Modelling doi: 10.3390/modelling6030078

Authors: Hui Zhang Lan Zhang Hua-Yang Dang

This paper presents a theoretical model of a thin, penny-shaped piezoelectric actuator bonded to an isotropic thermo-elastic substrate under coupled electrical-thermal-diffusive loading. The problem is assumed to be axisymmetric, and the peeling stress of the film is neglected in accordance with membrane theory, yielding a simplified equilibrium equation for the piezoelectric film. By employing potential theory and the Hankel transform technique, the surface strain of the substrate is analytically derived. Under the assumption of perfect bonding, a governing integral equation is established in terms of interfacial shear stress. The solution to this integral equation is obtained numerically using orthotropic Chebyshev polynomials. The derived results include the interfacial shear stress, stress intensity factors, as well as the radial and hoop stresses within the system. Finite element analysis is conducted to validate the theoretical predictions. Furthermore, parametric studies elucidate the influence of material mismatch and actuator geometry on the mechanical response. The findings demonstrate that, the performance of the piezoelectric actuator can be optimized through judicious control of the applied electrical-thermal-diffusive loads and careful selection of material and geometric parameters. This work provides valuable insights for the design and optimization of piezoelectric actuator structures in practical engineering applications.

Modelling doi: 10.3390/modelling6030077

Authors: Teguh Putranto Totok Yulianto Septia Hardy Sujiatanti Dony Setyawan Ahmad Fauzan Zakki Muhammad Zubair Muis Alie Wibowo Wibowo

This research explores the application of NiTiNOL-steel (NiTi–ST) wire ropes as nonlinear damping devices for mitigating vibrations in composite stiffened panels. A dynamic model is formulated by coupling the composite panel with a modified Bouc–Wen hysteresis representation and employing the first-order shear deformation theory (FSDT), based on Hamilton’s principle. Using the Galerkin truncation method (GTM), the model is converted into a system of nonlinear ordinary differential equations. The dynamic response to axial harmonic excitations is analyzed, emphasizing the vibration reduction provided by the embedded NiTi–ST ropes. Finite element analysis (FEA) validates the model by comparing natural frequencies and force responses with and without ropes. A newly developed experimental apparatus demonstrates that NiTi–ST cables provide outstanding vibration damping while barely affecting the system’s inherent frequency. The N3a configuration of NiTi–ST ropes demonstrates optimal vibration reduction, influenced by excitation frequency, amplitude, length-to-width ratio, and composite layering.

Modelling doi: 10.3390/modelling6030076

Authors: Guirong Wang Shuanglong Li Xiaojing Zhu Yuhuai Wang Jianfang Huang Yitao Zhong Zhipeng Wu

Inventory counting of logistics boxes in complex scenarios has always been a core task in intelligent logistics systems. To solve the problems of a high leakage rate and low computational efficiency caused by stacking, occlusion, and rotation in box detection against complex backgrounds in logistics environments, this paper proposes a lightweight, rotated object detection model: REW-YOLO (RepViT-Block YOLO with Efficient Local Attention and Wise-IoU). By integrating structural reparameterization techniques, the C2f-RVB module was designed to reduce computational redundancy in traditional convolutions. Additionally, the ELA-HSFPN multi-scale feature fusion network was constructed to enhance edge feature extraction for occluded boxes and improve detection accuracy in densely packed scenarios. A rotation angle regression branch and a dynamic Wise-IoU loss function were introduced to further refine localization and balance sample quality. Experimental results on the self-constructed BOX-data dataset demonstrate that the REW-YOLO achieves 90.2% mAP50 and 130.8 FPS, with a parameter count of only 2.18 M, surpassing YOLOv8n by 2.9% in accuracy while reducing computational cost by 28%. These improvements provide an efficient solution for automated box detection in logistics applications.

Modelling doi: 10.3390/modelling6030075

Authors: Ruiqing Chen Jieyu Dai Shuning Gu Lang Yang Laohu Long Jundong Wang

This study proposes a coupled constitutive model that captures the anisotropic failure characteristics and damage evolution of nickel-based single-crystal (SX) superalloys under various temperature conditions. The model accounts for both creep rate and material damage evolution, enabling accurate prediction of the typical three-stage creep curves, macroscopic fracture morphologies, and microstructural features under uniaxial tensile creep for specimens with different crystallographic orientations. Creep behavior of SX superalloys was simulated under multiple orientations and various temperature-stress conditions using the proposed model. The resulting creep curves aligned well with experimental observations, thereby validating the model’s feasibility and accuracy. Furthermore, a finite element model of cylindrical specimens was established, and simulations of the macroscopic fracture morphology were performed using a user-defined material subroutine. By integrating the rafting theory governed by interfacial energy density, the model successfully predicts the rafting morphology of the microstructure at the fracture surface for different crystallographic orientations. The proposed model maintains low programming complexity and computational cost while effectively predicting the creep life and deformation behavior of anisotropic materials. The model accurately captures the three-stage creep deformation behavior of SX specimens and provides reliable predictions of stress fields and microstructural changes at critical cross-sections. The model demonstrates high accuracy in life prediction, with all predicted results falling within a ±1.5× error band and an average error of 14.6%.

Modelling doi: 10.3390/modelling6030074

Authors: Surma H. Ibrahim Ali A. Shukur Rizgar H. Salih

This paper presents a novel four-dimensional autonomous conservative model characterized by an infinite set of equilibrium points and an unusual algebraic structure in which all eigenvalues of the Jacobian matrix are zero. The linearization of the proposed model implies that classical stability analysis is inadequate, as only the center manifolds are obtained. Consequently, the stability of the system is investigated through both analytical and numerical methods using Lyapunov functions and numerical simulations. The proposed model exhibits rich dynamics, including hyperchaotic behavior, which is characterized using the Lyapunov exponents, bifurcation diagrams, sensitivity analysis, attractor projections, and Poincaré map. Moreover, in this paper, we explore the model with fractional-order derivatives, demonstrating that the fractional dynamics fundamentally change the geometrical structure of the attractors and significantly change the system stability. The Grünwald–Letnikov formulation is used for modeling, while numerical integration is performed using the Caputo operator to capture the memory effects inherent in fractional models. Finally, an analog electronic circuit realization is provided to experimentally validate the theoretical and numerical findings.

Modelling doi: 10.3390/modelling6030073

Authors: Haiyang Ji Zhanqiang Liu Jinfu Zhao Bing Wang

The efficient thermal management of cutting tools is critical for ensuring dimensional accuracy, surface integrity, and tool longevity, especially in the high-speed dry machining process. However, conventional cooling methods often fall short in reaching the heat-intensive zones near the cutting inserts. This study proposes a novel internal cooling strategy that integrates triply periodic minimal surface (TPMS) structures into the toolholder, aiming to enhance localized heat removal from the cutting region. The thermal-fluidic behaviors of four TPMS topologies (Gyroid, Diamond, I-WP, and Fischer–Koch S) were systematically analyzed under varying coolant velocities using computational fluid dynamics (CFD). Several key performance indicators, including the convective heat transfer coefficient, Nusselt number, friction factor, and thermal resistance, were evaluated. The Diamond and Gyroid structures exhibited the most favorable balance between heat transfer enhancement and pressure loss. The experimental validation confirmed the CFD prediction accuracy. The results establish a new design paradigm for integrating TPMS structures into toolholders, offering a promising solution for efficient, compact, and sustainable cooling in advanced cutting applications.

Modelling doi: 10.3390/modelling6030072

Authors: Junyi Zou Haojun Yan Yunbing Yan Xianping Huang

The electromechanical braking (EMB) system is an important component of intelligent vehicles and is also the core actuator for longitudinal dynamic control in autonomous driving motion control. Therefore, we propose a new mechanism layout form for EMB and a feedforward second-order linear active disturbance rejection controller based on clamping force. This solves the problem of excessive axial distance in traditional EMB and reduces the axial distance by 30%, while concentrating the PCB control board for the wheels on the EMB housing. This enables the ABS and ESP functions to be integrated into the EMB system, further enhancing the integration of line control and active safety functions. A feedforward second-order linear active disturbance rejection controller (LADRC) based on the clamping force of the brake caliper is proposed. Compared with the traditional clamping force control methods three-loop PID and adaptive fuzzy PID, it improves the response speed, steady-state error, and anti-interference ability. Moreover, the LADRC has more advantages in parameter adjustment. Simulation results show that the response speed is increased by 130 ms, the overshoot is reduced by 9.85%, and the anti-interference ability is increased by 41.2%. Finally, the feasibility of this control algorithm was verified through the EMB hardware-in-the-loop test bench.

Modelling doi: 10.3390/modelling6030071

Authors: Alejandro Sandoval-Pineda Cesar Pedraza

Traffic crashes represent a major challenge for road safety, public health, and mobility management in complex urban environments, particularly in metropolitan areas characterized by intense traffic flows, high population density, and strong commuter dynamics. The development of short-term traffic crash prediction models represents a fundamental line of analysis in road safety research within the scientific community. Among these efforts, macro-level modeling plays a key role by enabling the analysis of the spatiotemporal relationships between diverse factors at an aggregated zonal scale. However, in cities like Bogotá, predicting short-term traffic crashes remains challenging due to the complexity of these spatiotemporal dynamics, underscoring the need for models that more effectively integrate spatial and temporal data. This paper presents a strategy based on deep learning techniques to predict short-term spatiotemporal traffic crashes in Bogotá using 2019 data on socioeconomic, land use, mobility, weather, lighting, and crash records across TMAU and TAZ zones. The results showed that the strategy performed with a model called SpatioConvGru-Net with top performance at the TMAU level, achieving R2 = 0.983, MSE = 0.017, and MAPE = 5.5%. Its hybrid design captured spatiotemporal patterns better than CNN, LSTM, and others. Performance improved at the TAZ level using transfer learning.

Modelling doi: 10.3390/modelling6030070

Authors: Taochun Yang Yating Jiang Xiaoyan Zhang Qinghai Liu Yin Wang

To clarify the potential failure modes of reinforced concrete (RC) beams under impact and understand their impact resistance safety, a comprehensive study was conducted by focusing on the failure mode discrimination and failure probability of RC beams under impact loads. This research utilized drop hammer impact tests, ABAQUS2022 software, and theoretical methods. The study examined three typical failure modes of RC beams under impact loads: flexural failure, flexural-shear failure, and shear failure. A discrimination criterion based on the flexural-shear capacity–effect curve was developed. Utilizing this criterion, along with the basic principles of structural reliability theory, the failure probability of RC beams under impact loads was calculated and analyzed using the Monte Carlo method. The results indicate that the criterion based on the flexural-shear capacity–effect curve can be used for discriminating failure modes of RC beams under impact loads. The impact velocity and stirrup ratio were identified as crucial factors that influenced the failure modes of RC beams under impact. Specifically, an increase in the stirrup spacing reduced the reliability of the RC beams under impact, while an increase in the stirrup ratio could significantly enhance their impact resistance. Furthermore, with a constant impact energy, an increase in beam span correlated with the improved reliability of RC beams under impact, where larger spans yielded a better impact resistance.

Modelling doi: 10.3390/modelling6030069

Authors: Tichen Huang Yuyan Jiang Rumeijiang Gan Fuyu Wang

As industrialization and economic growth accelerate, PM2.5 pollution has become a critical environmental concern. Predicting PM2.5 concentration is challenging due to its nonlinear and complex temporal dynamics, limiting the accuracy and robustness of traditional machine learning models. To enhance prediction accuracy, this study focuses on Ma’anshan City, China and proposes a novel hybrid model (QMEWOA-QCAM-BiTCN-BiLSTM) based on an “optimization first, prediction later” approach. Feature selection using Pearson correlation and RFECV reduces model complexity, while the Whale Optimization Algorithm (WOA) optimizes model parameters. To address the local optima and premature convergence issues of WOA, we introduce a quantum-enhanced multi-strategy improved WOA (QMEWOA) for global optimization. A Quantum Causal Attention Mechanism (QCAM) is incorporated, leveraging Quantum State Mapping (QSM) for higher-order feature extraction. The experimental results show that our model achieves a MedAE of 1.997, MAE of 3.173, MAPE of 10.56%, and RMSE of 5.218, outperforming comparison models. Furthermore, generalization experiments confirm its superior performance across diverse datasets, demonstrating its robustness and effectiveness in PM2.5 concentration prediction.

Modelling doi: 10.3390/modelling6030068

Authors: Tao Wu Tao Xue Yazhou Wang Kumar Tamma

In this paper, we develop a peridynamic computational framework to analyze thermomechanical interactions in fractured thin films subjected to ultrashort-pulsed laser excitation, employing nonlocal discrete material point discretization to eliminate mesh dependency artifacts. The generalized Cattaneo–Fourier thermal flux formulation uncovers contrasting dynamic responses: hyperbolic heat propagation (FT=0) generates intensified temperature localization and elevates transient crack-tip stress concentrations relative to classical Fourier diffusion (FT=1). A GSSSS (Generalized Single Step Single Solve) i-Integration temporal scheme achieves oscillation-free numerical solutions across picosecond-level laser–matter interactions, effectively resolving steep thermal fronts through adaptive stabilization. These findings underscore hyperbolic conduction’s essential influence on stress-mediated fracture evolution during ultrafast laser processing, providing critical guidelines for thermal management in micro-/nano-electromechanical systems.

Modelling doi: 10.3390/modelling6030067

Authors: Thenarasu M Sumesh Arangot Narassima M S Olivia McDermott Arjun Panicker

The study aims to increase productivity in the cold room door manufacturing industry by addressing non-value-adding operations, identifying bottlenecks, and reducing processing time through digital twin (DT)-based simulation. The goal is to eliminate the need for supply chain outsourcing and increase overall efficiency. The research involves developing a DT of the existing production process for five distinct categories of cold room doors: flush door, single door, double door, face-mounted door, and sliding door. Simulation was used to uncover problems at multiple stations, encompassing curing, welding, and packing. Lean principles were used to identify the causes of inefficiency, and the process was improved using TRIZ principles. These changes produced a 42.90% improvement in productivity, a 20% dependence reduction on outsourcing and an increase of 10.5% added inventory to the shortage demand level. The approach presented is provided for a particular manufacturer of cold room doors, but the methods and techniques used are generally applicable to other manufacturing companies to support systematic innovation. Combining DT simulation, lean techniques and TRIZ principles, this study presents a strong approach to addressing the productivity challenges in manufacturing. The incorporation of these methods has brought considerable operational efficiency and has minimised dependency on external outsourcing.

Modelling doi: 10.3390/modelling6030066

Authors: Fernando Iván Molina-Herrera Hugo Jiménez-Islas

This study presents a numerical comparison between Direct numerical simulation (DNS) and the standard κ-ε turbulence model to evaluate natural convection in a two-dimensional, differentially heated, air-filled cavity over the Rayleigh number range 103 to 1010. The objective is to assess the predictive capabilities of both methods across laminar and turbulent regimes, with a particular emphasis on the quantitative comparison of thermal characteristics under high Rayleigh number conditions. The Navier–Stokes and energy equations were solved using the finite element method with Boussinesq approximation, employing refined meshes near the hot and cold walls to resolve thermal and velocity boundary layers. The results indicate that for Ra ≤ 106, the κ-ε model significantly underestimates temperature gradients, maximum velocities, and average Nusselt numbers, with errors up to 19.39%, due to isotropic assumptions and empirical formulation. DNS, in contrast, achieves global energy balance errors of less than 0.0018% across the entire range. As Ra increases, the κ-ε model predictions converge to DNS, with Nusselt number deviations dropping below 1.2% at Ra = 1010. Streamlines, temperature profiles, and velocity distributions confirm that DNS captures flow dynamics more accurately, particularly near the wall vortices. These findings validate DNS as a reference solution for high-Ra natural convection and establish benchmark data for assessing turbulence models in confined geometries

Modelling doi: 10.3390/modelling6030065

Authors: Ming Huang Teng Tu Yueling Jing Fan Yang

To investigate the impermeability characteristics of composite geomembranes in rigid landfills, a three-dimensional finite element seepage analysis model, which incorporates a composite geomembrane, was established based on a case study of a rigid landfill project in Tongling. Utilizing the seepage mechanism of the composite geomembrane, the seepage distribution patterns of the hazardous waste leachate within the unit cell were computed under representative operating conditions. Different thickness amplification factor schemes for the equivalent treatment of the composite geomembrane were comparatively analyzed, considering both isotropic and anisotropic seepage conditions. The relationships between the seepage flow rate, velocity, and thickness amplification factor were determined. The results showed that the leachate experiences a rapid drop in the water head as it passes through the composite geomembrane, with a low seepage flow rate and velocity, highlighting the membrane’s significant impermeability effect. The finite element analysis indicated that thickness amplification of the composite geomembrane based on the flow equivalence is feasible to some degree, but treating the geomembrane as an anisotropic material during the equivalent process better approximates the actual conditions.

Modelling doi: 10.3390/modelling6030064

Authors: Ibrahim Kipngeno Rotich László E. Kollár

Wind turbine performance in cold regions is affected by icing which can lead to power reduction due to the aerodynamic degradation of the turbine blade. The development of airfoil shapes applied as blade sections contributes to improving the aerodynamic performance under a wide range of weather conditions. The present study considers inverse design coupled with numerical modelling to simulate the effects of varying airfoil thickness and maximum camber. The inverse design process was implemented in MATLAB R2023a, whereas the numerical models were constructed using ANSYS Fluent and FENSAP ICE 2023 R1. The inverse design process applied the modified Garabedian–McFadden (MGM) iterative technique. Shear velocities were calculated from the flow over an airfoil with slip conditions, and then this velocity distribution was modified according to the prevailing icing conditions to obtain the target velocities. A parameter was proposed to consider the airfoil thickness as well when calculating the target velocities. The airfoil generated was then exposed to various atmospheric conditions to check the improvement in the aerodynamic performance. The ice mass and lift-to-drag ratio were determined considering cloud characteristics under varying liquid water content (LWC) from mild to severe (0.1 g/m3 to 1 g/m3), median volume diameter (MVD) of 50 µm, and two ambient temperatures (−4 °C and −20 °C) that characterize freezing drizzle and in-cloud icing conditions. The ice mass on the blade section was not significantly impacted by modifying the shape after applying the process developed (i.e., <5%). However, the lift-to-drag ratio that describes the aerodynamic performance may even be doubled in the icing scenarios considered.

Modelling doi: 10.3390/modelling6030063

Authors: Jianlin Li Xupeng Qi Xiaoli Li Huijie Huang Jian Gao

To address thermal imbalance and ground temperature degradation in shallow geothermal heat pump (GSHP) systems in severely cold climates, this study analyzes a typical logistics building using an hourly dynamic load model. Multiyear simulations were conducted to investigate the coupling between building load variation and soil thermal response. The results indicate that with a cumulative heating load of 14.681 million kWh and cooling load of 6.3948 million kWh, annual heat extraction significantly exceeds heat rejection, causing ground temperature to decline by about 1 °C per year. Over five and ten years, the cumulative drops reached 2.65 °C and 4.71 °C, respectively, leading to a noticeable reduction in borehole heat exchanger performance and system COP. The study quantitatively evaluates ground temperature and heat exchange degradation, highlighting the key role of load imbalance. To mitigate long-term thermal deterioration, strategies such as load optimization, summer heat reinjection, and operational adjustments are proposed. The findings offer guidance for the design and sustainable operation of GSHP systems in cold regions.

Modelling doi: 10.3390/modelling6030062

Authors: Luiz Vicente Figueira de Mello Filho Felipe Pastori Lopes de Sousa Gustavo de Godoi William Machado Emiliano Felippe Benavente Canteras Vitor Eduardo Molina Júnior Jo?o Roberto Bertini Junior Yuri Alexandre Meyer

Efficient logistics and transport infrastructure are critical in contemporary urban and interurban scenarios due to their impact on economic development, environmental sustainability, and quality of life. This study explores the use of the Ant Colony Optimization (ACO) metaheuristic applied to the Vehicle Routing Problem (VRP) and the strategic positioning of service stations along major highways. Through a systematic mapping of the literature and practical application to a real-world scenario—specifically, a case study on the Bandeirantes Highway (SP348), connecting Limeira to São Paulo, Brazil—the effectiveness of ACO is demonstrated in addressing complex logistical challenges, including capacity constraints, route optimization, and resource allocation. The proposed method integrates graph theory principles, entropy concepts from information theory, and economic analyses into a unified computational model implemented using Python (version 3.12), showcasing its accessibility for educational and practical business contexts. The results highlight significant improvements in operational efficiency, cost reductions, and optimized service station placement, emphasizing the algorithm’s robustness and versatility. Ultimately, this research provides valuable insights for policymakers, engineers, and logistics managers seeking sustainable and cost-effective solutions in transport infrastructure planning and management.

Modelling doi: 10.3390/modelling6030061

Authors: Juan Ma Anyi Wang Philipp Junker Anas W. Alshawawreh Qingya Li Haoqi Xu Runzhuo Xue

Thermal barrier coatings have been widely used in industrial fields where thermal damage occurs, and they are crucial for insulation technology and for the safe service of high-temperature components. So, it is critical to accurately predict the reliability of thermal barrier coatings. In this work, an adaptive reliability analysis method based on radial basis functions is proposed, in which different shape parameters and subsets are used to initiate different radial basis function models for multiple predictions. An active learning function that comprehensively considers local uncertainty, limit state function information, and distance among samples is then used for sequential sampling, and the proposed method is validated via a four-branch series connection system. Finally, a reliability analysis is conducted on the failure of interface oxidation in thermal barrier coatings, which verifies the feasibility of the proposed method.

Modelling doi: 10.3390/modelling6030060

Authors: Said Chaabani Naoufel Azouz

In recent decades, the deployment of quadcopters has significantly expanded, particularly in outdoor applications such as parcel delivery. These missions require highly stable aerial platforms capable of maintaining balance under diverse environmental conditions, ensuring the safe operation of both the drone and its payload. This paper focuses on the stabilization of a quadcopter designed for outdoor use. A detailed dynamic model of a compact vertical takeoff and landing (VTOL) drone forms the basis for a non-linear control strategy targeting stability during the critical takeoff phase. The control law is designed using a quasi-linear parameter-varying (quasi-LPV) model that captures the system’s non-linear dynamics. Lyapunov theory and linear matrix inequalities (LMIs) are employed to validate the stability and design the controller. Numerical simulations demonstrate the controller’s effectiveness, and a comparative study is conducted to benchmark its performance against a reference quadrotor model.

Modelling doi: 10.3390/modelling6030059

Authors: Sel?uk Erol

Underground production and injection operations result in mechanical compaction and mineral chemical reactions that alter porosity and permeability. These changes impact the flow and, eventually, the long-term sustainability of reservoirs utilized for CO2 sequestration and geothermal energy. Even though mechanical and chemical deformations in rocks take place at the pore scale, it is important to investigate their impact at the continuum scale. Rock deformation can be examined using intergranular pressure solution (IPS) models, primarily for uniaxial compaction. Because the reaction rate parameters are estimated using empirical methods and the assumption of constant mineral saturation indices, these models frequently overestimate the rates of compaction and strain by several orders of magnitude. This study presents a new THMC algorithm by combining thermo-mechanical computation with a fractal approach and hydrochemical computations using PHREEQC to evaluate the pressure solution. Thermal stress and strain under axisymmetric conditions are calculated analytically by combining a derived hollow circle mechanical structure with a thermal resistance model. Based on the pore scale, porosity and its impact on the overall excessive stress and strain rate in a domain are estimated by applying the fractal scaling law. Relevant datasets from CO2 core flooding experiments are used to validate the proposed approach. The comparison is consistent with experimental findings, and the novel analytical method allows for faster inspection compared to numerical simulations.

Modelling doi: 10.3390/modelling6030058

Authors: Changgen Liu Xiaozhou Xia

The nonlocal macro–meso-scale damage (NMMD) model, implemented in the framework of the finite element method, has been demonstrated to be a promising numerical approach in simulating crack initiation and propagation with reliable efficacy and high accuracy. In this study, the NMMD model was further enhanced by employing an identical degradation mechanism for both the tensile and shear components of shear stiffness, thereby overcoming the limitation of equal degradation in shear and tensile stiffness inherent in the original model. Additionally, a more refined and physically sound seepage evolution function was introduced to characterize the variation in permeability in porous media with geometric damage, leading to the development of an improved NMMD model suitable for simulating coupled seepage–stress problems. The reliability of the enhanced NMMD model was verified by the semi-analytical solutions of the classical KGD problem. Finally, based on the modified NMMD model, the effects of preset fracture spacing and natural voids on hydraulic fracture propagation were investigated.

Modelling doi: 10.3390/modelling6030057

Authors: Gang Sun Hua Li Hongcheng Liu Fuchun Li Huanhuan Wang Jun Zhou Guangchuan Liang

Tight gas wells in Southwest oil and gas fields have significant production and high sand output intensity. The sand out of the wellhead has a certain erosion effect on the downstream pipeline, the equipment, and affects the normal production. This paper models and simulates the desander used at the wellhead according to the real parameters of the tight gas wellhead, and explores the effects of gas production, pressure, temperature, sand particle size, water content, and other factors on the desander’s sand removal efficiency. This paper combines the principle of fluid dynamics to analyze the internal mechanism of the effect trend and according to the simulation results uses the Pearson correlation coefficient quantification of the effect of each operating parameter to explore the optimal boundary condition parameters applicable to the desander. From the simulation results, it can be seen that the separation efficiency of the desander is the highest when the gas production rate is 4 × 104 m3/d, the pressure is 7 MPa, and the lower the working temperature is, the larger is the gravel particle size. Combined with the sand management problems occurring in the field of tight gas wells, suggestions are made for the optimization of the operating parameters and structure of the desander, which will provide a basis for supporting the rapid production and large-scale beneficial development of tight gas fields.

Modelling doi: 10.3390/modelling6030056

Authors: Nesma Khamis Nermine Harraz Hadi Fors

Lot sizing and cutting stock problems are critical for manufacturing companies seeking to optimize resource utilization and minimize waste. This paper addresses the interconnected nature of these problems, often occurring sequentially in industries involving cut items or packaging. We propose a novel mixed integer linear programming (MILP) model that integrates the capacitated lot sizing problem with the one-dimensional cutting stock problem within a multi-level manufacturing framework. The cutting stock problem is addressed using an arc flow formulation. Our model aims to minimize setup, production, holding, and waste material costs while incorporating capacity constraints, setup requirements, inventory balance, and the use of various cutting machines. The effectiveness of our model is demonstrated through numerical experiments using a commercial optimization package. While the model efficiently generates optimal solutions for most scenarios, larger instances pose challenges within the specified time limits. Sensitivity analysis is conducted to evaluate the effect of changing essential parameters of the integrated problem on model performance and to provide managerial insights for real-life applications.

Modelling doi: 10.3390/modelling6030055

Authors: Sy-Dan Dao Dang-Diem Nguyen Trong-Hiep Nguyen Ngoc-Lam Nguyen

This study presents a high-order shear deformation theory (HSDT)-based model for evaluating the energy harvesting performance of functionally graded material (FGM) beams integrated with a piezoelectric layer and subjected to a moving concentrated load at constant velocity. The governing equations are derived using Hamilton’s principle, and the dynamic response is obtained through the State Function Method with trigonometric mode shapes. The output voltage and harvested power are calculated based on piezoelectric constitutive relations. A comparative analysis with homogeneous isotropic beams demonstrates that HSDT yields more accurate predictions than the Classical Beam Theory (CBT), especially for thick beams; for instance, at a span-to-thickness ratio of h/L = 12.5, HSDT predicts increases of approximately 6%, 7%, and 12% in displacement, voltage, and harvested power, respectively, compared to CBT. Parametric studies further reveal that increasing the load velocity significantly enhances the strain rate in the piezoelectric layer, resulting in higher voltage and power output, with the latter exhibiting quadratic growth. Moreover, increasing the material gradation index n reduces the beam’s effective stiffness, which amplifies vibration amplitudes and improves energy conversion efficiency. These findings underscore the importance of incorporating shear deformation and material gradation effects in the design and optimization of piezoelectric energy harvesting systems using FGM beams subjected to dynamic loading.

Modelling doi: 10.3390/modelling6030054

Authors: Xuanqi Zhang Wenbin Shao Yongshou Liu Xin Fan Ruiyun Shi

The accuracy of the blade pitch angle (BPA) motion in controllable pitch propellers (CPPs) is considered crucial for the efficacy and reliability of marine propulsion systems. The pitch adjustment process of CPPs is highly complex and influenced by various uncertain factors. A parametric kinematic model for the pitch adjustment process for CPPs was established, incorporating the geometric dimensions and material surface friction coefficients caused during workpiece production as uncertainty parameters. The aim was to establish the correspondence between these uncertainty parameters and the BPA of CPPs. A large dataset was generated by batch calling on Adams. Based on the collected dataset, five surrogate models (e.g., deep neural network (DNN), Kriging, support vector regression (SVR), random forest (RF), and polynomial chaos expansion Kriging (PCK)) were constructed to predict the BPA. Among these, the DNN approach demonstrated the highest prediction accuracy. Accordingly, the influence of uncertainties on the BPA was investigated using the DNN model, focusing on variations in the slider width, crank pin diameter, crank disc diameter, piston rod–slider friction coefficient, crank pin–slider friction coefficient, and hub bearing–crank disc friction coefficient. The high-fidelity model established in this study can replace the kinematic model of the CPP pitch adjustment process, significantly improving computational efficiency. The research findings also provide important references for the design optimization of CPPs.

Modelling doi: 10.3390/modelling6030053

Authors: Antonio Lobo-Santos Joaquín Borrego-Díaz

The rapid growth in scientific knowledge has created a critical need for advanced systems capable of managing mathematical knowledge at scale. This study presents a novel approach that integrates ontology-based knowledge representation with large language models (LLMs) to automate the extraction, organization, and reasoning of mathematical knowledge from LaTeX documents. The proposed system enhances Mathematical Knowledge Management (MKM) by enabling structured storage, semantic querying, and logical validation of mathematical statements. The key innovations include a lightweight ontology for modeling hypotheses, conclusions, and proofs, and algorithms for optimizing assumptions and generating pseudo-demonstrations. A user-friendly web interface supports visualization and interaction with the knowledge graph, facilitating tasks such as curriculum validation and intelligent tutoring. The results demonstrate high accuracy in mathematical statement extraction and ontology population, with potential scalability for handling large datasets. This work bridges the gap between symbolic knowledge and data-driven reasoning, offering a robust solution for scalable, interpretable, and precise MKM.

Modelling doi: 10.3390/modelling6030052

Authors: Boxing Deng Siyuan Shao Guoqing Cheng Yujia Wang

This study addresses the limitations of existing maintenance decision-making approaches that predominantly rely on single-objective strategies for leased production systems with complex series–parallel configurations. An integrated opportunity-based adaptive maintenance strategy is proposed, and a multi-objective optimization model incorporating multiple maintenance alternatives is developed. First, a proportional hazards model to characterize the degradation-dependent failure rates of key components is used to characterize equipment failure rates, which inform the selection of maintenance actions. Second, the effects of virtual age and maintenance strategies on the residual value of leased equipment are analyzed, leading to the formulation of a net residual value model from the lessor’s perspective. Simultaneously, a customer cost model is established by considering both product quality loss and downtime loss. Finally, the NSGA II algorithm is employed to solve the proposed multi-objective optimization model, yielding optimal preventive maintenance intervals, opportunistic maintenance thresholds, preventive maintenance thresholds, and the corresponding Pareto front. A case study illustrates the strategy’s superior flexibility and practical applicability, with its effectiveness further validated through comparative analysis against traditional maintenance strategies.

Modelling doi: 10.3390/modelling6030051

Authors: Yudong Huang Tianju Wang Hongsheng Guo Yan Zhang Zhiwei Hao Xiaobing Lu Xuhui Zhang

The initiation condition of the shear band in gas hydrate-bearing sediment (GHBS) was analyzed in this study. First, the mathematical model considering the pore diffusion and stress conservation equations was constructed. The shear stress is assumed to be related to the porosity, shear strain, and shear strain ratio. The expansion of pores causes sediment softening, while the shear strain causes the stiffening of the sediment. The perturbation method was used to analyze the initiation condition of the shear band under porosity softening and strain stiffening based on the presented mathematical model. A numerical simulation was also performed. The development of the strain, stress, and porosity was analyzed. It is shown that the parameters of the sediment change with the strain and porosity. When the parameters are satisfied under certain conditions, the shear band will initiate and develop. The critical condition is when the porosity-softening effects overcome the strain-stiffening effects. In some special cases, the critical condition may be related to other factors, such as when strain softening induces other kinds of initiation of the shear band.

Modelling doi: 10.3390/modelling6020050

Authors: Raymond Leung Alexander Lowe Arman Melkumyan

Probabilistic models are used to describe random processes and quantify prediction uncertainties in a principled way. Examples include geotechnical and geological investigations that seek to model subsurface hydrostratigraphic properties or mineral deposits. In mining geology, model validation efforts have generally lagged behind the development and deployment of computational models. One problem is the lack of industry guidelines for evaluating the uncertainty and predictive performance of probabilistic ore grade models. This paper aims to bridge this gap by developing a holistic approach that is autonomous, scalable and transferable across domains. The proposed model assessment targets three objectives. First, we aim to ensure that the predictions are reasonably calibrated with probabilities. Second, statistics are viewed as images to help facilitate large-scale simultaneous comparisons for multiple models across space and time, spanning multiple regions and inference periods. Third, variogram ratios are used to objectively measure the spatial fidelity of models. In this study, we examine models created by ordinary kriging and the Gaussian process in conjunction with sequential or random field simulations. The assessments are underpinned by statistics that evaluate the model’s predictive distributions relative to the ground truth. These statistics are standardised, interpretable and amenable to significance testing. The proposed methods are demonstrated using extensive data from a real copper mine in a grade estimation task and are accompanied by an open-source implementation. The experiments are designed to emphasise data diversity and convey insights, such as the increased difficulty of future-bench prediction (extrapolation) relative to in situ regression (interpolation). This work enables competing models to be evaluated consistently and the robustness and validity of probabilistic predictions to be tested, and it makes cross-study comparison possible irrespective of site conditions.

Modelling doi: 10.3390/modelling6020049

Authors: Qian Xu Qian Huang Chuanxu Jiang Xin Li Yiming Wang

Video stabilization is a critical technology for enhancing video quality by eliminating or reducing image instability caused by camera shake, thereby improving the visual viewing experience. It has deeply integrated into diverse applications—including handheld recording, UAV aerial photography, and vehicle-mounted surveillance. Propelled by advances in deep learning, data-driven stabilization methods have emerged as prominent solutions, demonstrating superior efficacy in handling jitter while achieving enhanced processing efficiency. This review systematically examines the field of video stabilization. First, this paper delineates the paradigm shift from classical to deep learning-based approaches. Subsequently, it elucidates conventional digital stabilization frameworks and their deep learning counterparts along with establishing standardized assessment metrics and benchmark datasets for comparative analysis. Finally, this review addresses critical challenges such as robustness limitations in complex motion scenarios and latency constraints in real-time processing. By integrating interdisciplinary perspectives, this work provides scholars with academically rigorous and practically relevant insights to advance video stabilization research.

Modelling doi: 10.3390/modelling6020048

Authors: Steffen Wilbrandt Olaf Stenzel

We present a practical numerical model for calculating transmittance and reflectance of multilayer antireflection coatings taking third-order optical nonlinearities into account. Thereby, the impact of different types of discretization of the complex refractive index profile on the predicted system performance is investigated. Additionally, aspects of parallelism of the calculations are discussed. It is shown that the inclusion of nonlinearity is essential when large laser intensities are incident to the coating. The developed method is applied for the design of different antireflective coatings matching various types of targets.

Modelling doi: 10.3390/modelling6020047

Authors: Sergey D. Lavrov Andrey A. Guskov

This study introduces a comprehensive physical modeling framework for phototransistors based on quasi-two-dimensional transition metal dichalcogenides, with a particular emphasis on MoS2. By integrating electromagnetic simulations of optical absorption with semiconductor transport calculations, the model captures both dark and photocurrent behaviors across diverse operating conditions. For 20 nm MoS2 films, the model reproduces the experimental transfer characteristics with a threshold voltage accuracy better than 0.1 V and achieves quantitative agreement with photocurrent and dark current values across the full range of gate voltages, with the worst-case deviation not exceeding a factor of seven. Additionally, the model captures a three-order-of-magnitude increase in the photocurrent as the MoS2 thickness varies from 4 nm to 40 nm, reflecting the strong thickness dependence observed experimentally. A key insight from the study is the critical role of defect states, including traps, impurities, and interfacial imperfections, in governing the dark current and photocurrent under channel pinch-off conditions (Vg < −1.0 V). The model successfully replicates the qualitative trends observed in experimental devices, highlighting how small variations in film thickness, doping levels, and contact geometries can significantly influence device performance, in agreement with published experimental data. These findings underscore the importance of precise defect characterization and optimization of material and structural parameters for 2D-material-based phototransistors. The proposed modeling framework serves as a powerful tool for the design and optimization of next-generation phototransistors, facilitating the integration of 2D materials into practical electronic and optoelectronic applications.

Modelling doi: 10.3390/modelling6020046

Authors: Rafael Aredes Couto Igor Augusto Guimar?es Campos Elvys Dias Reis Daniel Hasan Dalip Flávia Spitale Jacques Poggiali Péter Ludvig

The durability of reinforced concrete (RC) structures is strongly influenced by carbonation, a phenomenon governed by material and environmental interactions. This study applied machine learning (ML) techniques—Random Forest (RF), Support Vector Regression (SVR), and Artificial Neural Networks (ANNs)—to predict carbonation depth using a synthetic dataset of 20,000 instances generated from the validated Possan equation. Model performances were evaluated across multiple scenarios, with compressive strength and exposure time identified as the most influential features, while relative humidity and exposure conditions had intermediate effects. SVR consistently captured linear and nonlinear trends, the ANN achieved the highest R2 values but showed minor overestimations, and RF exhibited lower adaptability to feature variations. The results highlight the applicability of ML models for durability assessments, particularly under complex conditions where traditional approaches are limited. Moreover, this study reinforces the strategic value of synthetic datasets in developing predictive models when experimental data collection is time-consuming or impractical. The methodologies developed here can be extended beyond carbonation modeling to other deterioration processes, supporting data-driven strategies for maintenance planning and resilience design in RC structures.

Modelling doi: 10.3390/modelling6020045

Authors: Ruiqiang Ma Yingxue Lu Xiaohui Yu Bin Yang

Utilizing the considerable cold energy in liquefied natural gas (LNG) through the organic Rankine cycle is a highly important initiative. A multi-stage Rankine-based power generation system using LNG cold energy for waste heat utilization was proposed in this study. Moreover, a comprehensive assessment method was used to select the working fluid for this proposed system. Not only were thermodynamic and economic indicators considered, but also the environmental impact of candidate working fluids was taken into account in the evaluation process. The optimal operating points of the system were determined using non-dominated sorting genetic algorithm II and TOPSIS methods, while employing Gray Relational Analysis was applied to compute the gray relational coefficients of candidate working fluids at the optimal operating points. In addition, four weighting methods were used to calculate the final gray correlation degree of the candidate working fluids by considering the weighting influence. The stability of the calculated gray correlation degree was observed by performing a standard deviation analysis. The results indicate that R245ca was chosen as the optimal working fluid due to its superior performance based on the entropy weighting method, the independent weighting coefficient method, and the mean weighting method. Simultaneously, R245ca exhibits the best specific net power output and levelized cost of energy values of 0.283 USD/kWh and 106.9 kWh/t, respectively, among all candidate working fluids. The gray correlation degree of R1233zd(E) is 0.948, exceeding that of R245ca under the coefficient of variation method. The gray correlation degree under the mean value method is the most stable, with a standard deviation of only 0.162, while the gray correlation degree under the coefficient of variation method exhibits the greatest fluctuation, with a standard deviation of 0.17, in the stability assessment.

Modelling doi: 10.3390/modelling6020044

Authors: Jingyi Li Yuqi Song Chengliang Tian Weizhong Tian

The k-nearest- neighbor (kNN) algorithm is crucial in data mining and machine learning, yet its deployment on large-scale datasets within cloud environments presents significant security and efficiency challenges. This paper is dedicated to advancing the resolution of these challenges and presents novel contributions to the development of efficient and secure exact kNN query schemes tailored for spatial datasets in cloud-based location services. Addressing existing limitations, our approach focuses on accelerating query processing while ensuring robust privacy preservation and public verifiability. Key contributions include the establishment of a formal framework underpinned by stringent security definitions, providing a solid groundwork for future advancements. Leveraging Paillier’s homomorphic cryptosystem and public-key signature techniques, our design achieves heightened security by safeguarding databases, query access patterns, and result integrity while enabling public verification. Additionally, our scheme enhances computational efficiency through optimized data-packing techniques and simplified Voronoi diagram-based ciphertext index construction, leading to substantial savings in computational and communication overheads. Rigorous and transparent theoretical analysis substantiates the correctness, security, and efficiency of our design, while comprehensive experimental evaluations confirm the effectiveness of our approach, showcasing its practical applicability and scalability across datasets of varying scales.

Modelling doi: 10.3390/modelling6020043

Authors: Miguel ?ngelo Lellis Moreira Maria Teresa Pereira Igor Pinheiro de Araújo Costa Carlos Francisco Sim?es Gomes Marcos dos Santos

Decision-making in complex environments, especially sustainable ones, requires flexible methodologies to handle multiple criteria and stakeholder perspectives. This study introduces the SAPEVO-H2 method (Simple Aggregation of Preferences Expressed by Ordinal Vectors—Hybrid and Hierarchical), an extensive model from the SAPEVO family, which offers multi-criteria analysis through a hierarchical structure of variables evaluated by groups partitioned into levels concerning their respective responsibilities. The proposal allows flexible analysis, considering inputs through ordinal and cardinal information. The validation of the methodology is demonstrated through a case study involving an automobile manufacturing company, which focuses on prioritizing sustainability projects based on multiple objectives aimed at minimizing polluting gas emissions. Within a hierarchical structure of five levels, the individual level results are presented. In addition, a sensitivity analysis is applied, exposing the most sensitive variables to changes concerning the highest levels. Then, we discuss the main contributions and limitations concerning the mathematical proposal and the conclusions and proposals for future work.

Modelling doi: 10.3390/modelling6020042

Authors: Pedro Jesús Rodríguez de Rivera Miriam Rodríguez de Rivera Fabiola Socorro Manuel Rodríguez de Rivera

This study presents an advanced model of thermal Resistances and heat Capacities model approach (RC model), applied to a custom-built skin calorimeter for the in vivo characterization of localized thermal behavior of the skin. The device integrates a heat flux sensor and a programmable thermostat, and is capable of measuring the heat flux, heat capacity, internal thermal resistance, and subcutaneous temperature of the skin, under both resting and exercising conditions. The model, refined through extensive experimental validation, incorporates the skin as part of the system and is adapted to three modes of operation: calibration base, ambient air, and direct skin contact. Simulations are used to analyze heat flux dynamics, optimize control parameters, and validate analytical expressions. Under resting conditions, the model enables the estimation of the skin’s heat capacity and thermal resistance. During exercise, it allows the determination of heat flux and internal temperature variations using simplified expressions. The system demonstrates high sensitivity (195.5 mV/W) and provides a robust, non-invasive method for extracting medically relevant thermal parameters from a 2 × 2 cm2 skin area.

Modelling doi: 10.3390/modelling6020041

Authors: Shiva Rezaei Akbarieh Dayou Ma Claudio Sbarufatti Andrea Manes

Due to environmental concerns and increasing energy needs, hydrogen is increasingly seen as a promising alternative to fossil fuels. Its advantages include minimal greenhouse gas emissions (depending on origin), high efficiency, and widespread availability. Various storage methods have been developed, with high-pressure storage being currently among the most common due to its cost-effectiveness and simplicity. Composite high-pressure vessels are categorized as type III or IV, with type III using an aluminum alloy liner and type IV utilizing a polymer liner. This paper investigates damage mechanisms in filament wound carbon fiber composite pressure vessels subjected to low-velocity impacts, focusing on two types of impactors (with different geometries) with varying impact energies. The initial section features experimental trials that capture various failure modes (e.g., matrix damage, delamination, and fiber breakage) and how different impactor geometries influence the damage mechanisms of composite vessels. A numerical model was developed and validated with experimental data to support the experimental findings, ensuring accurate damage mechanism simulation. The research then analyzes how the shape and size of impactors influence damage patterns in the curved vessel, aiming to establish a relationship between impactor geometry features and damage, which is crucial for the design and applications of carbon fiber composites in such an engineering application.

Modelling doi: 10.3390/modelling6020040

Authors: Aziida Nanyonga Keith Joiner Ugur Turhan Graham Wild

This study investigates the application of advanced deep learning models for the classification of aviation safety incidents, focusing on four models: Simple Recurrent Neural Network (sRNN), Gated Recurrent Unit (GRU), Bidirectional Long Short-Term Memory (BLSTM), and DistilBERT. The models were evaluated based on key performance metrics, including accuracy, precision, recall, and F1-score. DistilBERT achieved perfect performance with an accuracy of 1.00 across all metrics, while BLSTM demonstrated the highest performance among the deep learning models, with an accuracy of 0.9896, followed by GRU (0.9893) and sRNN (0.9887). Class-wise evaluations revealed that DistilBERT excelled across all injury categories, with BLSTM outperforming the other deep learning models, particularly in detecting fatal injuries, achieving a precision of 0.8684 and an F1-score of 0.7952. The study also addressed the challenges of class imbalance by applying class weighting, although the use of more sophisticated techniques, such as focal loss, is recommended for future work. This research highlights the potential of transformer-based models for aviation safety classification and provides a foundation for future research to improve model interpretability and generalizability across diverse datasets. These findings contribute to the growing body of research on applying deep learning techniques to aviation safety and underscore opportunities for further exploration.

Modelling doi: 10.3390/modelling6020039

Authors: Yongjun Wu Hongyun Kang Weipin Wang Shuli Zhao Xuening He Jingyao Chen

Accurate, efficient, and reliable traffic flow prediction is pivotal for highway operation and management. However, traffic flow series present nonlinear, heterogeneous, and stochastic characteristics, posing significant challenges to precise prediction. To address this issue, this paper proposes a novel wavelet-LNN model, integrating the strengths of wavelet decomposition and liquid neural networks (LNNs). Initially, multi-scale wavelet decomposition is applied to the original traffic flow data to yield approximation components and detailed components. Subsequently, each component is trained using the LNN. Ultimately, the predicted results of all components of the LNN models are aggregated to derive the final traffic flow prediction. The experiments conducted on four highway datasets demonstrate that the proposed wavelet-LNN model surpasses SVR, LSSVM, LSTM, TCN, and transformer models in prediction performance across R2, MSE, and MAE metrics. Notably, the wavelet-LNN model features the fewest parameters (<2% of typical deep learning models).

Modelling doi: 10.3390/modelling6020038

Authors: Erik-Josué Moreno-Mejía Daniel Canton-Enriquez Ana-Marcela Herrera-Navarro Hugo Jiménez-Hernández

Automatic surveillance systems have become essential tools for urban centers. These technologies enable intelligent monitoring that is both versatile and non-intrusive. Today, these systems can analyze various aspects, such as urban traffic, citizen behavior, and the detection of unusual activities. Most intelligent systems utilize photo sensors to gather information and assess situations. They analyze data sequences from these photo sensors over time to detect moving objects or other relevant information. In this context, background modeling approaches are crucial for efficiently detecting moving objects by differentiating between the foreground and background, which serves as the basis for further analysis. Although current methods are effective, the dynamic nature of outdoor environments can limit their performance due to numerous external variables that affect the collected information. This paper introduces a novel algorithm that uses mathematical morphology to create a background model by analyzing texture information in discrete spaces, leading to an efficient solution for the background subtraction task. The algorithm dynamically adjusts to global luminance conditions and effectively distinguishes texture information to label the foreground and background using morphological filters. A key advantage of this approach is its use of discrete working spaces, which enables faster implementation on standard hardware, making it suitable for a variety of devices. Finally, our proposal is tested against reference datasets of surveillance and common background subtraction algorithms, demonstrating that our method adapts better to outdoor conditions, making it more robust in detecting different moving objects.

Modelling doi: 10.3390/modelling6020037

Authors: Dang Diem Nguyen Sy Dan Dao Xuan Tung Nguyen Van Tan Giap

This study presents the development and application of the stochastic finite element method (SFEM) to analyze the static response of beams with a two-dimensional (2D) spatially varying elastic modulus. A 2D stationary stochastic field is employed to model the elastic modulus, capturing the material heterogeneity along both the longitudinal and vertical directions of the beam. The weighted integral method is applied to represent the random field as random variables and to compute the element stiffness matrices, while a first-order perturbation technique is utilized to estimate the statistical moments of the nodal displacement vector, including the mean and covariance matrix. This method enhances both computational efficiency and accuracy in capturing material heterogeneity compared to traditional approaches. The precision and effectiveness of the developed SFEM are evaluated through comparisons with Monte Carlo simulations (MCs), demonstrating strong agreement in the analysis of the coefficient of variation (COV) of displacement. A sensitivity analysis is conducted to examine the influence of the correlation length and dispersion of the stochastic field on the COV. The results indicate that the COV generally increases as these parameters grow, with the most significant variations occurring at small correlation lengths. As the correlation length becomes very large, the COV of displacement converges toward the standard deviation of the input stochastic field. Furthermore, the study reveals that the correlation length along the beam’s longitudinal axis has a more pronounced effect on the COV of displacement compared to the vertical correlation length.

Modelling doi: 10.3390/modelling6020036

Authors: Luis Josimar Vences-Reynoso Daniel Villanueva-Vasquez Roberto Alejo-Eleuterio Federico Del Razo-López Sonia Mireya Martínez-Gallegos Everardo Efrén Granda-Gutiérrez

Geometric optimization of carbon nanotubes (CNTs) is a fundamental step in computational simulations, enabling precise studies of their properties for various applications. However, this process becomes computationally expensive as the molecular structure grows in complexity and size. To address this challenge, this study utilized three deep-learning-based neural network architectures: Multi-Layer Perceptron (MLP), Bidirectional Long Short-Term Memory (BiLSTM), and 1D Convolutional Neural Networks (1D-CNNs). Simulations were performed using the CASTEP module in Material Studio to generate datasets for training the neural networks. While the final geometric optimization calculations were completed within Material Studio, the neural networks effectively generated preoptimized CNT structures that served as starting points, significantly reducing computational time. The results showed that the 1D-CNN architecture performed best for CNTs with 28, 52, 76, and 156 atoms, while the MLP outperformed others for CNTs with 84, 124, 148, and 196 atoms. Across all cases, computational time was reduced by 39.68% to 90.62%. Although the BiLSTM also achieved reductions, its performance was less effective than the other two architectures. This work highlights the potential of integrating deep learning techniques into materials science; it also offers a transformative approach to reducing computational costs in optimizing CNTs and presents a way for accelerated research in molecular systems.

Modelling doi: 10.3390/modelling6020035

Authors: Md. Mahfuzul Islam Shamim Abu Bakar bin Abdul Hamid Tadiwa Elisha Nyamasvisva Najmus Saqib Bin Rafi

This systematic review investigates the integration of artificial intelligence (AI) in cost estimation within project management, focusing on its impact on accuracy and efficiency compared to traditional methods. This study synthesizes findings from 39 high-quality articles published between 2016 and 2024, evaluating various machine learning (ML), deep learning (DL), regression, and hybrid models in sectors such as construction, healthcare, manufacturing, and real estate. The results show that AI-powered approaches, particularly artificial neural networks (ANNs)—which constitute 26.33% of the studies—, enhance predictive accuracy and adaptability to complex, dynamic project environments. Key AI techniques, including support vector machines (SVMs) (7.90% of studies), decision trees, and gradient-boosting models, offer substantial improvements in cost prediction and resource optimization. ML models, including ANNs and deep learning models, represent approximately 70% of the reviewed studies, demonstrating a clear trend toward the adoption of advanced AI techniques. On average, deep learning models perform with 85–90% accuracy in cost estimation, making them highly effective for handling complex, nonlinear relationships and large datasets. Machine learning models achieve an average accuracy of 75–80%, providing strong performance, particularly in industries like road construction and healthcare. Regression models typically deliver 70–80% accuracy, being more suitable for simpler cost estimations where the relationships between variables are linear. Hybrid models combine the strengths of different algorithms, achieving 80–90% accuracy on average, and are particularly effective in complex, multi-faceted projects. Overall, deep learning and hybrid models offer the highest accuracy in cost estimation, while machine learning and regression models still provide reliable results for specific applications.

Modelling doi: 10.3390/modelling6020034

Authors: Gustavo Mendes Platt Otávio Knevitz de Azevedo Francisco Bruno Souza Oliveira

The optimal design of distillation separation processes has become a fundamental tool in industries in order to minimize operating costs and investments. In many cases, the optimization stage has been carried out using metaheuristics, with the process simulation stage carried out externally to the optimization. This paper presents an optimal design methodology for separating the components of turpentine, a raw material of natural origin, based on coupling a distillation process simulator with the Firefly metaheuristic as an optimizer. Results were obtained for a distillation process to obtain α-pinene and β-pinene (two of the main components of turpentine), meeting purity criteria in the top products of the equipment while minimizing a measure of the total annualized cost. The results show that the tool developed—together with the Firefly algorithm—is capable of obtaining optimized results (although there is no guarantee of a global optimum) from a small set of initial design configurations.

Modelling doi: 10.3390/modelling6020033

Authors: Ishita Arora M. Gangadharappa

Human Activity Recognition (HAR) has recently attracted the attention of researchers. Human behavior and human intention are driving the intensification of HAR research rapidly. This paper proposes a novel Motion History Mapping (MHI) and Orientation-based Convolutional Neural Network (CNN) framework for action recognition and classification using Machine Learning. The proposed method extracts oriented rectangular patches over the entire human body to represent the human pose in an action sequence. This distribution is represented by a spatially oriented histogram. The frames were trained with a 3D Convolution Neural Network model, thus saving time and increasing the Classification Correction Rate (CCR). The K-Nearest Neighbor (KNN) algorithm is used for the classification of human actions. The uniqueness of our model lies in the combination of Motion History Mapping approach with an Orientation-based 3D CNN, thereby enhancing precision. The proposed method is demonstrated to be effective using four widely used and challenging datasets. A comparison of the proposed method’s performance with current state-of-the-art methods finds that its Classification Correction Rate is higher than that of the existing methods. Our model’s CCRs are 92.91%, 98.88%, 87.97.% and 87.77% which are remarkably higher than the existing techniques for KTH, Weizmann, UT-Tower and YouTube datasets, respectively. Thus, our model significantly outperforms the existing models in the literature.

Modelling doi: 10.3390/modelling6020032

Authors: Madhuri Patel Samir B. Patel Debabrata Swain Rishikesh Mallagundla

Passenger flow forecasting is crucial for optimizing urban transit operations, especially in developing countries such as India, where congestion, infrastructure constraints, and diverse commuter behaviors pose significant challenges. Despite its importance, limited research explored forecasting models for Indian urban transit systems, particularly incorporating the effects of holidays and disruptions caused by the COVID-19 pandemic. To address this gap, we propose TBATS Boosting, a novel hybrid forecasting model that integrates the statistical strengths of trigonometric, Box–Cox, ARMA, trend, and seasonal (TBATS) with the predictive power of LightGBM. The model is trained on a five-year real-world dataset from e-ticketing machines (ETM) in Thane Municipal Transport (TMT), incorporating holiday and pandemic-related variations. While Route 12 serves as a primary evaluation route, different station pairs are analyzed to validate their scalability across varying passenger demand levels. To comprehensively evaluate the proposed framework, a rigorous performance assessment was conducted using MAE, RMSE, MAPE, and WMAPE across station pairs characterized by heterogeneous passenger flow patterns. Empirical results demonstrate that the TBATS Boosting approach consistently outperforms benchmark models, including standalone SARIMA, TBATS, XGBoost, and LightGBM. By effectively capturing complex temporal dependencies, multiple seasonalities, and nonlinear relationships, the proposed framework significantly enhances forecasting accuracy. These advancements provide transit authorities with a robust tool for optimizing resource allocation, improving service reliability, and enabling data-driven decision making across varied and dynamic urban transit environments.

Modelling doi: 10.3390/modelling6020031

Authors: Mohammad Jifaturrohman I Utama Teguh Putranto Dony Setyawan I Suastika Septia Sujiatanti Dendy Satrio Noorlaila Hayati Luofeng Huang

Floating photovoltaic (FPV) systems offer a promising renewable energy solution, particularly for coastal waters. This preliminary numerical study proposes a single-array pentamaran configuration designed to maximize panel installation and enhance stability by reducing rolling motion. The study investigates the effect of mooring length on the motion behavior of FPV systems and actual line tension using the Boundary Element Method (BEM) in both frequency and time domains under irregular wave conditions. The results demonstrate that the mooring system significantly reduces all horizontal motion displacements, with reductions exceeding 90%. Even with a reduction of up to 51% in the unstretched mooring length, from the original design (304.53 m) to the shortest alternative (154.53 m), the motion response shows minimal change. This is supported by RMSE values of only 0.01 m/m for surge, 0.02 m/m for sway, and 0.09 deg/m for yaw. In the time-domain response, the shortened mooring line demonstrates improved motion performance. This improvement comes with the consequence of stronger nonlinearity in restoring forces and stiffness, resulting in higher peak tensions of up to 15.79 kN. Despite this increase, all configurations remain within the allowable tension limit of 30.69 kN, indicating that the FPV’s system satisfies safety criteria.

Modelling doi: 10.3390/modelling6020030

Authors: Sivasankaran Sivanandam Huey Tyng Cheong Aasaithambi Thangaraj

The goal of the present investigation is to explore the heater position and tilting angle of geometry on a buoyant convective stream and energy transport in a tilted, curved porous cavity. This work can be utilized in the field of solar panel construction and electrical equipment cooling. Since no study has explored the impact of the heater location in an inclined wavy porous chamber, three locations of the heater of finite length on the left sidewall, viz., the top, middle, and bottom, are explored. The stream through the porous material is explained by the Darcy model. The upper and lower walls, as well as the remaining area in the left wall, are covered with thermal insulation, while the curved right sidewall maintains the lower temperature. The governing equations and related boundary conditions are discretized by the finite difference approximations. The equations are then iteratively solved for different heater positions, inclinations, Darcy–Rayleigh number (RaD), and corrugation of the right walls. It is witnessed that the heater locations and cavity inclinations alter the stream and thermal fields within the curved porous domain. Furthermore, all heating zones benefit from improved heat conduction due to the right sidewall’s waviness and the tilted porous domain.

Modelling doi: 10.3390/modelling6020029

Authors: Anjala Wickramasinghe Mahinda Vilathgamuwa Ghavameddin Nourbakhsh Paul Corry

The integration of Distributed Energy Resources (DERs) into power grids presents significant challenges to grid performance, requiring innovative solutions for effective operation. Dynamic Operating Envelopes (DOEs) offer a promising approach by optimizing the use of existing infrastructure while ensuring compliance with network constraints. This paper reviews various DOE calculation methodologies, focusing on Optimal Power Flow (OPF)-based methods. Key findings include the role of DOEs in optimizing import and export limits, with critical factors such as forecast accuracy, network modelling, and the effects of mutual phase coupling in unbalanced networks identified as influencing DOE performance. The paper also explores the integration of DOEs into smart grid frameworks, examining both centralized and decentralized control strategies, as well as their potential for providing ancillary services. Challenges in scaling DOEs are also discussed, particularly regarding the need for accurate forecasts, computational resources, communication infrastructure, and balancing efficiency and fairness in resource allocation. Lastly, future research directions are proposed, focusing on the practical application of DOEs to improve grid performance and support network operations, as well as the development of more robust DOE calculation methodologies. This review provides a comprehensive overview of current DOE research and identifies avenues for further exploration and advancement.

Modelling doi: 10.3390/modelling6020028

Authors: Costica Lupascu Stelian Alaci Florina-Carmen Ciornei Ionut-Cristian Romanu Delia-Aurora Cerlinca Carmen Bujoreanu

One of the most well-known problems of dynamics is the “ladder problem”. In this paper, a theoretical model is proposed followed by the experimental validation of the predicted solution. The model refers to a rod of negligible thickness with the ends leaning frictionless on two walls. By approximating the rod as a segment, the problem is simplified, and the Lagrange equations can be applied. The experimental validation of the model had to address several challenges: the actual rod–wall contacts are singular points, friction cannot be neglected, and the rod’s motion must remain confined to the vertical plane. The physical “ladder” was designed as a cylindrical rod with two identical balls of well-controlled geometry, fixed at the ends. These spheres make contact with two half-cylinder grooves—one vertical and one horizontal—ensuring that the motion remains parallel to the vertical plane. The presence of dry friction in the sphere–groove contacts leads to a complex, strongly nonlinear differential equation of motion, requiring numerical methods of integration. A test-rig was designed and constructed for the experimental study of motion, and an aspect overlooked by the theoretical model was emphasised: the interruption of contact with the vertical wall. An excellent agreement was found between the experimental data and the theoretical results.

Modelling doi: 10.3390/modelling6020027

Authors: Aziida Nanyonga Hassan Wasswa Keith Joiner Ugur Turhan Graham Wild

The timely identification of probable causes in aviation incidents is crucial for averting future tragedies and safeguarding passengers. Typically, investigators rely on flight data recorders; however, delays in data retrieval or damage to the devices can impede progress. In such instances, experts resort to supplementary sources like eyewitness testimonies and radar data to construct analytical narratives. Delays in this process have tangible consequences, as evidenced by the Boeing 737 MAX accidents involving Lion Air and Ethiopian Airlines, where the same design flaw resulted in catastrophic outcomes. To streamline investigations, scholars advocate for natural language processing (NLP) and topic modelling methodologies, which organize pertinent aviation terms for rapid analysis. However, existing techniques lack a direct mechanism for deducing probable causes. To bridge this gap, this study trains and evaluates the performance of a transformer-based model in predicting the likely causes of aviation incidents based on long-input raw text analysis narratives. Unlike traditional models that classify incidents into predefined categories such as human error, weather conditions, or maintenance issues, the trained model infers and generates the likely cause in a human-like narrative, providing a more interpretable and contextually rich explanation. By training the model on comprehensive aviation incident investigation reports like those from the National Transportation Safety Board (NTSB), the proposed approach exhibits promising performance across key evaluation metrics, including BERTScore with Precision: (M = 0.749, SD = 0.109), Recall: (M = 0.772, SD = 0.101), F1-score: (M = 0.758, SD = 0.097), Bilingual Evaluation Understudy (BLEU) with (M = 0.727, SD = 0.33), Latent Semantic Analysis (LSA similarity) with (M = 0.696, SD = 0.152), and Recall Oriented Understudy for Gisting Evaluation (ROUGE) with a precision, recall and F-measure scores of (M = 0.666, SD = 0.217), (M = 0.610, SD = 0.211), (M = 0.618, SD = 0.192) for rouge-1, (M = 0.488, SD = 0.264), (M = 0.448, SD = 0.257), M = 0.452, SD = 0.248) for rouge-2 and (M = 0.602, SD = 0.241), (M = 0.553, SD = 0.235), (M = 0.5560, SD = 0.220) for rouge-L, respectively. This demonstrates its potential to expedite investigations by promptly identifying probable causes from analysis narratives, thus bolstering aviation safety protocols.

Modelling doi: 10.3390/modelling6020026

Authors: Evaggelos Kaselouris Vasilis Dimitriou

The integration of Finite Element Method (FEM) simulations with laser-based techniques has significantly advanced acoustic research by enhancing wave measurement, analysis, and prediction in complex solid media. This review examines the role of the FEM in laser-based acoustics for wave propagation, defect detection, biomedical diagnostics, and engineering applications. FEM models simulate ultrasonic wave generation and propagation in single-layer and multilayered structures, while laser-based experimental techniques provide high-resolution validation, improving modeling accuracy. The synergy between laser-generated ultrasonic waves and FEM simulations enhances defect detection and material integrity assessment, making them invaluable for non-destructive evaluation. In biomedical applications, the FEM aids in tissue characterization and disease detection, while in engineering, its integration with laser-based methods contributes to noise reduction and vibration control. Furthermore, this review provides a comprehensive synthesis of FEM simulations and experimental validation while also highlighting the emerging role of artificial intelligence and machine learning in optimizing FEM models and improving computational efficiency, which has not been addressed in previous studies. Key advancements, challenges, and future research directions in laser-based acoustic applications are discussed.

Modelling doi: 10.3390/modelling6020025

Authors: Mostafa Nofal Rania A. Elmanfaloty

The rise of telehealth in smart cities has introduced both opportunities and challenges, particularly in securing sensitive patient data and ensuring reliable authentication. This paper presents a chaos-based dynamic authentication scheme designed to address these challenges. Utilizing the inherent unpredictability and sensitivity of chaotic systems, the proposed method ensures robust protection against various attacks, including replay, brute-force, man-in-the-middle, collision, and parameter prediction. The scheme operates through a dynamic challenge–response mechanism using chaotic maps, which generate highly unpredictable authentication parameters. Simulations demonstrate the system’s strong resilience, minimal collision rate, and adaptability to diverse telehealth devices. By safeguarding sensitive telehealth data and promoting secure access control, this research provides a foundational framework for implementing secure authentication systems in smart cities. Future directions include real-world deployment and integration with advanced technologies like blockchain to further enhance security and scalability.

Modelling doi: 10.3390/modelling6010024

Authors: Yuhang Tian Yuan Feng Wei Gao

Mechanical metamaterials have become a critical research focus across various engineering fields. Recent advancements have pushed the development of reprogrammable mechanical metamaterials to achieve adaptive mechanical behaviours against external stimuli. The relevant designs strongly depend on a thorough understanding of the response spectrum of the original structure, where establishing an accurate virtual model is regarded as the most efficient approach to this end up to now. By employing an extended support vector regression (X-SVR), a powerful machine learning algorithm model, this study explores the uncertainty and sensitivity analysis and inverse study of re-entrant honeycombs under quasi-static compressive loads. The proposed framework enables accurate uncertainty quantification, sensitivity analysis, and inverse study, facilitating the related design and optimisation of metastructures when extended to responsive materials. The proposed framework is considered an effective tool for uncertainty quantification and sensitivity analysis, enabling the identification of key parameters affecting mechanical performance. Finally, the inverse study approach leverages X-SVR to swiftly obtain the required structural configurations based on targeted mechanical responses.

Modelling doi: 10.3390/modelling6010023

Authors: Petro Pukach Olha Chernukha Yurii Chernukha Myroslava Vovk

A three-dimensional mathematical model and simulation of the impurity diffusion process are developed under the given statistical characteristics of the system of internal stochastically disposed point sources of mass. These sources, possessing varying intensities, are located within the sub-strip according to a uniform distribution. The random source statistics are known, and the problem solution is expressed as the sum of the solution to the homogeneous problem and the convolution of Green’s function with the random point source system. The impurity concentration is averaged. Diffusive fluxes and the total amount of substance passing through any cross-sectional area over a specified time period are modeled using Fick’s laws. General and calculating formulas for averaged diffusive fluxes, including those applicable to steady-state regimes, are derived. A calculating formula for the total substance that has passed through the strip within a given time interval is obtained. A comprehensive software suite is developed to simulate the behavior of the averaged characteristics of the diffusion process influenced by the point source system. The second statistical moments of the impurity concentration are obtained and studied.

Modelling doi: 10.3390/modelling6010022

Authors: Chao-Qun Yu Sheng-Jie Duan Jing-Zhong Tong

A novel concrete-filled corrugated steel tubular (CFCST) column composed of corner steel bars and corrugated steel plates filled with concrete has been proposed recently. Columns with large height-to-width ratios are commonly used in practice, where they are often subjected to eccentric compression. However, there is a lack of research on their stability behavior under such conditions. This study presented a numerical analysis to evaluate the stability performance of CFCST columns under eccentric compression, with eccentricity ratios ranging from 0 to 2.0 and height-to-width ratios between 10 and 30. The numerical results indicated that the N–M interaction curve became less convex as the height-to-width ratio increased. Concrete strength and column width had a greater impact on the stability performance of the CFCST columns at low eccentricity ratios, while steel strength and steel bar width were more influential at high eccentricity ratios. The comparison between numerical and calculation results specified in AISC 360 and GB 50936 showed that both of them were unsuitable to estimate the stability performance of the column under eccentric compression. Finally, a formula was fitted, and the error was basically within 15%, which offered significantly improved accuracy over current design codes.

Modelling doi: 10.3390/modelling6010021

Authors: Avirut Puttiwongrak Thatree Deekaoropkun Khin Phyu Sin Krit Saowiang Pittaya Jamsawang Piti Sukontasukkul

This study addresses the critical issue of basal heave stability in deep excavations within Bangkok’s soft clay, particularly under conditions of confined groundwater recovery. Historical failures in excavation projects highlight the urgent need for effective stability assessments that account for fluctuating groundwater levels. Utilizing a comprehensive dataset derived from case studies and numerical simulations, this research employs the finite element method (FEM) to analyze the interactions between excavation depth, undrained shear strength, and groundwater dynamics. The findings reveal that groundwater recovery significantly influences effective stress, leading to increased uplift pressures that can destabilize excavation support systems. The numerical analyses indicate that Terzaghi’s method overestimates safety factors, while Bjerrum and Eide’s and Chang’s methods closely match numerical results, emphasizing the need for robust analysis that integrates groundwater effects to enhance stability assessments in urban excavations. Grouting techniques applied 10 m below the diaphragm wall significantly improved stability, with safety factors increasing by 63.47%, 87.86%, and 138.72% over various periods. This study contributes valuable insights into excavation design practices and provides empirical data that can inform future research aimed at mitigating hydraulic heave risks in urban environments. Ultimately, the findings advocate for the integration of advanced modeling techniques in geotechnical engineering to improve safety and structural integrity in excavation projects.

Modelling doi: 10.3390/modelling6010020

Authors: Camila Minchala-ávila Paul Arévalo Danny Ochoa-Correa

The increasing adoption of electric vehicles has introduced challenges in maintaining grid stability, energy efficiency, and economic optimization. Advanced control strategies are required to ensure seamless integration while enhancing system reliability. This study systematically reviews predictive control applications in energy systems, particularly in electric vehicle integration and bidirectional energy exchange. Using the PRISMA 2020 methodology, 101 high-quality studies were selected from an initial dataset of 5150 records from Scopus and Web of Science. The findings demonstrate that predictive control strategies can significantly enhance energy system performance, achieving up to 35% reduction in frequency deviations, 20–30% mitigation of harmonic distortion, and a 15–20% extension of battery lifespan. Additionally, hybrid approaches combining predictive control with adaptive learning techniques improve system responsiveness by 25% under uncertain conditions, making them more suitable for dynamic and decentralized networks. Despite these advantages, major barriers remain, including high computational demands, limited scalability for large-scale electric vehicle integration, and the absence of standardized communication frameworks. Future research should focus on integrating digital modeling, real-time optimization, and machine learning techniques to improve predictive accuracy and operational resilience. Additionally, the development of collaborative platforms and regulatory frameworks is crucial for large-scale implementation.

Modelling doi: 10.3390/modelling6010019

Authors: Alexandr Arbuz Nikita Lutchenko Rozina Yordanova

Equal-channel angular pressing (ECAP) is one of the most effective methods for obtaining ultrafine-grained structures in metals and alloys, significantly improving their mechanical properties. In this work, FEM modeling and development of a new design of the instrument for ECAP were carried out, followed by the production of real samples of working dies and casing. Four different designs of dies have been studied: with channel intersection angles of 90° and 45° and two schemes with the same angles and a spherical cavity to create back pressure. The main purpose of the study was to study the effect of dies geometry on the stress–strain state and pressing load, as well as to develop an optimal tool design that ensures the reliability and durability of the process. The simulation results showed that reducing the channel intersection angle to 45° increases the degree of accumulated deformation to 4.5 mm/mm but also increases the pressing load to 280 kN. The introduction of a spherical cavity contributes to a more uniform distribution of deformations, although the pressing load increases to 416 kN. Based on the data obtained, an improved tool design with a massive steel casing was developed and manufactured. The analysis and production of real samples confirmed its effectiveness and reliability, which will improve the ECAP process and obtain materials with improved characteristics while reducing operating costs.

Modelling doi: 10.3390/modelling6010018

Authors: Apostolos Palasis Antonios Liakopoulos George Sofiadis

In this paper, we compare three mathematical models for the mean velocity and Reynolds stress profiles for fully developed pressure-driven turbulent channel flow with the aim of assessing the level of accuracy of each model. Each model is valid over the whole boundary layer thickness (0 ≤y≤ δ), and it is formulated in terms of a law of the wall and a law of the wake. To calibrate the mathematical models, we use data obtained by direct numerical simulations (DNS) of pressure-driven turbulent channel flow in the range 182 ≤Reτ≤ 10,049. The models selected for performance evaluation are two models (Musker’s and AL84) originally developed based on high Reynolds boundary layer experimental data and Luchini’s model, which was developed when some DNS data were also available for wall-bounded turbulent flows. Differences are quantified in terms of local relative or absolute errors. Luchini’s model outperforms the other two models in the “low” and “intermediate” Reynolds number cases (Reτ= 182 to 5186). However, for the “high” Reynolds number cases (Reτ= 8016 and Reτ= 10,049). Luchini’s model exhibits larger errors than the other two models. Both Musker’s and AL84 models exhibit comparable accuracy levels when compared with the DNS datasets, and their performance improves as the Reynolds number increases.

Modelling doi: 10.3390/modelling6010017

Authors: Arulvalavan Tamilarasan Devaraj Rajamani

In the present research, the AlZnMgCu1.5 alloy was machined via an industrial-type Nd-YAG laser cutting process. The Box–Behnken design of response surface methodology was used to plan the trials. The experiments were carried out by varying the nitrogen pressure (4–10 bar), pulse energy (2.5–5.5 J), cutting speed (10–18 mm/min), and pulse width (1.5–2 ms). ANOVA was conducted to assess the impact of process factors on response characteristics. The ANOVA results suggest that nitrogen pressure has the greatest influence on the input process parameters. A detailed investigation was conducted to examine the effects of various parameters on kerf deviation. The metaheuristic algorithms (i.e., Giant Trevally Optimizer—GTO; and Zebra Optimization Algorithm—ZOA) were implemented to determine the optimum process parameters for producing the best performance measures. A comparative analysis demonstrated that the parametric value provided by the GTO algorithm, which adheres to the ZOA method, yielded the lowest response. Optimization using GTO resulted in a 6.71% improvement in kerf deviation prediction accuracy compared to experimental values, while ZOA achieved a 2.37% improvement. Furthermore, GTO demonstrated superior computational efficiency, converging in 5.687 s, significantly faster than the 11.548 s required by ZOA. The optimal solution suggested by the GTO algorithm is further verified using a confirmation test on the random settings. In addition, the surface morphology of the laser-cut kerf surfaces was analyzed using SEM images. Through this, it is confirmed that the metaheuristic algorithm of GTO is more suitable for finding the optimum process parameters.

Modelling doi: 10.3390/modelling6010016

Authors: Warisa Thangjai Sa-Aat Niwitpong Suparat Niwitpong Rada Somkhuean

The Birnbaum–Saunders (BS) distribution, defined only for non-negative values, is asymmetrical. However, it can be transformed into a normal distribution, which is symmetric. The BS distribution is particularly useful for analyzing data consisting of values greater than zero. This study aims to introduce six approaches for constructing confidence intervals for the difference and ratio of percentiles in Birnbaum–Saunders distributions containing zero values. The proposed approaches include the generalized confidence interval (GCI) approach, the bootstrap approach, the highest posterior density (HPD) approach based on the bootstrap method, the Bayesian approach, the HPD approach based on the Bayesian method, and the method of variance estimates recovery (MOVER) approach. To assess their performance, a Monte Carlo simulation study is conducted, focusing on coverage probability and average length. The results indicate that the MOVER approach and the HPD approach based on the Bayesian method perform better than other approaches for constructing confidence intervals for the difference between percentiles. Moreover, the GCI and Bayesian approaches outperform others when constructing confidence intervals for the ratio of percentiles. Finally, daily wind speed data from the Rayong and Prachin Buri provinces are used to demonstrate the efficacy of the proposed approaches.

Modelling doi: 10.3390/modelling6010015

Authors: Reza Shojaei Mehr Esmaeil Mohammadian Bishe Bijan Farhanieh Hossein Afshin

Analyzing wildfire behavior is crucial due to its significant environmental repercussions. Among the various influencing factors, terrain slope and wind velocity are pivotal in governing fire spread characteristics. In the present study, we investigate the influence of negative terrain slopes (up to −45°), backward wind velocities (up to 2 m/s), and their combined effects on the surface fire spread rate using the Wildland-Urban Fire Dynamics Simulator (WFDS). Wind velocity in backward flows reduces the rate of spread by 40% at 30° angles, primarily due to the suppression of radiative heat transfer leading to reduced preheating unburnt areas. However, this effect reduces on lower slopes. The key findings reveal a significant increase in fire intensity and the rate of spread when the terrain slope exceeds 20°. The fire front shape evolves from a relatively flat rounded U-shape to a V-shape; it is shown that a downward slope slightly affects the spread rate, and the fire front shape stays flat.

Modelling doi: 10.3390/modelling6010014

Authors: Panagiota Katsimpini

This study explores the performance of a novel curved steel damper system in lessening the seismic response of elevated steel tanks. It specifically examines two types of tanks, broad and tall, by analyzing their behavior during past earthquakes. Non-linear time history analyses were executed using various ground motion records to evaluate the dynamic characteristics and structural responses of the tank systems. The application of the curved steel damper, placed between the tank container and its supporting structure, resulted in a significant reduction in base shear forces and deformations of the tank walls when compared to traditional designs. The findings highlight the effectiveness of the damping system, showing that the curved damper leads to decreased maximum displacement and base shear forces during seismic activities. This research contributes essential knowledge for the seismic design of elevated steel tanks and proposes an innovative, cost-efficient strategy for enhancing their earthquake resilience.

Modelling doi: 10.3390/modelling6010013

Authors: Shruthi Polipu Jiju Gillariose

The Bivariate Odd Lindley Half-Logistic (BOLiHL) distribution with progressive Type-II censoring provides a powerful statistical tool for analyzing dependent data effectively. This approach benefits society by enhancing engineering systems, improving healthcare decisions, and supporting effective risk management, all while optimizing resources and minimizing experimental burdens. In this paper, the likelihood function derived under progressive Type-II censoring is generalized for the BOLiHL distribution. The well-known maximum likelihood estimation method and Bayesian estimation are applied to evaluate the parameters of the distribution. A study utilizing simulation techniques is performed to evaluate the performance of the estimators, using statistical analysis metrics for censored observations under a progressive Type-II censoring scheme with varying sample sizes, failure times, and censoring schemes. Additionally, a real dataset is studied to validate the proposed model, delivering impactful analyses for practical applications.

Modelling doi: 10.3390/modelling6010012

Authors: Nurlan Zhangabay Timur Tursunkululy Akmaral Utelbayeva Uliya Abdikerova Murat Sultanov

This manuscript presents a theoretical study of a newly developed energy-efficient external wall structure in comparison with a traditional ventilated facade. To conduct numerical studies based on mathematical models of the heat transfer of water vapor filtration through a multilayer filler structure with ventilated and non-ventilated air gaps, a calculation method was developed that additionally considers the presence of heat-reflecting screens and different variations in the geometric parameters of air gaps and thermal insulation layers. The study results demonstrated that the new energy-efficient multilayer wall structure was 6.1–7.2% more efficient in terms of heat transfer resistance than the traditional one, and due to the presence of heat-reflecting screens, the efficiency increased to 15.2–16.3% depending on the geometric parameters of the air and thermal insulation layers of the wall structure. In addition, in all the considered variants of the filler structure geometry (i.e., with closed and ventilated air gaps), there were water vapor condensation zones, but it was established that according to the value of the inadmissibility of moisture accumulation in multilayer wall structures, over the annual period of operation, the structures complied with the standard climatic conditions of Shymkent. The results of this study thus positively complement the existing catalog of energy-efficient wall structures, and the new wall structure can be used while considering the necessary geometric parameters of air and heat-insulating layers when designing buildings in the corresponding climatic conditions.

Modelling doi: 10.3390/modelling6010011

Authors: Michael Niebler Stylianos Chrisopoulos Roberto Cudmani Daniel Rebstock

The importance of using sophisticated interface models to obtain realistic numerical solutions of soil–structure interaction (SSI) problems has been recognised in recent decades. With this aim, various advanced interface models have been developed, which assume that the same advanced constitutive model can describe the soil behaviour inside and outside the shear zone. These models fail to adequately address the experimentally observed stick–slip transition, assuming permanent sticking between the soil and structure. Furthermore, the influence of interface roughness requires model parameter adjustments, e.g., in the critical state of the soil, which are questionable from a physical point of view. To overcome these shortcomings, we propose a general relationship to describe the evolution of the shear strain in the shear zone as a function of the surface roughness, the density, and the normal stress. This relationship, which assumes a stick–slip transition at the interface, can be combined with an advanced constitutive model to describe soil–structure interface behaviour using the same set of model parameters as for the surrounding soil. Depending on the surface roughness of the interface, this transition leads to a localisation within the soil in the shear zone (for rough surfaces) or at the contact surface (for smooth surfaces). The proposed model was validated using interface shear tests from the literature on dry granular soils. A hypoplastic constitutive model was used in the simulations. The comparison of experimental and calculated results demonstrates the ability of the proposed model to realistically reproduce shear stress and relative displacements, including the stick–slip transition observed in the experiments. This instils confidence in the model’s reliability and accuracy, thus providing a reliable numerical tool for SSI analyses.

Modelling doi: 10.3390/modelling6010010

Authors: Muhammad Ahsan Khan Fabio Addona Luca Chiapponi Nicolò Merli Renata Archetti

This paper investigates the flow dynamics of a turbulent fountain with negative buoyancy using a Computational Fluid Dynamics (CFD) model, developed using OpenFOAM® and calibrated against laboratory experiments. The simulations effectively replicate the geometry and buoyancy fluxes of the fountain, showing a fairly good agreement between the numerical and experimental velocity fields. These simulations are then used to investigate momentum and buoyancy fluxes for various source fluid densities. We find a dominant out-upward momentum transfer in the body of the fountain, while it is mainly out-downward below the inlet section. Furthermore, the vertical flux is almost twice the radial flux, while the tangential components are negligible on the inner side of the fountain. For small density differences between the fountain and the surrounding environment, we find a greater diffusion of the source fluid, while both the vertical and radial salt fluxes increase with increasing density of the fountain. The data generated serve as a significant resource for the development of future CFD models.

Modelling doi: 10.3390/modelling6010009

Authors: Khalil Abbal Mohammed El-Amrani Oussama Aoun Youssef Benadada

Particle swarm optimization (PSO), an important solving method in the field of swarm intelligence, is recognized as one of the most effective metaheuristics for addressing optimization problems. Many adaptive strategies have been developed to improve the performance of PSO. Despite these advances, a key problem lies in defining the configuration criteria of the adaptive algorithm. This study presents an adaptive variant of PSO that relies on fitness landscape analysis, particularly via ruggedness factor estimation. Our approach involves adaptively updating the cognitive and acceleration factors based on the estimation of the ruggedness factor using a machine learning-based method and a deterministic way. We tested them on global optimization functions and the feature selection problem. The proposed method gives encouraging results, outperforming native PSO in almost all instances and remaining competitive with state-of-the-art methods.

Modelling doi: 10.3390/modelling6010008

Authors: Oussama Abderrahmane Dambri Arash Azarnoush Dimitrios Makrakis Gabriel Levesque Maja Witter Abdelhakim Senhaji Hafid

This paper presents the development of a computer simulation framework, designed as a cost–effective and technically efficient alternative to experimental studies. The framework focuses on the Bio–Neural Dust System proposed in our previous works, which consists of two components: a light–emitting bio–nanosensor and an opsin–expressing genetically modified neuron. This innovative system holds significant potential for applications in neuroscience and biotechnology research. Programmed in Python, the framework provides researchers with a virtual tool to test and evaluate the Bio–Neural Dust System, enabling the prediction of outcomes for future in vivo experiments. This approach not only conserves resources, but also offers scientists a flexible and accessible means to investigate the complex interactions within the system prior to real–world applications. The framework’s adaptability and potential for diverse research applications highlight its importance in advancing the field of bio–nanotechnology.

Modelling doi: 10.3390/modelling6010007

Authors: Fernando Iván Molina-Herrera Luis Isai Quemada-Villagómez Mario Calderón-Ramírez Gloria María Martínez-González Hugo Jiménez-Islas

Grain storage in silos plays a fundamental role in preserving the quality and safety of agricultural products. This study presents a comparative evaluation of two-dimensional (2D) and three-dimensional (3D) mathematical models to predict the temperature and moisture distribution during unventilated corn storage in cylindrical silos with conical roofs. The models incorporate external temperature fluctuations, solar radiation, grain moisture equilibrium with air humidity via sorption isotherm (water activity), and grain respiration to simulate real-world storage conditions. The 2D model offers computational efficiency and is suitable for preliminary assessments but simplifies natural convection effects and underestimates axial temperature gradients. Conversely, the 3D model provides a detailed representation of heat and moisture transfer phenomena, capturing complex interactions such as buoyancy-driven flow and localized effects of solar radiation. The results reveal that temperature and moisture accumulation are more pronounced in the upper regions of the silo, driven by solar radiation and natural convection, with significant implications for large-scale silos where thermal inertia plays a key role. This dual modeling approach demonstrates that while the 2D model is valuable for quick evaluations, the 3D model is essential for comprehensive insights into thermal and moisture gradients. The findings support informed decision-making in silo design, optimization, and management, enhancing grain storage strategies globally.

Modelling doi: 10.3390/modelling6010006

Authors: Bilal Bencharif Mohamed Amine Beghoura Emrah Demir

Green logistics has gained significant attention in recent years due to increasing pollution levels and their negative effects. This area of research is crucial as governments and countries worldwide recognize the severity of pollution and its detrimental effects. Despite progress, significant gaps remain due to the lack of advanced models that consider additional factors and the influence of speed on their outcomes. This paper presents a case study on the Volume-based Pollution-Routing Problem with Time Windows (VPRPTW). The objective is to minimize CO⁢2 emissions and improve customer satisfaction using a fleet of delivery vehicles. We propose a mathematical model and a probabilistic Tabu Search (TS) algorithm to solve the studied VPRPTW. The study revealed a decrease in daily fleet size from 16 to 12, indicating improved operational efficiency. In our study, we evaluate the impact of vehicle speed on fuel consumption and compare the results with a constant route speed to those obtained at varying speeds. Computational experiments reveal a significant difference of over 20% between fixed and variable speed assumptions. Additionally, we confirm that distance alone does not always correlate with energy consumption and CO⁢2 emissions. This highlights the importance of considering variable speeds in routing problems to assist logistics companies, urban planners, and policymakers achieve more accurate and environmentally friendly transportation solutions.

Modelling doi: 10.3390/modelling6010005

Authors: Rostislav Svidler Roman Rinberg Sascha Mueller Lothar Kroll

Fibre-reinforced polymers based on natural fibers, such as flax fibers, exhibit pronounced nonlinear orthotropic material behavior. This presents a significant challenge in finite element analysis (FEA) simulations, as the nonlinear constitutive models available in commercial FEA tools are difficult to apply and fail to capture all the material’s specific characteristics. Relying on initial or reduced secant moduli in linear quasi-static analyses of deformations or stress states can result in inaccurate outcomes and overly optimistic strength predictions, particularly in compression-dominated cases. However, with appropriate modifications, classical laminate theory (CLT) can be adapted for nonlinear analysis. This involves iteratively updating the components of the stiffness matrix for the unidirectional (UD) ply during the calculation process based on the current strain state and stress interactions. This study presents and discusses a computational algorithm for the FEA software ABAQUS/CAE 2019, which incorporates material-related orthotropic nonlinearities and stress-dependent interactions within the CLT framework. The algorithm represents a single-scale material model at the meso level (UD ply) and is based on the concept of orthotropic elasto-damage within the framework of continuum damage mechanics (CDM) theory. Numerical implementation is achieved through a user-defined field (USDFLD) subroutine, accompanied by a pre-processing Python script for managing experimental data, computing data fields, and calculating parameters. As shown below, this type of implementation appears justified compared to a user material subroutine (UMAT) subroutine in terms of computational efficiency and practicality.

Modelling doi: 10.3390/modelling6010004

Authors: Bauyrzhan Rakhadilov Nazerke Muktanova Aidar Kengesbekov Nurtoleu Magazov

This paper discusses the process of high-velocity oxygen fuel (HVOF) spraying with modeling of the gas flow parameters and behavior of WC-Co-Cr powder particles of different fractions (up to 20 µm, 21–35 μm and 36–45 μm). It was found that the temperature of the gas stream reaches a maximum of about 2700 °C, after which it gradually decreases, and the pressure in the combustion chamber (before the exit of gases through the nozzle) reaches maximum values, exceeding 400,000 Pa, and the pressure at the exit of the nozzle stabilizes at about 100,000 Pa, which corresponds to the standard atmospheric pressure. The gas velocity increases to 1300–1400 m/s and then decreases to 400 m/s at a distance of about 150 mm. It was determined that powder particles of the 21–35 µm fraction provide more stable parameters of velocity and temperature. Small particles (up to 20 µm) lose velocity and temperature faster as they advance, which deteriorates the coating quality, which was also experimentally confirmed. All results obtained from the HVOF process modeling fully align with the data from experimental studies.

Modelling doi: 10.3390/modelling6010003

Authors: Geraldo Cesar Rosario de Oliveira Vania Aparecida Rosario de Oliveira Carlos Alexis Alvarado Silva Erick Siqueira Guidi Fernando de Azevedo Silva

This study presents an experimental and numerical investigation into the stress field in cylinders manufactured from photosensitive resin using the Masked Stereolithography (MSLA) technique. For material characterization, tensile and bending test data from resin specimens were utilized. The stress field in resin disks was experimentally analyzed using photoelasticity and Digital Image Correlation (DIC) methods, subjected to compressive loads, according to the cylinder–plane contact model. Images were captured during the experiments using polarizing film and a low-cost CPL lens, coupled to a smartphone. The experimental results were compared with numerical and analytical simulations, where the formation of fringes and regions indicating the direction and magnitude of normal and shear stresses were observed, with variations ranging from 0.6% to 8.2%. The convergence of the results demonstrates the feasibility of using parts produced with commercially available photosensitive resin on non-professional printers for studying contact theory and stress fields. In the future, this methodology is intended to be applied to studies on stress in gears.

Modelling doi: 10.3390/modelling6010002

Authors: Mahmoud Shaban

A frequency-reconfigurable MIMO antenna with high gain, low mutual coupling and highly suppressed side lobe level (SLL) for applications in 24 GHz ISM band sensing and automotive radar systems was designed, modeled, and simulated. The reconfigurability feature was modeled with the implementation of a varactor diode in the model to alter the frequency in a wide band around 24 GHz. The design features 2- and 4-port MIMO antenna each comprising a 1 × 8 microstrip patch array. At the core of achieving both a high gain of 16 dBi and high isolation of 38.4 dB at a resonance frequency of 24.120 GHz lies the integration of a metamaterial absorber, comprising an optimized split-ring unit cell to effectively mitigate interference among the MIMO elements. Noteworthy impedance bandwidths of the sensor antenna span from 23.8 to 24.3 GHz, catering to diverse frequency requirements. The proposed sensor antenna feature a half-power beamwidth of 74° in the E-plane and 11° in the H-plane and an SLL of −24 dB at 24.120 GHz showing its robust performance characteristics across multiple operational dimensions.

Modelling doi: 10.3390/modelling6010001

Authors: Panagiota Katsimpini

This study investigates the seismic performance of two-, four-, and six-story composite buildings equipped with viscous wall dampers, focusing on structures with concrete-filled steel tubular (CFST) columns and steel beams. Through nonlinear time history analyses using sequential ground motions, the research evaluates the effectiveness of viscous wall dampers in mitigating seismic demands. Results demonstrate significant reductions in both interstory drift ratios and peak floor accelerations across all building heights when dampers are installed. The study particularly highlights the dampers’ effectiveness in controlling drift demands in lower and middle floors while managing acceleration amplification at upper levels. The findings validate the integration of viscous wall dampers into mid-rise composite structures and underscore the importance of considering sequential ground motions in seismic performance evaluations.

Modelling doi: 10.3390/modelling5040106

Authors: Leonid Legashev Sergey Tolmachev Irina Bolodurina Alexander Shukhman Lyubov Grishina

Surrogate modeling technology is used to create lightweight analogs of resource- and calculation-intensive software, provided that the problem can be reduced to the regression problem. In this article, we construct a surrogate model for predicting annual energy consumption using the open-source EnergyPlus software and various sampling techniques. A general algorithm for an error-based adaptive sampling technique to build the surrogate model is presented. The best results were shown by the composite Mixed Sampling method with a data refining window the size of 70% and a LightGBM regression model. The best attained metrics values are as follows: MSE = 7.76, RMSE = 1.47, MAE = 0.98 and R2 = 0.99. For a small number of iterations, an error-based adaptive sampling technique with hyperparameter tuning is preferable to the static sampling approach. For a large number of iterations, both techniques show approximately good predictive results of the built surrogate model. After hyperparameter tuning was performed, the average value of the MSE metric decreased from 43.43 to 7.76. A gas thickness feature greater than 0.015 had no positive effect on energy-saving optimization. For temperatures on a summer day of 30 degrees and above, there was a sharp increase in energy consumption. The maximum dry bulb temperature on a winter and summer day and the wind speed on a winter day were the most important features of the built surrogate model with 492, 483 and 443 gain values of the feature importance method, respectively.

Modelling doi: 10.3390/modelling5040105

Authors: Alexey Shcherbakov Alexander Gudenko Andrey Sliva Daria Gaponova Artem Marchenkov Alexey Goncharov

The relevance of creating specialized computer programs that convert a virtual 3D model of an object into machine code (G-code) for controlling the process of 3D printing products from wire raw materials is substantiated. It is shown that for wire-based additive technologies, a fundamentally important requirement is to ensure the continuity of the surfacing trajectory within one section. A method for determining a continuous surfacing trajectory is proposed, the implementation of which requires two stages: performing a numerical analysis of a two-dimensional region with boundary conditions describing this section; and running a heuristic algorithm for the movement of the surfacing head, in which the direction of movement is selected based on the results of the analysis. The procedure for setting boundary conditions and an algorithm for numerically solving the boundary value problem of determining the field of the “height” function for each section are described. The principles of operation of the heuristic algorithm for selecting the direction of head movement based on the calculated height field and continuous determination of the proximity of adjacent layers and section boundaries are disclosed. An analysis of the algorithm operation is carried out using a section with holes as an example, and the potential of using numerical methods to calculate the change in the temperature field during the surfacing process is shown.

Modelling doi: 10.3390/modelling5040104

Authors: Farima Salamian Amirmohammad Paksaz Behrooz Khalil Loo Mobina Mousapour Mamoudan Mohammad Aghsami Amir Aghsami

Efficient management of hospital evacuations and pharmaceutical supply chains is a critical challenge in modern healthcare, particularly during emergencies. This study addresses these challenges by proposing a novel bi-objective optimization framework. The model integrates a Mixed-Integer Linear Programming (MILP) approach with advanced machine learning techniques to simultaneously minimize total costs and maximize patient satisfaction. A key contribution is the incorporation of a Gated Recurrent Unit (GRU) neural network for accurate drug demand forecasting, enabling dynamic resource allocation in crisis scenarios. The model also accounts for two distinct patient destinations—receiving hospitals and temporary care centers (TCCs)—and includes a specialized pharmaceutical supply chain to prevent medicine shortages. To enhance system robustness, probabilistic demand patterns and disruption risks are considered, ensuring supply chain reliability. The solution methodology combines the Grasshopper Optimization Algorithm (GOA) and the ɛ-constraint method, efficiently addressing the multi-objective nature of the problem. Results demonstrate significant improvements in cost reduction, resource allocation, and service levels, highlighting the model’s practical applicability in real-world scenarios. This research provides valuable insights for optimizing healthcare logistics during critical events, contributing to both operational efficiency and patient welfare.

Modelling doi: 10.3390/modelling5040103

Authors: Sergey Osipov Ivan Komarov Olga Zlyvko Andrey Vegera George Gertsovsky

Currently, about a thousand micro gas turbine units of small and medium capacity are in operation in the Russian Federation, which are used as an autonomous power source at critical infrastructure facilities. During long-term operation, the component parts of the micro GTU may fail and require replacement or repair. The lack of spare parts and design documentation for their production makes it impossible to operate. As a way to solve the problem, the reverse engineering process can be used to produce components. One of the stages of reverse engineering is to determine the geometric parameters of the object. The fastest and most accurate way to obtain geometric characteristics in the reverse engineering process is 3D scanning. Three-dimensional scanning technology is used to obtain a solid 3D model of the prototype surface, based on which design documentation is subsequently developed. This article presents the results of a study of the influence of the parameters of the distance between polygonal grid points and the scanner exposure on the detailing of the outer surface and the geometric parameters of the resulting polygonal model. As a result of this study, the dependence of the final file size and the time spent on scanning and processing on the distance between the points of the polygonal grid and the model was established. Based on the dependence of the parameters, recommendations were obtained for choosing the distance between the points of the polygonal grid of laser 3D scanning. Also, after performing the stages of reverse engineering, the methodology for creating solid models and design documentation of parts of power equipment units using 3D scanning technology was improved.

Modelling doi: 10.3390/modelling5040102

Authors: Mohammed A. Namuq Ezideen A. Hasso Mohammed A. Jamal Koran A. Namuq Yibing Yu

Currently, most oil and gas wells are drilled by continuously transmitting downhole measured information (directional and geological information) in real-time to the surface to monitor and steer the well along a pre-defined path. The intelligent drill pipe method can transmit data over longer distances and at a higher rate than other methods, such as mud pulse telemetry, acoustic telemetry, and electromagnetic telemetry. Nevertheless, it is expensive and requires boosters along the drill string. In the available literature, academic research rarely addresses the data transmission process in boreholes using intelligent drill pipes. Furthermore, there is a need for an effective and validated model to study various controllable parameters to enhance the efficiency of the intelligent drill pipe telemetry without the need to develop several physical lab or field prototypes. This paper presents the development of a model based on MATLAB Simulink to simulate the process of data transmission in boreholes utilizing intelligent drill pipes. Laboratory experimental prototype measurements have been used to test the model’s effectiveness. A good correlation is found between the measured lab data and the model’s predictions for the signals transmitted contactless through intelligent drill pipes with a correlation coefficient (R2) above 0.9. This model can enhance data transmission efficiency via intelligent drill pipes, study different concepts, and eliminate the need to develop several unnecessarily expensive and time-consuming physical lab prototypes.

Modelling doi: 10.3390/modelling5040101

Authors: Shuguang Zhao Yurong Han Qicheng Xu Ziping Wang Yinghao Shan

Hydrogen energy plays an increasingly vital role in global energy transformation. However, existing electric–hydrogen coupled integrated energy systems (IESs) face two main challenges: achieving stable operation when integrated with large-scale networks and integrating optimal dispatching code with physical systems. This paper conducted comprehensive modeling, optimization and joint simulation verification of the above IES. Firstly, a low-carbon economic dispatching model of an electric–hydrogen coupled IES considering carbon capture power plants is established at the optimization layer. Secondly, by organizing and selecting representative data in the optimal dispatch model, an electric–hydrogen coupled IES planning model considering the integration of wind, photovoltaic (PV), diesel and storage is constructed at the physical layer. The proposed electric–hydrogen coupling model mainly consists of the following components: an alkaline electrolyzer, a high-pressure hydrogen storage tank with a compressor and a proton exchange membrane fuel cell. The IES model proposed in this paper achieved the integration of optimal dispatching mode with physical systems. The system can maintain stable control and operation despite unpredictable changes in renewable energy sources, showing strong resilience and reliability. This electric–hydrogen coupling model also can integrate with large-scale IES for stable joint operation, enhancing renewable energy utilization and absorption of PV and wind power. Co-simulation verification showed that the optimized model has achieved a 29.42% reduction in total system cost and an 83.66% decrease in carbon emissions. Meanwhile, the simulation model proved that the system’s total harmonic distortion rate is controlled below 3% in both grid-connected and islanded modes, indicating good power quality.

Modelling doi: 10.3390/modelling5040100

Authors: Olga S. Stolbova Oleg V. Stolbov

This paper presents a model of the bending behavior of a bi-layer cantilever composed of titanium nickelide and a magnetoactive elastomer embedded with magnetically hard particles. The cantilever is initially subjected to an external magnetic field in its high-temperature state, followed by cooling to a low-temperature state before the magnetic field is removed. This sequence results in residual bending deformation. Basic relations describing the material behavior of titanium nickelide and the magnetoactive elastomer are presented. A variational formulation for the problem under consideration is written down. The problem is solved numerically using the finite element method. The influence of the applied magnetic field magnitude and the thickness of the titanium nickelide layer on the cantilever deflection magnitude is studied. The dependence of the residual cantilever deflection on the applied magnetic field is obtained. The possibility of this structure as a controllable gripping element for applications in robotics and micro-manipulation is demonstrated.

Modelling doi: 10.3390/modelling5040099

Authors: Julio Hernández-Ramírez Juan Segundo-Ramírez Nancy Visairo-Cruz C. Alberto Nú?ez Guitiérrez

This paper presents a finite-difference-based method for numerically deriving the DQ impedance model of power electronics-based power systems, specifically tailored for stability analysis. The proposed method offers a computationally efficient alternative to traditional approaches by directly applying finite-difference approximations to the large-signal dynamic system, without relying on repetitive time-domain simulations or small-signal analytical models. This method eliminates the need for additional models or complex procedures to compute the steady-state solution, streamlining the impedance modeling process. The accuracy, efficiency, and precision of the proposed method are evaluated through comparative studies with analytical and time-domain perturbation methods. Results demonstrate that the proposed approach provides accuracy comparable to analytical models while significantly reducing computational effort, outperforming perturbation methods in both speed and precision. These findings highlight the practical value of the proposed method for real-time and large-scale system analysis, making it a robust tool for power systems stability assessment.

Modelling doi: 10.3390/modelling5040098

Authors: Angelo M. Tusset Jonierson A. Cruz Jose M. Balthazar Maria E. K. Fuziki Giane G. Lenzi

This work presents a non-linear mathematical model of a machining system subjected to a non-ideal vibration source. Computer simulations have shown chaotic behavior for specific parameters of the proposed mathematical model. The chaotic behavior is proven using time histories, phase diagrams, bifurcation diagrams, and the Lyapunov exponent. Considering that cutting tool vibration in the machining process is one of the main problems of productivity and machining accuracy, the introduction of a magnetorheological damper was considered in the proposed model to reduce the vibration amplitudes of the cutting tool and suppress the chaotic behavior. Hysteresis was considered in the magnetorheological damper model and its application in the system as both a passive and active absorber. The active control strategy considered the application of two non-linear control signals: feedforward to maintain the vibration with a desired behavior and state feedback to drive the system to the desired behavior. The numerical results demonstrated that the proposed controls efficiently reduced the vibration amplitude by introducing the MR damper. Active control has proven effective in controlling the force of the MR damper by varying the electrical voltage applied to the damper coil.

Modelling doi: 10.3390/modelling5040097

Authors: Ivan Smolyanov Evgeniy Shmakov

The development of digital twins for power transformers has become increasingly important to predict possible operating modes and reduce the likelihood of faults. The accuracy of these predictions relies heavily on the numerical models used, which must be both simple and computationally efficient. This work focuses on creating a simplified numerical model for a template oil-immersed power transformer (100 MVA, 230/69 KV). The study investigates how the number of elements and the strategies used to set up the mesh in the domain of interest influence the results, aiming to identify the key parameters that affect the outcomes. Furthermore, a significant effect of resolving thermal boundary layers on the accurate identification of hot spots is demonstrated. Two approaches to resolving thermal boundary layers are explored in this work. This study presents a comprehensive analysis of three numerical models for conjugate heat transfer simulations, each with distinct features and computational domain compositions. The results show that the addition of extra calculation domains leads to the emergence of new vortex structures, affecting the velocity profile at the channel inlet and altering the location of hot spots. This study provides valuable insights into the configuration and composition of calculated domains in numerical models of oil-immersed power transformers, essential for the accurate prediction of hot spot temperatures and ensuring reliable operation.

Modelling doi: 10.3390/modelling5040096

Authors: Rita I. Babicheva Aleksander S. Semenov Artem A. Izosimov Elena A. Korznikova

In the study, the combined molecular dynamics and Monte Carlo (MD/MC) simulation was used to investigate the short-range ordering effect on tensile deformation of bicrystals with grain boundaries (GBs) Σ3(11¯2)[110]. Three different equiatomic high-entropy alloys, namely, ZrTiNbV, ZrTiNbTa and ZrTiNbHf, were considered. The tensile loading at 300K was applied in the direction perpendicular to the GBs’ planes. The stress–strain response as well as the structure evolution of the alloys with initial random distribution of atoms were compared with results obtained for the corresponding materials relaxed during the MD/MC procedure. It was revealed that the distribution of atoms in the alloys significantly affects the deformation process. Ordered clusters of Nb atoms are able to suppress the dislocation sliding and twin formation increasing the yield strength of ZrTiNbV. On the contrary, in ZrTiNbTa, the twinning mechanism is dominant in the case of the ordered structure due to the absence of Nb clusters and the presence of areas enriched with Zr atoms, which ease nucleation of dislocations and twins. Since Hf decreases the stability of the body-centered cubic lattice, the main deformation mechanism of ZrTiNbHf is the stress-induced phase transition; however, Nb clusters inside grains of the relaxed alloy slightly delay this process.

Modelling doi: 10.3390/modelling5040095

Authors: Ruben Hernandez Ramon Garcia-Hernandez Francisco Jurado

In this paper, we address the modeling, simulation, and control of a rotary inverted pendulum (RIP). The RIP model assembled via the MATLAB (Matlab 2021a)®/Simulink (Simulink 10.3) Simscape (Simscape 7.3)™ environment demonstrates a high degree of fidelity in its capacity to capture the dynamic characteristics of an actual system, including nonlinear friction. The mathematical model of the RIP is obtained via the Euler–Lagrange approach, and a parameter identification procedure is carried out over the Simscape model for the purpose of validating the mathematical model. The usefulness of the proposed Simscape model is demonstrated by the implementation of a variety of control strategies, including linear controllers as the linear quadratic regulator (LQR), proportional–integral–derivative (PID) and model predictive control (MPC), nonlinear controllers such as feedback linearization (FL) and sliding mode control (SMC), and artificial intelligence (AI)-based controllers such as FL with adaptive neural network compensation (FL-ANC) and reinforcement learning (RL). A design methodology that integrates RL with other control techniques is proposed. Following the proposed methodology, a FL-RL and a proportional–derivative control with RL (PD-RL) are implemented as strategies to achieve stabilization of the RIP. The swing-up control is incorporated into all controllers. The visual environment provided by Simscape facilitates a better comprehension and understanding of the RIP behavior. A comprehensive analysis of the performance of each control strategy is conducted, revealing that AI-based controllers demonstrate superior performance compared to linear and nonlinear controllers. In addition, the FL-RL and PD-RL controllers exhibit improved performance with respect to the FL-ANC and RL controllers when subjected to external disturbance.

Modelling doi: 10.3390/modelling5040094

Authors: Sameer Salasakar Sabyasachi Prakash Ganesh Thakur

Well placement optimization refers to the identification of optimal locations for wells (producers and injectors) to maximize net present value (NPV) and oil recovery. It is a complex challenge in all phases of production (primary, secondary and tertiary) of a reservoir. Reservoir simulation is primarily used to solve this intricate task by analyzing numerous scenarios with varied well locations to determine the optimum location that maximizes the targeted objective functions (e.g., NPV and oil recovery). Proxy models are a computationally less expensive alternative to traditional reservoir simulation techniques since they approximate complex simulations with simpler models. Previous review papers have focused on analyzing various optimization algorithms and techniques for well placement. This article explores various types of proxy models that are the most suitable for well placement optimization due their discrete and nonlinear natures and focuses on recent advances in the area. Proxy models in this article are sub-divided into two primary classes, namely data-driven models and reduced order models (ROMs). The data-driven models include statistical- and machine learning (ML)-based approximations of nonlinear problems. The second class, i.e., a ROM, uses proper orthogonal decomposition (POD) methods to reduce the dimensionality of the problem. This paper introduces various subcategories within these two proxy model classes and presents the successful applications from the well placement optimization literature. Finally, the potential of integrating a data-driven approach with ROM techniques to develop more computationally efficient proxy models for well placement optimization is also discussed. This article is intended to serve as a comprehensive review of the latest proxy model techniques for the well placement optimization problem. In conclusion, while proxy models have their own challenges, their ability to significantly reduce the complexity of the well placement optimization process for huge reservoir simulation areas makes them extremely appealing. With active research and development occurring in this area, proxy models are poised to play an increasingly central role in oil and gas well placement optimization.

Modelling doi: 10.3390/modelling5040093

Authors: José Luis Díaz Palencia

This study investigates the steady, two-dimensional boundary layer flow of a Casson fluid over an inclined nonlinear stretching surface embedded within a Forchheimer porous medium. The governing partial differential equations are transformed into a set of ordinary differential equations through similarity transformations. The analysis incorporates the effects of an external uniform magnetic field, gravitational forces, thermal radiation modeled by the Rosseland approximation, and first-order homogeneous chemical reactions. We consider several dimensionless parameters, including the Casson fluid parameter, magnetic parameter, Darcy and Forchheimer numbers, Prandtl and Schmidt numbers, and the Eckert number to characterize the flow, heat, and mass transfer phenomena. Analytical solutions for the velocity, temperature, and concentration profiles are derived under simplifying assumptions, and expressions for critical physical quantities such as the skin friction coefficient, Nusselt number, and Sherwood number are obtained.

Modelling doi: 10.3390/modelling5040092

Authors: Vladislav Semenyuk Ildar Kurmashev Dmitriy Alyoshin Liliya Kurmasheva Vasiliy Serbin Alessandro Cantelli-Forti

This article explores the challenges of integrating two deep learning neural networks, YOLOv5 and RT-DETR, to enhance the recognition of unmanned aerial vehicles (UAVs) within the optical-electronic channels of Sensor Fusion systems. The authors conducted an experimental study to test YOLOv5 and Faster RT-DETR in order to identify the average accuracy of UAV recognition. A dataset in the form of images of two classes of objects, UAVs, and birds, was prepared in advance. The total number of images, including augmentation, amounted to 6337. The authors implemented training, verification, and testing of the neural networks exploiting PyCharm 2024 IDE. Inference testing was conducted using six videos with UAV flights. On all test videos, RT-DETR-R50 was more accurate by an average of 18.7% in terms of average classification accuracy (Pc). In terms of operating speed, YOLOv5 was 3.4 ms more efficient. It has been established that the use of RT-DETR as the only module for UAV classification in optical-electronic detection channels is not effective due to the large volumes of calculations, which is due to the relatively large number of parameters. Based on the obtained results, an algorithm for combining two neural networks is proposed, which allows for increasing the accuracy of UAV and bird classification without significant losses in speed.

Modelling doi: 10.3390/modelling5040091

Authors: Prakash KC Maryam Naghibolhosseini Mohsen Zayernouri

The failure of overhead transmission lines in the United States can lead to significant economic losses and widespread blackouts, affecting the lives of millions. This study focuses on analyzing the failure of transmission lines, specifically considering the effects of wind, ambient temperature, and current demands, incorporating minimal and significant pre-existing damage. We propose a multiphysics framework to analyze the transmission line failures across sensitive and affected states of the United States, integrating historical data on wind and ambient temperature. By combining numerical simulation with historical data analysis, our research assesses the impact of varying environmental conditions on the reliability of transmission lines. Our methodology begins with a deterministic approach to model temperature and damage evolution, using phase-field modeling for fatigue and damage coupled with electrical and thermal models. Later, we adopt the probability collocation method to investigate the stochastic behavior of the system, enhancing our understanding of uncertainties in model parameters, conducting sensitivity analysis to identify the most significant model parameters, and estimating the probability of failures over time. This approach allows for a comprehensive analysis of factors affecting transmission line reliability, contributing valuable insights into improving power line’s resilience against environmental conditions.

Modelling doi: 10.3390/modelling5040090

Authors: Sergei Lazarev Dmitrii Protasov Dmitrii Konovalov Irina Khorokhorina Oleg Abonosimov

The article formulates the state of the problem of improving the theoretical calculation of the nanofiltration kinetic characteristics in the time cycle of separation of industrial solutions containing copper(II), iron(III), trisodium phosphate and OP-10 (a wetting agent used in electroplating, a product of treating a mixture of mono- and dialkylphenols with ethylene oxide) using the equations of convective diffusion, hydrodynamics and mass transfer. To calculate the kinetic characteristics of the nanofiltration process, the mathematical model was improved by numerically solving the equations of convective diffusion, the Navier–Stokes equation and the flow continuity equation in a polar coordinate system with initial and boundary conditions. The theoretical results obtained in the process of an analytical solution of the system of equations allow calculating changes in concentrations in the permeate and retentate tracts and the permeate volume during nanofiltration separation. The acceptability of the developed nanofiltration method for separating solutions is assessed by comparing the calculated data according to the mathematical model with the experimental data obtained on the nanofiltration unit during separation of solutions containing copper(II), iron(III), trisodium phosphate and OP-10.

Modelling doi: 10.3390/modelling5040089

Authors: Oussama Aoun

Particle Swarm Optimization (PSO) is a widespread evolutionary technique that has successfully solved diverse optimization problems across various application fields. However, when dealing with more complex optimization problems, PSO can suffer from premature convergence and may become stuck in local optima. The primary goal is accelerating convergence and preventing solutions from falling into these local optima. This paper introduces a new approach to address these shortcomings and improve overall performance: utilizing a reinforcement deep learning method to carry out online adjustments of parameters in a homogeneous Particle Swarm Optimization, where all particles exhibit identical search behaviors inspired by models of social influence among uniform individuals. The present method utilizes an online parameter control to analyze and adjust each primary PSO parameter, particularly the acceleration factors and the inertia weight. Initially, a partially observed Markov decision process model at the PSO level is used to model the online parameter adaptation. Subsequently, a Hidden Markov Model classification, combined with a Deep Q-Network, is implemented to create a novel Particle Swarm Optimization named DPQ-PSO, and its parameters are adjusted according to deep reinforcement learning. Experiments on different benchmark unimodal and multimodal functions demonstrate superior results over most state-of-the-art methods regarding solution accuracy and convergence speed.

Modelling doi: 10.3390/modelling5040088

Authors: Alexander P. Lyapin Ilya V. Kudryavtsev Sergey G. Dokshanin Andrey V. Kolotov Alexander E. Mityaev

The current engineering theories on bending vibrations and the stability of beam structures are based on solving eigenvalue problems through similarly formulated differential equations. Solving the eigenvalue problem for engineering calculations is particularly laborious, especially for non-classical supports, where factors like the stiffness of supports, axial forces, or temperature must be considered. In this case, the solution can be obtained only by numerical methods using specially created programs, which makes it difficult to select supports for a given planar beam structure in engineering practice. This work utilizes established solutions from eigenvalue problems in the theory of vibrations and stability of beams, incorporating factors such as axial forces, temperature, and support stiffness. This combined solution is applicable to beam structures of any type and cross-section, as it is determined solely by the selected support conditions (stiffness) and loading (axial force, temperature). Approximation of eigenvalue problem solutions through continuous functions allows the readers to use them for the analytical solution of the design problem of choosing a support system to ensure the frequency of vibrations and stability of the planar beam structure. At the same time, the known solutions given in the reference books on bending vibrations and stability become their particular solutions. This approach is applicable to solving problems of vibrations and loss of stability of various types (torsional, longitudinal, etc.), and is also applicable in other disciplines where solving problems for eigenvalues is required.

Modelling doi: 10.3390/modelling5040087

Authors: Qiang Du Ruikang Ke Xiangwei Bai Cheng Du Zhaoqian Luo Yao Huang Lang Du Senqi Pei Dezhi Zeng

Due to the failure of string seals, gas can leak and result in the abnormal annulus pressure in gas wells, so it is necessary to relieve the pressure in gas wells. In the process of pressure relief, the leaked gas enters the annulus, causes a the great disturbance to the annulus flow field, and thus reduces the protection performance of the annular protection fluid in the string. In order to investigate the influence of gas leakage on the annular flow field, a VOF finite element model of the gas-liquid two-phase flow disturbed by gas leakage in a casing was established to simulate the transient flow field in the annular flow disturbed by gas leakage, and the influences of leakage pressure differences, leakage direction, and leakage time on annular flow field disturbance and wall shear force were analyzed. The analysis results showed that the larger leakage pressure difference corresponded to the faster diffusion rate of the leaked gas in the annulus, the faster the flushing rate of the leaked gas against the casing wall, and a larger shear force on the tubing wall was detrimental to the formation of the corrosion inhibitor film on the tubing wall and casing wall. Under the same conditions, the shear action on the outer wall of tubing in the leakage direction of 90° was stronger than that in the leakage directions of 135° and 45° and the diffusion range was also larger. With the increase in leakage time, leaked gas further moved upward in the annulus and the shear effect on the outer wall of tubing was gradually strengthened. The leaked acid gas flushed the outer wall of casing, thus increasing the peeling-off risk of the corrosion inhibitor film. The study results show that the disturbance law of gas leakage to annular protection fluid is clear, and it was suggested to reduce unnecessary pressure relief time in the annulus to ensure the safety and integrity of gas wells.

Modelling doi: 10.3390/modelling5040086

Authors: Pedro M. S. Santos Belmiro P. M. Duarte Nuno M. C. Oliveira Ricardo A. L. Mendes José L. S. A. Campos Jo?o M. C. Silva

This paper investigates the production of nanoparticles via detonation. To extract valuable knowledge regarding this route, a phenomenological model of the process is developed and simulated. This framework integrates the mathematical description of the detonation with a model representing the particulate phenomena. The detonation process is simulated using a combination of a thermochemical code to determine the Chapman–Jouguet (C-J) conditions, coupled with an approximate spatially homogeneous model that describes the radial expansion of the detonation matrix. The conditions at the C-J point serve as initial conditions for the detonation dynamic model. The Mie–Grüneisen Equation of State (EoS) is used, with the “cold curve” represented by the Jones–Wilkins–Lee Equation of State. The particulate phenomena, representing the formation of metallic oxide nanoparticles from liquid droplets, are described by a Population Balance Equation (PBE) that accounts for the coalescence and coagulation mechanisms. The variables associated with detonation dynamics interact with the kernels of both phenomena. The numerical approach employed to handle the PBE relies on spatial discretization based on a fixed-pivot scheme. The dynamic solution of the models representing both processes is evolved with time using a Differential-Algebraic Equation (DAE) implicit solver. The strategy is applied to simulate the production of alumina nanoparticles from Ammonium Nitrate Fuel Oil aluminized emulsions. The results show good agreement with the literature and experience-based knowledge, demonstrating the tool’s potential in advancing understanding of the detonation route.

Modelling doi: 10.3390/modelling5040085

Authors: Daniela Ambrosino Haoqi Xie

This paper proposes an integrated approach to define the best consignment strategy for storing containers in an export yard of a maritime terminal. The storage strategy identifies the rules for grouping homogeneous containers, which are defined simultaneously with the assignment of each group of containers to the available blocks (bay-locations) in the yard. Unlike recent literature, this study focuses specifically on weight classes and their respective limits when establishing the consignment strategy. Another novel aspect of this work is the integration of a data-driven algorithm and operations research. The integrated approach is based on unsupervised learning and optimization models and allows us to solve large instances within a few seconds. Results obtained by spectral clustering are treated as input datasets for the optimization models. Two different formulations are described and compared: the main difference lies in how containers are assigned to bay-locations, shifting from a time-consuming individual container assignment to the assignment of groups of containers, which offers significant advantages in computational efficiency. Experimental tests are organized into three campaigns to evaluate the following: (i) The computational time and solution quality (i.e., space utilization) of the proposed models; (ii) The performance of these models against a benchmark model; (iii) The practical effectiveness of the proposed solution approach.