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Modelling, Volume 7, Issue 4 (August 2026) – 54 articles

Cover Story (view full-size image): Additive manufacturing has enabled the widespread fabrication of lattice mechanical metamaterials, but the resulting structures inevitably deviate from their nominal designs. Because their wave attenuation performance relies on accurately predicted phononic bandgaps, understanding the sensitivity of dispersion analyses to geometric and modelling discrepancies is critical. This work investigates how finite element modelling errors affect the predicted dispersion behaviour of lattice metastructures. The results identify the most critical sources of error and provide practical guidelines for reliable simulations, while offering qualitative insight into how geometry-related imperfections may influence the dynamic response of manufactured metamaterials. View this paper
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15 pages, 4449 KB  
Article
Investigation on Cryogenic Creep Damage Behavior of NEPE Propellant
by Jinghui Li, Xueren Wang, Chuanfei Song, Zhipeng Zhao and Yanchao Wang
Modelling 2026, 7(4), 176; https://doi.org/10.3390/modelling7040176 - 21 Aug 2026
Viewed by 278
Abstract
Most existing creep studies on NEPE propellant focus on room and high temperatures, lacking systematic investigation into low-temperature creep damage. In this work, uniaxial creep tests at −10 °C, −30 °C and −50 °C under three stress levels were conducted. All specimens show [...] Read more.
Most existing creep studies on NEPE propellant focus on room and high temperatures, lacking systematic investigation into low-temperature creep damage. In this work, uniaxial creep tests at −10 °C, −30 °C and −50 °C under three stress levels were conducted. All specimens show complete three-stage creep behavior. Higher stress accelerates interface debonding and shortens rupture life, while low temperature restricts molecular chain movement and suppresses damage growth. Combined with continuum damage mechanics and strain-equivalence hypothesis, a modified time-hardening creep model embedded with the Kachanov damage-evolution equation is established. All fitting coefficients of determination exceed 0.989. A FORTRAN UMAT subroutine is developed on ABAQUS (version 2024) for numerical simulation, using SDV1 and SDV8 to output creep strain and damage variables respectively. Simulation strain curves match experimental data well and reproduce full-range creep evolution. Damage remains low for most of the service time and surges only in the final 5–10% of the lifetime. The proposed model and subroutine accurately characterize the low-temperature creep and damage evolution of NEPE propellant, supporting grain structural integrity analysis and long-term storage life prediction. Full article
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19 pages, 1333 KB  
Article
Surrogate-Assisted Genetic Optimization for Inverse Identification of Hyperelastic Material Parameters from Membrane Inflation Data
by Sabir Hussain, Saif Shakeel, Affan Khan, Mohammad Rashid Zafar, Arshad Hussain Khan, Thimmappa Shetty Guruprasad and Vishwanath Managuli
Modelling 2026, 7(4), 175; https://doi.org/10.3390/modelling7040175 - 20 Aug 2026
Viewed by 325
Abstract
Soft deformable materials such as elastomers, biological tissues, and polymeric membranes are widely used in modern engineering applications including biomechanics, soft robotics, and flexible electronics. Accurate identification of their constitutive parameters is therefore essential for reliable mechanical modeling and design. Membrane inflation or [...] Read more.
Soft deformable materials such as elastomers, biological tissues, and polymeric membranes are widely used in modern engineering applications including biomechanics, soft robotics, and flexible electronics. Accurate identification of their constitutive parameters is therefore essential for reliable mechanical modeling and design. Membrane inflation or bulge tests are commonly used for this purpose, where material parameters are typically identified from pressure–deflection measurements. However, such measurements generally require optical systems to capture membrane deformation, which increases experimental complexity. In this work, we propose a surrogate-assisted inverse identification framework for determining hyperelastic material parameters using pressure–volume data obtained from membrane inflation tests, thereby eliminating the need for optical deformation measurements. To reduce the computational cost associated with repeated forward simulations, an Artificial Neural Network (ANN) surrogate model is trained using numerically generated pressure–volume data from finite-element simulations. The trained ANN efficiently predicts the pressure response of the membrane for different material parameters and volume influx values. A Genetic Algorithm (GA) is then employed to identify the optimal parameters by minimizing the discrepancy between measured and predicted responses. The proposed GA–ANN framework is demonstrated for the Mooney–Rivlin hyperelastic model and accurately recovers material parameters for both noise-free and noisy datasets, providing a computationally efficient and robust methodology for the characterization of soft membranes. Full article
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19 pages, 13091 KB  
Article
Numerical Simulation Analysis of Gas–Liquid Two-Phase Flow in a Downhole Coupled Intensified Mixing Structure
by Zewei Zheng, Hongbao Liang, Junjie Huang, Boyu Zhang, Zhen Zhang and Peiang Huang
Modelling 2026, 7(4), 174; https://doi.org/10.3390/modelling7040174 - 19 Aug 2026
Viewed by 319
Abstract
To address the challenge of efficiently blending low-mutual-solubility gas–liquid two-phase systems, a composite structure comprising a Venturi and a static mixer was designed, and its flow field characteristics were analyzed using computational fluid dynamics (CFD) simulations. The results indicate that positioning the static [...] Read more.
To address the challenge of efficiently blending low-mutual-solubility gas–liquid two-phase systems, a composite structure comprising a Venturi and a static mixer was designed, and its flow field characteristics were analyzed using computational fluid dynamics (CFD) simulations. The results indicate that positioning the static mixer at the exit of the Venturi diffusion section yields optimal performance. This configuration prevents disruption of the jet premix flow field and facilitates the uniform dispersion of gas–liquid mixtures throughout the entire domain via six sets of SK-type single-spiral static mixer (SK) units following the initial blending. The composite structure exhibits a three-tier synergistic mechanism characterized by “suction–premix–mixing intensification”: the negative pressure zone within the throat tube induces suction of the gas phase, the diffusion section converts pressure energy to enhance shearing and crushing, and the static mixing section disrupts the axial jet through cutting and swirling effects, thereby generating secondary vortices. This process ultimately achieves uniform dispersion of gas and liquid across the entire domain. The structure’s lack of moving parts addresses the issues of low efficiency and unstable flow fields associated with traditional devices. This design facilitates enhanced crude oil recovery and low-pressure reservoir gas injection drilling. Full article
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14 pages, 903 KB  
Communication
Event-Triggered Security Control for High-Order Fully Actuated Systems Under DoS Attacks
by Qian Wang and Xiaohu Li
Modelling 2026, 7(4), 173; https://doi.org/10.3390/modelling7040173 - 18 Aug 2026
Viewed by 208
Abstract
This paper investigates the problem of event-triggered secure regulation for high-order fully actuated (HOFA) systems subject to stochastic denial-of-service (DoS) attacks. Through a suitable state transformation, the original HOFA plant is recast into an error-state representation. A dual-dynamic event-triggered control (DETC) law is [...] Read more.
This paper investigates the problem of event-triggered secure regulation for high-order fully actuated (HOFA) systems subject to stochastic denial-of-service (DoS) attacks. Through a suitable state transformation, the original HOFA plant is recast into an error-state representation. A dual-dynamic event-triggered control (DETC) law is devised, which operates solely during DoS sleep intervals. By employing Lyapunov-based arguments, sufficient conditions are derived to ensure the practical stability of the closed-loop system for both attack and sleep phases. Moreover, a strictly positive lower bound on the minimum inter-event interval is established, thereby ruling out Zeno phenomena. Numerical experiments confirm the effectiveness of the proposed approach. Full article
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15 pages, 8700 KB  
Article
Electromagnetic−Thermo−Mechanical Coupling Analysis of Armature−Rail Contact Behavior in Electromagnetic Railgun
by Dongke Li, Yong Liu, Wanying Wang, Dongying Wang and Tao Zhang
Modelling 2026, 7(4), 172; https://doi.org/10.3390/modelling7040172 - 18 Aug 2026
Viewed by 276
Abstract
To address the critical role of armature–rail contact in electromagnetic railguns, a comprehensive electromagnetic–thermal–mechanical coupled model is developed. In contrast to existing coupled railgun models, this work uniquely introduces the dynamic mechanical contact state and contact resistance as coupling variables and explicitly accounts [...] Read more.
To address the critical role of armature–rail contact in electromagnetic railguns, a comprehensive electromagnetic–thermal–mechanical coupled model is developed. In contrast to existing coupled railgun models, this work uniquely introduces the dynamic mechanical contact state and contact resistance as coupling variables and explicitly accounts for the interference−fit process during armature loading, enabling a full−cycle simulation from assembly to launch. The simulation results are compared with open−bore experimental measurements, and the model is applied to simulate the launch process. The results reveal a characteristic evolution of contact resistance: a rapid initial decrease followed by a gradual increase, maintaining relatively stable conditions until muzzle exit. Mechanistically, the early−stage decrease is attributed to transverse Lorentz forces that enlarge the contact area, while the later−stage stability is governed by thermal expansion, preserving contact pressure. Parametric studies further elucidate the influence of operating conditions on contact resistance. Full article
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25 pages, 34199 KB  
Article
Numerical Investigation of Stepped Ram-Air Inlets for Air Capture and Thermal Management in a UAV Power Cabin
by Qiu Zhang, Xin Qiao and Xinmin Chen
Modelling 2026, 7(4), 171; https://doi.org/10.3390/modelling7040171 - 18 Aug 2026
Viewed by 245
Abstract
Unmanned aerial vehicles (UAVs) used in low-altitude mobility and electric aviation are increasingly required to carry higher payloads, operate for longer durations and maintain reliable performance under constrained installation conditions. In compact power cabins, batteries, controllers, power distribution units and auxiliary actuators are [...] Read more.
Unmanned aerial vehicles (UAVs) used in low-altitude mobility and electric aviation are increasingly required to carry higher payloads, operate for longer durations and maintain reliable performance under constrained installation conditions. In compact power cabins, batteries, controllers, power distribution units and auxiliary actuators are densely arranged, making cabin thermal management a critical design issue. In this study, a full-scale conjugate flow and heat transfer model is developed for the power cabin of a UAV and validated against thermal management experiments. The validated model is then used to examine how a conventional rectangular ram-air inlet and a proposed stepped ram-air inlet affect air capture, internal flow organization and temperature distribution. The inlet area of the rectangular configuration is first varied to establish a baseline, after which the transition arc ratio, spacing ratio and area ratio of the stepped inlet are parametrically investigated. The results show that increasing the rectangular inlet area from 0.002 to 0.008 m2 increases the total captured mass flow rate from 0.258 to 1.084 kg/s, whereas the cabin average temperature decreases by 0.34 °C. By contrast, the cabin maximum temperature decreases nonlinearly, with a 27.2% reduction when the area increases from 0.004 to 0.006 m2. These results indicate that air capture and the cabin average temperature alone are insufficient to evaluate cooling effectiveness in a compact multi-source cabin. For the stepped inlet, the transition arc ratio controls the turning of the incoming flow, the spacing ratio governs shielding and backflow between adjacent inlet sections, and the area ratio redistributes the dominant inlet sections. The best-performing stepped-inlet configuration among the tested cases increases the captured mass flow rate by 32.8% compared with the rectangular baseline under the same opening constraint and improves the utilization of cooling air around high heat load components. This study demonstrates that ram-air inlet design for UAV power cabins should be treated as a coupled problem of the mass flow capture, internal flow path and component-level thermal response. Full article
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33 pages, 44090 KB  
Article
Dynamic Modeling and Self-Tuning Fuzzy Skyhook Control of a Metro Vehicle with a Flexible Carbody and Semi-Active Suspension
by Hao Song, Wei Han, Yi You, Wei Min and Jianxu Shi
Modelling 2026, 7(4), 170; https://doi.org/10.3390/modelling7040170 - 17 Aug 2026
Viewed by 244
Abstract
Lightweight metro carbodies may exhibit elastic modes within ride-comfort-relevant frequency bands, limiting semi-active suspension controllers tuned offline for nominal conditions. This study proposes a skyhook-based parameter self-tuning fuzzy control (PSTFC) strategy for lateral secondary suspension. Its rule base and membership functions remain fixed, [...] Read more.
Lightweight metro carbodies may exhibit elastic modes within ride-comfort-relevant frequency bands, limiting semi-active suspension controllers tuned offline for nominal conditions. This study proposes a skyhook-based parameter self-tuning fuzzy control (PSTFC) strategy for lateral secondary suspension. Its rule base and membership functions remain fixed, whereas two input quantization factors and one output scaling factor are updated online from the carbody lateral velocity and carbody–bogie relative lateral velocity, enabling state-dependent adaptation without increasing fuzzy-inference complexity. A rigid–flexible coupled multibody model is developed using Craig–Bampton component-mode synthesis and validated against field vibration measurements from a Type-A metro lead car. The controller is evaluated using ADAMS/Rail–MATLAB co-simulation, with robustness examined through repeated stochastic simulations and variations in vehicle speed, passenger load, track-irregularity intensity, and suspension parameters. The flexible model reproduces the measured location-dependent spectral characteristics more accurately than the rigid-carbody model. Under nominal conditions, PSTFC reduces the rear-carbody lateral-acceleration RMS from 0.1341 to 0.1015 m/s2 and the Sperling ride comfort index from 1.5485 to 1.2864, corresponding to improvements of 24.3% and 16.9% over passive suspension. Relative to fixed-parameter fuzzy skyhook control, the two indicators are further reduced by 5.8% and 4.7%, respectively. The improvement persists across the investigated off-nominal conditions without controller retuning. These results demonstrate that state-dependent parameter scaling improves the adaptability of fuzzy skyhook control while retaining a compact inference structure, providing a computationally tractable approach to flexible-carbody vibration suppression. Full article
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29 pages, 7391 KB  
Article
A Hybrid Momentum-Based Optimization and Gaussian Process Regression Modeling Framework with MEREC-CR Weighting for Sustainable Turning Operations
by Emonena Ithipri, Festus I. Ashiedu, Ikuobase Emovon, Olusegun D. Samuel, Manjunath Patel Gowdru Chandrashekarappa, Davannendran Chandran and Ganesh Ravi Chate
Modelling 2026, 7(4), 169; https://doi.org/10.3390/modelling7040169 - 17 Aug 2026
Viewed by 403
Abstract
Sustainable machining of composite materials requires optimizing conflicting responses influenced by limited experimental datasets, trade-offs, nonlinear process variables, and response variability. This study proposes a hybrid framework (Gaussian Process Regression—Method based on the Removal Effects of Criteria—Criteria Reliability—Momentum-Based Optimization Algorithm: GPR–MEREC-CR–MOA) to address [...] Read more.
Sustainable machining of composite materials requires optimizing conflicting responses influenced by limited experimental datasets, trade-offs, nonlinear process variables, and response variability. This study proposes a hybrid framework (Gaussian Process Regression—Method based on the Removal Effects of Criteria—Criteria Reliability—Momentum-Based Optimization Algorithm: GPR–MEREC-CR–MOA) to address these challenges in turning composite materials (PA66, PA66 + GF30, and PA66 + MoS2). The GPR model learns from small datasets to capture nonlinear relationships between machining variables (workpiece material, tool approach angle, tool nose radius, cutting speed, feed rate, depth of cut) and performance characteristics (surface roughness, cutting force, vibration, tool wear rate, temperature, sound pressure level, specific cutting energy, and material removal rate). The MEREC-CR method considers experimental dispersion and response variability to enhance the robustness of the multi-response aggregation model. The weighted responses determined by MEREC were optimized by exploring the operating ranges of machining variables using MOA. The GPR model accurately predicts eight performance characteristics (R2 ≥ 0.973). The GPR–MEREC-CR–MOA model identified optimal conditions for PA66 + MoS2 and composite material (tool angle = 93°, nose radius = 0.40 mm, cutting speed = 200 m/min, feed rate = 0.300 mm/rev, depth of cut = 1.08 mm), resulting in a composite performance index (CPI) of 0.9265 and a 30.2% improvement over the best experimental datasets from Taguchi L27 design. The tool wear rate, specific cutting energy, and vibration have a significant impact on overall machining performance. Feed rate has the strongest influence on CPI, as confirmed by Partial Rank Correlation Coefficients analysis. Monte Carlo-driven uncertainty analysis validates the optimal solution with a 95% confidence level for CPI between 0.8859 and 0.9451. External validation with nine independent cases confirmed the GPR model’s strong generalizability (R2 = 0.811–0.998). Benchmarking showed that MOA achieves solution quality comparable to GA, PSO, and GWO while reducing computational time by 66–86%, making it suitable for real-time optimization. The proposed hybrid framework provides an alternative data-driven decision support approach for evaluating sustainable machining parameters using limited experimental datasets of polymer composites. Full article
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26 pages, 28226 KB  
Article
CFD Modelling and Perturbation-Based Analytical Approach for Rapid Tank Farm Failure Time Prediction Under Wind-Influenced Fire-Induced Domino Effects
by Rafat Al-Waked, Asher Ahmed Malik and Mohammad Shakir Nasif
Modelling 2026, 7(4), 168; https://doi.org/10.3390/modelling7040168 - 15 Aug 2026
Cited by 1 | Viewed by 512
Abstract
Fire-induced domino effects in tank farms can be catastrophic, particularly under wind conditions. However, due to multiple evolutionary stages, Computational Fluid Dynamics (CFD)-based modelling of wind-influenced, fire-induced domino effects and tank farm Time to Failure (TTF) calculation remain computationally expensive. This study addresses [...] Read more.
Fire-induced domino effects in tank farms can be catastrophic, particularly under wind conditions. However, due to multiple evolutionary stages, Computational Fluid Dynamics (CFD)-based modelling of wind-influenced, fire-induced domino effects and tank farm Time to Failure (TTF) calculation remain computationally expensive. This study addresses this gap by using Fire Dynamics Simulator (FDS) to model fire-induced domino effects in a tank farm and perform detailed tank farm TTF calculations across multiple wind speeds and primary pool fire scenarios. The FDS results showed that increasing wind speed from 0 to 8 m/s altered domino escalation, increasing incident heat flux on the downwind in-line tank by more than sevenfold (a 35% reduction in tank farm TTF). A new perturbation-based analytical formulation was then proposed for rapid determination of tank farm TTF under wind effects, without requiring complete CFD simulations of pool fire escalation. The formulation updates tank farm TTF under the no-wind baseline solution with wind-influenced perturbative correction terms. The proposed formulation agreed with the detailed CFD modelling-based calculation, with a mean relative error of 2.8% across all primary fire scenarios and wind conditions. This formulation provides a practical basis for rapid assessment of domino effects due to pool fire under wind conditions. However, it is calibrated for one specific six-tank configuration and crosswind directions and is not yet general. Full article
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26 pages, 956 KB  
Article
Optimal Item Placement for Information Retrieval in Stochastic Paired Comparison Models Under Special Comparison Structures
by László Gyarmati, Csaba Mihálykó and Éva Orbán-Mihálykó
Modelling 2026, 7(4), 167; https://doi.org/10.3390/modelling7040167 - 14 Aug 2026
Viewed by 275
Abstract
Paired comparison models are examined from the perspective of the placement of objects within specific comparison structures. For both pairwise comparison matrix-based models and stochastic models, previous studies have examined which comparison structures maximize the amount of information that can be recovered from [...] Read more.
Paired comparison models are examined from the perspective of the placement of objects within specific comparison structures. For both pairwise comparison matrix-based models and stochastic models, previous studies have examined which comparison structures maximize the amount of information that can be recovered from incomplete comparisons. In this paper, we investigate how the amount of extracted information can be increased in stochastic paired comparison models—primarily the Bradley–Terry model—by way of exploiting prior information about the ranking of the objects, if such information is available. We examine several comparison structures to identify the optimal placement of objects within each structure with respect to information recovery and evaluability. The investigated structures are the star graph, the union of two star graphs, and the union of two edge-disjoint spanning trees. Parameters are estimated using the maximum likelihood method. The applied evaluation metrics are the Euclidean distance, Pearson, Spearman, and Kendall correlations, called similarity metrics. Moreover, the rate of evaluable datasets and an inconsistency index is also computed. We found that, in almost all cases, all four similarity metrics identified the same placement as optimal. Our results show that, for the star graph, placing an object of medium strength at the center and comparing all other object to it maximizes the amount of information recovered from the comparisons. For the union of two star graphs, placing objects that occupy middle positions in the ranking at the centers also outperforms the commonly used best–worst centered placement. However, the union of two edge-disjoint spanning trees provides, on average, even better information recovery based on all investigated metrics. We also examined the proportion of evaluable datasets and found it to be higher when medium-strength objects were placed at the centers. Finally, we compared the findings obtained from the stochastic models with those from pairwise comparison matrix-based models and observed strong agreement between the two approaches. Full article
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19 pages, 21595 KB  
Article
Prior-Guided Histogram Equalization for Tunnel Image Enhancement Under Non-Uniform Illumination
by Guang Yang, Haoyue Yang and Yongjun Wu
Modelling 2026, 7(4), 166; https://doi.org/10.3390/modelling7040166 - 14 Aug 2026
Viewed by 631
Abstract
Non-uniform illumination in tunnel environments severely degrades image quality, posing substantial challenges to visual monitoring and intelligent transportation systems. While histogram equalization (HE) remains prevalent due to its computational simplicity, its non-linear pixel transformations frequently induce over-enhancement, artifacts, and structural distortions. This paper [...] Read more.
Non-uniform illumination in tunnel environments severely degrades image quality, posing substantial challenges to visual monitoring and intelligent transportation systems. While histogram equalization (HE) remains prevalent due to its computational simplicity, its non-linear pixel transformations frequently induce over-enhancement, artifacts, and structural distortions. This paper proposes Prior-Guided Histogram Equalization (PGHE), a lightweight enhancement framework that integrates conventional HE with Retinex-based illumination priors. Within the Retinex decomposition paradigm, PGHE constructs a contrast illumination map from the ratio between the HE-enhanced image and the original input. A Prior Correction Module (PCM) subsequently refines this map via relative total variation regularization, thereby restoring spatial coherence and alleviating local discontinuities introduced by HE. The corrected map is then applied to the original image to obtain the final enhanced result. Extensive evaluation on the LOL low-light benchmarks and a proprietary tunnel dataset comprising 247 real-world frames shows that PGHE offers favorable trade-offs among contrast enhancement, structural fidelity, and brightness preservation: it is particularly strong in brightness preservation and Entropy, while its PSNR/SSIM on LOL and its NIQE on the tunnel dataset are comparable to, but not always the best among, the compared methods. Furthermore, the proposed PCM functions as a plug-in module that improves existing HE variants with measurable gains in Structural Similarity and perceived naturalness at a modest cost in Absolute Mean Brightness Error. Full article
(This article belongs to the Section Modelling in Artificial Intelligence)
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24 pages, 1843 KB  
Article
A Solver-Independent Declarative Material Layer for Compile-Time Integration of Symbolic Constitutive Models
by Rahil Miten Doshi and Matthias Markl
Modelling 2026, 7(4), 165; https://doi.org/10.3390/modelling7040165 - 14 Aug 2026
Viewed by 329
Abstract
Constitutive models define how physical properties depend on evolving state variables, and consequently have a strong influence on computational simulations. However, material descriptions are commonly embedded within solver implementations, limiting their reusability and exchangeability. We introduce a declarative material layer that separates state-dependent [...] Read more.
Constitutive models define how physical properties depend on evolving state variables, and consequently have a strong influence on computational simulations. However, material descriptions are commonly embedded within solver implementations, limiting their reusability and exchangeability. We introduce a declarative material layer that separates state-dependent material descriptions from numerical solvers and that integrates material behavior into the generated solver code. Material properties are represented symbolically, allowing constitutive relations to be defined independently of discretization methods and reused across different simulation frameworks without solver-specific modifications. A reference implementation demonstrates the compile-time integration of this approach into code-generated solvers for one reference code generation backend. Flow and thermal diffusion benchmarks show that identical constitutive descriptions can be applied consistently across different numerical methods while preserving physical behavior. Performance measurements reveal that the computational impact depends on the interaction between constitutive model complexity and solver characteristics. The proposed declarative material layer opens up the possibility of reusable and solver-independent integration of state-dependent constitutive models into high-performance simulation workflows. Full article
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25 pages, 25893 KB  
Article
NURBS-Driven Modelling of Interface Geometric Errors in Aero-Engine Casings for Assembly Analysis
by Xiaole Guan, Xin Jin and Zhijing Zhang
Modelling 2026, 7(4), 164; https://doi.org/10.3390/modelling7040164 - 13 Aug 2026
Viewed by 267
Abstract
Assembly-oriented geometric models of aero-engine casings require the spatial distribution of deviations at mating interfaces. Conventional scalar descriptors, including flatness, axial runout, and radial runout, cannot retain this information. This study proposes a measurement-driven integrated modelling method based on measured point clouds. After [...] Read more.
Assembly-oriented geometric models of aero-engine casings require the spatial distribution of deviations at mating interfaces. Conventional scalar descriptors, including flatness, axial runout, and radial runout, cannot retain this information. This study proposes a measurement-driven integrated modelling method based on measured point clouds. After boundary completion, gross-error removal, and Gaussian filtering, the interface morphology is reconstructed as a tensor-product cubic B-spline surface in unit-weight non-uniform rational B-spline (NURBS) form. The reconstructed surface is then integrated with the nominal computer-aided design (CAD) model. Validation was performed using two cuboidal specimens and three representative casing flange surfaces. The relative differences between the reconstructed and measured flatness values of the cuboidal specimens were 8.58% and 1.04%. At the withheld verification points of the casing flange surfaces, the mean absolute reconstruction errors were 0.0022 mm, 0.0017 mm, and 0.0049 mm. These results show that measured interface morphology can be transferred into a CAD-compatible component model while retaining its spatial characteristics. The present study provides a geometric basis for subsequent assembly analysis. Full article
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18 pages, 1652 KB  
Article
Sustainable Roofing in Hot Climates: A Comparative Lifecycle Assessment of Residential Buildings in Saudi Arabia
by Raheemat O. Yussuf, Omar S. Asfour, Ahmed Abd El Fattah and Muhammad Asif
Modelling 2026, 7(4), 163; https://doi.org/10.3390/modelling7040163 - 11 Aug 2026
Viewed by 408
Abstract
Roofing systems strongly influence the energy performance and environmental footprint of buildings, particularly in hot–arid climates such as Saudi Arabia, where cooling dominates electricity demand; however, the comparative lifecycle environmental performance of alternative roofing strategies remains underexplored in this specific climatic and market [...] Read more.
Roofing systems strongly influence the energy performance and environmental footprint of buildings, particularly in hot–arid climates such as Saudi Arabia, where cooling dominates electricity demand; however, the comparative lifecycle environmental performance of alternative roofing strategies remains underexplored in this specific climatic and market context. This study therefore aims to evaluate and compare the environmental performance of four sustainable roofing strategies against a conventional flat roof (FR) baseline in order to provide evidence-based guidance for climate-specific roofing selection in Saudi Arabia. This study conducts a comparative cradle-to-grave lifecycle assessment (LCA) of four sustainable roofing strategies considering the hot–arid climate of Saudi Arabia. Green roof (GR), cool roof (CR), solar photovoltaic roof (SPV), and roof canopy (RC) were assessed using the ReCiPe 2016 method in the SimaPro software. The environmental impacts of these strategies were assessed across product, construction, use, and end-of-life stages relative to conventional flat roofs (FRs). The results indicate that the production stage consistently contributes the highest environmental impacts, with increases ranging from 30 to 3000% for GR, CR, and RC and exceeding 10,000% for SPV. On the other hand, the use stage offers the greatest reductions ranging from 10 to 200%, particularly for SPV and CR, due to operational energy savings and electricity generation. Overall, CR demonstrates the most balanced environmental performance, combining high impact reductions with minimal trade-offs, while SPV provides significant climate and fossil resource benefits but increases mineral resource use. These findings highlight the importance of climate-specific and resource-conscious selection of roofing strategies in Saudi Arabia and provide a transferable comparative LCA framework that can inform sustainable roofing decisions in other hot–arid and hot–humid regions, in support of the Kingdom’s Vision 2030 objectives for sustainable urban development. Full article
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32 pages, 7394 KB  
Article
Collaborative Robust Multi-Objective Optimization of Electrode Air-Flotation Drying Under Equipment Aging Uncertainty
by Juchen Hong, Xue Feng and Zhengyun Ren
Modelling 2026, 7(4), 162; https://doi.org/10.3390/modelling7040162 - 9 Aug 2026
Viewed by 243
Abstract
In the wet-process stage of lithium-ion battery manufacturing, double-sided coating combined with air-flotation drying can reduce repeated drying operations, thereby helping improve production throughput. However, the requirements of air-flotation drying for equipment stability, together with the coupling among process parameters such as temperature, [...] Read more.
In the wet-process stage of lithium-ion battery manufacturing, double-sided coating combined with air-flotation drying can reduce repeated drying operations, thereby helping improve production throughput. However, the requirements of air-flotation drying for equipment stability, together with the coupling among process parameters such as temperature, air velocity, and tension, substantially increase the difficulty of process-parameter calibration. As critical components degrade over time, deviations arise between nominal process parameters and actual operating conditions, introducing non-negligible uncertainty and further complicating parameter recalibration. This paper proposes a collaborative robust multi-objective optimization algorithm to obtain stable and reliable process-parameter combinations under limited computational resources. Specifically, multi-objective optimization models are first established. Then, the operating condition of new equipment is approximately formulated as an undisturbed auxiliary optimization problem, whereas the operating condition of aged equipment with parameter perturbations is formulated as a robust optimization problem; surrogate models are constructed for both problems. Finally, search information from the auxiliary problem is used to guide the evolution of the robust optimization problem, thereby improving its optimization efficiency. Experimental results demonstrate that the proposed algorithm can obtain robust Pareto solutions with favorable convergence and diversity while consuming fewer resources, providing engineers with reliable references for selecting suitable process parameters. Full article
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20 pages, 581 KB  
Article
Modelling of Davenport and Kaimal Wind Spectra with a Stochastic Differential Operator in Multiple Frequency Domains
by Guo-Kang Er, Chang Tian and Haofan Wu
Modelling 2026, 7(4), 161; https://doi.org/10.3390/modelling7040161 - 7 Aug 2026
Viewed by 365
Abstract
Accurate probabilistic analysis of wind-induced structural vibration is essential for accurately analyzing structural safety and serviceability. Though the FPK equation offers a tool for analysis, its application is challenged by the noise characteristics of wind spectra, such as the Davenport and Kaimal spectra. [...] Read more.
Accurate probabilistic analysis of wind-induced structural vibration is essential for accurately analyzing structural safety and serviceability. Though the FPK equation offers a tool for analysis, its application is challenged by the noise characteristics of wind spectra, such as the Davenport and Kaimal spectra. Using the conventional second-order linear filter model to fit Davenport and Kaimal spectra tends to underestimate their spectral energy in the mid-to-high-frequency range. To address this limitation, this paper proposes an improved second-order filter model that enhances fidelity without increasing filter dimensionality. This model is complemented by an optimization strategy based on the idea that the frequency range is partitioned, which generates three models specifically for low-, mid-, and high-frequency ranges. These models can better fit Davenport and Kaimal spectra in a much larger frequency range compared to the conventional model. The effectiveness of the proposed models is validated through numerically analyzing a linear SDOF stochastic oscillator and a nonlinear stochastic SDOF oscillator in various cases. The results demonstrate that the proposed models maintain exceptional accuracy across a wide range of structural natural frequencies. Full article
(This article belongs to the Section Modelling in Engineering Structures)
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19 pages, 10800 KB  
Article
Sound Absorption and Transmission Loss of Lightweight Powders Under Longitudinal Vibration: Application of a Frequency-Dependent Complex Modulus to a One-Dimensional Beam Model
by Shuichi Sakamoto, Hiroaki Soeta, Yosuke Kubo, Okuda Taichi and Odashima Takeomi
Modelling 2026, 7(4), 160; https://doi.org/10.3390/modelling7040160 - 7 Aug 2026
Viewed by 266
Abstract
A powder layer was treated as a one-dimensional beam undergoing longitudinal vibration, and the loss factor was derived from the damping ratio based on Rayleigh damping, thereby introducing frequency dependence into the complex modulus. The transfer matrix of the powder layer was subsequently [...] Read more.
A powder layer was treated as a one-dimensional beam undergoing longitudinal vibration, and the loss factor was derived from the damping ratio based on Rayleigh damping, thereby introducing frequency dependence into the complex modulus. The transfer matrix of the powder layer was subsequently formulated based on the complex modulus, and the validity and effectiveness of the proposed model were evaluated by comparing the calculated and measured values of transmission loss and sound-absorption coefficient. A loss correction was introduced to account for energy dissipation associated with viscous boundary-layer effects and other dissipative mechanisms. A parametric study of the loss correction was conducted, and the correction was quantitatively incorporated through curve fitting based on the root mean square error (RMSE). Comparison of theoretical and experimental transmission loss values revealed that the increasing trend in transmission loss at high frequencies was captured by the proposed model. In the comparison between the experimental and theoretical sound absorption coefficients, this evaluation approach places greater emphasis on the average degree of agreement across the full measurement frequency range rather than at specific frequency points. Consequently, the loss correction yielding the minimum error across the entire frequency range was selected, which occasionally resulted in differences in peak values near the first-order peak frequency. Full article
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16 pages, 2466 KB  
Article
Impact of Geometric and Modelling Discrepancies on the Dispersion Dynamics of Lattice Metastructures
by Krishnaraj Vilasraj Bhat, Ignacio Martínez-Terés, Pablo Pflueger Tejero, Juan García-Martínez and Francisco J. Montans
Modelling 2026, 7(4), 159; https://doi.org/10.3390/modelling7040159 - 6 Aug 2026
Viewed by 349
Abstract
Mechanical metamaterials (MMMs) are periodic architectures engineered to achieve extraordinary macroscopic mechanical properties. A primary objective in their design is wave propagation isolation, achieved through the generation of phononic bandgaps. These bandgaps are highly sensitive to the geometric features of the underlying unit [...] Read more.
Mechanical metamaterials (MMMs) are periodic architectures engineered to achieve extraordinary macroscopic mechanical properties. A primary objective in their design is wave propagation isolation, achieved through the generation of phononic bandgaps. These bandgaps are highly sensitive to the geometric features of the underlying unit cell, which is frequently based on a lattice topology. While additive manufacturing has become the predominant approach for fabricating these MMMs, a persistent challenge remains: standard finite element (FE) models based on nominal designs may differ from both the manufactured geometry and its numerical representation. In this context, manufacturing-induced geometric deviations and FE modelling discrepancies can both lead to dispersion characteristics that diverge from the intended behaviour. The present work focuses on the latter through a controlled numerical sensitivity study. This work assesses the impact of these FE modelling errors on the dynamic response of lattice metastructures by simulating structural deviations through conditional node addition and relocation. Specifically, we investigate the influence of two distinct scenarios that lead to significantly different outcomes: nodes subjected to Floquet–Bloch periodic boundary conditions, and interior nodes unaffected by these boundary constraints. Finally, a quantitative threshold for the maximum permissible modeling error is established for each case. Full article
(This article belongs to the Section Modelling in Mechanics)
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25 pages, 11632 KB  
Article
Hierarchical Clustering and Schur Complement for Automatic Hyperspectral Band Selection
by Valérie N’Guessan Gboulouhonon Komenan N’dri, Kacoutchy Jean Ayikpa, Pierre Gouton and Vincent Oria
Modelling 2026, 7(4), 158; https://doi.org/10.3390/modelling7040158 - 5 Aug 2026
Viewed by 388
Abstract
Band selection is a crucial step in hyperspectral imaging to reduce spectral redundancy and processing costs whilst retaining information useful for classification. Most existing approaches require the number of bands to be retained to be set manually or rely on parameters that are [...] Read more.
Band selection is a crucial step in hyperspectral imaging to reduce spectral redundancy and processing costs whilst retaining information useful for classification. Most existing approaches require the number of bands to be retained to be set manually or rely on parameters that are difficult to adjust. This work proposes the Clustering-Unified Schur complement for Diversity with Hierarchical Clustering (CUSD-HC). This fully unsupervised band selection method combines Ward’s hierarchical clustering with a greedy selection based on the Schur complement. Bands are grouped by spectral similarity, and then a representative band is chosen from each group to preserve diversity and informational content. The number of bands is determined automatically using a multi-detector k-fold criterion combined with an intrinsic dimension threshold estimated via PCA. Evaluated on six benchmark datasets using four classifiers (SVM-RBF, Random Forest, XGBoost, LightGBM), CUSD-HC achieves an average rank of between 2.7 and 3.3 among nine compared methods, placing it consistently among the leading group. The Nemenyi test shows no statistically significant difference between CUSD-HC and the top-ranked competitors, while CUSD-HC significantly outperforms the weakest baselines (p < 0.05); unlike the best-ranked alternatives, it reaches this level of performance without any manual selection of the number of bands, which is determined automatically from the data. An inter-scene transferability experiment on the WHU-Hi datasets shows a maximum degradation of 3.9 points in overall accuracy (OA), and the transferred bands even outperform the native selection in three cases out of six. Furthermore, the selected bands naturally cover the main spectral regions (visible, near-infrared, and SWIR), which facilitates the interpretation of results for applications such as precision agriculture and environmental monitoring. Full article
(This article belongs to the Topic Computer Vision and Image Processing, 3rd Edition)
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18 pages, 1924 KB  
Article
Context-Gated Graph Modelling for Traffic Flow Forecasting
by Yuzhuo Zhang, Jialin Liang, Ziqiong Yuan, Zanzan Dai and Yaozheng Kang
Modelling 2026, 7(4), 157; https://doi.org/10.3390/modelling7040157 - 5 Aug 2026
Viewed by 215
Abstract
Traffic states evolve on irregular sensor graphs and vary with calendar context, yet the original ASTGCN does not explicitly model how the contribution of different graph receptive fields changes across traffic periods. This paper proposes CD-MRFG, a context-gated extension of ASTGCN that encodes [...] Read more.
Traffic states evolve on irregular sensor graphs and vary with calendar context, yet the original ASTGCN does not explicitly model how the contribution of different graph receptive fields changes across traffic periods. This paper proposes CD-MRFG, a context-gated extension of ASTGCN that encodes hour-of-day, day-of-week and weekend information and uses the resulting representation to weight Chebyshev graph-convolution orders in each spatio-temporal block. Under a common 12-step forecasting protocol, CD-MRFG reduced the overall MAE and RMSE of the reproduced ASTGCN baseline from 18.66 and 31.05 to 16.98 and 28.59 on PEMS03, from 22.79 and 35.02 to 20.82 and 32.77 on PEMS04, and from 18.88 and 28.83 to 17.24 and 26.84 on PEMS08. Three-seed experiments confirmed lower mean MAEs on PEMS04 (p = 0.028) and PEMS08 (p = 0.042), although the corresponding RMSE differences did not reach the 0.05 significance threshold. Ablation, gate-weight, sensitivity, complexity and convergence analyses showed that temporal context was the main source of the improvement and that the gate provided a model-internal view of order selection with moderate overhead. CD-MRFG remains less accurate than several stronger recent baselines, so its value is a bounded and interpretable extension of ASTGCN rather than a universal state-of-the-art replacement. Full article
(This article belongs to the Section Modelling in Artificial Intelligence)
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28 pages, 6016 KB  
Article
Surrogate Modeling and Optimization of a Dual-Band Circular Patch Antenna with a C-Shaped Slot Using MLP Neural Networks
by Ksenija Mladenović, Ivan Milovanović, Zoran Stanković, Olivera Pronić Rančić and Nebojša Dončov
Modelling 2026, 7(4), 156; https://doi.org/10.3390/modelling7040156 - 4 Aug 2026
Viewed by 231
Abstract
This paper presents an efficient framework for surrogate modeling and rapid optimization of a dual-band circular patch antenna with a C-shaped slot (DB-CPAC) using multilayer perceptron (MLP) neural networks. Although highly accurate, traditional full-wave electromagnetic simulations are computationally expensive for geometric optimization due [...] Read more.
This paper presents an efficient framework for surrogate modeling and rapid optimization of a dual-band circular patch antenna with a C-shaped slot (DB-CPAC) using multilayer perceptron (MLP) neural networks. Although highly accurate, traditional full-wave electromagnetic simulations are computationally expensive for geometric optimization due to complex slot-induced surface current perturbations. To address this limitation, a hybrid optimization framework based on Latin Hypercube Sampling (LHS) is proposed, combining the developed MLP model with a Method-of-Moments (MoM) simulator. The surrogate model uses an advanced modular architecture consisting of an ensemble of MLP neural networks for regressing center frequencies and classification MLP modules with a softmax output layer to estimate the probabilities of achieving bandwidth and gain targets. All networks are trained using the Levenberg–Marquardt algorithm with early stopping on data generated by a dedicated DB-CPAC_MoM_Sim software package. The proposed LHS-based optimizer employs the surrogate model for rapid global search and targeted local optimization before final MoM verification. Results show that this hybrid approach achieves an order-of-magnitude acceleration of the optimization process compared to conventional MoM methods while maintaining high accuracy. Full article
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19 pages, 6315 KB  
Article
Stochastic Dynamic Response Analysis of Spherical Roller Thrust Bearings Based on Improved Deep Neural Network
by Chenyao Wan, Zheng Li, Xiaoqian Ma, Yongshou Liu and Wei Sun
Modelling 2026, 7(4), 155; https://doi.org/10.3390/modelling7040155 - 4 Aug 2026
Viewed by 303
Abstract
The roller–raceway contact response is a key factor affecting stress concentration, fatigue initiation, and raceway spalling in spherical roller thrust bearings. Uncertainty analysis of this response is therefore important for revealing how practical parameter fluctuations affect bearing contact behavior and for supporting robust [...] Read more.
The roller–raceway contact response is a key factor affecting stress concentration, fatigue initiation, and raceway spalling in spherical roller thrust bearings. Uncertainty analysis of this response is therefore important for revealing how practical parameter fluctuations affect bearing contact behavior and for supporting robust bearing design and operating-condition optimization. In this paper, a multibody dynamic model of a spherical roller thrust bearing is established by explicitly considering the main internal contact pairs, including roller–raceway, roller–flange, roller–cage, and cage–guide interactions. The model is used to obtain the transient roller–raceway contact loads under coupled axial loading and rotational motion. The resulting contact loads are introduced into a finite element contact model to evaluate the dynamic contact stress response of the inner raceway. To assess the effects of random uncertainties on this response, an improved deep neural network (DNN) surrogate model is developed. An attention mechanism deep neural network (AM-DNN) is improved by incorporating feature importance information from random forest (RF) into its attention mechanism, and the resulting model is denoted by RF-AM-DNN. Validation on the generated dataset demonstrates that the proposed RF-AM-DNN outperforms conventional surrogate models in prediction accuracy. Finally, the RF-AM-DNN is used to investigate the uncertainty characteristics of dynamic contact stress in spherical roller thrust bearings under multiple uncertainty factors. Full article
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26 pages, 10962 KB  
Article
A Macro-Constitutive Damage Modelling Framework for Biomass-Modified Cement Mortars Under Compressive Loading: Experimental Calibration and Sustainability Assessment
by Omid Hassanshahi, Nima Azimi, Mohammad Bakhshi, Diāna Bajāre and Shaghayegh Karimzadeh
Modelling 2026, 7(4), 154; https://doi.org/10.3390/modelling7040154 - 3 Aug 2026
Cited by 1 | Viewed by 511
Abstract
The integration of bio-based constituents into cementitious materials requires robust predictive models capable of describing mechanical degradation while supporting sustainability-driven material design. This study presents a macro-constitutive damage modelling framework for biomass-modified cement mortars subjected to monotonic compressive loading, combining experimental characterisation, continuum [...] Read more.
The integration of bio-based constituents into cementitious materials requires robust predictive models capable of describing mechanical degradation while supporting sustainability-driven material design. This study presents a macro-constitutive damage modelling framework for biomass-modified cement mortars subjected to monotonic compressive loading, combining experimental characterisation, continuum damage mechanics (CDM), and life-cycle assessment (LCA). The calibrated parameters are interpreted in terms of meso-scale mechanisms, but the study does not constitute a direct imaging-based multiscale characterisation. Mortars containing 0–10% dried microalgal biomass as a partial replacement for binder mass were investigated through their complete compressive stress–strain response. A scalar damage variable was employed to model stiffness degradation and progressive microcrack evolution, enabling the identification of elastic-modulus reduction, damage-initiation thresholds, softening behaviour, and residual load-bearing capacity. A thermodynamically consistent Mazars-type damage model was calibrated against the measured envelopes and internally verified by reproducing the same pre-peak and post-peak responses, with coefficients of determination ranging from 0.979 to 0.996. Increasing biomass content reduced the 28-day compressive strength from 47.8 to 23.7 MPa and the elastic modulus from 27.5 to 14.9 GPa, while increasing the damage level at peak load from 0.26 to 0.46 and promoting a more gradual post-peak softening response. The calibrated law provides a compact constitutive representation within the tested replacement range; independent external validation is still required before extrapolation to other biomass types, mixture proportions, or curing regimes. In parallel, a cradle-to-gate LCA quantified global warming, acidification, eutrophication, ozone depletion, and abiotic depletion potentials. An integrated carbon-efficiency index was used to relate mechanical performance to environmental impact. Biomass replacement reduced global warming potential by up to 7.7% but increased eutrophication potential, highlighting a clear performance–environment trade-off. Despite the reduction in mechanical properties, all mixtures satisfied masonry-unit strength requirements, supporting the application of biomass-modified mortars in low-carbon concrete masonry units. The proposed framework demonstrates how experimentally calibrated damage models can support the structural assessment and sustainable development of emerging bio-based cementitious materials. Full article
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45 pages, 3615 KB  
Review
Discrete Element Method in Agricultural Machinery Design: A Critical Review of Applications, Validation Practices, and Implementation Challenges
by Gustavo de Mello, Ricardo Rodrigues Magalhães and Fernando Elias de Melo Borges
Modelling 2026, 7(4), 153; https://doi.org/10.3390/modelling7040153 - 31 Jul 2026
Cited by 1 | Viewed by 722
Abstract
The discrete element method (DEM) has become an important numerical tool for investigating the interactions between agricultural machinery and granular agricultural materials. By enabling the analysis of particle-scale dynamics and macroscopic system behavior, the DEM provides valuable support for the design, optimization, and [...] Read more.
The discrete element method (DEM) has become an important numerical tool for investigating the interactions between agricultural machinery and granular agricultural materials. By enabling the analysis of particle-scale dynamics and macroscopic system behavior, the DEM provides valuable support for the design, optimization, and performance evaluation of agricultural equipment. This paper presents a comprehensive review of advances in the application of the DEM in agricultural machinery, with particular emphasis on material modeling, parameter calibration strategies, and the simulation of machine operational processes. First, the establishment of DEM models for major agricultural materials, including soil, seeds, and plant residues, is analyzed, highlighting commonly adopted contact models and calibration methodologies. Second, the application of the DEM in the simulation of key agricultural operations, such as soil tillage, material conveying, and harvesting processes, is examined to identify current capabilities and limitations. Finally, the main technical challenges and future research directions are discussed, focusing on improving model accuracy, validation practices, and integration with experimental and industrial workflows. Among the studies analyzed, the results showed varying performance when comparing experimental and simulated values, with the best results exhibiting a relative difference of less than 1%. However, persistent challenges regarding transferability and computational cost limit industrial-scale adoption. This review aims to provide an organized framework to guide future developments and promote the effective use of the DEM in the design and optimization of agricultural machinery. Full article
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30 pages, 6553 KB  
Article
Multi-Criteria Decision-Making Framework for Rock Burst Risk Assessment Under Uncertainty: An Integrated Fault Tree–Bayesian Network–Fuzzy Grey Relational Approach
by Chutong Hao, Qingwei Xu, Kaili Xu, Tianwei Shi, Bingjun Li, Yaping Zhu and Wanjun Niu
Modelling 2026, 7(4), 152; https://doi.org/10.3390/modelling7040152 - 29 Jul 2026
Viewed by 389
Abstract
This study develops an integrated risk assessment framework to trace the evolution from multi-factor coupling to systemic failure, using coal mine rock burst as a case study. First, a fault tree containing 56 basic events is established from statistical analysis of accident cases [...] Read more.
This study develops an integrated risk assessment framework to trace the evolution from multi-factor coupling to systemic failure, using coal mine rock burst as a case study. First, a fault tree containing 56 basic events is established from statistical analysis of accident cases from 2010 to 2024. Expert judgment is then combined with fuzzy theory to assign probabilities to basic events, which are further analyzed through a Bayesian Network. Next, differentiated importance measures, including Birnbaum Importance and Fussell–Vesely Importance, are calculated at multiple levels, and gray relational analysis is used to identify the most critical basic events. Results show that management-related factors, particularly insufficient monitoring and inadequate hazard identification, play dominant roles in risk propagation. The Bow-Tie model is subsequently applied to examine inadequate hazard identification in greater depth and to propose targeted preventive measures. Finally, by integrating the comprehensive accident model with chaos theory across the four dimensions of human, machine, environment, and management, the study reveals the internal mechanism of disaster evolution under multi-factor coupling. Validation against objective data confirms the reliability of both probability assignment and critical-event identification. Full article
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18 pages, 5956 KB  
Article
Numerical Investigation of Tip Shape Classification in Dynamic Atomic Force Microscopy Based on the XGBoost Model: A Simulation-Based Study
by Zixuan Zhang, Beirong Han and Xilong Zhou
Modelling 2026, 7(4), 151; https://doi.org/10.3390/modelling7040151 - 29 Jul 2026
Viewed by 322
Abstract
Dynamic atomic force microscopy (AFM) is a key technique for nanoscale characterization and mechanical property measurement, where the geometric shape of the probe tip critically determines imaging quality and measurement accuracy. This study proposes a tip shape classification framework based on the dynamic [...] Read more.
Dynamic atomic force microscopy (AFM) is a key technique for nanoscale characterization and mechanical property measurement, where the geometric shape of the probe tip critically determines imaging quality and measurement accuracy. This study proposes a tip shape classification framework based on the dynamic response of the AFM microcantilever. First, a dimensionless dynamic model of the microcantilever is established, and its vibrational response is solved using a finite-difference scheme. For conical, spherical, and flat tip geometries, interaction force models are provided under both non-contact and tapping-mode AFM. Based on these formulations, multidimensional dynamic feature parameters, including amplitude, phase, virial, and root-mean-square force, are extracted. On this basis, an XGBoost-based classifier is constructed for tip shape identification, and the model’s decision-making mechanism is further interpreted through a SHAP-based explainability framework combined with dimensionality reduction and visualization techniques. Results show that, under non-contact conditions, the overall classification accuracy on the test set reaches 96.7%, with a 100% recognition rate for conical tips. Under tapping-mode conditions, the classification accuracies for conical, spherical, and flat tips are 100%, 85.5%, and 98.3%, respectively. The results demonstrate the feasibility of identifying tip shapes from dynamic responses using simulated data, thereby establishing a theoretical and methodological basis for future experimental validation and the development of tip diagnostic techniques. Full article
(This article belongs to the Section Modelling in Mechanics)
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24 pages, 4940 KB  
Article
Enhanced Disturbance Rejection in Diesel Generator Speed Control Using Adaptive Cascaded LADRC
by Yi Zang and Yuan Ding
Modelling 2026, 7(4), 150; https://doi.org/10.3390/modelling7040150 - 25 Jul 2026
Viewed by 400
Abstract
Diesel generator sets are key frequency-supporting units in islanded microgrids and shipboard power systems, where rapid speed recovery under abrupt load variations is essential for maintaining power quality. However, conventional linear active disturbance rejection control (LADRC) is limited by the disturbance-estimation and noise-amplification [...] Read more.
Diesel generator sets are key frequency-supporting units in islanded microgrids and shipboard power systems, where rapid speed recovery under abrupt load variations is essential for maintaining power quality. However, conventional linear active disturbance rejection control (LADRC) is limited by the disturbance-estimation and noise-amplification trade-off of a single observer, while fixed parameters restrict its adaptability under varying operating conditions. To address these limitations, this paper proposes an RBF neural-network-optimized cascaded LADRC method, termed RBF-CLADRC. A mechanism-based torque balance model is first established, with uncertain mechanical coupling, friction losses, and load variations lumped into the total disturbance. A residual-disturbance cascaded observer is then constructed, in which the first linear extended state observer estimates the total disturbance and the second further reconstructs the residual estimation error. Unlike conventional ML-based ADRC methods that directly tune multiple gains, the proposed RBFNN adjusts only a common controller bandwidth within a prescribed interval, while all observer and feedback gains are generated through predefined analytical relationships. This low-dimensional adaptation preserves coordinated gain variation, reduces online computational complexity, and facilitates real-time implementation. Lyapunov analysis shows that the observer and tracking errors are uniformly ultimately bounded under bounded disturbance rates and converge exponentially for constant disturbances. Finally, comparative simulations in MATLAB/Simulink demonstrate that the proposed method achieves better dynamic response and disturbance-rejection performance than conventional LADRC and other benchmark controllers. Full article
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29 pages, 22307 KB  
Article
Transport Characteristics of Coal Fines and Anti-Deposition Structural Optimization in Standing Valves of Coalbed Methane Drainage Pumps
by Yicheng Wang, Wanzhong Li, Jianning Xu, Yapeng Li and Liaobo Li
Modelling 2026, 7(4), 149; https://doi.org/10.3390/modelling7040149 - 23 Jul 2026
Viewed by 373
Abstract
Stable drainage of coalbed methane wells is essential for reducing reservoir pressure and promoting methane desorption. However, coal fines carried by produced water tend to accumulate and deposit within the standing valves of drainage pumps. To address this common problem, this study investigates [...] Read more.
Stable drainage of coalbed methane wells is essential for reducing reservoir pressure and promoting methane desorption. However, coal fines carried by produced water tend to accumulate and deposit within the standing valves of drainage pumps. To address this common problem, this study investigates the transport characteristics of coal fines within the standing valve during the liquid-dominated water-pumping stage of the plunger upstroke, with the standing valve fully open. Theoretical calculations, numerical simulations, and settling experiments were conducted for three coal fines size fractions of 60–100, 100–200, and 200–400 mesh to validate the model’s predictive capability for coal fines motion. The results show that the RNG k–ε model has the lowest mean absolute relative error, at 14.50%. A solid–liquid two-phase flow model was employed to comparatively analyze five valve seat cone angles ranging from 105° to 165° and representative inlet velocities of 0.1–0.4 m/s. The results indicate that the mixture within the standing valve accelerates markedly while passing through the narrow clearance between the valve ball and the valve seat and then decelerates in the region above the valve ball. The region above the valve ball and the valve seat transition region are the primary locations of instantaneous coal fines enrichment. Increasing the inlet velocity generally enhances coal fines transport capacity and reduces the local maximum solid-phase volume fraction. Larger coal fines particles exhibit more pronounced inertial deviation and a higher degree of local enrichment, whereas smaller particles show stronger flow-following behavior and a more dispersed spatial distribution. The results further indicate that, within the investigated structural range, the 150° valve seat cone angle provides the best overall balance between coal fines transport capacity and hydraulic resistance. Ultimately, the findings provide a theoretical foundation and methodological reference for understanding the anti-clogging mechanisms of CBM pump standing valves, optimizing structural parameters, and guiding the blockage-resistant design of downhole flow components. Full article
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21 pages, 3684 KB  
Article
Knowledge-Organized and Retrieval-Augmented Intelligent Decision-Making Model for Remote Monitoring of Power System Secondary Equipment
by Longxing Jin, Luemou Ju, Xu Zhang, Zhengfei Lu, Tinghuang Wang, Jingyang Zhou and Kangli Liu
Modelling 2026, 7(4), 148; https://doi.org/10.3390/modelling7040148 - 23 Jul 2026
Viewed by 354
Abstract
To address the challenges in remote monitoring of power system secondary equipment, including dispersed multi-source heterogeneous corpora, inconsistent terminology, non-standardized expressions, unstable knowledge granularity, and fragmented evidence retrieval, a knowledge-organized and retrieval-augmented intelligent decision-making model is proposed in this paper. First, heterogeneous textual [...] Read more.
To address the challenges in remote monitoring of power system secondary equipment, including dispersed multi-source heterogeneous corpora, inconsistent terminology, non-standardized expressions, unstable knowledge granularity, and fragmented evidence retrieval, a knowledge-organized and retrieval-augmented intelligent decision-making model is proposed in this paper. First, heterogeneous textual resources, including defect records, standards and operating procedures, maintenance logs, typical cases, and abnormal operation reports, are transformed into retrievable, reusable, and traceable knowledge units through text cleaning, terminology normalization, semantic chunking, and metadata annotation. Monitoring issues are then uniformly represented and modeled as structured retrieval requests. A hybrid retrieval scheme is further developed by integrating keyword retrieval, vector retrieval, hierarchical index backtracking, and unified re-ranking. On this basis, an evidence-constrained retrieval-augmented output mechanism is introduced to generate structured results containing anomaly assessment, evidence-based interpretation, handling recommendations, and source traceability, thereby forming an intelligent auxiliary analysis workflow with expert-system-oriented support for duty-operation scenarios. Results show that the proposed model improves evidence retrieval over baseline retrieval settings and achieves better assisted-analysis performance than direct LLM output and conventional RAG. It effectively improves evidence matching accuracy, completeness of evidence organization, and stability of source traceability, indicating its scenario-level feasibility for intelligent auxiliary analysis and decision-support tasks in remote monitoring of power system secondary equipment. Full article
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31 pages, 26403 KB  
Article
Wind Pressure Coefficient Distribution and Shape Factor of Wind Load of Plastic Greenhouse Cluster in Valley Terrain Based on CFD Simulation
by Jing Xu, Zhengming Liao, Xiaoying Ren, Tianyang Liu and Zongmin Liang
Modelling 2026, 7(4), 147; https://doi.org/10.3390/modelling7040147 - 23 Jul 2026
Viewed by 445
Abstract
Understanding wind load characteristics of greenhouse clusters in valley terrain is essential for ensuring structural safety in high-altitude agricultural regions. This study investigates the wind pressure coefficient distribution of plastic greenhouse clusters located in a representative high-altitude valley region (Case sourced from Tibet, [...] Read more.
Understanding wind load characteristics of greenhouse clusters in valley terrain is essential for ensuring structural safety in high-altitude agricultural regions. This study investigates the wind pressure coefficient distribution of plastic greenhouse clusters located in a representative high-altitude valley region (Case sourced from Tibet, China) using computational fluid dynamics simulations. Numerical models incorporating realistic topographic features and representative cluster layouts (2 × 3, 3 × 3, and 3 × 5) were established to evaluate surface wind pressure coefficient distribution and wind load shape factors. The results indicate that valley terrain modifies the incoming wind field through terrain-induced acceleration and possible flow separation. Compared with flat-terrain assumptions, wind load shape factors show noticeable deviations, particularly in windward, roof, and leeward regions. First-row and peripheral greenhouses consistently experience the largest wind loads due to direct wind exposure, while interior greenhouses are significantly influenced by aerodynamic shielding effects from upstream structures. As cluster density increases, shielding effects reduce wind pressure magnitude and result in a more stable pressure distribution within the interior region of the cluster. The correction coefficient derived in this study should be regarded as site-specific indicators for the selected valley terrain, greenhouse layout, and wind direction, rather than as generally applicable design coefficients. Full article
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