Modelling doi: 10.3390/modelling7050203

Authors: Deniz Kenan Kılıç

The deployment of multiple Autonomous Underwater Vehicles (AUVs) for large-scale oceanic search and mapping missions is frequently constrained by inefficient task assignment and strict collision avoidance protocols. Traditional deconfliction methods block adjacent operational regions, significantly reducing the feasible search area and delaying the exploration of high-priority zones. Although this limitation is widely acknowledged in recent surveys, the direct integration of physical search-pattern geometry into the assignment constraints themselves remains largely unexplored. To address this gap, a mathematical model for dynamic task assignment executed across macro- and micro-cycles is proposed. The objective is formulated to maximize search rewards based on finding likelihood and temporal efficiency. To bypass the restrictive nature of neighboring-region exclusion constraints, a novel integration of alternating narrowing and widening spiral patterns is introduced, combined with depth-based layer assignment for transiting AUVs. The relaxation is validated at two levels. At the constraint level, systematic Monte Carlo simulations over 50 trials show that the pattern-aware method attains a statistically significant reward improvement over a standard strict-adjacency baseline (paired t(49)=7.15, p<0.001) while remaining free of assignment-level conflicts. At the trajectory level, the narrowing and widening sweeps and the depth-layered transits are explicitly simulated and scored with a single physical conflict metric applied identically to every method. This analysis shows that the relaxed constraint alone is not physically sufficient: executing the alternating spiral geometry reduces sonar-interference events from 2.36 to 0.52 per run, and an additional phase-admissibility condition is required to eliminate them. A regime analysis establishes that the mechanism is valid when the region side exceeds approximately four sonar ranges. The results indicate that physical search-pattern geometry can be embedded in assignment constraints to recover most of an unconstrained heuristic’s early-discovery advantage while remaining deconflicted, within an explicitly characterized operating envelope.

Modelling doi: 10.3390/modelling7050202

Authors: Yi-Da Chung Keh-Chin Chang

Accumulation of carbon deposits on coke-oven walls is an inherent challenge. The air injection technique for removing them is becoming widely adopted in coke-oven operations. A physical model that simulates the turbulent reacting flow of this carbon-deposit removal process is necessary to serve as a numerical analysis tool. Due to a lack of available measurement data for the rate of carbon deposit removal in coke ovens, benchmark data from thermogravimetric experiments were used to validate a developed turbulent combustion model. This study compares the simulation performance of one-film and two-film models for the reaction of carbon deposits and air, as well as turbulence–reaction interactions, these being the eddy dissipation model and a beta-shape probability density function (PDF) method. The physical model using the SST k-ω turbulence model, the two-film model for carbon–air reactions, and a beta-shape PDF method can account for turbulence–reaction interactions and simulate turbulent burning carbon-deposit tests in TG experiments. This model can simulate carbon deposit removal in coke ovens through air injection.

Modelling doi: 10.3390/modelling7050201

Authors: Xi Qin Mei Li Zhiqiang Xie Yanjie Zhang Min Yuan

This paper develops a three-dimensional refined finite-element model for the typical concrete lining of the Dianzhong Water Diversion Project tunnel, investigates the temperature and stress fields of the lining, and systematically analyzes the influences of various temperature-control measures and construction conditions on both fields. The interface between the surrounding rock and the lining is simulated using thin-layer contact elements. The results show that the rock temperature beyond a depth of 6 m is not affected by concrete hydration. The maximum temperature of the lining poured in the inner section is 6.36 °C higher than that poured at the entrance section. Concrete with micro-expansion and low adiabatic temperature rise, as well as pouring during low-temperature seasons, is beneficial for the anti-cracking safety degree of the lining. The temperature stress increases with the pouring temperature: when the pouring temperature rises by 4 °C, the minimum cracking safety factor decreases by 0.25. For this project section, the appropriate segmented length of the lining structure ranges from 8 m to 10 m. These results can provide guidance for the construction of tunnel linings to improve their anti-cracking safety degree.

Modelling doi: 10.3390/modelling7050200

Authors: Markel Alaña Julen Bastardo Asier Astarloa Gorka Aguirre Aitor Olarra Jokin Muñoa

Hydrostatic rotary tables are widely used in the machine tool industry for high-precision machining applications. The standard design approach relies on two-dimensional (2D) Reynolds finite element models that treat the bearing gap as a rigid, uniform scalar per ring. Nevertheless, at the scale of these machines, elastic deformations become comparable to the oil film thickness. In this study, a monolithic three-dimensional elasto-hydraulic model is compared with the standard 2D benchmark for a 5.5 m diameter cast iron table with two concentric bearing rings, over a load sweep (115–230 t) and six clamping-rectangle configurations. At the nominal load, the 2D model underestimates the inner-ring mean film by 21%, overestimates the minimum outer-ring film by 30%, and underestimates the pumping power by 24%, all percentages growing with load. Independently of load, clamping configuration alone produces an inner-ring film dispersion of up to 88% of the 2D value and a ring load-sharing ratio varying by a factor of 2.8. These effects are invisible to the 2D framework and, in the most compact configuration, sufficient to collapse the oil film. These results indicate that the 2D model, while adequate for preliminary sizing, cannot substitute for the coupled model when verifying guideway safety margins.

Modelling doi: 10.3390/modelling7050199

Authors: Jassiel V. H. Fontes Irving D. Hernández Edry A. G. Cisneros Lucas Duarte da Silva Edgar Mendoza Rodolfo Silva

Inland navigation is crucial for agricultural transport in the Brazilian Amazon; however, computational fluid dynamics (CFD) methodologies are needed to evaluate the effects of seasonal water-depth changes on regional vessel performance. This paper presents a CFD study of the effects of water-depth variation on the hydrodynamics and effective power of an agricultural cargo vessel. A multiphase CFD approach was applied and validated against benchmark data for ultra-shallow-water conditions. A simplified geometry of a single pusher–barge convoy in the 1:1 configuration was considered. The effects of five water depths and three vessel speeds on the CFD results were investigated. These results show that in shallower waters, blockage effects, gap flow changes, and flow velocity variation play a relevant role in vessel hydrodynamics. A reduction in water depth is one of the determinants of changes in wall shear stress, flow velocity and hydrodynamic pressure exerted on the hull. Moreover, results demonstrated that reducing the water-depth-to-draft ratio from H/T= 6.0 to H/T = 1.2 increased total resistance and, consequently, effective power demand by approximately 16% and 14% for the lower and higher speeds evaluated, respectively. Limitations and considerations for the application of the proposed approach to investigate other agricultural cargo vessels are discussed. Existing benchmark data for ultra-shallow waters can be crucial for validating numerical approaches such as the one presented in this work, expanding the possibilities of innovation.

Modelling doi: 10.3390/modelling7050198

Authors: Wenxing Sun Yanjun Ma Junwen Yao Yun Chen Xutao Chen Yongfei Ma Yupeng Zou

Kinematic modelling is essential for evaluating hybrid manipulators that require both stiffness and spatial adaptability. This paper proposes a modular 3-UPU (universal joint–prismatic joint–universal joint) hybrid serial–parallel manipulator for confined-space tool operations, with offshore jacket tubular-joint maintenance used as a representative application background. The mechanism connects several 3-UPU parallel units in series; each unit provides two rotational degrees of freedom and one translational degree of freedom for local steering and axial adjustment. Screw theory and the modified Grübler–Kutzbach formula are used to analyze module mobility, and a geometric kinematic model is established to map module pose to actuator displacement. Actuator commands are generated for cylindrical and planar surface-following trajectories and verified using a CAD-based Simscape Multibody virtual prototype. The maximum model-to-model relative position discrepancies are 1.07% and 1.45%, showing consistency between the analytical actuation model and the rigid-body virtual prototype under the considered conditions.

Modelling doi: 10.3390/modelling7050197

Authors: Miao Chen Guowei Li Lei Si Jinheng Gu

Efficient and safe path planning is the core prerequisite for realizing the autonomous crushing operation of the hydraulic crushing robotic arm in the mine chute. Foundational sampling-based algorithms, specifically standard RRT* and Informed RRT*, have problems such as unattainable targets, high computational redundancy, and hydraulic commutation shock in this highly constrained context. Therefore, this paper proposes a novel path planning method based on an improved Informed RRT* algorithm. Firstly, an axis-aligned bounding box (AABB) is constructed to approximately replace the obstacles, which not only facilitates collision detection but also enables the end of the robotic arm to accurately reach the target point. Secondly, an adaptive hierarchical strategy based on inverse kinematics perception and an artificial potential field guidance mechanism are used to construct the elevated obstacle-crossing corridor, achieving dimensionality-reduced path search and reducing ineffective collision detection. Finally, cubic non-uniform B-spline and seven-segment S-shaped velocity planning are combined to complete trajectory smoothing. Simulation results show that the success rate of the proposed planning algorithm is 100%, the number of generated nodes is reduced by 90.1%, and the trajectory achieves C2 continuity, providing command-level smoothing to act as a feedforward mitigation against potential hydraulic oscillations. Path-planning experiments are carried out on the hydraulic crushing robotic arm, and the average positioning error of the end robotic arm reaching position is 30 mm, meeting the accuracy requirements and providing a reliable solution for the safe operation of heavy-duty robotic arms.

Modelling doi: 10.3390/modelling7050196

Authors: Ruoxi Lin Fayou A Haifeng Jia Zhang Luo Shiqiang He Shiqun Yan

Background: To elucidate the hydraulic response, progressive deformation, and wetting-induced swelling effects of high-fill expansive soil slopes throughout the rainfall–cessation process. Methods: A high-fill expansive soil slope in Jianshui, Yunnan Province, China, was selected as the study case. A three-dimensional coupled saturated–unsaturated seepage and wetting-induced swelling model was established to simulate the evolution of pore-water pressure, displacement, maximum shear strain increment, and factor of safety during 24 h of continuous rainfall followed by 48 h without rainfall. Results: During rainfall, the shallow part of the slope exhibited a pronounced pore-water pressure response. Displacement and shear strain were mainly concentrated in the middle and lower portions of the slope, near the platform transitions, and around the slope toe. Throughout the rainfall–cessation process, the factor of safety generally exhibited a decreasing trend. Wetting-induced swelling further intensified slope deformation and shear strain concentration. At 72 h, the maximum total displacement increased from 92.5 mm without considering wetting-induced swelling to 139.0 mm when wetting-induced swelling was considered, representing an increase of approximately 50.3%. After rainfall ceased, pore-water pressure and displacement remained essentially stable when wetting-induced swelling was neglected. When wetting-induced swelling was considered, matric suction increased during approximately the first 0–9 h after rainfall cessation, whereas slope displacement continued to increase after the end of rainfall and gradually stabilized only after approximately 9 h. These results indicate that the hydraulic state and deformation of the slope continued to adjust after rainfall cessation. Conclusions: Wetting-induced swelling not only increased shear deformation and reduced slope stability but also altered the post-rainfall displacement response, causing deformation adjustment to persist after rainfall cessation. Neglecting wetting-induced swelling, or evaluating slope stability solely at the end of rainfall, may therefore underestimate the actual slope deformation and overlook the continued evolution of pore-water pressure and displacement, ultimately leading to an underestimation of the final deformation magnitude and potential instability risk.

Modelling doi: 10.3390/modelling7050195

Authors: Tuo Zhou Xing Jiang

This paper investigates prescribed-performance containment control of nonlinear multi-agent systems with multiple leaders under a fixed directed graph. To reconcile follower-specific physical containment envelopes, multi-leader targets determined by the communication graph, and the virtual errors available for distributed feedback, the inverse-Laplacian transfer principle is used to construct sufficient virtual-error bounds. Nonlinear evaluation and convex averaging also generate a possibly nonvanishing nonlinear averaging residual at the containment target. The controller therefore couples the allocated barrier feedback with a directional robust term that dominates this residual in the Lyapunov estimate. For every maximal Filippov solution, a barrier Lyapunov analysis based on an improper integral establishes forward completeness, invariance of the allocated virtual and prescribed physical envelopes, and asymptotic physical containment. Finally, simulation studies across multiple configurations and two direct comparisons with existing methods verify the theoretical results.

Modelling doi: 10.3390/modelling7050194

Authors: Hualong Li Ao Zhang Lianheng Zhao Yong Mei Yunhou Sun Feng Li Huajie Wu Bingde Li Li Liu

This study addresses the challenges of slow attenuation and significant hazards associated with explosive shock waves confined within conventional underground tunnel walls. A novel serrated passive shock-attenuating tunnel design is proposed, grounded in the principle of viscous dissipation within the boundary layer. The investigation encompasses both experimental analyses and numerical simulations. The study found that shock waves in smooth tunnels primarily propagate as one-dimensional plane waves, resulting in concentrated energy and gradual attenuation. Conversely, the serrated tunnel geometry generated a continuous reflection, scattered and vortex formation due to abrupt geometric discontinuities, led to distortion and fragmentation of the shock front and the emergence of a three-dimensional discrete pressure field. Through turbulent dissipation mechanisms, energy is rapidly transformed into small-scale vortices, effectively reducing wave velocity and markedly diminishing the forward peak pressure. Under conditions of high-equivalent explosions, the serrated structure demonstrates enhanced efficacy in energy dissipation and peak pressure attenuation, significantly curtailed the effective propagation distance of high-pressure shock waves. Optimization of the serration spacing identified 30 cm as the optimal interval, minimizing stress peaks both centrally and at the tunnel entrance, thereby maximizing wave attenuation. Comparative analysis between simulation and experimental was resulted that corroborates the wave-attenuation performance of the serrated design, offering a critical foundation for the development of blast-resistant underground structures.

Modelling doi: 10.3390/modelling7050193

Authors: Agris Šostaks Artūrs Sproģis Aleksandrs Saveļjevs Dāvids Liepa

Many scientific and engineering domains, including machine learning, software engineering, operations research, and logistics optimization, are characterized by a fragmented landscape of problem variants, methodological approaches, and application-specific requirements. This diversity makes it difficult to systematically understand, compare, and select appropriate solution approaches, particularly when real-world industry needs must be translated into formal problem definitions and scientific methods. The Electric Vehicle Routing Problem (EVRP) provides a representative example: the literature spans numerous problem variants and a wide range of exact, heuristic, learning-based, and hybrid methods, yet there is no clear structure for linking practical requirements to relevant solution approaches through scientific evidence. We propose a dual-taxonomy framework that structures problem features and solution features as complementary conceptual spaces. Using this structure, industry requirements and scientific publications are annotated with shared taxonomy elements. Publications provide traceable links between problem features and solution methods reported in the mapped literature, while requirements provide an industry-facing entry point into the problem space. In a real-world EVRP case study, we demonstrate how the framework can support method exploration, reveal mismatches between industrial needs and the mapped research corpus, and identify gaps in the requirement set, taxonomy, and analyzed literature corpus. This provides a transparent and extensible pathway from practical problem descriptions to relevant scientific evidence and candidate solution approaches.

Modelling doi: 10.3390/modelling7050192

Authors: Artur Zaporozhets Vladyslav Khaidurov

Accurate and computationally efficient numerical modelling of shallow-water flows is essential for flood prediction and hydrodynamic risk assessment. This study develops an implicit finite-difference scheme for the numerical solution of the two-dimensional shallow-water equations. First, the main numerical approaches used for shallow-water modelling, including finite-difference, finite-volume, finite-element, and discontinuous Galerkin methods, are analysed in terms of accuracy, stability, treatment of discontinuities, and computational requirements. Based on this analysis, an implicit finite-difference formulation is developed that uses central approximations for spatial derivatives and averages flow variables at cell boundaries. The nonlinear terms are treated using Newton linearization, resulting in an iterative scheme that allows larger time steps than explicit formulations constrained by the Courant–Friedrichs–Lewy condition. The proposed method is implemented in MATLAB as a computational module for two-dimensional hydrodynamic simulations. Its performance is demonstrated on a test problem that describes the propagation of an initially localised disturbance in a rectangular computational domain with rigid boundaries. The numerical results demonstrate stable wave propagation, conservation of the modelled flow dynamics, and physically consistent boundary reflections. The developed approach provides a computational basis for further integration of shallow-water hydrodynamic models with spatial data and geographic information systems for flood forecasting and risk assessment. The implicit scheme allowed the release of time steps Δt = 0.1, 0.5 and 0.9, which significantly exceeds the limit stability of the explicit scheme, which, due to the Courant–Friedrichs–Lévy conditions, was limited to the value Δt ≤ 0.01. The simulation results show that the developed scheme provides stable wave growth and physically correct separation from impermeable boundaries for all investigated time step indicators. The obtained water depth profiles at times t = 10, 15, 20 and 25 s illustrate the correct evolution of the initial combustion: the wave front expands symmetrically while preserving the conservative properties of the model hydrodynamics. The numerical solution demonstrates the accuracy and robustness of the proposed implicit finite-difference scheme, even when using time steps that are almost two orders of magnitude larger than those allowed by explicit methods. The results confirm that the developed approach is a robust and computationally efficient tool for hydrodynamic modelling, intended for further integration with geographic information systems in behaviour prediction and risk assessment tasks.

Modelling doi: 10.3390/modelling7050191

Authors: Ioan Tamașag Irina Beșliu-Băncescu Dumitru Amarandei

This paper presents an analytical—mechanistic model for determining local friction and normal force components acting on the rake and flank surfaces during oblique cutting. The proposed formulation integrates the tool geometry by considering both the constructive angles of the cutting tool and the functional angles resulting from the cutting conditions, including cutting speed, feed rate, and depth of cut. The transformation from the oblique cutting coordinate system to the dynamometer reference system is performed using successive rotation matrices based on Euler angles. The model is formulated as a system of three equations with four unknown local force components F,FN,Fα,FNα, which is analytically resolved by combining the measured cutting force components Fx,Fy,Fz with an experimentally determined friction coefficient. The geometric direction parameters derived from the Euler angles enable the decomposition of the measured global forces into local friction and normal force components acting on the active tool surfaces. The model is further extended to functional geometry by accounting for changes in the effective tool orientation under actual cutting conditions. The internal consistency of the proposed formulation is supported through several particular cases, including orthogonal cutting and zero-angle geometry. Experimental validation was carried out using P20 carbide inserts and AISI 1045 steel. The obtained results showed good agreement between the analytically reconstructed force components, the measured cutting forces, and the friction coefficient values identified experimentally, supporting the applicability of the proposed model for local force evaluation in oblique cutting.

Modelling doi: 10.3390/modelling7050190

Authors: Chunxu Qin Yiran Ma Huijuan Liang Zhifan Wang Liqiang Liu Huichun Hua Jie Bai

The end-winding insulation structure of stator windings in pumped-storage generator units is complex, with pronounced electric field concentration under out-of-phase conditions, making them critical concerns in insulation design and condition-based maintenance. Although the finite element method (FEM) offers reliable accuracy, the strong nonlinearity of the anti-corona layer results in a computation time exceeding 104 seconds per single solution, rendering it impractical for parameter optimization and rapid on-site assessment. This paper proposes a fast prediction method for end-region potential distribution based on a deep neural network (DNN). Taking a 334 MW unit as the research object, a three-dimensional electroquasistatic finite element model with six stator coils is established and validated through power-frequency withstand voltage and ultraviolet imaging experiments. Training samples are generated via design of experiments (DoE), and a multilayer DNN surrogate model with a 7-dimensional input (comprising 3D spatial coordinates and four physical parameters) and a 1-dimensional output is constructed to directly reconstruct the spatial potential field at the end region. The results demonstrate that the surrogate model achieves a maximum relative error of less than 2% along the entire path compared with the high-fidelity FEM solutions, with a single prediction time of approximately 38 s—representing a speedup factor of approximately 272—while also exhibiting good generalization capability. This method provides a feasible technical approach for rapid reconstruction of end-region field distribution and optimization of insulation structures.

Modelling doi: 10.3390/modelling7050189

Authors: Siyuan Chen Yaokuan Peng Yao Tong Xinyuan Jin Lipu Zhang

Installed-capacity shares are widely used to describe power-sector transition, but per-kWh life cycle assessment (LCA) depends on delivered generation. This study develops and tests a static, annual-average generation-weighted structural diagnostic framework linking capacity-to-generation conversion, technology impact factors, scenario simulation, uncertainty analysis, optimization-boundary diagnostics, and regional proxy analysis. The lcpy Simple LCA capacity mix supplies six pedagogical S0–S5 stress-test scenarios, while UK official capacity and generation observations provide a 2020–2024 observational backcast. Relative to raw capacity shares, fixed 2024 capacity-factor weighting reduces mean generation-share error by 60.1%, and a prior-year capacity-factor model reduces it by 72.3%; these improvements are interpreted as arithmetic and structural evidence, not as evidence of dispatch-model forecasting skill. In the scenario set, generation weighting lowers GWP100 by 13.55–22.59%; the low-fossil S2 scenario gives the lowest GWP100, 0.09011 kg CO2-eq kWh−1, 50.01% below S0, and remains lowest in the tested climate-change sensitivity analyses. Multi-indicator rankings are less stable, with S2, S3, and S4 forming a low-burden group rather than a method-invariant optimum. Applying the same weighted-sum calculation to 2024 generation structures for China, the UK, and the EU gives a central-proxy China GWP100 of 0.7497 kg CO2-eq kWh−1; this is a proxy-based structural diagnostic, not a validated regionalized LCA. The results relocate the assessment focus from installed capacity to delivered generation while identifying time-varying utilization and region-specific inventories as necessary extensions.

Modelling doi: 10.3390/modelling7050188

Authors: Shirong Pi Shilong Gan Tao Cheng Panpan Guo Yangsheng Wang Tianshe Sun Yixian Wang

Water-decking can buffer and redistribute borehole loading, but the coupled effects of axial charge segmentation, radial decoupling, and peripheral-hole spacing across scales remain insufficiently quantified. A cross-scale three-dimensional multi-material Arbitrary Lagrangian–Eulerian (ALE) framework coupled with the Riedel–Hiermaier–Thoma (RHT) damage model was developed for intact granite and applied at single-hole, double-hole, and full-face scales following specimen-scale calibration and numerical consistency checks. Increasing the segment count from four to six reduced the charge-section peak pressure from 283.0 to 257.0 MPa while increasing the water-section peak from 24.5 to 50.7 MPa. Increasing the radial decoupling coefficient from 1.00 to 1.31 reduced the numerical damage span from 55.6 to 33.7 cm. The spacing–decoupling assessment identified the six-segment configuration with Kd = 1.31 and 65 cm spacing as a condition-specific combination that maintained inter-hole damage connectivity while limiting outward disturbance. In the full-face model, multi-hole stress-wave interaction occurred at approximately 0.48–0.52 ms. The D ≥ 0.19 and D ≥ 0.90 damaged regions occupied 2.154% and 0.348% of the representative section, respectively. These results support a sequential axial–radial–spatial regulation framework linking pressure redistribution and inter-hole interaction to full-face stress and damage evolution, providing a basis for smooth-blasting parameter selection under the investigated intact-granite conditions.

Modelling doi: 10.3390/modelling7050187

Authors: Zhenle Dong Xiangpeng Luan Pengxiang Zhang Yilong Jia

Valve-controlled hydraulic servo systems have been broadly utilized in applications requiring fast response and high power, where input constraints represent one of the major limitations on control performance. To tackle this problem, this study proposes an adaptive asymptotic tracking control method considering input constraints. First, a nonlinear mathematical model of the valve-controlled hydraulic servo system is established and transformed into an integrator form to facilitate controller derivation. Second, a tracking controller is designed based on the robust integral of the sign of the error (RISE) method, and an adaptive law for the robust gain is developed. This method not only realizes asymptotic tracking but also guarantees that the control input magnitude remains within the prescribed bounds. The controller stability is rigorously analyzed via Lyapunov theory. Finally, the validity of the proposed control method is confirmed by comparative simulations. The results show that the amplitude of the control input can be effectively limited, and the tracking accuracy is further improved.

Modelling doi: 10.3390/modelling7050186

Authors: Xiaofeng Sun Zhengyang Lu Pengfei Ni Jingyu Qu

Proppant transport and placement in rough fractures strongly influence hydraulic fracture conductivity, while the mechanisms by which fracture-wall heterogeneity affects particle migration and deposition remain insufficiently understood. In this study, a Eulerian–Eulerian two-fluid model coupled with fractal fracture reconstruction is developed to investigate proppant transport and placement in rough fractures. Rough fracture surfaces with different fractal dimensions are generated using the spectral synthesis method, and a modified cosine-weighted transition algorithm is proposed to improve geometric continuity and mesh stability between the inlet and rough fracture regions. The effects of fracture roughness, injection velocity, particle size, particle density, and sand concentration on sand-bank evolution are systematically investigated. The results reveal that fracture roughness has a non-monotonic influence on proppant deposition: moderate roughness enhances near-wall disturbances and particle resuspension, reducing sand-bank accumulation, whereas excessive roughness increases particle interception, collision, and local flow disturbance, resulting in localized deposition. Increasing injection velocity from 0.15 to 0.8 m/s decreases the equilibrium sand-bank height by approximately 44%. Increasing particle diameter from 0.25 to 0.85 mm increases the maximum sand-bank height from 2.23 to 25.64 cm, while increasing sand concentration from 1 to 10 increases the maximum sand-bank height from 3.97 to 15.01 cm. Although rough and smooth fractures have identical average apertures, roughness-induced contraction–expansion channels redistribute particle trajectories and promote deeper fracture placement. This study provides insights into proppant transport mechanisms in heterogeneous fractures.

Modelling doi: 10.3390/modelling7050185

Authors: Nikola Čajová Kantová Alexander Backa Juraj Drga Alexander Čaja

Particulate matter from small-scale combustion systems remains a concern, as fine and submicron particles are difficult to remove by inertial separation alone. Electrostatic precipitators (ESP) are a promising option for this application. However, the effective aerodynamic utilization of the available collecting area depends on the internal distribution of particle-laden flue gas. This study numerically investigates the gas-flow distribution and aerodynamic particle transport in a four-tube ESP, designed to increase the collecting surface area relative to a conventional tubular arrangement. Three geometrical configurations were evaluated using computational fluid dynamics: a basic four-tube model without flow guidance, a model with nine radial inserts, and a model with a screw-type guiding structure positioned in the T-junction region. The basic geometry showed strongly non-uniform flow distribution, with a maximum-to-minimum tube-average velocity ratio of 3.31 and a coefficient of variation of approximately 51%. Radial inserts reduced these values to 1.95 and 27%, respectively, while the screw-type structure provided the most uniform distribution, with corresponding values of 1.75 and 20%. Particle-velocity fields indicated that the guiding elements promoted a more even particle supply to the four tubes. The results demonstrate that inlet-flow conditioning is essential for the effective aerodynamic utilization of the enlarged collecting area in multi-tube ESPs.

Modelling doi: 10.3390/modelling7050184

Authors: Subha Ghosh Charilaos Paraskevoulakos Alexander Michel

Digital volume correlation (DVC) is widely used to extract internal displacement and strain fields from X-ray computed tomography (XCT) data, yet the limits imposed by the material’s own texture remain poorly quantified. This paper quantifies the individual and combined effects of particle volume fraction, particle geometry, and imaging noise on DVC accuracy. Sixteen specimens with prescribed volume fractions (0.25–10%) and particle shapes (spherical and angular) were generated using the discrete element method (DEM), loaded elastically in uniaxial compression, and converted into synthetic three-dimensional image datasets with and without additive Gaussian noise. Global DVC was performed in AVIZO and compared against the exact DEM ground truth. Under noise-free conditions, mean nodal displacement errors fall below 5% once the volume fraction exceeds 1%, whereas errors of 10–25% occur below this value; adding Gaussian noise with a variance of 0.001 raises the practical threshold to approximately 4%. Angular particles consistently outperform spherical particles at an equal volume fraction, a difference explained quantitatively by their 1.4-times-larger specific interfacial area and correspondingly higher image gradient. Median filtering favours spherical microstructures, whereas the Non-Local Means filter performs consistently across all microstructures. The results provide a priori guidelines for assessing DVC feasibility directly from microstructural descriptors.

Modelling doi: 10.3390/modelling7050183

Authors: Xiaofei Zhu Yaping Wang Xuebing Wei Lili Wan Zihui Zhao Yujun Meng

Modern manufacturing enterprises are increasingly transitioning to multi-variety, small-batch production. This shift introduces significant scheduling challenges, particularly due to the job hierarchy constraints inherent in assembling multi-level intermediate parts. Furthermore, non-machining preparation times—such as tool switching, material handling, and equipment standby—significantly impact production efficiency. To address these challenges, this paper investigates the flexible job shop batch scheduling problem by integrating order and operation consolidation under strict job hierarchy constraints. To mathematically formulate the scheduling problem with non-serial operation precedence networks and dynamic batching, we develop a mixed-integer programming model. The primary objective is to simultaneously minimize the maximum completion time (makespan) and total tardiness. To solve this efficiently, an Improved Grey Wolf Optimization (IGWO) algorithm is proposed. The algorithm features a novel two-tier coding scheme tailored for consolidation logic and employs a hybrid population initialization strategy to enhance initial solution quality. Moreover, it improves the standard hunting mechanism, utilizes Variable Neighborhood Search (VNS) for local exploitation, and independently applies a Simulated Annealing (SA) dynamic acceptance mechanism to balance global exploration and local exploitation. Extensive experiments using small-, medium-, and large-scale industrial data from a power station valve manufacturer validate the effectiveness of the proposed model and algorithm in optimizing complex batch scheduling schemes.

Modelling doi: 10.3390/modelling7050182

Authors: Fernando I. Molina-Herrera María L. López-González Luis I. Quemada-Villagómez Shafqat Hussain Mario A. Sandoval-Hernández Hugo Jiménez-Islas

This study presents a numerical investigation of natural convection in a two-dimensional inclined square cavity filled with air and subjected to differential heating. The effects of the Rayleigh number and cavity inclination on heat transfer and flow behavior were investigated for 103 ≤ Ra ≤ 109 and inclination angles of 0°, 15°, 30°, and 45°. The dimensionless Navier–Stokes and energy equations were solved using the finite-element method under the Boussinesq approximation with a steady laminar formulation. A structured quadrilateral mesh with boundary-layer refinement was employed near the differentially heated walls. Mesh-refinement tests and comparisons with benchmark data for the classical square cavity were used to assess the numerical accuracy of the model. The results show that the average Nusselt number increases with the Rayleigh number, reflecting the progressive intensification of buoyancy-driven heat transfer. The effect of inclination is non-monotonic and depends on the Rayleigh number. At Ra = 104, the highest average Nusselt number is obtained at 45°, whereas for Ra ≥ 105, the maximum is consistently observed at 15°. At Ra = 109, the average Nusselt number is 54.475, 55.617, 53.224, and 49.408 for inclination angles of 0°, 15°, 30°, and 45°, respectively. The results indicate that moderate cavity inclination can enhance heat transfer by favorably modifying the interaction between buoyancy and the imposed thermal gradient, whereas larger inclinations progressively reduce the heat-transfer rate. The present results provide a systematic characterization of the coupled effects of Rayleigh number and cavity inclination within the scope of the steady two-dimensional formulation considered.

Modelling doi: 10.3390/modelling7050181

Authors: Kai Zhang Zhenyu Zhang Xu Yang Guangkui Liu

The large-scale integration of renewable energy has compelled coal-fired power plants to operate under deep peak-shaving conditions, significantly increasing the failure risk of Circulating Fluidized Bed (CFB) boiler heating surfaces due to severe thermal and pressure fluctuations. To address the limitations of traditional static risk evaluations, this study proposes a novel dynamic risk assessment framework integrating a Spatial–Temporal Graph Convolutional Network (STGCN) and a Dynamic Bayesian Network (DBN). The STGCN, enhanced with an operation-adaptive dynamic cross-attention delay module, predicts spatiotemporal temperature and pressure variations across the high-temperature heating surfaces. The predicted variables are incorporated into the DBN as dynamic evidence, which utilizes Noisy-OR logic and an embedded Weibull physical degradation model to continuously quantify cumulative failure probabilities. Case study results demonstrate that the STGCN outperforms traditional LSTM and RNN baselines in prediction accuracy. Furthermore, the DBN effectively maps the distinct degradation characteristics of individual boiler components, accurately identifying the water wall and superheater as having the highest failure risks and the largest fluctuations in marginal failure probability during rapid load cycling. This integrated data-driven approach provides highly accurate, real-time risk predictions, offering essential decision-making support for the predictive maintenance and safe flexible operation of CFB boilers.

Modelling doi: 10.3390/modelling7050180

Authors: Stylianos Vasileios Kontomaris Ioannis Psychogios Anna Malamou Andreas Stylianou

Accurate AFM nanoindentation analysis requires models that account for the rounded apex of real pyramidal indenters. Although exact force-indentation equations for n-sided blunt pyramids exist, their numerical complexity limits routine use. In this work, a simple closed-form analytical approximation is developed that directly relates force to indentation depth for blunt pyramidal indenters. The method employs first-order Maclaurin series expansions of the geometric terms and the generic indentation differential equation, yielding a closed-form second-degree polynomial expression that is readily implemented in AFM data analysis. Comparison with the exact solutions showed that the approximation error decreases with indentation depth and is governed by the pyramid geometry rather than the tip radius. Simulated and experimental AFM data confirmed accurate Young’s modulus estimation above a geometry-dependent validity threshold. For a four-sided blunt pyramidal indenter, the proposed criterion predicts minimum indentation depths ranging from approximately 10.4 Rc for θ = 15° to 2.4 Rc for θ = 45° where Rc is the tip radius and θ is the pyramid’s semi-included angle. Application of the model to simulated AFM datasets yielded Young’s modulus values between 18.5 and 19.8 kPa for a true modulus of 20 kPa, corresponding to errors below 8% in all examined cases. Furthermore, the closed-form equation provided very good agreement with AFM nanoindentation data obtained from human prostate cancer cells. It is also shown that the generic derived equation includes the case of a spheroconical indenter as a limiting case. Young’s modulus is obtained directly from the quadratic coefficient, eliminating the need for tip-radius calibration. In addition, the formulation is applicable to heterogeneous materials, providing an effective local modulus through the weighted mean value theorem for integrals. The approach offers a practical and computationally efficient alternative for AFM data processing, improving the robustness of modulus estimation for soft biological materials.

Modelling doi: 10.3390/modelling7050179

Authors: Kristina Božić-Tomić Miljan Kovačević Ljubo Marković Suzana Koprivica

Accurate prediction of pile base resistance is essential for the safe and economical design of deep foundations, particularly in soft soils where load-transfer mechanisms are highly nonlinear and uncertain. This study develops a comparative, probabilistic, and interpretable machine learning framework for predicting pile unit base resistance using five input variables: applied load, settlement, effective pile length, axial stiffness, and SPT value. A Gaussian Process Regression model with an automatic relevance determination (ARD) Exponential kernel achieved the best performance, with RMSE = 262.11 kPa, R2 = 0.943 on an independent test set, and 95% prediction intervals with 96.46% coverage. Beyond record-level evaluation, a leave-one-pile-out validation (the first grouped validation applied to this database) showed harder generalization to entirely unseen piles, driven mainly by a per-pile level offset rather than shape mismatch (within-pile correlation = 0.975). A sequential next-stage scheme, calibrating this level from a pile’s early loading stages, then predicted its remaining segments with consistently strong agreement (Willmott’s d = 0.76–0.83), supporting practical extension of partial load tests. Interpretability was assessed using ARD, SHAP, permutation/ablation importance, and partial dependence/accumulated local effects analysis, identifying settlement as the dominant predictor. The framework combines accuracy, calibrated uncertainty, interpretability, and validated segment-level extrapolation for reliability-oriented pile assessment.

Modelling doi: 10.3390/modelling7050178

Authors: Xueping Song Xi Liao Shuyu Zhang Jicun Zhang Shanglei Jiang

Deploying prohibited-item detectors on resource-constrained X-ray security inspection terminals is not equivalent to selecting the smallest available YOLO scale: excessive compression can reduce feature capacity, whereas medium-scale detectors may retain avoidable computational redundancy. This study therefore investigates a deployment-oriented operating point through coordinated backbone compression, feature compensation, and class-sensitive optimization. YOLO-SMV and YOLO-EMV are developed from YOLOv8m and YOLO11m by combining MobileNetV3-Small backbone reconstruction, SE/ECA-based channel recalibration, and a VF-BCE objective for difficult and underrepresented categories. A three-seed full-factorial study on YOLO11m shows that VF-BCE provides the largest individual accuracy gain and that ECA repeatedly recovers part of the performance lost in the compressed VF-BCE pathway. The accuracy-oriented ECA+VF-BCE configuration reaches 0.93842±0.00720 mAP50, whereas the deployment-oriented YOLO-EMV reaches 0.92744±0.00768; the latter trades 1.098±0.061 percentage points of mAP50 for a reduction from 20.03 M to 12.04 M parameters and from 67.9 G to 28.8 G FLOPs. Under the common seed-41 SIXray protocol, YOLO-EMV also achieves higher mAP50 than standard YOLO11n, YOLO11s, and YOLO11m, demonstrating that the selected operating point is not reproduced simply by choosing a smaller baseline. Published SIXray results are reported separately as protocol-aware literature context rather than as a cross-paper ranking. Additional OPIXray and PIDray experiments provide multi-benchmark evidence for the component interactions under heavy occlusion and long-tailed class distributions. The deployment-oriented YOLO-EMV model has also been integrated into customs security inspection equipment.

Modelling doi: 10.3390/modelling7050177

Authors: Dongyang Song Pengyue Na Yulai Zhao Dong Yang Mohammed Meiirbekov Haitao Luo

This study addresses the inherently low damping and vibration susceptibility of carbon fiber reinforced polymer (CFRP) laminated cantilever plates by developing a comprehensive dynamic modeling and active vibration control framework. An electromechanical coupling model incorporating macro-fiber composite (MFC) actuators and sensors is established using the first-order shear deformation theory (FSDT) and the assumed mode method, with virtual springs introduced to account for non-ideal clamped boundary conditions. A reduced-order state-space model is then derived through model reduction, and a linear quadratic Gaussian (LQG) controller is designed for optimal state estimation and feedback control. The theoretical model is systematically validated via convergence analysis, ANSYS finite element simulations, and LMS impact hammer testing. The results demonstrate that, with the relative errors of the first four natural frequencies controlled within 2%, the theoretical mode shapes are highly consistent with those obtained from ANSYS simulations. An active vibration control experimental platform is established, and the effectiveness of the control strategy is verified under dual-spectrum harmonic and impact excitations. The results show that the designed LQG controller can effectively suppress multi-modal vibrations, substantially attenuating the response amplitudes of dominant modes and significantly accelerating the transient vibration convergence. This study addresses the challenge of precisely characterizing actual non-ideal clamped boundary conditions. Through model order reduction and closed-loop LQG control experiments, it provides a comprehensive set of theoretical methodologies, numerical solution strategies, and engineering-oriented experimental schemes for the electromechanical coupling dynamic modeling and optimal vibration suppression of CFRP thin-walled composite structures.

Modelling doi: 10.3390/modelling7040176

Authors: Jinghui Li Xueren Wang Chuanfei Song Zhipeng Zhao Yanchao Wang

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.

Modelling doi: 10.3390/modelling7040175

Authors: Sabir Hussain Saif Shakeel Affan Khan Mohammad Rashid Zafar Arshad Hussain Khan Thimmappa Shetty Guruprasad Vishwanath Managuli

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.

Modelling doi: 10.3390/modelling7040174

Authors: Zewei Zheng Hongbao Liang Junjie Huang Boyu Zhang Zhen Zhang Peiang Huang

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.

Modelling doi: 10.3390/modelling7040173

Authors: Qian Wang Xiaohu Li

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.

Modelling doi: 10.3390/modelling7040172

Authors: Dongke Li Yong Liu Wanying Wang Dongying Wang Tao Zhang

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.

Modelling doi: 10.3390/modelling7040171

Authors: Qiu Zhang Xin Qiao Xinmin Chen

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.

Modelling doi: 10.3390/modelling7040170

Authors: Hao Song Wei Han Yi You Wei Min Jianxu Shi

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.

Modelling doi: 10.3390/modelling7040169

Authors: Emonena Ithipri Festus I. Ashiedu Ikuobase Emovon Olusegun D. Samuel Manjunath Patel Gowdru Chandrashekarappa Davannendran Chandran Ganesh Ravi Chate

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.

Modelling doi: 10.3390/modelling7040168

Authors: Rafat Al-Waked Asher Ahmed Malik Mohammad Shakir Nasif

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.

Modelling doi: 10.3390/modelling7040167

Authors: László Gyarmati Csaba Mihálykó Éva Orbán-Mihálykó

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.

Modelling doi: 10.3390/modelling7040166

Authors: Guang Yang Haoyue Yang Yongjun Wu

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.

Modelling doi: 10.3390/modelling7040165

Authors: Rahil Miten Doshi Matthias Markl

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.

Modelling doi: 10.3390/modelling7040164

Authors: Xiaole Guan Xin Jin Zhijing Zhang

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.

Modelling doi: 10.3390/modelling7040163

Authors: Raheemat O. Yussuf Omar S. Asfour Ahmed Abd El Fattah Muhammad Asif

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.

Modelling doi: 10.3390/modelling7040162

Authors: Juchen Hong Xue Feng Zhengyun Ren

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.

Modelling doi: 10.3390/modelling7040161

Authors: Guo-Kang Er Chang Tian Haofan Wu

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.

Modelling doi: 10.3390/modelling7040160

Authors: Shuichi Sakamoto Hiroaki Soeta Yosuke Kubo Okuda Taichi Odashima Takeomi

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.

Modelling doi: 10.3390/modelling7040159

Authors: Krishnaraj Vilasraj Bhat Ignacio Martínez-Terés Pablo Pflueger Tejero Juan García-Martínez Francisco J. Montans

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.

Modelling doi: 10.3390/modelling7040158

Authors: Valérie N’Guessan Gboulouhonon Komenan N’dri Kacoutchy Jean Ayikpa Pierre Gouton Vincent Oria

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.

Modelling doi: 10.3390/modelling7040157

Authors: Yuzhuo Zhang Jialin Liang Ziqiong Yuan Zanzan Dai Yaozheng Kang

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.

Modelling doi: 10.3390/modelling7040156

Authors: Ksenija Mladenović Ivan Milovanović Zoran Stanković Olivera Pronić Rančić Nebojša Dončov

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.

Modelling doi: 10.3390/modelling7040155

Authors: Chenyao Wan Zheng Li Xiaoqian Ma Yongshou Liu Wei Sun

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.

Modelling doi: 10.3390/modelling7040154

Authors: Omid Hassanshahi Nima Azimi Mohammad Bakhshi Diāna Bajāre Shaghayegh Karimzadeh

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.

Modelling doi: 10.3390/modelling7040153

Authors: Gustavo de Mello Ricardo Rodrigues Magalhães Fernando Elias de Melo Borges

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.

Modelling doi: 10.3390/modelling7040152

Authors: Chutong Hao Qingwei Xu Kaili Xu Tianwei Shi Bingjun Li Yaping Zhu Wanjun Niu

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.

Modelling doi: 10.3390/modelling7040151

Authors: Zixuan Zhang Beirong Han Xilong Zhou

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.

Modelling doi: 10.3390/modelling7040150

Authors: Yi Zang Yuan Ding

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.

Modelling doi: 10.3390/modelling7040149

Authors: Yicheng Wang Wanzhong Li Jianning Xu Yapeng Li Liaobo Li

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.

Modelling doi: 10.3390/modelling7040148

Authors: Longxing Jin Luemou Ju Xu Zhang Zhengfei Lu Tinghuang Wang Jingyang Zhou Kangli Liu

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.

Modelling doi: 10.3390/modelling7040147

Authors: Jing Xu Zhengming Liao Xiaoying Ren Tianyang Liu Zongmin Liang

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.

Modelling doi: 10.3390/modelling7040146

Authors: Chang-Yong Song

This study presents a structural design sensitivity analysis and metamodeling framework for a 30-ft class modular pontoon boat utilizing High-Density Polyethylene (HDPE) and an aluminum alloy (Al-5083) frame. Finite element analysis (FEA) was performed under the design load conditions specified by the Korean Register (KR) rules for high-speed light craft. Based on the FEA simulation results, a design sensitivity analysis was conducted using an L81(311) orthogonal array design matrix (OADM) to identify the quantitative influence of structural thicknesses on the hull weight and maximum stresses. The best design combination among the OADM experiments successfully achieved a 31.9% weight reduction while strictly satisfying the allowable stress criteria. Furthermore, Kriging metamodels with four different correlation functions (Gaussian, Exponential, Matérn linear, and Matérn cubic) were constructed to predict the structural responses efficiently. A comparative analysis of the approximation accuracy revealed that the Matérn linear function provided the most robust predictive performance, yielding the highest average cross-validation coefficient of determination (R2) of 0.971 across all performance metrics. The predictive accuracy of the selected metamodel was further verified by leave-one-out cross-validation in terms of root mean square error (RMSE) and mean absolute error (MAE). The findings confirm that the Kriging metamodel employing the Matérn linear correlation function is highly suitable for capturing the complex structural behavior of hybrid-material marine structures.

Modelling doi: 10.3390/modelling7040145

Authors: Hamid Reza Soltani Motlagh A. M. Amer Nourhan I. Ghoneim Ahmed M. Megahed Amr M. Abdallah Seyed Behbood Issa-Zadeh

This research presents a physics-informed deep learning framework for investigating the magnetohydrodynamic flow of a dissipative non-Newtonian micropolar nanofluid induced by a stretching sheet, incorporating Stefan blowing, internal heat generation, and the zero nanoparticle mass flux condition. The physical model consists of the interplay between the microrotation dynamics, resistance of porosity on the microrotation, Brownian diffusion, and thermophoretic transport phenomenon. The numerical solutions for the nonlinear yielded equations that result from the above interaction are obtained by employing a PINN that considers the laws of physics and boundary conditions. With this technique, the flow behavior, temperature, concentration, and microrotation fields can be predicted accurately without requiring huge datasets. This shows the ability of PINNs to numerically treat highly-coupled nonlinear transport equations in a very efficient manner compared to other traditional methods. The important discoveries from this study include that the porous and magnetic factors increased the skin friction coefficient, but the magnetic effect and viscous dissipation decreased the rate of heat transfer, and the thermophoresis effect decreased the rate of mass transfer while the Brownian effect increased it. The precision of the PINN algorithm is confirmed by comparison of the results with the earlier findings, which proves very high accuracy and hence the robustness of the current computing framework. Results of this research are useful for the development of some thermal management systems, energy converters, cooling methods, chemical reaction processes, fuel cell technology, porous media reactors, and ocean engineering involving the transport of complicated non-Newtonian nanofluids.

Modelling doi: 10.3390/modelling7040144

Authors: Yajuan Wang Yuehong Wang Gao Zhang Junde Guo Xiyao Liu

To enhance the thermal performance of a Stirling air conditioner, this study applies Schmidt-based dimensionless analysis to systematically investigate the influence of key structural parameters on its cooling and heating characteristics. A dimensionless thermodynamic framework is established under the ideal isothermal assumptions of the Schmidt model to investigate the effects of temperature ratio, swept volume ratio, dead volume ratio, and phase angle on a Stirling system. The results indicate that increasing the temperature ratio enhances the thermodynamic driving potential; however, excessive temperature ratios introduce stronger irreversibilities, resulting in saturation or even degradation of effective cooling performance. The dimensionless cooling capacity increases significantly with phase angle, rising from 0.25 at α = 50° to 0.65 at α = 120°, while heating capacity peaks at α ≈ 71.6° with εe = 0.18. The p–v diagram analysis reveals optimal work output at α ≈ 75°, where the cycle area reaches 20.8, representing a 44.4% increase from the value at 15°. Performance saturation occurs at τ > 3 and κ > 6 for cooling and beyond κ > 4 for heating. Within the assumptions of the ideal Schmidt model, the results suggest that medium-to-high temperature ratios (τ ≈ 3–4) combined with moderate swept volume ratios (κ ≈ 6–8) provide the optimal balance between thermodynamic performance and structural compactness; these parameter combinations should be regarded as theoretical design references for ideal operating conditions rather than directly applicable engineering optimization guidelines.

Modelling doi: 10.3390/modelling7040143

Authors: Naveed Ashraf Ghulam Abbas Umar Farooq Jason Gu

Three-port DC-to-DC converters based on the SEPIC-boost circuit have gained remarkable attraction in standalone applications such as DC micro grids having PV panels as roof-tops in electric boats, electric and hybrid vehicles, LED driving circuits, telecommunication systems, and medical and industrial electronics devices. Such a combination of SEPIC-boost in a single converter eliminates the use of three separate DC-to-DC converters to charge the batteries and to supply power from the PV module or batteries to the load. All such modes of operation in a single package make the converter compact by reducing the number of solid-state devices and passive components. It also enables the reduction in conversion losses and hence improves the system’s overall conversion efficiency. The control of a single circuit becomes simple and effective in terms of power management by detecting the solar irradiation and state of charge (SOC) of the battery. It enables the continuous flow of power to the load from PV modules or batteries, which is determined by the SOC of the battery and the available level of solar irradiation. This article develops the dynamic or state-space modeling of the combined operation of the SEPIC-boost-based DC-to-DC converter, which has not yet been developed in the literature. The development of systems based on separate dynamic SEPIC or boost modeling cannot meet the requirements of all operating modes. A state-space model of the combined operation of the SEPIC-boost converter enables evaluating the performance of such an energy management system during its various operating modes effectively. The validity of the developed model is recognized with results gained from MATLAB/Simulink and electronics-based Multisim computer software.

Modelling doi: 10.3390/modelling7040142

Authors: Tatiana Kin Aleksey Budnikov Yury Gamin Anna Khakimova Ivan Soloviev

This study conducts a preliminary FE simulation of screw piercing and screw rolling processes for producing bimetallic pipes with variable inner and outer positioning and thickness of the corrosion-resistant steel CL (13Cr and 18Cr10Ni grades) as a rational first step before experimental testing. The results demonstrate that a favorable stress–strain state is formed in both processes under the selected deformation parameters (there are no high tensile stresses in the area of high strains and low temperatures). Shape change analysis confirmed that the pipe geometric dimensions according to simulation are sufficiently close to the target values, with only minor deviations in wall thickness and ovality. The change in CL thickness during piercing ranges from 34% to 51% and increases with the elongation ratio. In the rolling process, it reaches approximately 55–56%. The CL position, its thickness and the material choice significantly influence the deformation heating intensity within the bonding of base and clad materials, as well as the magnitude of the forces acting on the tool in contact with the CL. The obtained results can serve as a methodology that lays the groundwork for experimental verification and the further technology implementation, while minimizing risks and costs.

Modelling doi: 10.3390/modelling7040141

Authors: Guoyuan Wang Wenbo Fan Yinhe Sun Bowen Hu Liyuan Yu Zhaoyang Song

Fractures exert a significant influence on rock mass deformation and seepage pathways, thereby posing a serious challenge to the safe and efficient extraction of deep mines. This problem is particularly evident in deep mines located near the sea, where fractures are extensively developed. For such mines, the overlying seawater represents a considerable potential risk to mining safety. Therefore, investigating the distribution characteristics of deep fractures and clarifying the coupling relationships among the fracture, stress, seepage, and temperature fields are important for ensuring safe and efficient production in deep mines near the sea. Taking the auxiliary shaft of the Sanshandao Gold Mine as the engineering case, this study uses extensive measured fracture data, determines fracture locations by their centroids, and adopts kernel density estimation to non-parametrically characterize the fracture spatial distribution. Fourier convolution is then employed to rapidly reconstruct fracture positions in the discrete fracture network (DFN) model. The results demonstrate that the proposed kernel density estimation method can effectively identify the spatial distribution characteristics of fractures. Subsequently, the fracture field of the underground rock mass is reconstructed by the Monte Carlo method, and a thermal–hydro–mechanical multi-field coupling model incorporating the fracture field is established. The numerical results indicate that fluid flow is primarily concentrated along fractures, and that heat transfer within fractures is markedly faster than that in the rock matrix. The presence of fractures significantly affects the stress field of the underground rock mass, and their influence on the stress distribution increases as fracture length becomes greater. Accordingly, the effects of fractures should not be neglected in numerical analyses. The findings provide reliable support for mine stability calculations and safety evaluations.

Modelling doi: 10.3390/modelling7040140

Authors: Fabien Beaumont Guillaume Polidori Mohammed Lachi

Despite growing interest in sustainable construction materials, unfired clay bricks still exhibit limited thermal insulation performance. This study investigates the enhancement of perforated raw earth bricks through the integration of a bio-based phase change material (PCM) derived from coconut oil to improve thermal damping and heat storage capacity. A numerical analysis was conducted on several configurations, including a solid reference brick, a hollow brick with air-filled cavities, and bricks incorporating one, two, or three rows of PCM encapsulated in polylactic acid (PLA) tubes. Results show a progressive improvement in thermal performance with increasing PCM content showing that the three-row PCM configuration achieved the best dynamic thermal behavior. Thermal gradient and enthalpy analyses revealed the combined effects of the thermal conductivity of PLA and raw earth and the latent heat storage capacity of the PCM. Replacing 17 PCM tubes with a single container of equivalent volume further improved performance while reducing system complexity and cost, decreasing the decrement factor by nearly 50% compared with the three-row configuration. These findings demonstrate the potential of PCM-enhanced raw earth bricks for passive thermal regulation in sustainable buildings, although experimental validation remains necessary.

Modelling doi: 10.3390/modelling7040139

Authors: Oscar H. Sierra-Herrera Mario Eduardo González Niño Carlos E. Pinto-Salamanca Wilman Alonso Pineda Muñoz Jersson X. Leon-Medina

Wind turbines are critical components in renewable energy systems, where early fault detection is essential to ensure reliable operation and reduce maintenance costs. Vibration-based monitoring using multichannel signals provides rich information about the dynamic behavior of the system, although it also introduces challenges related to high dimensionality and feature redundancy. This paper proposes a machine learning-based methodology for fault classification that combines Discrete Wavelet Transform (DWT) for time–frequency feature extraction with Linear Discriminant Analysis (LDA) for dimensionality reduction within a structured processing pipeline. The approach incorporates a Group K-Fold cross-validation strategy to prevent data leakage and ensure a reliable evaluation when working with segmented signals. Experimental results show that the proposed framework achieves high classification performance, reaching a mean accuracy of 98.84±1.16% and a weighted F1-score of 0.9905±0.0089 using a Support Vector Machine (SVM) classifier over five Group K-Fold splits. The results also indicate that dimensionality reduction plays a critical role in improving class separability, having a greater impact than the specific choice of wavelet transform. Findings demonstrate that the proposed DWT–LDA-based approach provides an effective solution for rotor imbalance detection in the laboratory-scale wind turbine evaluated in this study.

Modelling doi: 10.3390/modelling7040138

Authors: Carolina Lima da Silva Luiz Carlos Lobato dos Santos George Simonelli

Accurate prediction of natural gas thermophysical properties is essential for applications in production and transportation engineering, including reservoir simulation and flow modeling. Although machine learning (ML) techniques have been widely used, most studies focus on the estimation of these properties, with limited integration into practical applications. In this study, we propose a supervised model based on a Backpropagation Neural Network for simultaneous estimation of four interdependent properties: compressibility factor (Z), viscosity (μ), density (ρ) and gas formation volume factor (Bg). The multi-output model was trained on 58,165 data points generated from thermodynamic correlations, using pressure, temperature, composition (mole fractions of N2, CO2 and H2S), and gas specific gravity as inputs. The results yielded RMSE values of 5.56 × 10−4, 3.24 × 10−5, 3.01 × 10−2, and 6.33 × 10−4 for Z, μ, ρ and Bg, respectively, with R2 coefficients close to unity. The model’s applicability was evaluated by integrating the Z-factor into pressure drop calculations in pipelines using the Cullender and Smith method, resulting in a mean percentage error of 3.78%, close to the traditional method (3.83%). The results indicate that the model is an efficient and consistent alternative, highlighting the potential for integrating ML with classical hydraulic models.

Modelling doi: 10.3390/modelling7040137

Authors: Mohammed Mawlana Amin Hammad

Simulation optimization has been used to analyze construction operations and support planning decisions under uncertainty. It enables the identification of effective planning strategies throughout a project’s lifecycle. However, the use of stochastic simulation to evaluate alternative strategies results in higher computational demands and the generation of inferior solutions within the resulting optimal solutions. This study examines the feasibility of overcoming these issues by implementing variance reduction techniques into a discrete-event simulation optimization framework. Three variance reduction techniques are evaluated in a case study: Common Random Numbers, Antithetic Variates, and a combined application of both. While these techniques are well established in simulation, their impact on the optimization performance of construction problems has not been fully explored. The results show that VRT not only reduces the computational effort required to evaluate planning strategies but also provides better planning strategies. Among the evaluated techniques, the combined approach demonstrates the best improvements. Overall, the study highlights that variance reduction techniques can make simulation optimization frameworks more practical and reliable for complex construction projects.

Modelling doi: 10.3390/modelling7040136

Authors: Laura Paola Villalobos-Baquero Juan Camilo Mosquera-Jiménez Oscar Danilo Montoya

This paper introduces a methodology for evaluating the voltage stability margin in high-voltage direct-current (HVDC) systems, which analyzes the singularity of the power flow Jacobian matrix—computed via the Newton—Raphson method—and identifies saddle-node bifurcations. The continuation power flow method is employed to model progressive load increases, enabling the continuous tracking of power flow solutions and the determination of voltage collapse points. Within this framework, the system’s behavior is analyzed under contingency conditions, particularly transmission line outages, assessing its capability to maintain secure operating conditions under increasing demand scenarios. The main objective is to identify the most critical line in the system, defined as that which leads to the greatest reduction in loadability when unavailable, prior to voltage collapse. This approach allows for the early identification of structural vulnerabilities, supporting decision-making processes aimed at risk mitigation and operating cost optimization. The proposed methodology is validated using two systems: the six-terminal CIGRE-B4 HVDC system and an 11-node HVDC test feeder.

Modelling doi: 10.3390/modelling7040135

Authors: Nikola Mirkov Milada Pezo Rastko Jovanović Martina Balać Ognjen Peković

This study presents the analysis of global dynamics and stability (e.g., coexisting attractors, Hopf bifurcation boundary) for a nonlinear rotor system with an automatic ball balancer (ABB). The presence of nonlinearity, anisotropy and non-ideal dynamics makes this system not fully understood. The Lagrangian is written explicitly in terms of the displacement of the rotor centre and the angular positions of the balls (x,y,ψ,φj). The kinetic energy separates into structural, unbalance coupling, and ball coupling blocks, and the Rayleigh dissipation function covers both support damping and race drag. The three families of equations of motion (translational, spin, ball) are compacted into the matrix form and solved numerically. Non-dimensionalisation introduces the seven groups (Ω,μun,μb,ε,β^,D^,Δ) with Δ being the anisotropy parameter. The results document bistability between the clustered and balanced ball configurations depending solely on ball initial conditions rather than rotor displacement, together with a basin of attraction analysis in which the balanced basin occupies only approximately 20% of ball initial-condition space. A three-dimensional stability map reveals a previously unreported phenomenon: narrow islands of stability at very low race damping, suggesting that effective balancing may not always require dissipation, alongside a two-lobe Hopf bifurcation boundary with a disconnected instability pocket. Anisotropy study uncovers that the rotor’s response is dominated by quasi-periodic torus attractor across almost the entire (93.5%) parameter space rather than the simple periodic balancing usually assumed, with a clean analytical rule identifying exactly when support asymmetry will resonantly amplify vibration. Together these findings point to design principles on ball seeding, damping selection, and permissible anisotropy.

Modelling doi: 10.3390/modelling7040134

Authors: Kumari Gamage Buddhika Weerasinghe Shasha Wang Sabrina Fawzia

In-plane curved steel beams with circular hollow sections (CHSs) are widely gaining appeal in bridges. Strengthening such elements for increased demand or decreased strength due to environmental effects or fatigue, without affecting the usage of structure, is a timely need. Carbon fiber-reinforced polymer (CFRP) materials have been a promising solution for such situations. This paper investigates the flexural behavior of CFRP-strengthened vertically curved steel beams with CHSs. Sixteen such beams, each with a span of 1200 mm and having four different radii of curvature, i.e., 0 m, 2000 mm, 4000 mm, and 6000 mm, and retrofitted with a range of CFRP bond lengths, are considered. Numerical models of these beams are developed and validated using the results of tests performed by the authors, and the validated models were used to simulate bond characteristics and structural performance. Optimum performance was noted in the specimens strengthened with CFRP fibers attached in the axial direction of the members, irrespective of their curvature. On average, strength enhancements of 21% and 14% were obtained in CFRP-strengthened straight and curved beams, respectively. Detailed bond characteristics presented in this paper under transverse loads yield important data for researchers, designers and material developers to strengthen in-plane curved steel members.

Modelling doi: 10.3390/modelling7040133

Authors: Fangqian Wu Xueping Song Lin Yuan Shanglei Jiang Yuwen Sun

Due to the low stiffness characteristics, thin-walled parts are prone to force-induced deformation during the peripheral milling process, which severely restricts machining accuracy and efficiency. In existing studies, for curved thin-walled parts, the Finite Element Method (FEM) is usually adopted for deformation prediction. However, the traditional FEM usually requires a considerable amount of computing time, owing to the high model complexity and batch parameter evaluations. Therefore, this study proposes a method of constructing a surrogate model based on a small amount of FEM simulation data. Firstly, a peripheral milling cutting force model is established to obtain the instantaneous milling force. Secondly, a finite element model considering the material removal effect is constructed, and an iterative solution strategy is introduced to calculate the force-induced deformation. Finally, an Enhanced Latin Hypercube Sampling (ELHS) method is used to generate training samples, and the Elliptic Basis Function Neural Network (EBFNN) is selected as the surrogate model to establish a nonlinear mapping relationship between machining parameter combinations and force-induced deformation. This method enables rapid prediction of deformation at any machining position on curved thin-walled parts, reducing the computation time from hours to seconds while maintaining prediction accuracy.

Modelling doi: 10.3390/modelling7040132

Authors: Shuichi Sakamoto Yoshiaki Kojima Kenta Saito Zulhafiz Syazmi Bin Roslan Shui Miyata Ryuki Kiuchi

Rice straw, a byproduct of global rice production (~530 million tons annually), is generated at 80–100 million tons per year, yet a significant portion is incinerated or discarded, causing environmental problems. This study investigated the sound absorption properties of straw from IR8, a high-yielding long-grain rice variety. The normal incidence sound absorption coefficient was measured at three bulk densities (0.140, 0.150, and 0.160 g/cm3) for bundled rice straw structures. Cross-sectional images obtained using a micro-computed tomography (CT) scanner were then used to theoretically estimate the sound absorption coefficient. Each CT cross-section, oriented perpendicular to the incident sound wave direction, was modeled as a clearance between two parallel planes. The characteristic impedance and propagation constant were calculated from this model, and the normal incidence sound absorption coefficient was determined using the transfer matrix method with measured tortuosity incorporated. The experimental and theoretical absorption peaks showed similar trends across bulk densities. A parameter study was also conducted by scaling cross-sectional images according to the diameter ratios of Koshihikari short-grain rice straw and Yumekaori wheat straw relative to IR8. Additionally, reducing the number of CT images to as few as ten adequately approximated the full dataset for a 20 mm thick sample.

Modelling doi: 10.3390/modelling7040130

Authors: Shang Wang Yajuan Zhang Linjie Li

The Traveling Salesman Problem (TSP) is a fundamental NP-hard combinatorial optimization problem with broad applications in logistics, scheduling, and satellite mission planning. While Ant Colony Optimization (ACO) offers distributed search and positive feedback, conventional variants suffer from premature convergence and quadratic construction costs that limit scalability. We propose the Globally Adaptive Ant Colony System (GACS), which integrates three synergistic mechanisms: (1) K-nearest neighbor candidate-list pruning that reduces per-step construction complexity from O(n) to O(K); (2) a globally adaptive pheromone weighting scheme that dynamically calibrates reinforcement intensity as the search matures; and (3) an adaptive stagnation recovery mechanism that applies pheromone smoothing to escape local optima. Numerical experiments demonstrate that GACS consistently outperforms four traditional ACO baselines under an equivalent time budget. On a large benchmark set from TSPLIB, GACS achieves highly competitive results against various state-of-the-art metaheuristics, with non-parametric statistical tests confirming its significant superiority in both solution quality and convergence rank. Ablation and sensitivity analyses verify that all three mechanisms are individually indispensable and that the framework is robust to parameter perturbation. Specifically, the evaporation rate and stagnation threshold are identified as the most critical parameters affecting performance, while the smoothing and adaptive range parameters exhibit low sensitivity. These results establish GACS as a lightweight, scalable, and adaptable framework for the TSP.

Modelling doi: 10.3390/modelling7040131

Authors: Ying Huang Zhiqiang Xin Zhiming Cai Songyang Liu Yanming Xu

Recognizing that efficient and high-fidelity simulation of wind farms in mountainous terrain remains a significant challenge, this study adopted an integrated Large Eddy Simulation (LES) and Dynamic Wake Meandering (DWM) approach to conduct medium-fidelity fluid–structure interaction analysis of a wind farm situated on multiple-hill terrain. Furthermore, a comparative investigation with a flat wind farm was conducted to elucidate the coupled effects of turbine layout and terrain conditions on wake characteristics and structural loads. Results show that the terrain-induced vortical structures in the mountainous wind farm significantly enhance the wake meandering amplitude and expansion rate, leading to higher overall turbulence intensity compared to the flat wind farm. Due to the higher wake recovery rate in the mountainous wind farm, the power gain from lateral offset is more limited. Both wind farms reach their maximum power output at a lateral offset of one turbine rotor diameter (1D) under the present setup, beyond which no further increase is observed. The streamwise decay of the terrain-induced flow acceleration effect is identified as the primary cause of power differences among front-row turbines located on distinct hills within the mountainous wind farm. Furthermore, the terrain-induced vortices create more non-uniform inflow conditions in the mountainous wind farm, causing certain turbines to exhibit peak short-term equivalent fatigue loads with a distribution pattern distinct from the flat wind farm. Due to the generally higher turbulence intensity, all turbines in the mountainous wind farm experience increased fatigue loads compared to the flat wind farm.

Modelling doi: 10.3390/modelling7040129

Authors: Tuo Zhou

In this paper, a class of distributed event-triggered (ET) control strategy is proposed to address the average consensus problem for multi-agent systems (MAS). Compared with the existing ET control methods with fixed connected communication links, underlying topology considered here is jointly connected, which is more adaptable to the needs of practicality. In order to save communication energy resources among agents, an improved integral-type event-triggered (ITET) strategy is chosen to guarantee that the entire system reaches an agreement on the desired state and no Zeno behavior occurs. Finally, two simulation examples are given to investigate the effectiveness of the proposed control strategy.

Modelling doi: 10.3390/modelling7040128

Authors: Ahmed Y. Zakariya Ahmed F. Tayel Shehab Ahmed

Energy-efficient operation of railway systems is of great importance for both environmental and economic reasons. Minimizing net energy consumption helps to achieve such energy-efficient operation. In this paper, the train’s speed profile and headway between trains are controlled to achieve lower traction energy consumption and higher train synchronization for better regenerative braking energy utilization. Eventually, the net energy consumption, defined as the difference between the traction energy consumption and the utilization of regenerative braking energy, is minimized. Two optimization problems are defined to solve the problem efficiently. The first main problem is to find the optimal speeds at each segment of the railway track. The second sub-problem’s objective is to find the optimal values of travel time, dwell time, and headway for every suggested solution to the main problem. Both problems are solved using the genetic algorithm. Numerical results are based on the actual operation data of the Beijing Metro Yizhuang Line in China. In the numerical results, the proposed strategy of dividing the problem into two problems and the use of variable headway shows an enhancement in reducing net energy consumption by 7.5% compared to other strategies in the literature.

Modelling doi: 10.3390/modelling7040127

Authors: Ismail Ekmekci Faruk Oral Cemil Koyunoğlu

Accurate characterization of wind-speed distributions is essential for preliminary wind-resource assessment, vertical wind-profile evaluation, and energy-yield estimation. This study presents a CFD-assisted reconstruction and validation framework that integrates two-parameter Weibull statistics with class-conditioned OpenFOAM v13 simulations to reconstruct wind-speed distributions at different measurement heights. Hourly wind-speed records measured at 10 m and 30 m at the Sakarya–Esentepe station during the period of 2009–2010 were used. The 2009 dataset was employed to estimate the Weibull shape and scale parameters by maximum likelihood estimation, while the 2010 dataset was reserved for independent validation. To ensure methodological consistency between statistical wind characterization and steady CFD modeling, the fitted Weibull distribution was discretized into representative wind-speed classes. For each class, a steady Reynolds-averaged Navier–Stokes simulation was performed in OpenFOAM under neutral atmospheric boundary-layer assumptions using the standard k–ε turbulence model, a logarithmic inlet velocity profile, and rough-wall boundary treatment. The class-wise CFD velocity responses extracted at 10 m and 30 m were then weighted by the corresponding Weibull class probabilities to reconstruct height-specific wind-speed probability distributions. The reconstructed distributions showed good agreement with the measured and fitted Weibull references. The RMSE values obtained by CFD for measurements at heights of 10 m and 30 m on the measurement mast were 0.45 m s−1 and 0.52 m s−1, respectively, and the Pearson correlation coefficients were 0.97 and 0.96, respectively; these values indicate that the CFD analyses are reliable. For the Lilliefors-adjusted Kolmogorov–Smirnov statistics, there is no value higher than 0.06. The differences between the reference and CFD-reconstructed AEP estimates were +0.40% at 10 m and −1.97% at 30 m. These findings indicate that the proposed Weibull–OpenFOAM framework provides a reproducible engineering approach for CFD-assisted wind-speed distribution reconstruction and height-specific consistency assessment. However, the method should be interpreted as a class-conditioned reconstruction framework rather than a stand-alone transient atmospheric wind prediction model.

Modelling doi: 10.3390/modelling7040126

Authors: Chen Xu Yang Yang Xiaojiang Gu Yijun Mao

The snapshot proper orthogonal decomposition (POD) method relies on synchronously sampled datasets, significantly limiting its utility for analyzing asynchronous measurements in unsteady flow studies. This paper proposes a frequency-domain proper orthogonal decomposition (FDPOD) method tailored for mode extraction and flow field reconstruction from asynchronously sampled data. The FDPOD framework integrates three key components: frequency-domain transformation to decouple phase discrepancies inherent in asynchronous sampling, power spectral density (PSD) analysis combined with segmented ensemble averaging to suppress spectral leakage errors, and eigenvalue decomposition of energy-ranked frequency components to identify dominant coherent structures. Validated through numerical simulations of a subsonic jet and experimental measurements from a low-speed mixed-flow fan, the method demonstrates exceptional performance under asynchronous conditions: cumulative energy errors are reduced to 0.3% across the first 50 modes, while flow field reconstruction achieves 99.5% accuracy. Dominant mode structures exhibit remarkable consistency with those derived from synchronous conditions, with hot-wire measurement errors remaining below 0.03% for both asynchronous and temporally shuffled datasets. These results position FDPOD as a robust and practical tool for analyzing complex unsteady flows where synchronous data acquisition proves impractical, particularly in large-scale or spatially distributed measurement systems.

Modelling doi: 10.3390/modelling7040125

Authors: Juraj Kováč Peter Malega Pavlo Vaulin

Virtual reality can support the preparation and rehearsal of assembly tasks by providing a safe and repeatable digital representation of workstations. This study presents the development and laboratory feasibility validation of a geometry- and procedure-oriented VR simulation model for the assembly and disassembly of end-effectors on an industrial robot. The workflow was implemented using the Almega AX-V6 robotic workstation as a case study and included geometric acquisition of the real robot, CAD modelling in SolidWorks, redesign of the original end-effector connection using a quick-change flange concept, creation of two alternative end-effector models, modelling of the laboratory workspace in SketchUp, and scene enhancement in Twinmotion. The resulting robot and environment models were integrated in Pixyz Review and deployed through an Oculus Rift-based VR setup. Compared with the original flange concept, which required twelve screws, the redesigned training concept used two screws and two nuts, reducing the number of fastening elements by 66.7% and the number of screw positions by 83.3%. The VR implementation supported visual inspection, controller-based placement and alignment, and symbolic confirmation of fastening steps; it did not include force feedback, threaded fastening physics, automatic error scoring, or quantified transfer-of-training evaluation. Laboratory feasibility validation confirmed correct asset integration, spatial correspondence with the physical workplace, and functional executability of the target exchange sequence. The results show that the workflow is useful as a case-study pipeline for CAD-to-VR modelling and assembly rehearsal, while controlled user studies are still required before claims about training effectiveness can be made.

Modelling doi: 10.3390/modelling7040124

Authors: Steven D. Harris Christopher D. Gill Roger D. Chamberlain

Orchestration of Asymmetric Multiprocessing Platforms (AMPs), such as ARM big.LITTLE, frequently relies on the heuristic assumption of cluster independence, wherein high-performance (“Big”) and high-efficiency (“Little”) cores operate as computationally orthogonal resources. These cores are partitioned into “islands” of separate power/performance clusters, operating on independent/voltage frequency rails. However, these platforms share resources, including Last-Level Cache (LLC), main memory, and interconnects across all cores. Therefore, we assume that islands interact, operating in a functionally “coupled state.” To conduct a measure-theoretic evaluation of this assumption, we apply the Boltzmann uniqueness theorem, recently demonstrated to be the singular method to determine the veracity of this assumption. Mathematically, we define an “uncoupled” system as one whose joint resource measurement is strictly the convolution of its subsystem measures. We evaluate two distinct AMP topologies—Orange Pi 5 and Cubie A7A under controlled saturation—and demonstrate a systemic failure of convolution commutativity. We subsequently expand this investigation to high-performance x86 hybrid architectures via the Intel i7-12800H platform. Our findings, characterized by significant negative power correlations and the failure of predictive convolution models, constitute a counterexample for cluster independence. We identify shared architectural resources, specifically the LLC and shared power rails, as the likely physical mechanisms of “architectural entanglement,” rendering traditional additive performance models underspecified.

Modelling doi: 10.3390/modelling7040123

Authors: Shunzuo Qiu Qin Liu Yan Yang Qianqi Xiao Yan Jiang

To solve the problem that the theory of in situ separation and sand removal of marine hydrate is not perfect enough, the formulas of fluid tangential velocity and particle radial migration were derived based on the separation theory of rotating fluid and equilibrium orbit. Under certain assumptions, theoretical prediction models of fluid tangential velocity, particle radial migration and separated particle size under different operation and physical parameters were established. Then the theoretical results were compared with the numerical simulation results. The results show that the key factors affecting the tangential velocity are the inlet spiral pitch, the number of spiral blades, the diameter of the overflow pipe, the thickness of the spiral blades, and the main diameter of the desander. The tangential velocity is proportional to the flow rate. When the particle diameter is fixed, the radial migration velocity of the particle decreases with the increase in the rotation radius. When the rotation radius is fixed, the radial migration velocity of particles increases with the increase in particle diameter. The larger the hydrate particle size, the shorter the time to reach the center, and the larger the sand particle size, the shorter the time to reach the wall. The particle size is inversely proportional to the tangential velocity of the fluid in the equilibrium orbit. The determination of fluid velocity, liquid–solid density difference and particle size is the key factor affecting particle equilibrium trajectory and particle size separation. The numerical simulation results are basically consistent with the theoretical values. The obtained results enrich the theoretical model of hydrate in situ sand removal.

Modelling doi: 10.3390/modelling7030122

Authors: Jiaren Sun Yating Jiang Shuai Teng Zongchao Liu Nuo Chen

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.

Modelling doi: 10.3390/modelling7030121

Authors: Ming-Lei Ma Cheng-Da Yu Ji-Long Chai Guo-Wen Xu Biao Wu Jing-Zhong Tong Qing-Hua Li

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.

Modelling doi: 10.3390/modelling7030120

Authors: Rogério F. F. Lopes Christian J. Silva Rodrigo R. Menéres Pedro J. S. C. P. Sousa Pedro M. G. P. Moreira João S. Silva Rodrigo S. Andrade

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.

Modelling doi: 10.3390/modelling7030119

Authors: Shuichi Sakamoto Kenta Saito Yoshiaki Kojima Ryuki Kiuchi Shui Miyata

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.

Modelling doi: 10.3390/modelling7030118

Authors: Dianchao Wang

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.

Modelling doi: 10.3390/modelling7030117

Authors: Haoran Song Lipu Zhang

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.

Modelling doi: 10.3390/modelling7030116

Authors: Jinzhao Fan Bixiao Zhang Jiazhen Liu Yufei Cai Hong Shi

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.

Modelling doi: 10.3390/modelling7030115

Authors: Yi Guo Chun Li Yang Lv Liuxiao Li Yangfan Lu Kai Wen

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.

Modelling doi: 10.3390/modelling7030114

Authors: Tianxue Yang Dongpo Zhao

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.

Modelling doi: 10.3390/modelling7030113

Authors: Olivier Plé Anna Lushnikova Xiaohui Jia

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.

Modelling doi: 10.3390/modelling7030112

Authors: Amrita Bhadoriya Manish R. Betheja Mrudul Y. Jani Vivek Panwar Vishal Pradhan

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.

Modelling doi: 10.3390/modelling7030111

Authors: D. M. Li Zhi-Yan Zhong Liu Yang Bi-He Yuan Ying Zhang

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.

Modelling doi: 10.3390/modelling7030110

Authors: Zhihao Zhao Xiran Wang Leyi Shi Juan Wang

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.

Modelling doi: 10.3390/modelling7030109

Authors: Luca Vaccino Alana K. Lund Shirley J. Dyke Mohsen Azimi Ethan Vallerga

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.

Modelling doi: 10.3390/modelling7030108

Authors: Douglas M. Rieger Alisson L. Daga Ervin K. Lenzi Marcelo K. Lenzi

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.

Modelling doi: 10.3390/modelling7030107

Authors: Bin Cai Sri Sritharan Eugene S. Takle Chris Milliren

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%.

Modelling doi: 10.3390/modelling7030106

Authors: Jenny Vanessa Rojas-Báez María Fernanda Laverde-Rojas Oscar Danilo Montoya

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 N−1 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.

Modelling doi: 10.3390/modelling7030105

Authors: Yifei Wang Jiatian Gan Jun Yang Ning Zhang Jingang Wang Xingyu Zhang Pengcheng Zhao

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.

Modelling doi: 10.3390/modelling7030104

Authors: Hexing Zheng Jinguo Liu Haitao Gu Fang Shi Kexin Zhang

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.