Journal Description
Modelling
Modelling
is an international, peer-reviewed, open access journal on theory and applications of modelling and simulation in engineering science, published bimonthly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within ESCI (Web of Science), Scopus, Ei Compendex, EBSCO and other databases.
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 22.7 days after submission; acceptance to publication is undertaken in 3.6 days (median values for papers published in this journal in the first half of 2026).
- Journal Rank: JCR - Q2 (Engineering, Multidisciplinary) / CiteScore - Q2 (Mathematics (miscellaneous))
- Recognition of Reviewers: APC discount vouchers, optional signed peer review and reviewer names are published annually in the journal.
Impact Factor:
1.8 (2025);
5-Year Impact Factor:
1.8 (2025)
Latest Articles
Finite Element Simulation of Production Process of Bimetallic Pipes by Screw Rolling
Modelling 2026, 7(4), 142; https://doi.org/10.3390/modelling7040142 - 10 Jul 2026
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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.
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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.
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Open AccessArticle
Study on the Fine Reconstruction of Fracture Field and Coupling Mechanism of Thermal–Fluid–Solid Multiple Fields in Deep Rock Mass
by
Guoyuan Wang, Wenbo Fan, Yinhe Sun, Bowen Hu, Liyuan Yu and Zhaoyang Song
Modelling 2026, 7(4), 141; https://doi.org/10.3390/modelling7040141 - 9 Jul 2026
Abstract
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.
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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.
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Open AccessArticle
Numerical Study of Sustainable Bio-Based Bricks with Integrated Phase Change Materials for Enhanced Thermal Performance
by
Fabien Beaumont, Guillaume Polidori and Mohammed Lachi
Modelling 2026, 7(4), 140; https://doi.org/10.3390/modelling7040140 - 8 Jul 2026
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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
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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.
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Rotor Imbalance Classification in Wind Turbines Using Multichannel Vibration Analysis and a DWT–LDA Framework
by
Oscar H. Sierra-Herrera, Mario Eduardo González Niño, Carlos E. Pinto-Salamanca, Wilman Alonso Pineda Muñoz and Jersson X. Leon-Medina
Modelling 2026, 7(4), 139; https://doi.org/10.3390/modelling7040139 - 7 Jul 2026
Abstract
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
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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 and a weighted F1-score of 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.
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(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Modelling)
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Integrated Prediction of Thermophysical Properties of Natural Gas Using Machine Learning and Its Application to Pressure Drop Modeling
by
Carolina Lima da Silva, Luiz Carlos Lobato dos Santos and George Simonelli
Modelling 2026, 7(4), 138; https://doi.org/10.3390/modelling7040138 - 6 Jul 2026
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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
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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.
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(This article belongs to the Section Modelling in Artificial Intelligence)
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Enhancing Construction Simulation Optimization Performance Through Variance Reduction Techniques
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Mohammed Mawlana and Amin Hammad
Modelling 2026, 7(4), 137; https://doi.org/10.3390/modelling7040137 - 5 Jul 2026
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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
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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.
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(This article belongs to the Special Issue Optimization in Engineering: Models and Algorithms)
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Voltage Stability Analysis in HVDC Systems Using Jacobian Singularity and Saddle-Node Bifurcations
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Laura Paola Villalobos-Baquero, Juan Camilo Mosquera-Jiménez and Oscar Danilo Montoya
Modelling 2026, 7(4), 136; https://doi.org/10.3390/modelling7040136 - 5 Jul 2026
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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
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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.
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(This article belongs to the Special Issue Modelling of Nonlinear Dynamical Systems)
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Global Dynamics and Stability of Automatic Ball Balancers Under Anisotropy and Non-Ideal Excitation
by
Nikola Mirkov, Milada Pezo, Rastko Jovanović, Martina Balać and Ognjen Peković
Modelling 2026, 7(4), 135; https://doi.org/10.3390/modelling7040135 - 4 Jul 2026
Abstract
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
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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 . 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 with 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 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 ( ) 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.
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(This article belongs to the Special Issue Modelling of Nonlinear Dynamical Systems)
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Experimental and Numerical Investigation of CFRP-Strengthened In-Plane Curved Steel Beams with Circular Hollow Cross-Section Subjected to Transverse Load
by
Kumari Gamage, Buddhika Weerasinghe, Shasha Wang and Sabrina Fawzia
Modelling 2026, 7(4), 134; https://doi.org/10.3390/modelling7040134 - 1 Jul 2026
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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
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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.
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(This article belongs to the Section Modelling in Engineering Structures)
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A Method for Rapidly Predicting Force-Induced Deformation During the Peripheral Milling of Curved Thin-Walled Parts
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Fangqian Wu, Xueping Song, Lin Yuan, Shanglei Jiang and Yuwen Sun
Modelling 2026, 7(4), 133; https://doi.org/10.3390/modelling7040133 - 1 Jul 2026
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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.
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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.
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Open AccessArticle
Experimental and Theoretical Estimation of Sound Absorption Coefficients from CT Scan Images of Long-Grain Rice Straw
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Shuichi Sakamoto, Yoshiaki Kojima, Kenta Saito, Zulhafiz Syazmi Bin Roslan, Shui Miyata and Ryuki Kiuchi
Modelling 2026, 7(4), 132; https://doi.org/10.3390/modelling7040132 - 1 Jul 2026
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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
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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.
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(This article belongs to the Section Modelling in Engineering Structures)
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Numerical Study on Wake Characteristics and Fatigue Loads of Turbine Arrays with Different Layouts in Multiple Hills Terrain
by
Ying Huang, Zhiqiang Xin, Zhiming Cai, Songyang Liu and Yanming Xu
Modelling 2026, 7(4), 131; https://doi.org/10.3390/modelling7040131 - 30 Jun 2026
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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
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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.
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(This article belongs to the Topic Theoretical, Numerical and Experimental Studies on Clean Energy and Combustion, 2nd Edition)
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A Globally Adaptive Ant Colony System with Stagnation Recovery and Candidate-List Search for Traveling Salesman Problems
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Shang Wang, Yajuan Zhang and Linjie Li
Modelling 2026, 7(4), 130; https://doi.org/10.3390/modelling7040130 - 30 Jun 2026
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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
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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 to ; (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.
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(This article belongs to the Special Issue Optimization in Engineering: Models and Algorithms)
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Integral-Type Event-Triggered Average Consensus over Jointly Connected Topologies
by
Tuo Zhou
Modelling 2026, 7(4), 129; https://doi.org/10.3390/modelling7040129 - 29 Jun 2026
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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
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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.
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Open AccessArticle
Enhanced Strategy for Optimizing Net Energy Consumption of Railway Systems Using Speed Profile and Variable Headway
by
Ahmed Y. Zakariya, Ahmed F. Tayel and Shehab Ahmed
Modelling 2026, 7(4), 128; https://doi.org/10.3390/modelling7040128 - 28 Jun 2026
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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
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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.
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Open AccessArticle
CFD-Assisted Validation of Weibull-Based Wind-Speed Reconstruction Using OpenFOAM
by
Ismail Ekmekci, Faruk Oral and Cemil Koyunoğlu
Modelling 2026, 7(4), 127; https://doi.org/10.3390/modelling7040127 - 25 Jun 2026
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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
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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.
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Open AccessArticle
Frequency-Domain Proper Orthogonal Decomposition for Asynchronously Sampled Unsteady Flow Fields
by
Chen Xu, Yang Yang, Xiaojiang Gu and Yijun Mao
Modelling 2026, 7(4), 126; https://doi.org/10.3390/modelling7040126 - 25 Jun 2026
Abstract
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
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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.
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(This article belongs to the Section Modelling in Mechanics)
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Development and Laboratory Feasibility Validation of a Virtual Reality Simulation Model for Robotic End-Effector Assembly Training
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Juraj Kováč, Peter Malega and Pavlo Vaulin
Modelling 2026, 7(4), 125; https://doi.org/10.3390/modelling7040125 - 23 Jun 2026
Abstract
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
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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.
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(This article belongs to the Special Issue Modelling and Simulation in Virtual Reality)
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Open AccessArticle
Measure-Theoretic Diagnostics of Architectural Entanglement in Asymmetric Multiprocessing Systems: A Boltzmann Uniqueness Approach
by
Steven D. Harris, Christopher D. Gill and Roger D. Chamberlain
Modelling 2026, 7(4), 124; https://doi.org/10.3390/modelling7040124 - 23 Jun 2026
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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
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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.
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Open AccessArticle
Theoretical Study on the Separation of New Hydrate Downhole In Situ Desander
by
Shunzuo Qiu, Qin Liu, Yan Yang, Qianqi Xiao and Yan Jiang
Modelling 2026, 7(4), 123; https://doi.org/10.3390/modelling7040123 - 23 Jun 2026
Abstract
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
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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.
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(This article belongs to the Section Modelling in Engineering Structures)
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