Kiuchi and Shui Miyata
Modelling 2026, 7(3), 119; https://doi.org/10.3390/modelling7030119 - 18 Jun 2026
Viewed by 243
Abstract
This study aims to establish a simple theoretical method for estimating the sound absorption characteristics of randomly packed granular materials. Using insights gained from existing mathematical models for regular packing and methods utilizing CT images, we propose the “single-clearance” model, a theoretical model [...] Read more.
This study aims to establish a simple theoretical method for estimating the sound absorption characteristics of randomly packed granular materials. Using insights gained from existing mathematical models for regular packing and methods utilizing CT images, we propose the “single-clearance” model, a theoretical model that estimates the sound absorption coefficient. It calculates the volume of voids and the surface area of spheres in a granular material based on the material particle size and packing density; the volume and surface area are then used to simplify the packing structure of the granular material to a clearance between two planes. The model is then validated by comparing its obtained theoretical sound absorption coefficients with experimental values and theoretical values derived from CT images. In random packing structures with small variations in porosity relative to the direction of sound propagation, the effect of accounting for this variation on the sound absorption coefficient is negligible. In the single-clearance model, the sound absorption coefficient calculated using a packing density of 0.65 for the random packing structure generally agrees with that derived from CT images at all particle sizes. Thus, the sound absorption coefficient can be estimated simply using particle size and packing density. Full article
(This article belongs to the Section Modelling in Engineering Structures)
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19 pages, 3022 KB  
Article
A Dual-Regime Kinetic Model of Accelerated CO2 Sequestration in Cement-Based Materials Across Industrial Waste-Heat Temperatures
by Dianchao Wang
Modelling 2026, 7(3), 118; https://doi.org/10.3390/modelling7030118 - 16 Jun 2026
Viewed by 295
Abstract
Accelerated carbonation of cement-based materials offers a promising route for CO2 sequestration driven by waste heat co-emitted from cement and power plants; however, existing kinetic models typically describe the low-temperature gas–liquid–solid regime near 100 °C and the high-temperature gas–solid regime near 600 [...] Read more.
Accelerated carbonation of cement-based materials offers a promising route for CO2 sequestration driven by waste heat co-emitted from cement and power plants; however, existing kinetic models typically describe the low-temperature gas–liquid–solid regime near 100 °C and the high-temperature gas–solid regime near 600 °C in isolation, limiting their applicability to plant-scale reactor design. This study proposes a unified dual-regime kinetic framework spanning 20–700 °C. The low-temperature branch couples Henry’s-law CO2 solubility, a sigmoidal water-film stability function, and an Arrhenius ionic reaction term, whereas the high-temperature branch integrates shrinking-core surface reaction and product-layer diffusion with an attenuation term near the CaCO3 decomposition onset. Seven parameters were calibrated by bounded least squares against a 51-point temperature dataset compiled from the author’s previously published carbonation experiments. The calibrated model reproduced the bimodal temperature dependence of the carbonation degree (R2 = 0.62; RMSE = 0.083), with peaks near 100 °C and 640 °C, and predicted reactor volumes of order-of-magnitude 150–200 m3 for a 1 Mt/y cement plant under three waste-heat operating points. The framework bridges particle-scale kinetic and plant-scale design, and identifies mixing as the dominant operational sensitivity at the clinker-cooler condition. Full article
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21 pages, 5782 KB  
Article
Constraint-Aware Robustness and Multi-Objective Synthesis of Multi-Layer DUV Interference Coatings
by Haoran Song and Lipu Zhang
Modelling 2026, 7(3), 117; https://doi.org/10.3390/modelling7030117 - 15 Jun 2026
Viewed by 290
Abstract
The evolution of 193 nm deep-ultraviolet (DUV) lithography toward high numerical aperture (NA > 1.35) presents challenges approaching physical limits for antireflective (AR) coatings on strongly curved lens elements. In this study, a full-stack multi-objective optimization framework is developed by coupling the Non-dominated [...] Read more.
The evolution of 193 nm deep-ultraviolet (DUV) lithography toward high numerical aperture (NA > 1.35) presents challenges approaching physical limits for antireflective (AR) coatings on strongly curved lens elements. In this study, a full-stack multi-objective optimization framework is developed by coupling the Non-dominated Sorting Genetic Algorithm II (NSGA-II) with the Transfer Matrix Method (TMM) to optimize a 7-layer LaF3/MgF2 system on strongly curved substrates (R=150 mm). The model integrates material dispersion, thermo-optic effects, deposition flux deviations, and manufacturing thickness constraints. Following 1500 generations of optimization and TOPSIS-based decision-making, the selected Pareto optimal solution achieves a full-aperture average reflectance of 1.3633% and a radial uniformity of 9.5037%. The design further exhibits high environmental robustness with a thermal drift of 0.0019% and a residual stress of 39.23 MPa. These results demonstrate that the proposed method overcomes the critical process bottleneck of achieving full-aperture uniformity below 10% on strongly curved optics. This framework provides a general paradigm for the robust design of next-generation ultra-precision DUV optical systems, effectively balancing theoretical depth with engineering feasibility. Full article
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23 pages, 4055 KB  
Article
Topology Optimization of MIMO Cooling Plates for Discrete Heat Sources in GPUs
by Jinzhao Fan, Bixiao Zhang, Jiazhen Liu, Yufei Cai and Hong Shi
Modelling 2026, 7(3), 116; https://doi.org/10.3390/modelling7030116 - 14 Jun 2026
Viewed by 546
Abstract
With the rising integration of high-performance GPUs, localized hotspots induced by discrete heat sources present severe thermal challenges. Traditional single-inlet–single-outlet liquid cold plates can scarcely meet the heat dissipation requirements of inhomogeneous high heat fluxes. This study systematically investigates the effects of nine [...] Read more.
With the rising integration of high-performance GPUs, localized hotspots induced by discrete heat sources present severe thermal challenges. Traditional single-inlet–single-outlet liquid cold plates can scarcely meet the heat dissipation requirements of inhomogeneous high heat fluxes. This study systematically investigates the effects of nine multiple-inlet–multiple-outlet (MIMO) configurations, ranging from single-inlet–single-outlet to three-inlet–three-outlet, on cold plate hydrothermal performance. An innovative stepwise optimization strategy, topology optimization (TO)-driven channel layout combined with fin-enhancement (FE)-based fine regulation, is proposed and verified to precisely regulate surface temperature distribution of discrete heat sources. The results show that the three-inlet–three-outlet configuration C-3 exhibits the optimal comprehensive performance among the nine configurations. Compared with the worst configuration A-2, C-3 reduces the pressure drop by 58.37% to only 147.18 Pa and yields the highest PEC, striking the optimum trade-off between heat transfer enhancement and fluid flow resistance. Through multi-inlet flow distribution and multi-outlet heat extraction, C-3 accurately suppresses heat accumulation in high heat flux regions, limiting the maximum temperature to merely 29.82 °C and drastically narrowing the substrate temperature difference from 8.69 °C to 2.12 °C. In comparison with the traditional cold plate (TCP), the optimized cold plate (OCP) realizes a 17.42% increase in performance evaluation criterion (PEC). Furthermore, the fin-enhanced optimized cold plate (FEOCP) reduces the temperature standard deviation by 54.15% relative to TCP, significantly enhancing temperature uniformity with only an additional pressure drop penalty of 5.43%. This study reveals the regulation mechanism of MIMO configurations on the flow field distribution of liquid cold plates and verifies the effectiveness of the TO-FE optimization framework, thus providing highly valuable engineering solutions for the high-efficiency, uniform-temperature and low-resistance heat dissipation of high-power electronic devices. Full article
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23 pages, 2895 KB  
Article
A Hybrid Modelling and Simulation Framework for Energy-Efficient Operation of Heated Crude Oil Pipelines Under Small-Batch and Multi-Condition Operation
by Yi Guo, Chun Li, Yang Lv, Liuxiao Li, Yangfan Lu and Kai Wen
Modelling 2026, 7(3), 115; https://doi.org/10.3390/modelling7030115 - 12 Jun 2026
Viewed by 329
Abstract
Heated crude oil pipelines transporting high-pour-point, high-viscosity, and high-wax-content crude oil are increasingly operated under small-batch and multi-condition scenarios. Under such conditions, fixed-parameter models and experience-based operating strategies may fail to accurately describe the evolving thermo-hydraulic state, resulting in inaccurate temperature-safety assessment and [...] Read more.
Heated crude oil pipelines transporting high-pour-point, high-viscosity, and high-wax-content crude oil are increasingly operated under small-batch and multi-condition scenarios. Under such conditions, fixed-parameter models and experience-based operating strategies may fail to accurately describe the evolving thermo-hydraulic state, resulting in inaccurate temperature-safety assessment and conservative energy use. To address this problem, this study develops a hybrid modelling and simulation framework for the energy-efficient operation of heated crude oil pipelines. The framework integrates operating-state perception, online parameter inversion, transient thermo-hydraulic simulation, data assimilation, and rolling optimization. First, an online parameter inversion method based on inverse problem solving is established to dynamically identify the overall heat-transfer coefficient and friction correction factor from Supervisory Control and Data Acquisition (SCADA) measurements. Second, a transient thermo-hydraulic simulation and data-assimilation model is constructed to predict pressure, temperature, and safety margins under changing boundary conditions. Third, a constraint-aware rolling optimization strategy is introduced to coordinate heating and pumping operations while satisfying temperature and pressure constraints. The proposed framework is validated using a practical crude oil pipeline. Under a representative low-flow-rate condition, online parameter inversion corrects the overestimation of the thermo-hydraulic state by the fixed-parameter model: the total temperature drop along the pipeline is revised from 33.12 °C to 35.65 °C, and the minimum station-inlet oil temperature is revised from 24.77 °C to 21.61 °C. After optimization is introduced, the total operating energy consumption decreases from 11,715.65 kW to 11,287.43 kW, corresponding to a reduction of 3.66%, while all temperature and pressure constraints remain satisfied. Under time-varying boundary conditions, the rolling optimization strategy further adjusts heating-furnace operation according to variations in inlet flow rate, inlet oil temperature, and ambient temperature, thereby reducing cumulative heating energy consumption while maintaining safe operation. The results demonstrate that the proposed framework provides an implementable modelling and simulation approach for online state assessment, transient prediction, and energy-efficient operation of heated crude oil pipelines under variable operating conditions. Full article
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13 pages, 3057 KB  
Article
Trajectory Tracking Control for Piezoelectric-Driven EVC Systems via Damping Enhancement and Frequency-Domain Shaping
by Tianxue Yang and Dongpo Zhao
Modelling 2026, 7(3), 114; https://doi.org/10.3390/modelling7030114 - 11 Jun 2026
Viewed by 305
Abstract
To address the issues of pronounced resonance, limited control bandwidth, and insufficient trajectory tracking accuracy in piezoelectric-driven elliptical vibration-assisted cutting (EVC) systems under high-frequency vibration, this paper proposes a trajectory tracking control strategy combining damping control with frequency-domain shaping. First, a damping-control strategy [...] Read more.
To address the issues of pronounced resonance, limited control bandwidth, and insufficient trajectory tracking accuracy in piezoelectric-driven elliptical vibration-assisted cutting (EVC) systems under high-frequency vibration, this paper proposes a trajectory tracking control strategy combining damping control with frequency-domain shaping. First, a damping-control strategy is integrated into the control system to refine the plant’s inherent dynamic properties, suppressing the resonance peak and elevating the system’s stability margin. Second, to enhance the system bandwidth and dynamic response, a high-gain PID controller is designed via frequency shaping. Additionally, given that the nominal model becomes high-order after implementing the damping controller, proportional gain is used for approximate equivalence with the system transfer function, lowering the model order and streamlining controller design. Next, a disturbance observer (DOB) is introduced to estimate and compensate for the unmodeled dynamics in the feedforward path in real time, further improving the trajectory tracking accuracy. Finally, taking the designed piezoelectric-driven EVC device as the controlled plant, the system frequency response is obtained through sweep excitation experiments, based on which the nominal model is identified, and the controller parameters are determined. The experimental results demonstrate that the proposed control strategy effectively suppresses resonance effects, increases system bandwidth, and reduces the trajectory tracking error. In the complex harmonic superposition trajectory tracking experiment, the steady-state tracking error is maintained within ±0.09 μm. These results demonstrate that the proposed approach markedly improves the system’s dynamic response and trajectory tracking performance, thereby providing technical support for high-precision fabrication of micro/nano-structured surfaces. Full article
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20 pages, 34425 KB  
Article
Molecular Dynamics Modeling of a CNT–CMC–Cement Mixture: Understanding Its Molecular Mechanical and Physical Properties at the Molecular Scale
by Olivier Plé, Anna Lushnikova and Xiaohui Jia
Modelling 2026, 7(3), 113; https://doi.org/10.3390/modelling7030113 - 9 Jun 2026
Viewed by 353
Abstract
Carbon nanotubes (CNTs) are commonly used to reinforce and functionalize cement matrices, thereby imparting new properties. To facilitate the introduction of CNTs into inorganic matrices such as cement, the use of a master batch is advantageous. In this approach, the CNTs are premixed [...] Read more.
Carbon nanotubes (CNTs) are commonly used to reinforce and functionalize cement matrices, thereby imparting new properties. To facilitate the introduction of CNTs into inorganic matrices such as cement, the use of a master batch is advantageous. In this approach, the CNTs are premixed with a carboxymethyl cellulose (CMC) to form this master batch, which enables homogeneous dispersion and simplifies the mixing of all components (cement, CNTs, CMC, and water). The system, a CNT–CMC–cement mixture, is modeled here by using a molecular dynamics simulation. Three models were constructed for comparative analysis: pristine tobermorite 11Å (T11) for hydrated cement paste, T11 with embedded CNT (T11 + CNT), and T11 with both CNT and CMC (T11 + CNT + CMC). All models were first equilibrated to obtain stable and low-energy configurations. Subsequently, three types of loading conditions were applied to investigate mechanical and physical properties: tension, compression, and heating. Under mechanical loading, both the stress–strain response and the resulting piezoelectric effect were analyzed. Under thermal loading, the focus was on thermally induced polarization. The simulation was used to elucidate the role of CNTs and polymer modification (CMC) at the atomistic scale. Full article
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27 pages, 1387 KB  
Article
A Carbon-Tax-Based Dual-Warehouse Inventory Model with Deterioration and Investment in Preservation Technology
by Amrita Bhadoriya, Manish R. Betheja, Mrudul Y. Jani, Vivek Panwar and Vishal Pradhan
Modelling 2026, 7(3), 112; https://doi.org/10.3390/modelling7030112 - 5 Jun 2026
Viewed by 418
Abstract
This study develops an inventory model for deteriorating products within a dual-warehouse system under carbon tax regulation. The framework is motivated by supply chains for perishable goods where storage constraints, product deterioration, environmental costs, and financing decisions arise simultaneously. The model considers an [...] Read more.
This study develops an inventory model for deteriorating products within a dual-warehouse system under carbon tax regulation. The framework is motivated by supply chains for perishable goods where storage constraints, product deterioration, environmental costs, and financing decisions arise simultaneously. The model considers an owned warehouse and a rented warehouse with higher holding cost, where the rented facility is utilized first. To capture realistic operational conditions, the model integrates time-dependent holding costs, trend-based demand, preservation technology investment to reduce deterioration, and a two-tier trade credit scheme. Carbon tax is incorporated as an environmental cost component, while preservation technology directly influences the deterioration rate, creating a trade-off between investment and waste reduction. The proposed model is examined through numerical analysis based on parameter settings representative of perishable products such as organic dairy items. The objective is to determine the optimal replenishment cycle time, preservation investment, and order quantity that minimize the total cost within the dual-warehouse system. Numerical results indicate an average optimal cycle time of approximately 0.57 years, preservation investment of about 1.32 dollars, and order quantity near 459 units. The average total cost is around 1056 dollars, with a minimum observed cost of approximately 964 dollars. The findings highlight the significant impact of preservation technology and carbon taxation on profitability and sustainability. Full article
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33 pages, 11080 KB  
Article
Quasi-RVE Contact Modeling of Rough Flange–Gasket Interfaces for Micro-Leakage Channel Geometry Characterization
by D. M. Li, Zhi-Yan Zhong, Liu Yang, Bi-He Yuan and Ying Zhang
Modelling 2026, 7(3), 111; https://doi.org/10.3390/modelling7030111 - 5 Jun 2026
Viewed by 482
Abstract
This paper focuses on the characterization of the micro-leakage channel geometry in the flange-gasket rough contact interface of hazardous chemicals transport vehicles. This work represents the first step in a multi-physics simulation framework for optical-fiber-based micro-leakage monitoring. Directly establishing a full-scale contact model [...] Read more.
This paper focuses on the characterization of the micro-leakage channel geometry in the flange-gasket rough contact interface of hazardous chemicals transport vehicles. This work represents the first step in a multi-physics simulation framework for optical-fiber-based micro-leakage monitoring. Directly establishing a full-scale contact model from micron-scale rough peaks and valleys to the decimeter-scale flange structure would lead to extremely high computational costs; a nonlinear contact model based on quasi-representative volume element (quasi-RVE) and quasi-periodic boundary condition (quasi-PBC) is proposed in this paper. Quasi-RVE refers to a local region selected from the overall rough surface. Unlike a traditional RVE that requires strict geometric periodicity, the quasi-RVE is only approximately consistent with the overall surface with respect to key morphological parameters and volume parameters. Quasi-PBC only imposes in-plane displacement compatibility constraint on the relative side boundary without imposing periodic constraints in the peak-valley height direction. In this paper, the average interface gap and its distribution are selected as the geometric descriptors of the micro-leakage channel, and the reliability of the contact model is verified by comparing with the existing experimental and numerical results. On this basis, the influences of surface roughness, gasket material and loading conditions on the geometric characteristics of the micro-leakage channel are further analyzed. The results show that the lower stiffness gasket is easier to fit with the rough flange surface under the same load conditions, so as to obtain a larger contact area and a smaller average gap. The quasi-RVE contact model established in this paper can effectively reduce the computational scale of contact analysis of the rough sealing interface, and provide reliable channel geometric information for subsequent micro-leakage fluid simulation and optical fiber signal response simulation. Full article
(This article belongs to the Special Issue The 5th Anniversary of Modelling)
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26 pages, 1505 KB  
Article
TADS-DQN: A Trigger-Based Adaptive Deception Strategy Evolution Method Using Deep Q-Networks
by Zhihao Zhao, Xiran Wang, Leyi Shi and Juan Wang
Modelling 2026, 7(3), 110; https://doi.org/10.3390/modelling7030110 - 1 Jun 2026
Viewed by 339
Abstract
As an active defense paradigm, cyber deception technology effectively misleads attackers by constructing deceptive network environments, thereby increasing the cost of attack operations and introducing uncertainty into their decision-making, while providing defenders with critical response time. However, existing deception strategies are mostly based [...] Read more.
As an active defense paradigm, cyber deception technology effectively misleads attackers by constructing deceptive network environments, thereby increasing the cost of attack operations and introducing uncertainty into their decision-making, while providing defenders with critical response time. However, existing deception strategies are mostly based on predefined static rules derived from expert knowledge and lack the ability to adapt to dynamic attack scenarios autonomously and intelligently. This limitation results in poor adaptability and suboptimal performance of the strategy. To solve these issues, this paper proposes an Adaptive Cyber Deception Defense System (ACDDS). Different from off-the-shelf MDP/DQN frameworks in existing adaptive defense, the core innovation of ACDDS is a scenario-customized Trigger-based Adaptive Deception Strategy evolution method using Deep Q-Networks (TADS-DQN). We specifically formulate the dynamic deception strategy optimization as a cyber-deception-tailored Markov Decision Process (MDP). In this model, the state of the system is represented as a state matrix, and the attack behavior defines the environment for agent interaction. The TADS-DQN method employs a trigger-based mechanism: when a threat to real services is detected, a Deep Q-Network agent is activated. This agent takes the current system state as input and outputs the optimal reconfiguration action. The simulation results indicate that, compared to the baseline methods, TADS-DQN provides more stable defense performance, as evidenced by a smaller fluctuation range and a lower standard deviation of the attack success rate. At the same time, it achieves a reduction in the hit rate against real services that is competitive with the baseline methods. Full article
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28 pages, 3786 KB  
Article
HabSim: Modeling Disruptions, Propagation, Detection and Repair in Deep Space Habitats
by Luca Vaccino, Alana K. Lund, Shirley J. Dyke, Mohsen Azimi and Ethan Vallerga
Modelling 2026, 7(3), 109; https://doi.org/10.3390/modelling7030109 - 31 May 2026
Viewed by 410
Abstract
Establishing long-term human settlements in deep space presents significant challenges. Environmental conditions, such as extreme temperature fluctuations, micrometeorite impacts, seismic activity, and exposure to solar and cosmic radiation, pose obstacles to the design and operation of habitat systems. Prolonged mission duration and vast [...] Read more.
Establishing long-term human settlements in deep space presents significant challenges. Environmental conditions, such as extreme temperature fluctuations, micrometeorite impacts, seismic activity, and exposure to solar and cosmic radiation, pose obstacles to the design and operation of habitat systems. Prolonged mission duration and vast distances from Earth introduce further complications in the form of delayed communication and limited resources, making Earth independence through appropriate autonomous management systems especially desirable. Enabling the modeling and simulation of the consequences of disruptions and faults, and their propagation through the various habitat subsystems, is critically needed for the development of resilience-based design frameworks and methods for autonomous operation. While existing simulation tools can assist in modeling isolated aspects of damage, the integration of damage propagation and the capacity to enable detection and repair are rarely considered in a computational model. This paper introduces and demonstrates an architecture designed specifically to enable the modeling and integration of faults and damage, as well as their cascading effects. By combining physics-based and phenomenological models, our approach balances computational efficiency with model fidelity. After describing the modeling approach and corresponding architecture, we demonstrate its application within HabSim, a system-level space habitat model developed by the NASA-funded Resilient Extraterrestrial Habitat Institute (RETHi), as a simulation-based design aid suited to early-phase trade studies. Fire hazard propagation within a lunar habitat is used as an illustrative example of how the architecture supports modeling of disruption consequences, propagation, detection, and repair, and of how HabSim can be leveraged for stochastic simulations to support resilience assessment. Resilience-focused studies that apply this architecture can quantify and compare design alternatives. Full article
(This article belongs to the Special Issue The 5th Anniversary of Modelling)
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24 pages, 3831 KB  
Article
Estimation of Thermal Diffusivity in the Inverse Heat Transfer Problem for a Polymer Plate
by Douglas M. Rieger, Alisson L. Daga, Ervin K. Lenzi and Marcelo K. Lenzi
Modelling 2026, 7(3), 108; https://doi.org/10.3390/modelling7030108 - 31 May 2026
Viewed by 227
Abstract
This study investigates the inverse estimation of the effective thermal diffusivity of a polytetrafluoroethylene (PTFE) plate subjected to oscillatory heating from a hot plate with on–off control. Transient temperature measurements at four internal positions were used to evaluate three modeling strategies: a constant-diffusivity [...] Read more.
This study investigates the inverse estimation of the effective thermal diffusivity of a polytetrafluoroethylene (PTFE) plate subjected to oscillatory heating from a hot plate with on–off control. Transient temperature measurements at four internal positions were used to evaluate three modeling strategies: a constant-diffusivity formulation with a prescribed Dirichlet boundary condition, a position-dependent effective diffusivity formulation, (x), and a constant-diffusivity model with a Robin boundary condition to account for thermal contact resistance. The constant-diffusivity Dirichlet model, when fitted to all data simultaneously, was unable to reproduce the experimental thermal response satisfactorily. When fitted separately at each thermocouple position, the estimated effective diffusivity increased systematically with position change, indicating that the experimental response could not be represented by a single scalar parameter under the adopted Dirichlet formulation. Variable-(x) models improved the fit, especially the exponential and rational expressions, which reproduced the apparent saturating spatial trend more effectively. However, these functions should be interpreted as empirical effective representations rather than intrinsic constitutive laws for PTFE. The Robin-boundary model with constant diffusivity also provided a comparable fit, suggesting that interfacial thermal resistance at the PTFE–hot plate contact may explain part of the apparent spatial variation inferred by the Dirichlet models. These results indicate that internal temperature measurements under realistic transient heating are not sufficient to uniquely distinguish between distributed effective diffusivity and boundary-contact resistance effects. Therefore, the estimated diffusivity values should be interpreted as model-dependent effective parameters rather than direct measurements of intrinsic PTFE thermal diffusivity. Full article
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23 pages, 5601 KB  
Article
Benefits of Using Tall Wind Turbine Towers in Wind-Rich Regions
by Bin Cai, Sri Sritharan, Eugene S. Takle and Chris Milliren
Modelling 2026, 7(3), 107; https://doi.org/10.3390/modelling7030107 - 30 May 2026
Viewed by 567
Abstract
While conventional wind towers operate at heights of 80 to 90 m across many regions, including the United States, emerging tower technologies enable higher hub heights that are expected to reduce the levelized cost of energy (LCOE) and increase profit margins. This paper [...] Read more.
While conventional wind towers operate at heights of 80 to 90 m across many regions, including the United States, emerging tower technologies enable higher hub heights that are expected to reduce the levelized cost of energy (LCOE) and increase profit margins. This paper investigates whether increased hub heights, as well as different turbine technologies, deliver measurable economic and performance benefits in wind-rich regions using measured and simulated wind data. First, a model for estimating hourly and monthly energy production is validated with data from a site in Minnesota. To evaluate the advantages of tall towers, the model is extended to estimate the annual energy production (AEP) at various hub heights across multiple sites using different wind datasets. The results confirm that simulated data can be effectively used for predicting AEP and capacity factors in wind-rich regions. Next, it is demonstrated that increasing the hub height by 20 m yielded an average 11% increase in AEP and an 18% reduction in LCOE. Finally, the integration of advanced turbine technologies with taller towers shows the potential to reduce the LCOE of wind power by 23% while increasing profit margins by over 40%. Full article
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22 pages, 847 KB  
Article
Estimation of the Voltage Stability Margin in Power Systems Under Transmission Line Contingencies Using a Convex Formulation and a Heuristic Approach
by Jenny Vanessa Rojas-Báez, María Fernanda Laverde-Rojas and Oscar Danilo Montoya
Modelling 2026, 7(3), 106; https://doi.org/10.3390/modelling7030106 - 30 May 2026
Viewed by 377
Abstract
Voltage stability under transmission line contingencies is a critical concern in modern power systems, as the growing electricity demand and the large-scale integration of renewable energy sources increasingly challenge the security of network operation. This paper addresses the problem of estimating the voltage [...] Read more.
Voltage stability under transmission line contingencies is a critical concern in modern power systems, as the growing electricity demand and the large-scale integration of renewable energy sources increasingly challenge the security of network operation. This paper addresses the problem of estimating the voltage stability margin under N1 transmission line contingencies through three solution methodologies: a nonlinear programming formulation solved via an interior-point algorithm (IPOPT) with a multi-start strategy, a recursive heuristic approach based on successive Newton–Raphson power flow solutions with progressive load scaling, and a convex second-order cone programming relaxation. The proposed methods are validated on the IEEE 9-, 14-, 30-, and 57-bus test systems, thereby covering networks of varying topological complexity and redundancy. A comparative analysis evaluates the accuracy of each approach against a nonlinear programming reference, as well as their computational efficiency under a comprehensive set of contingency scenarios. The results indicate that the heuristic method achieves higher precision, while the convex formulation offers a substantially faster solution, with both approaches demonstrating robustness in cases where the nonlinear programming method fails to converge. Full article
(This article belongs to the Special Issue Optimization in Engineering: Models and Algorithms)
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19 pages, 23582 KB  
Article
Lithium-Ion Battery SOH Prediction Method Based on Multidimensional Feature Data Fusion
by Yifei Wang, Jiatian Gan, Jun Yang, Ning Zhang, Jingang Wang, Xingyu Zhang and Pengcheng Zhao
Modelling 2026, 7(3), 105; https://doi.org/10.3390/modelling7030105 - 28 May 2026
Viewed by 310
Abstract
Aiming at the problem that the degradation mechanism of lithium-ion batteries is complex during aging and that a single feature is difficult to fully characterize the battery state of health (SOH), this paper proposes an SOH prediction method for lithium-ion batteries based on [...] Read more.
Aiming at the problem that the degradation mechanism of lithium-ion batteries is complex during aging and that a single feature is difficult to fully characterize the battery state of health (SOH), this paper proposes an SOH prediction method for lithium-ion batteries based on multidimensional HF weighted fusion. First, health features (HF) are extracted from the battery charge–discharge data, and the Pearson correlation coefficient is used to analyze the correlation between each HF and SOH. Based on this, a weighted fused feature matrix is constructed. Then, through the collaborative modeling of a convolutional neural network (CNN) and a bidirectional long short-term memory (BiLSTM), the joint extraction of local features and temporal features from multidimensional HF is realized. Meanwhile, manta ray foraging optimization (MRFO) is introduced to optimize key hyperparameters. Finally, experiments are conducted based on the CALCE dataset, and the prediction performance of the proposed method is evaluated through comparisons with different prediction models and an ablation experiment on HF fusion strategies. The results show that the proposed method achieves good prediction results on the CS2-35, CS2-36, and CS2-37 test batteries, with the lowest MAE of 1.134% and the highest R2 of 0.963. Full article
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21 pages, 12506 KB  
Article
A Weak Magnetic Anomaly Signal Enhancement Method Based on an Adaptive Variable-Structure Stochastic Resonance System
by Hexing Zheng, Jinguo Liu, Haitao Gu, Fang Shi and Kexin Zhang
Modelling 2026, 7(3), 104; https://doi.org/10.3390/modelling7030104 - 26 May 2026
Cited by 1 | Viewed by 335
Abstract
Magnetic anomaly detection (MAD) is a passive technique for detecting ferromagnetic targets, but weak magnetic anomaly signals are often submerged in background noise. Existing stochastic resonance (SR)-based MAD methods mainly focus on target detection and generally provide limited capability for waveform and amplitude [...] Read more.
Magnetic anomaly detection (MAD) is a passive technique for detecting ferromagnetic targets, but weak magnetic anomaly signals are often submerged in background noise. Existing stochastic resonance (SR)-based MAD methods mainly focus on target detection and generally provide limited capability for waveform and amplitude reconstruction. To address this problem, this paper proposes a weak magnetic anomaly signal enhancement method based on an adaptive variable-structure stochastic resonance (AVSSR) system. A potential function capable of switching among monostable, bistable, and multistable structures is designed to improve the adaptability of SR processing under different noise conditions. The noisy vector magnetic signals are processed by the AVSSR system, and the normalized sliding-window standard deviation is combined with a scaling factor to reconstruct the magnetic anomaly signal’s waveform and amplitude. The system parameters are optimized using the differential evolution algorithm. Simulation results show that the proposed method can effectively reconstruct magnetic anomaly signals under Gaussian white noise and colored 1/fα noise, even at an input SNR of −15 dB. Comparisons with the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method and an adaptive multistable SR method demonstrate better waveform preservation and more stable amplitude reconstruction. Experimental results using measured Bt signals further verify its practical applicability. Full article
(This article belongs to the Special Issue Optimization in Engineering: Models and Algorithms)
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16 pages, 3218 KB  
Article
Successive Overrelaxation–Progressive Interpolation for Loop Subdivision Surfaces
by Yusuf Fatihu Hamza and Mukhtar Fatihu Hamza
Modelling 2026, 7(3), 103; https://doi.org/10.3390/modelling7030103 - 26 May 2026
Viewed by 277
Abstract
The Loop subdivision scheme is one of the most widely used approximation subdivision methods for generating smooth surfaces. However, the limiting surface of the Loop subdivision scheme does not interpolate the vertices of the original mesh and may exhibit shrinkage in certain cases. [...] Read more.
The Loop subdivision scheme is one of the most widely used approximation subdivision methods for generating smooth surfaces. However, the limiting surface of the Loop subdivision scheme does not interpolate the vertices of the original mesh and may exhibit shrinkage in certain cases. To overcome this limitation, we propose the Successive Overrelaxation–Progressive Iterative Approximation (SOR-PIA) method, which adjusts the positions of the original vertices so that the corresponding limit surface of the Loop subdivision scheme can interpolate the vertices of the given mesh. The optimal relaxation parameter for the SOR-PIA method is also provided. Compared to classical PIA, Weighted PIA (W-PIA), Hermitian and skew-Hermitian PIA (HSS-PIA), and Weighted Hermitian and skew-Hermitian PIA (WHSS-PIA), the proposed method converges faster while maintaining accuracy, as demonstrated by numerical examples. Full article
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28 pages, 10819 KB  
Article
Dynamic Behavior and Computational Investigation of Tunnel Blasting Subjected to Varying Geostresses
by Hualong Li, Yong Mei, Yunhou Sun, Zixun Wu, Shengyi Cong and Shaojun Cao
Modelling 2026, 7(3), 102; https://doi.org/10.3390/modelling7030102 - 26 May 2026
Viewed by 753
Abstract
To examine the dynamic response of tunnel floor slabs subjected to blasting under varying stress conditions, a numerical model was developed to simulate blasting effects at different tunnel depths. This model integrated Hopkinson bar experiments conducted under confining pressure with the Riedel–Hiermaier–Thoma (RHT) [...] Read more.
To examine the dynamic response of tunnel floor slabs subjected to blasting under varying stress conditions, a numerical model was developed to simulate blasting effects at different tunnel depths. This model integrated Hopkinson bar experiments conducted under confining pressure with the Riedel–Hiermaier–Thoma (RHT) constitutive framework. The study subsequently investigated the effects of geostress fields, tunnel depth and tunnel inclination on the propagation characteristics of stress waves. Additionally, the mechanisms stress wave transmission and the damage evolution within the rock mass were analyzed. Results from the numerical simulations reveal that increasing the charge depth diminishes the dissipation of post-blasting stress waves toward the free surface, thereby concentrating stress wave propagation within the rock mass and substantially amplifying shock wave intensity and impact loading. Moreover, elevated stress levels in the surrounding rock increase the peak stress wave amplitude, constrain damage propagation on the tunnel’s upper side, and redirect more stress waves toward deeper regions of the model. Increasing tunnel inclination was also found to intensify stress concentration and augment stress wave intensity. Notably, at a tunnel inclination of 5°, stress wave intensity attains its maximum; beyond this angle, the development of stress waves exhibits irregular patterns. Full article
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15 pages, 4206 KB  
Article
Dynamic Simulation of Complex Multiple-Crack Evolution Under Blast Loading Using a Nonlocal Macro-Meso-Scale Consistent Damage Model
by Qianxu Yang, Guangda Lu and Xiaozhou Xia
Modelling 2026, 7(3), 101; https://doi.org/10.3390/modelling7030101 - 25 May 2026
Viewed by 455
Abstract
An explicit dynamic framework based on the Nonlocal Macro-Meso-scale Consistent Damage (NMMD) model is proposed to simulate complex multiple-crack evolution in quasi-brittle materials subjected to blast loading. Three numerical examples—a single-edge-notched half-plate, a thick ring, and a hollow mortar cylinder containing a small [...] Read more.
An explicit dynamic framework based on the Nonlocal Macro-Meso-scale Consistent Damage (NMMD) model is proposed to simulate complex multiple-crack evolution in quasi-brittle materials subjected to blast loading. Three numerical examples—a single-edge-notched half-plate, a thick ring, and a hollow mortar cylinder containing a small borehole—are analyzed. The results show that crack initiation, propagation, branching, and coalescence can be naturally captured by the proposed framework without remeshing. Reliable predictions are obtained only when sufficient mesh resolution is used to resolve nonlocal interactions and the time step satisfies the explicit stability criterion. Comparisons indicate that fewer but more dominant crack paths are predicted by the model, suggesting a conservative tendency in estimating the number of fragments. Crack-path selection is significantly influenced by material heterogeneity, which enables secondary cracks to evolve into dominant crack paths. Crack multiplication and network connectivity are promoted by increased blast pressure, whereas crack complexity and spatial extent are reduced by higher damping coefficients. Full article
(This article belongs to the Section Modelling in Mechanics)
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26 pages, 5313 KB  
Article
Mathematical Modeling and Comparative Evaluation of PI and PID Speed Controllers for Electric Vehicle Traction Systems
by Oleg Lyashuk, Dmytro Mironov, Pavlo Maruschak, Volodymyr Dzyura and Viktor Shevchuk
Modelling 2026, 7(3), 100; https://doi.org/10.3390/modelling7030100 - 20 May 2026
Viewed by 535
Abstract
Although PI and PID controllers are mature control laws, their effect on energy-related variables is rarely isolated in a complete electric vehicle traction model when the plant, controller tuning basis and driving conditions are kept unchanged. A full-system MATLAB/Simulink model was developed, comprising [...] Read more.
Although PI and PID controllers are mature control laws, their effect on energy-related variables is rarely isolated in a complete electric vehicle traction model when the plant, controller tuning basis and driving conditions are kept unchanged. A full-system MATLAB/Simulink model was developed, comprising a DC motor with PWM H-bridge, reduction gear, vehicle dynamics and a lithium-ion battery with SOC monitoring. Fixed-gain PI and PID configurations were compared under FTP75, with US06 added as a dynamic-cycle assessment. Speed tracking was evaluated using RMSE, MAE, IAE and ITAE, while energy behavior was assessed through SOC depletion, battery voltage, current and braking-command signals. Under FTP75, both controllers achieved nearly identical tracking accuracy, with an overall RMSE of 0.1525 km/h across the active intervals. Despite this kinematic equivalence, PID reduced SOC depletion by 0.980 percentage points over 4.963 km and produced a less intense but more distributed braking command. The additional 600 s US06 simulation did not confirm a general PID advantage: both controllers reached the same maximum speed and showed practically identical tracking accuracy, while PID did not reduce SOC depletion. The results show that the derivative channel changes the control-command pattern, but it does not automatically improve kinematic or energy performance under fixed-gain tuning. Full article
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27 pages, 7085 KB  
Article
Hybrid Mechanistic–Data-Driven Virtual Metering Models and Methodologies for Conventional Gas Fields
by Minhao Wang, Zhenjia Wang, Gangping Chen, Jun Zhou, Jian Luo, Fang Qin, Yue Wu, Pan Zhou and Chuqi Lin
Modelling 2026, 7(3), 99; https://doi.org/10.3390/modelling7030099 - 19 May 2026
Viewed by 866
Abstract
Virtual flow metering (VFM) serves as an effective alternative to traditional physical flow meters, significantly reducing gas-field metering costs and operational complexity. However, conventional VFM typically employs a single-modeling approach, failing to address metering requirements across varying production conditions and data types. Focusing [...] Read more.
Virtual flow metering (VFM) serves as an effective alternative to traditional physical flow meters, significantly reducing gas-field metering costs and operational complexity. However, conventional VFM typically employs a single-modeling approach, failing to address metering requirements across varying production conditions and data types. Focusing on wellhead choke equipment, four mechanistic models (MModels) based on choke-flow dynamics are constructed using piecewise linear regression, alongside six machine learning models. Hyperparameters are optimized via grid search and cross-validation, establishing a hybrid mechanistic and data-driven multi-model VFM method for gas wells. Systematic testing utilizes field data from gas wells in the Southwest Oil and Gas Field, with the Shapley additive explanations (SHAP) method quantifying feature contributions. MModel results indicate superior overall performance by the temperature-difference piecewise linear model, yielding a training R2 of 0.91 and a mean test error of 4.59%. Under different valve-position conditions, the downstream-temperature piecewise linear model demonstrates better predictive capability when the valve position is equal to 100, whereas the valve-position piecewise linear model achieves higher accuracy when the valve position is less than 100. MLModel results reveal that among ten feature parameters, “Date” and “Valve Position Indication” contribute most significantly to prediction accuracy, accounting for over 50% of cumulative contribution in GBoost (extreme gradient boosting) and CatBoost (categorical boosting) models. Notably, the XGBoost model exhibits optimal predictive performance, achieving a training R2 of 0.979 and a mean test error of merely 0.13%. Random sampling results show coefficient of variation values below 0.1 for all metrics, demonstrating exceptional robustness, providing an effective technical solution and solid theoretical support for gas-field VFM. Full article
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23 pages, 2831 KB  
Article
A Novel Short-Term Wind Power Forecasting Model Based on Improved Ensemble Learning
by He Jiang, Tianhui Shi, Qingzheng Li and Xinyu Wang
Modelling 2026, 7(3), 98; https://doi.org/10.3390/modelling7030098 - 19 May 2026
Viewed by 377
Abstract
The development of renewable energy is vital for addressing future climate change and environmental degradation. Nevertheless, the irregular and fluctuating essential features of wind power presents a considerable barrier to grid operational stability. Hence, precise prediction of wind energy output is crucial for [...] Read more.
The development of renewable energy is vital for addressing future climate change and environmental degradation. Nevertheless, the irregular and fluctuating essential features of wind power presents a considerable barrier to grid operational stability. Hence, precise prediction of wind energy output is crucial for improving power system management, boosting the reliability of the supply, and minimizing reserve expenditure. This study presents a predictive model designed for predicting short-term wind speeds using a stacking ensemble approach, which is based on an enhanced Multi-Feature Zebra Optimization Algorithm (IZOA-Stacking). In the data preprocessing phase, to minimize computational costs and prevent overfitting, a module tailored to the various features affecting wind power is developed for the IZOA-Stacking model. Grey relational analysis and Pearson correlation analysis are employed to determine and filter feature correlations. Critically, the preprocessing module demonstrates strong robustness: the One-Class Support Vector Machine (OneSVM) model is applied to identify and replace 100% of anomalous wind speed data, which leads to a substantial and measurable increase in feature correlation and overall model performance. For instance, when retaining wind speed features, the One-Class Support Vector Machine (OneSVM) model is employed to eliminate anomalous wind speed data. During model construction, a stacking ensemble learning strategy integrates multiple prediction models, including Long Short-Term Memory (LSTM) net-works, Extreme Gradient Boosting (XGBoost), ridge regression (RR), and Residual Networks (ResNets). This integration leverages the predictive strengths of each model. Additionally, the improved Zebra Optimization Algorithm (ZOA) optimizes the hyperparameters of each constituent model, further enhancing forecasting accuracy. The findings suggest that the proposed model demonstrates better performance than reference competitor models with regard to predictive accuracy. Full article
(This article belongs to the Section Modelling in Artificial Intelligence)
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23 pages, 733 KB  
Article
Ordinal Probit Modeling of Injury Severity Risks at Visually Obstructed Intersections with Bootstrap Validation
by Irfan Ullah, Ahmed Farid and Khaled Ksaibati
Modelling 2026, 7(3), 97; https://doi.org/10.3390/modelling7030097 - 19 May 2026
Viewed by 438
Abstract
Road intersection crashes remain a major contributor to injuries due to complex conflict patterns and multimodal interactions. Among the factors influencing intersection safety, inadequate intersection sight distance (ISD) attributed to roadside sight obstructions can limit drivers’ ability to respond to conflicting movements, potentially [...] Read more.
Road intersection crashes remain a major contributor to injuries due to complex conflict patterns and multimodal interactions. Among the factors influencing intersection safety, inadequate intersection sight distance (ISD) attributed to roadside sight obstructions can limit drivers’ ability to respond to conflicting movements, potentially affecting crash injury outcomes. Despite its importance, visual obstruction has rarely been examined as a distinct context in traffic crash injury severity modeling. This study investigates crash injury severity at visually obstructed intersections using an ordinal probit modeling framework applied to 951 intersection crashes documented with sight obstruction as a contributing factor in Wyoming over the period 2014 through 2023. Crash data were analyzed to identify the effects of driver behavior, vehicle characteristics, roadway geometry, environmental conditions, and traffic control on ordered injury severity outcomes ranging from property damage only (PDO) to fatal and serious injury. Nonparametric bootstrap resampling with 1000 iterations was employed to assess parameter stability and construct empirical confidence intervals. Average marginal effects were estimated to quantify the change in probability of each injury severity level associated with key predictors. The results indicate that alcohol involvement produces the largest severity shift, reducing the probability of PDO outcomes by 51.2 percentage points while increasing the probability of fatal and serious injury by 34.2 percentage points. Hillcrest grade locations increase fatal and serious injury risk by 14.4 percentage points, while adverse road surface conditions, including snowy, icy, and wet pavements, consistently reduce fatal and serious injury probability by 12.5 to 15.1 percentage points, reflecting behavioral adaptation to visually salient hazard cues. Bootstrap validation confirms strong parameter stability across all estimates, with 94% of parameters showing bootstrap standard errors within 25% of their asymptotic counterparts. By formally establishing visually obstructed intersections as a dedicated severity modeling context and integrating systematic bootstrap validation, this study contributes both substantive and methodological insights to support evidence-based prioritization of intersection safety improvements. Full article
(This article belongs to the Special Issue Advanced Modelling Techniques in Transportation Engineering)
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21 pages, 5741 KB  
Article
Improved WCSPH-DEM Coupling for Analyzing Fluid–Solid Interactions
by Changjun Zou and Zhihua Shi
Modelling 2026, 7(3), 96; https://doi.org/10.3390/modelling7030096 - 15 May 2026
Viewed by 290
Abstract
Fluid–structure interaction (FSI) research is crucial for applications in fields such as naval engineering, geological hazards, and biomechanics. Traditional grid-based methods (such as CFD) often face challenges in simulating large-deformation flow fields and complex boundary conditions, where mesh distortion can compromise simulation accuracy. [...] Read more.
Fluid–structure interaction (FSI) research is crucial for applications in fields such as naval engineering, geological hazards, and biomechanics. Traditional grid-based methods (such as CFD) often face challenges in simulating large-deformation flow fields and complex boundary conditions, where mesh distortion can compromise simulation accuracy. Building upon the DualSPHysics5.2 framework, this study leverages the strengths of weakly compressible SPH (WCSPH) in modeling free surface flows and large-deformation fluids, as well as the discrete element method (DEM), for accurately describing particle collisions and fragmentation behaviors. We propose an improved MSPH-DEM coupling algorithm that incorporates moving least squares (MLS) correction for kernel function gradient optimization. This algorithm utilizes MLS-based gradient correction to achieve smoother fluid surfaces as well as bidirectional coupling between fluids and particles. Experimental validation demonstrates that in dam break simulations, this method reduces pressure errors. In the dam break impacting a cube experiment, it enhances accuracy, while in the dam break impacting a baffle experiment, the horizontal displacement of marker points closely aligns with the experimental values from Liao et al. This approach effectively improves the accuracy of the simulations of FSI problems, offering a more reliable numerical simulation methodology for engineering applications such as geological hazard prevention. Full article
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39 pages, 13762 KB  
Article
Comparative Study of Different Time Integration Algorithms for Solving Kinematic Problems
by Wei Xu, Yi-Fan Li and Yong-Ou Zhang
Modelling 2026, 7(3), 95; https://doi.org/10.3390/modelling7030095 - 15 May 2026
Viewed by 348
Abstract
This study selects five numerical methods: the explicit Leap-Frog scheme, the implicit Crank–Nicolson scheme, the explicit second-order Runge–Kutta scheme, the implicit Newmark-β scheme, and the implicit Bathe scheme. These methods are compared through representative dynamic cases in terms of solution accuracy and computational [...] Read more.
This study selects five numerical methods: the explicit Leap-Frog scheme, the implicit Crank–Nicolson scheme, the explicit second-order Runge–Kutta scheme, the implicit Newmark-β scheme, and the implicit Bathe scheme. These methods are compared through representative dynamic cases in terms of solution accuracy and computational efficiency. The results demonstrate that implicit schemes maintain numerical convergence even with relatively large time steps. The findings also indicate that, although the actual convergence accuracy of the given schemes varies slightly among motion models of different dimensions, it remains close to the theoretical second-order accuracy. Different time integration schemes exhibit distinct numerical accuracies when applied to multi-dimensional motion problems. Overall, under identical time step sizes, the Bathe time integration scheme demonstrates slightly superior computational accuracy and error stability compared to other schemes considered. The numerical efficiency of time integration schemes also varies across dimensions and problem types. The actual computational time does not scale linearly with the time step size and is partially influenced by the complexity of the solution algorithm employed. In general, when solution accuracy is comparable, the Leap-Frog scheme shows marginally higher efficiency in explicit simulations, whereas the Crank–Nicolson scheme proves more efficient in implicit simulations. Full article
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26 pages, 30414 KB  
Article
Experimental and Numerical Verification of Continuous Carbon-Fibre Additively Manufactured Structures
by Ivica Smojver, Darko Ivančević, Fran Ušurić, Moritz Kuhtz and Andreas Hornig
Modelling 2026, 7(3), 94; https://doi.org/10.3390/modelling7030094 - 15 May 2026
Viewed by 583
Abstract
This study investigates the mechanical behaviour of continuous carbon-fibre-reinforced additively manufactured composite structures aimed at applications in aeronautical structures, through a combination of experimental testing and numerical simulation. Tensile, compressive, and shear tests established stiffness and failure characteristics, while finite element analyses were [...] Read more.
This study investigates the mechanical behaviour of continuous carbon-fibre-reinforced additively manufactured composite structures aimed at applications in aeronautical structures, through a combination of experimental testing and numerical simulation. Tensile, compressive, and shear tests established stiffness and failure characteristics, while finite element analyses were used for a preliminary calibration-based reproduction of the measured coupon response, with an emphasis on the initial elastic part of the impact event. The integration of measured data with structural modelling provides a clearer understanding of load transfer and damage initiation in continuous-fibre AM, supporting more accurate simulation-based design of additively manufactured composite components. Experimental results show pronounced anisotropy, and a stable, rate-dependent impact response. The preliminary numerical model based on CT-derived homogenized properties accurately reproduces the initial part of the measured quasi-static and dynamic responses. Full article
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19 pages, 4663 KB  
Article
Modeling and Analysis of Key Structural Parameters of Infrared Line Drawing Device for Oil and Gas Pipeline Cutting Operations
by Yong Chen, Ping Xiong and Ding Yang
Modelling 2026, 7(3), 93; https://doi.org/10.3390/modelling7030093 - 14 May 2026
Viewed by 356
Abstract
To address the issues associated with traditional multi-point surveying processes in the dead-end cutting for oil and gas pipelines—such as cumbersome procedures, high error rates, lengthy emergency repair cycles, and difficulties in ensuring welding precision—an infrared line drawing device has been developed that [...] Read more.
To address the issues associated with traditional multi-point surveying processes in the dead-end cutting for oil and gas pipelines—such as cumbersome procedures, high error rates, lengthy emergency repair cycles, and difficulties in ensuring welding precision—an infrared line drawing device has been developed that enables rapid positioning, long-distance high-precision alignment, and accurate marking of cutting locations. This paper establishes mathematical models for the centering deflection mechanism and the marking mechanism, and derives theoretical solutions for key structural parameters. Thirteen finite element models were constructed using Abaqus to simulate operating conditions involving different pipe diameters and link lengths. A variance-based uniformity metric was employed to quantify structural stress stability, and optimal parameters were determined based on the principle that smaller variance indicates more uniform stress distribution and closer to ideal component service life. The results indicate that the optimal length of the three mounting bolts is 85 mm, with a maximum deflection angle of 9.25°, which meets the requirements. A spring extension of 5 mm for the marking pen can accommodate the compensation needs for marking on DN300 to DN500 pipes. An optimal set of connecting rod parameters across pipe diameters has been determined, with a 240 mm connecting rod capable of covering more than 75% of operating conditions. This device and its parameters are expected to contribute to first-pass compliance and reduce downtime, providing efficient and precise technical support for the maintenance and emergency repair of oil and gas pipelines. Full article
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