Modelling, Volume 6, Issue 3 (September 2025) – 19 articles

As industrialization and economic growth accelerate, PM_2.5 pollution has become a critical environmental concern. Predicting PM_2.5 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 PM_2.5 concentration prediction. Full article

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 ($F_T=0$) generates intensified temperature localization and elevates transient crack-tip stress concentrations relative to classical Fourier diffusion ($F_T=1$). 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. Full article

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. Full article

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 Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article