Modelling, Volume 6, Issue 4 (December 2025) – 21 articles

Tandem cylinders, widely used in heat exchangers, water storage units, and electronic cooling, require optimized flow and heat transfer to enhance engineering performance. However, the combined effects of various factors in tandem configurations remain insufficiently explored. This study proposes an innovative approach that integrates multiple parameters to systematically investigate the influence of surface pattern characteristics and rotational speed on the fluid dynamics and heat transfer performance of tandem cylinders. Numerical simulations are conducted to evaluate the effects of various pattern dimensions (w/D = 0.12–0.18), surface shapes (square, triangular, and dimpled grooves), rotational speeds (|Ω| ≤ 1), and frequencies (N = 2–10) on fluid flow and heat transfer efficiency at Re = 200. The study aims to establish the relationship between the complexity of the coupling effects of the considered parameters and the heat transfer behavior as well as fluid dynamic variations. The results demonstrate that, under stationary conditions, triangular grooves exhibit larger vortex structures compared to square grooves. When a positive rotation is applied, coupled with increases in w/D and N, square grooves develop a separation vortex at the front. Furthermore, the square and dimpled grooves exhibit significant phase control capabilities in the time evolution of lift and drag forces. Under conditions of w/D = 0.12 and w/D = 0.18, the C_L of the upstream cylinder decreases by 17.2% and 20.8%, respectively, compared to the standard smooth cylinder. Moreover, the drag coefficient C_D of the downstream cylinder is reduced to half of the initial value of the upstream cylinder. As the surface amplitude increases, the C_D of the smooth cylinder surpasses that of the other groove types, with an approximate increase of 8.8%. Notably, at Ω = −1, the downstream square-grooved cylinder’s C_L is approximately 12.9% lower than that of other groove types, with an additional 6.86% reduction in amplitude during counterclockwise rotation. When N increases to 10, the of the upstream square-grooved cylinder at w/D = 0.18 decreases sharply by 20.9%. Conversely, the upstream dimpled-groove cylinder significantly enhances at w/D = 0.14 and N = 4. However, the upstream triangular-groove cylinder achieves optimal stability at w/D ≥ 0.16. Moreover, at w/D = 0.18 and N = 6, square grooves show the most significant enhancement in vortex mixing, with an increase of approximately 42.7%. Simultaneously, the local recirculation zones in dimpled grooves at w/D = 0.14 and N = 6 induce complex and geometry-dependent heat transfer behaviors. Under rotational conditions, triangular and dimpled grooves exhibit superior heat transfer performance at N = 6 and w/D = 0.18, with TPI values exceeding those of square grooves by 33.8% and 28.4%, respectively. A potential underlying mechanism is revealed, where groove geometry enhances vortex effects and heat transfer. Interestingly, this study proposes a correlation that reveals the relationship between the averaged Nusselt number and groove area, rotational speed, and frequency. These findings provide theoretical insights for designing high-efficiency heat exchangers and open up new avenues for optimizing the performance of fluid dynamic systems. Full article

Short-range forces enable peridynamics to simulate impact, yet it demands a computationally expensive contact search and includes no intrinsic damping. A significantly more efficient solution is the coupled dual-horizon peridynamics–discrete element method approach, which provides a robust framework for modeling fracture. The peridynamics component handles the nonlocal continuum mechanics capabilities to predict material damage and fracture, while the discrete element method captures discrete particle behavior. Whereas existing peridynamics–discrete element method approaches assign discrete element method particles to many or all surface peridynamics points, the proposed method integrates dual-horizon peridynamics with a single discrete element particle representing each object. Contact forces are computed once per discrete element pair and mapped to overlapping peridynamics points in proportion to shared volume, conserving linear momentum. Benchmark sphere-on-plate impact demonstrates prediction of peak contact force, rebound velocity, and plate deflection within 5% of theoretical results found in the literature, while decreasing neighbour-search cost by more than an order of magnitude. This validated force-transfer mechanism lays the groundwork for future extension to fully resolved fracture and fragmentation. Full article

This study has investigated the structural and seismic performance of monolithic stone columns in the historical Mosque–Cathedral of Córdoba, with a focus on the earliest section constructed during the reign of Abd al-Rahman I (VIII century). An advanced 3D finite element (FE) model has been developed to assess the effects of geometric imperfections and component interactions on the stability of columns under both vertical and horizontal static loading. Three distinct modelling strategies have been employed in OpenSees 3.7.1, incorporating column inclination and contact elements to simulate mortar interfaces. Material properties have been calibrated using experimental data and in situ observations. The gravitational analysis has shown no significant damage in any of the configurations, aligning with the observed undamaged state of the structure. Conversely, horizontal analyses have revealed that tensile damage has predominantly occurred at the lower shaft. The inclusion of contact elements has led to a significant reduction in lateral resistance, highlighting the importance of accounting for friction and interface behaviour. Column inclination has been found to have a significant influence on failure patterns. These findings have highlighted the critical role of detailed modelling in evaluating structural vulnerabilities. Such features are generally included in the numerical modelling and evaluation of heritage buildings. Consequently, they can contribute to a better understanding of the seismic behaviour of historic masonry structures. Full article

Rapid urbanization and global climate change are leading to intensified Urban Heat Island (UHI) in tropical regions. This study examined and analyzed urban ventilation corridors to mitigate UHI, paying particular attention to the building arrangement and wind environment. The comprehensive review emphasizes the importance of macro-scale urban planning, including the orientation of street grids and the design of breezeways and air paths. After analyzing these strategies, CFD simulations were applied to the design of high-rise buildings in Semarang and residential areas in Jakarta. These studies revealed that in high-rise building areas in Semarang, the proposed design configuration resulted in a 62% increase in ground-level wind speeds. A further analysis of residential areas in Jakarta revealed that the most comfortable location within a house was in the second row, facing the wind, where the distance between houses was 8.5 m, and the average velocity was 2.78 m/s. Research conducted in this area may contribute to the development of more sustainable and resilient urban areas in tropical climates, as well as assist local governments in planning for these areas. Full article

Beta regression models are a class of models used frequently to model response variables in the interval $(0, 1)$. Although there are articles in which these models are used to model clustered and longitudinal data, the prediction of random effects is limited, and residual analysis has not been implemented. In this paper, a random intercept beta regression model is proposed for the complete analysis of this type of data structure. We proposed some types of residuals and formulate a methodology to obtain the best prediction of random effects. This model is developed through the parameterisation of beta distribution in terms of the mean and dispersion parameters. A log-likelihood function is approximated by the Gauss–Hermite quadrature to numerically integrate the distribution of random intercepts. A simulation study is used to investigate the performance of the estimation process and the sampling distributions of the residuals. Full article

Heat exchangers are widely used process equipment in industrial sectors, making the study of their temperature dynamics particularly appealing due to the nonlinearities involved. Model-free approaches enable the use of input and output data to generate specific and accurate estimations for each proposed system. In this work, a model-free identification strategy is proposed using a convolutional neural network to estimate the system’s behavior. Notably, the model does not rely on direct temperature measurements; instead, temperature is inferred from other system signals such as reference, flow, and control inputs. This data-driven approach offers greater specificity and adaptability, often outperforming manufacturer-provided coefficients whose performance may vary from design expectations. The results yielded an $R^2$ index of 0.9951 under nominal conditions and 0.9936 when the system was subjected to disturbances. Full article

Graphite nodularity is a key indicator for evaluating the microstructure quality of ductile iron and plays a crucial role in ensuring product quality and enhancing manufacturing efficiency. Existing research often only focuses on a single type of feature and fails to utilize multi-source information in a coordinated manner. Single-feature methods are difficult to comprehensively capture microstructures, which limits the accuracy and robustness of the model. This study proposes a hybrid estimation model for the graphite nodularity of ductile cast iron based on multi-source feature extraction. A comprehensive feature engineering pipeline was established, incorporating geometric, color, and texture features extracted via Hue-Saturation-Value color space (HSV) histograms, gray level co-occurrence matrix (GLCM), Local Binary Pattern (LBP), and multi-scale Gabor filters. Dimensionality reduction was performed using Principal Component Analysis (PCA) to mitigate redundancy. An improved watershed algorithm combined with intelligent filtering was used for accurate particle segmentation. Several machine learning algorithms, including Support Vector Regression (SVR), Multi-Layer Perceptron (MLP), Random Forest (RF), Gradient Boosting Regressor (GBR), eXtreme Gradient Boosting (XGBoost) and Categorical Boosting (CatBoost), are applied to estimate graphite nodularity based on geometric features (GFs) and feature extraction. Experimental results demonstrate that the CatBoost model trained on fused features achieves high estimation accuracy and stability for geometric parameters, with R-squared (R²) exceeding 0.98. Furthermore, introducing geometric features into the fusion set enhances model generalization and suppresses overfitting. This framework offers an efficient and robust approach for intelligent analysis of metallographic images and provides valuable support for automated quality assessment in casting production. Full article

To meet the stringent reliability requirements of rotor blades in turbomachines, greater effort should be devoted to improving both aerodynamic and structural performance in blade design. This paper introduces an aero-structural multi-disciplinary design optimization (MDO) method for compressor rotor blades using a discrete adjoint method and an equivalent stress model (ESM). The principles of the ESM are firstly introduced, and its accuracy in calculating equivalent stress is validated through comparison with a commercial program. Both the aerodynamic performance and the maximum equivalent stress (MES) are selected as optimization objectives. To modify the blade profile, the steepest descent optimization method is utilized, in which the necessary sensitivities of the cost function to the design parameters are calculated by solving the adjoint equations. Finally, the aero-structural MDO of a transonic compressor rotor, NASA Rotor 67, is conducted, and the Pareto solutions are obtained. The optimization results demonstrate that the adiabatic efficiency and the MES are competitive in improving multi-disciplinary performance. For most of the Pareto solutions, the MES can be considerably reduced with increased adiabatic efficiency. Full article

The construction industry remains one of the most hazardous sectors despite its economic importance, with high-altitude fall accidents being the most prevalent and deadly type of incident. This paper aimed to study and analyze the accident data of the past accident cases in China and find out the key causes and rules of the accidents. This research analyzed 1223 Chinese accident reports (2014–2023) using Latent Dirichlet Allocation topic modeling to identify causal factors, followed by Apriori algorithm correlation analysis to reveal accident causation patterns. This study comprehensively uses topic model, association rules and visualization methods to systematically analyze the causes of high-altitude fall accidents. The research identified 24 distinct accident cause topics across personnel, equipment, management, and environmental dimensions. Key findings revealed that incorrect use of labor protective equipment, inadequate safety inspections, and failure to implement safety management protocols were persistent issues throughout the study period. Notably, the post COVID-19 pandemic introduced new safety challenges, with the intensity of topics related to “subject of responsibility for safety production has not been implemented” showing significant post-pandemic increases. These findings highlight the evolving nature of construction safety challenges and the need for targeted interventions to address persistent and emerging risks. Full article

With the frequent occurrence of stuck pipe incidents during the ultra-deep well drilling operation, the hydraulic-while-drilling (HWD) jar has become a critical component of the bottom hole assembly (BHA). However, during jarring operations for stuck pipe release, the drill string experiences severe vibrations induced by the impact loads from the jar, which significantly alter the stress state and dynamic response of the threaded connections—the structurally weakest elements—under cyclic dynamic loading, often leading to fracture failures. here, a thread failure incident of a hydraulic jar in an ultra-deep well in the Tarim Basin, Xinjiang, is investigated. A drill string dynamic impact model incorporating the actual three-dimensional wellbore trajectory is established to capture the time-history characteristics of multi-axial loads at the threaded connection during up and down jarring. Meanwhile, a three-dimensional finite element model of a double-shouldered threaded connection with helix angle is developed, and the stress distribution of the joint thread is analyzed on the boundary condition acquired from the time-history characteristics of multi-axial loads. Numerical results indicate that the axial compression induces local bending of the drill string during down jarring, resulting in significantly greater bending moment fluctuations than in up jarring and a correspondingly higher amplitude of circumferential acceleration at the thread location. Among all thread positions, the first thread root at the pin end consistently experiences the highest average stress and stress variation, rendering it most susceptible to fatigue failure. This study provides theoretical and practical insights for optimizing drill string design and enhancing the reliability of threaded connections in deep and ultra-deep well drilling. Full article

As one of the most important finishing machining means of internal helical gear, the residual stress that appears during profile grinding plays an important role in transmission performance and the service internal helical gear. In this research, the residual stress simulation model of internal helical gear profile grinding is established to optimize and predict grinding parameters by means of a neural network. The grinding process parameters (including grinding depth, grinding feed speed, and grinding wheel linear speed) are taken as variable factors. Through experimental verification, the maximum error of the simulation value is 12.8%. The radial basis function (RBF) neural network is introduced, and simulation data samples are used to train and test the residual stress prediction model. Three groups of unknown grinding parameters are predicted, and the relative errors between the predicted and measured values are 5.16%, 1.63%, and 3.39%, respectively. The results demonstrate that the RBF neural network residual stress prediction model proposed in this paper is accurate and feasible. At the same time, the residual stress prediction method provides a theoretical basis for optimizing and controlling the precision of internal helical gear profile grinding. Full article

High-pressure, high-volume fracturing in unconventional reservoirs often induces perforation erosion damage, endangering operational safety. This paper employs fluid–solid coupling theory to analyze the flow characteristics of fracturing fluid inside the casing during fracturing. Combined with strength theory, the stress distribution and variation law are investigated, revealing the mechanical mechanism of casing perforation erosion damage. The results indicate that the structural discontinuity at the entrance of the perforation tunnel causes an increase in fracturing-fluid velocity, and this is where the most severe erosion happens. The stress around the perforation is symmetrically distributed along the perforation axis. The casing inner wall experiences a combined tensile–compressive stress state, while non-perforated regions are under pure tensile stress, with the maximum amplitudes occurring in the 90° and 270° directions. Although the tensile and compressive stress do not exceed the material’s allowable stress, the shear stress exceeds the allowable shear stress, indicating that shear stress failure is likely to initiate at the perforation, inducing erosion. Moreover, under the impact of fracturing fluid, the contact forces at the first and second interfaces of the casing are unevenly distributed, reducing cement bonding capability and compromising casing integrity. The findings provide a theoretical basis for optimizing casing selection. Full article

This study investigates the effect of incorporating an electromagnetic harvester inside the bluff body of a 2-DoF hybrid harvester in comparison to a standalone piezoelectric harvester for various external loads. The harvester is excited through a vortex-induced vibration owing to the resultant wake vortices created behind the bluff body. The coupled dynamics of the two harvester components are modeled, and numerical simulations are conducted to evaluate the system’s performance under varying electrical loads. Numerical results show that at high, optimum electrical load, the standalone piezoelectric harvester outperforms the hybrid harvester. Nevertheless, for small electrical loads, the results show that the hybrid harvester outperforms the standalone PZT harvester by up to 18% in peak power output, while reducing the bandwidth by approximately 10% compared to the standalone piezoelectric harvester. Optimal spring stiffness values were identified, with the hybrid harvester achieving its maximum output power at a spring stiffness of 83.56 N/m. These findings underscore the need for careful design considerations, as the hybrid harvester may not achieve enhanced power output and bandwidth under higher electrical loads. Full article

Bi₂Sr₂CaCu₂O_8+x (Bi2212) high-temperature superconductor exhibits broad application prospects in strong magnetic fields, superconducting magnets, and power transmission due to its exceptional electrical properties. However, during practical applications, Bi2212 superconducting round wires are prone to mechanical loading effects, leading to crack propagation and degradation of superconducting performance, which severely compromises their reliability and service life. To elucidate the damage mechanisms under mechanical loading and their impact on critical current, this study establishes a two-dimensional model with existing cracks based on phase field fracture theory, simulating crack propagation behaviors under varying conditions. The results demonstrate that crack nucleation and propagation paths are predominantly governed by stress concentration zones. The transition zone width of cracks is controlled by the phase field length scale parameter. By incorporating electric fields into the phase field model, coupled mechanical-electrical simulations reveal that post-crack penetration causes significant current shunting, resulting in a marked decline in current density. The research quantitatively explains the mechanism of critical current degradation in Bi2212 round wires under tensile strain from a mechanical perspective. Full article

The paper presents a comparative analysis of various machine learning algorithms for the classification of epoxy composites reinforced with basalt fiber and modified with inorganic fillers. The classification is based on key thermophysical characteristics, in particular, the mass fraction of the filler, temperature, and thermal conductivity coefficient. A dataset of 16,056 interpolated samples was used to train and evaluate more than a dozen models. Among the tested algorithms, the MLP neural network model showed the highest accuracy of 99.7% and balanced classification metrics F1-measure and G-Mean. Ensemble methods, including XGBoost, CatBoost, ExtraTrees, and HistGradientBoosting, also showed high classification accuracy. To interpret the results of the MLP model, SHAP analysis was applied, which confirmed the predominant influence of the mass fraction of the filler on decision-making for all classes. The results of the study confirm the high effectiveness of machine learning methods for recognizing filler type in composite materials, as well as the potential of interpretable AI in materials science tasks. Full article

In the research and development system of bat-like flapping-wing flying robots, lift modeling and numerical analysis are the key theoretical basis, which will directly affect the construction of the body structure and flight control system. However, due to the complex three-dimensional flapping motion mechanism of bats and the flexible deformation characteristics of their wing membranes, the existing lift theory lacks a mature calculation method suitable for bionic flapping-wing flying robots. In this paper, the wing membrane deformation mechanism of a bat-like flapping-wing flying robot is studied, and the coupling effect of wing membrane motion and deformation on flight parameters is analyzed. A set of calculation methods for flexible morphing wing membrane lift is improved by using a quasi-steady model and the blade element method. By comparing and analyzing the theoretical calculation and experimental results under various working conditions, the error is less than 4%, which proves the effectiveness of this method. Full article

This study aims to accurately characterize the nonlinear stress–strain evolution of rocks under uniaxial compression considering crack propagation. First, the rock meso-structure was generalized into intact rock unit cells, crack propagation damage unit cells, and pore unit cells according to phenomenological theory. A mesoscopic rock stress model considering crack propagation was established based on the static equilibrium relationship of the unit cells, and the effective stress of the crack propagation damage unit cells was solved based on fracture mechanics. Then, the geometric damage theory and conservation-of-energy principle were introduced to construct the damage evolution equation for rock crack propagation. On this basis, the effective stress of the damage unit cells and the crack propagation damage equation were incorporated into the rock meso-structure static equilibrium equation, and the effect of nonlinear deformation in the soft rock compaction stage was considered to establish a rock damage constitutive model based on mesoscopic crack propagation evolution. Finally, methods for determining model parameters were proposed, and the effects of the model parameters on rock stress–strain curves were explored. The results showed that the theoretical model calculations agreed well with the experimental results, thus verifying the rationality of the damage constitutive model and the clear physical meaning of the model parameters. Full article

Accurate identification of plastic polymers is essential for effective recycling, quality control, and environmental monitoring. This study assesses how spectral derivative preprocessing affects the classification of six common plastic polymers: Polyethylene Terephthalate (PET), Polyvinyl Chloride (PVC), Polypropylene (PP), Polystyrene (PS), and both High- and Low-Density Polyethylene (HDPE and LDPE), based on Fourier Transform Infrared (FTIR) spectroscopy data acquired at a resolution of 8 ${cm}^{-1}$. Using Savitzky–Golay derivatives (orders 0, 1, and 2), five machine learning algorithms, namely Multilayer Perceptron (MLP), Extremely Randomized Trees (ET), Linear Discriminant Analysis (LDA), Support Vector Classifier (SVC), and Random Forest (RF), were tested within a strict framework involving stratified repeated cross-validation and a final hold-out test set to evaluate generalization. The first spectral derivative notably improved the model performance, especially for MLP and SVC, and increased the stability of the ET, LDA, and RF classifiers. The combination of the first derivative with the ET model provided the best results, achieving a mean F1-score of 0.99995 (±0.00033) in cross-validation and perfect classification (1.0 in Accuracy, F1-score, Cohen’s Kappa, and Matthews Correlation Coefficient) on the independent test set. LDA also performed very well, underscoring the near-linear separability of spectral data after derivative transformation. These results demonstrate the value of derivative-based preprocessing and confirm a robust method for creating high-precision, interpretable, and transferable machine learning models for automated plastic polymer identification. Full article

This work presents an analytical 2D model for estimating eddy current losses in the permanent magnets (PMs) of a coaxial magnetic gear (CMG), with a focus on loss minimization through magnet segmentation. The model is applied under various operating conditions, including different rotational speeds, load levels, and segmentation configurations, to derive empirical expressions for eddy current losses in both the inner and outer rotors. A 1D lumped-parameter thermal model is then used to predict the steady-state temperature of the PMs, incorporating empirical correlations for the thermal convection coefficient. Both models are validated against finite element analysis (FEA) simulations. The analytical eddy current loss model exhibits excellent agreement, with a maximum error of 2%, while the thermal model shows good consistency, with a maximum temperature deviation of 5%. The results confirm that eddy current losses increase with rotational speed but can be significantly reduced through magnet segmentation. However, achieving an acceptable thermal performance at high speeds may require a large number of segments, particularly in the outer rotor, which could influence the manufacturing cost and complexity. The proposed models offer a fast and accurate tool for the design and thermal analysis of CMGs, enabling early-stage optimization with minimal computational effort. Full article

The numerical method was employed to analyze the transient pressure characteristics of a metro train passing through a tunnel in high-altitude regions. The transient pressure evolution inside and outside the train under varying ambient pressures is analyzed and compared. The findings indicate that while ambient pressure minimally impacts the waveform of the exterior transient pressure, it significantly influences the peak value. Specifically, as ambient pressure rises, the maximum transient pressure (P-max) and the peak-to-peak transient pressure (ΔP) on the train’s exterior surface increase linearly, whereas the minimum transient pressure (P-min) decreases linearly. Moreover, this study analyzed pressure changes within the metro train under varying ambient pressures to assess their impact on passengers’ ear comfort. The trend of pressure peak reduction and delay inside the metro train with a certain degree of airtightness remains well aligned for different ambient pressures. In areas of high altitude with low atmospheric pressure, the requirements for the tightness performance of the train are lower. Full article

Emerging technologies are revolutionizing power system operation and maintenance. Intelligent state perception is pivotal for stable grid operation, with small object detection technology being vital for identifying minor hazards in power facilities. However, challenges like small object size, low resolution, occlusion, and low confidence arise in small object detection for power operation and maintenance. This paper proposes PyraFAN, a feature fusion method designed for small object detection, and introduces a cloud-edge collaborative inference based smart detection method. This method boosts detection accuracy while ensuring real-time performance. Additionally, a graph-guided distillation method is developed for edge models. By quantifying model performance and task similarity, multi-model collaborative training is realized to improve detection accuracy. Experimental results show that compared with standalone edge models, the proposed method improves detection accuracy by 6.98% and reduces the false negative rate by 19.56%. The PyraFAN module can enhance edge model detection accuracy by approximately 12.2%. Updating edge models via cloud model distillation increases the mAP@0.5 of edge models by 2.7%. Compared to cloud models, the cloud-edge collaboration method reduces average inference latency by 0.8%. This research offers an effective solution for improving the accuracy of deep learning based small object detection in power operation and maintenance within cloud-edge computing environments. Full article