Modelling doi: 10.3390/modelling7030087

Authors: Mao Zhu Hanyi Wang

Hydraulic fracture geometry is of great importance for evaluating stimulation effectiveness and supporting the efficient development of unconventional oil and gas reservoirs, and it can be estimated from field shut-in water hammer signals. However, field signals are commonly characterized by strong noise, pronounced non-stationarity, strong dependence on manual extraction of effective response segments, and limited automation in inversion analysis. To address these issues, this study develops an integrated automated interpretation framework for shut-in water hammer analysis, which combines an adaptive shape-preserving Kalman filter for non-stationary signal denoising, an automatic response segment identification method, and a particle swarm optimization-based inversion strategy for fracture geometry estimation. The framework is validated using field high-frequency pressure data from hydraulically fractured wells. The results show that the proposed denoising method improves the signal-to-noise ratio from 11.99 dB to 25.05 dB while preserving key transient features. The response segments can be extracted efficiently, with runtimes of 0.84–1.22 s and onset errors within 0–5 s. For a representative fracturing stage, the relative errors of the inverted fracture half-length and fracture height are 6.21% and 3.04%, respectively. The proposed framework provides a low-cost and field-applicable tool for fracture evaluation and engineering decision-making.

Modelling doi: 10.3390/modelling7030086

Authors: Paloma B. Jimenez-Vara Flor Y. Rentería-Baltiérrez Luis E. Jasso-Ramos Jesús G. Puente-Córdova

Poly(ethylene terephthalate) (PET) composites reinforced with reduced graphene oxide (rGO) were investigated in order to elucidate the influence of nanofiller concentration and compatibilization on the viscoelastic relaxation behavior across the glass transition. Composites containing 0.1 and 0.5 wt% rGO were prepared by melt blending, and selected systems incorporated 5 wt% of an ionomeric polyester (PETi) as compatibilizer to enhance interfacial adhesion. The thermomechanical response was characterized using dynamic mechanical analysis (DMA) as a function of temperature. Experimental results revealed a strong dependence of stiffness, damping, and glass transition behavior on filler concentration and interfacial interactions. While low rGO loading produced minor changes, the incorporation of 0.5 wt% rGO significantly increased the glassy modulus and shifted the glass transition temperature, indicating restricted segmental mobility. Compatibilized systems exhibited further stiffness enhancement and modified relaxation dynamics due to improved stress transfer and interphase development. To capture the distributed nature of the relaxation processes, the glass transition region was modeled using a fractional Zener model (FZM) with two spring-pot elements within a cooperative relaxation framework. The model successfully reproduced the experimental E′ and tanδ curves and revealed systematic variations in the fractional exponents and cooperative parameters. The results demonstrate that the introduction of rGO and compatibilizer progressively transforms the relaxation spectrum of PET from a relatively uniform segmental process into a heterogeneous, interfacially mediated viscoelastic response that is naturally described by fractional rheology.

Modelling doi: 10.3390/modelling7030085

Authors: Haiwei Li Xi Zhang Fansen Kong Guoqiu Song Lie Cao

To improve the assembly efficiency and productivity of complex aircraft components, the optimization of an assembly line was investigated in this study. A hierarchical hybrid multi-objective optimization algorithm (HHMOA) was proposed using an improved non-dominated sorting genetic algorithm II and an enhanced longest processing time algorithm. The algorithm incorporates a two-layer framework for global–local optimization; an information entropy-based problem formulation with three objectives, including line balance rate, load balance index and assembly complexity smoothness index; and a hybrid initialization strategy for high-quality initial solutions. Based on the assembly line datasets of different scales, the algorithm performance was verified by comparing the hypervolume and the calculation efficiency using HHMOA and three benchmark algorithms, and the sensitivity analyses verified the algorithm robustness. For an actual aircraft component assembly line, the optimizations carried out with the given process time, number of workstations and precedence relationships indicate that the balance rate of the optimized line increased 72%, and the load balance index and the assembly complexity smoothing index were reduced by 80.3% and 92% respectively, which proved the reliability of the hybrid algorithm in optimizing the aircraft component assembly line. Finally, the optimization analyses with various workstation numbers and assembly process times suggest that reducing the workstations and adopting robotic automated processing can improve the aircraft component assembly line.

Modelling doi: 10.3390/modelling7030084

Authors: Jassiel V. H. Fontes Irving D. Hernández Edgar Mendoza Rodolfo Silva

A significant number of regional boats are used in the Brazilian Amazon to perform a range of social activities. However, the estimation of their propulsion parameters still requires exploring technically supported methods if the efficiency and sustainability of inland navigation is to be optimized. This study explores various approaches for estimating the total resistance and effective propulsive power required by regional boats. The research examines the real case of a rabeta, a regional boat commonly used in the Brazilian Amazon, by analyzing the applicability at full scale of two approaches: the conventional Mercier–Savitsky pre-planing method and a multiphase computational fluid dynamics (CFD) approach. Using experimental data, such as boat speed and the patterns of boat-generated waves, computational analysis and the comparison of results, respectively, were carried out. It was found that for the case considered, the CFD results underpredicted the conventional approach in less than 10% for the minimum and maximum drafts considered, suggesting that both approaches are useful for estimating the effective power of artisanal boats. However, the use of CFD has the potential to visualize a greater number of parameters, such as the generated waves during vessel motion, which can facilitate the optimization of the hydrodynamics of boats, thus contributing to the sustainability of inland navigation in the region. The procedure employed in this study can be further extended to estimate the propulsive parameters of other regional vessels in the Amazon and similar areas.

Modelling doi: 10.3390/modelling7030083

Authors: Narendra Kumar Kolla Pandu Ranga Vundavilli

Accurate detection of cardboard boxes is essential to mobile manipulators to perform pick-and-place operations in warehouses. Conventional object detection methods like YOLOv11 struggle in low-texture and occluded environments. This paper presents YOLO-REFB, a novel object detection framework for real-time cardboard box detection in robotic manipulation using a dual-arm mobile robot (DAMR) operating in indoor warehouse environments. The proposed approach enhances the network by integrating the Rectangular Edge Fusion Block (REFB) into the YOLOv11 architecture; it focuses on learning the geometric and structural features of cardboard boxes. Enhanced edge information extraction and feature fusion improve training stability and localization accuracy. A custom dataset of 3501 annotated images, collected under varied conditions, was utilized. The images were randomly assigned to training and validation sets while keeping an 80:20 ratio. They were manually annotated and trained using Roboflow software, ensuring precise alignment of bounding boxes with cardboard box edges for accurate comparison with existing YOLO models. The model outperformed existing YOLO variants (YOLOv8n and YOLOv5n) in terms of precision (89.29%), recall (83.95%), and F1-score (86.54%). YOLO-REFB achieved improved localization metrics, including mean Average Precision (mAP)@0.5 (91.68%) and mAP@0.5:0.95 (68.61%). The inclusion of REFB was essential to performance gains, enabling effective detection of objects in challenging environments. Future developments may include 3D pose estimation and multi-object grasp planning for advanced robotic manipulation.

Modelling doi: 10.3390/modelling7030082

Authors: Ladislav Zjavka

Self-contained local forecasting of wind and solar series can improve operational planning of wind farms and photovoltaic (PV) plant day-cycles in addition to numerical models, which are mostly behind time due to high simulation costs. Unstable electricity production requires balancing the availability of renewable energy (RE) with unpredictable user consumption to achieve effective usage. Artificial intelligence (AI) predictive modelling can minimise the intermittent uncertainty in wind and solar resources by trying to eliminate specific problems in RE-detached system reliability and optimal utilisation. The proposed 24 h day-training and prediction scheme comprises the starting detection and the following similarity re-assessment of sampling day-series intervals. Two-point professional weather stations record standard meteorological variables, of which the most relevant are selected as optimal model inputs. Automatic two-layer altitude observation captures key relationships between hill- and lowland-level data, which comply with pattern progress. New biologically inspired differential learning (DfL) is designed and developed to integrate adaptive neurocomputing (evolving node tree components) with customised numerical procedures of operator calculus (OC) based on derivative transforms. DfL enables the representation of uncertain dynamics related to local weather patterns. Angular and frequency data (wind azimuth, temperature, irradiation) are processed together with the amplitudes to solve simple 2-variable partial differential equations (PDEs) in binomial nodes. Differentiated data provide the fruitful information necessary to model upcoming changes in mid-term day horizons. Additional PDE components in periodic form improve the modelling of hidden complex patterns in cycle data. The DfL efficiency was proved in statistical experiments, compared to a variety of elaborated AI techniques, enhanced by selective difference input preprocessing. Successful LSTM-deep and stochastic tree learning shows little inferior model performances, notably in day-ahead estimation of chaotic 24 h wind series, and slightly better approximation of alterative 8 h solar cycles. Free parametric C++ software with the applied archive data is available for additional comparative and reproducible experiments.

Modelling doi: 10.3390/modelling7030081

Authors: Ivica Glavan Ivan Gospić Igor Poljak

Air-to-air heat pumps are a key technology for improving energy efficiency and reducing carbon emissions in residential buildings, yet their optimal control remains challenging under real-world conditions. This study evaluates the performance of a hybrid physical–LSTM model for controlling an air-to-air heat pump in a residential building in Zadar, Croatia. The hybrid framework integrates a first-order energy balance model of the building envelope with LSTM-based temperature correction using adaptive weighting. The physical model was calibrated and validated against 52,128 real IoT measurements collected during the 2024/2025 heating season, achieving high accuracy (RMSE ≈ 0.076 °C). Rolling one-day and continuous multi-day closed-loop simulations (up to 15 days) show that the hybrid model yields slightly lower RMSE in long-term runs compared to the pure physical model. However, this apparent statistical improvement is accompanied by systematic underestimation of indoor temperature and significantly higher simulated energy consumption. The results indicate that the observed effect originates from an implicit virtual heat flux introduced by the LSTM correction, which affects thermodynamic consistency in closed-loop operation. The findings highlight that short-term error metrics such as RMSE alone are insufficient for evaluating hybrid models intended for model predictive control (MPC). The main contribution of this study is the explicit demonstration and quantification of an implicit virtual heat flux generated by the LSTM correction in closed-loop multi-day operation, which leads to misleading statistical improvements while causing significant thermodynamic inconsistency and energy overconsumption. In 15-day continuous simulations the hybrid model (ω = 0.05–0.10) caused an indoor temperature underestimation of 1.25–1.31 °C and increased simulated electricity consumption by more than 300% (316 kWh vs. 72 kWh) compared to the physical model. These results have direct implications for the development of reliable digital twins and model predictive control strategies in residential HVAC systems.

Modelling doi: 10.3390/modelling7030080

Authors: Mohammad Khalid Hasan Nabil Jubayer Ahmed Sajid Ivan Grgić Jure Marijić Saiaf Bin Rayhan

Bird strike events on rotating jet engine fan blades pose significant risks to aviation safety, yet high-fidelity numerical simulations remain computationally expensive, limiting their use in parametric design studies. This study develops a physics-guided machine learning surrogate framework for predicting bird strike response on rotating Ti-6Al-4V fan blades, systematically comparing Lagrangian (gelatin-based, Mooney–Rivlin) and Smoothed Particle Hydrodynamics (SPH, water-like) formulations. A total of 100 explicit dynamic simulations were conducted in ANSYS LS-DYNA (R2) (50 per formulation), varying bird impact velocity and blade angular speed. Random Forest, Support Vector Regression, Polynomial Regression, and XGBoost regression models were trained and evaluated using five-fold cross-validation. Results demonstrate that SPH-based surrogates achieve superior predictive accuracy, with Random Forest yielding R2 = 0.9938 for maximum deformation and R2 = 0.9962 for total energy dissipation. In contrast, Lagrangian-based stress surrogates exhibited severe performance degradation (R2 = 0.24) due to mesh-dependent numerical noise. The trained surrogates achieved computational speed-up factors of 104–105 relative to direct simulation. These findings establish that surrogate model reliability is fundamentally governed by the numerical quality of the training data, providing guidance for integrating machine learning with impact simulation workflows in aero-engine blade design.

Modelling doi: 10.3390/modelling7030079

Authors: Baolu Yang Liangming Wang

To address the insufficient parameter estimation accuracy and poor filtering convergence caused by noise in radar trajectory measurement data, this paper proposes a joint framework combining SW-STPSO adaptive wavelet denoising and an improved Unscented Kalman Filter (UKF). First, SW-STPSO preprocesses noisy data using a sliding-window strategy and improved particle swarm optimization to adapt wavelet parameters to local noise characteristics. Then, the improved UKF adopts exponential-decay adaptive Q adjustment and covariance matrix positive-definite regularization to achieve high-precision estimation of ballistic parameters, including position, velocity, and ballistic coefficient. Simulation results show that: (1) SW-STPSO denoising improves subsequent parameter-estimation accuracy by more than 60% compared with the case without denoising; (2) the improved UKF achieves 37% faster convergence and 42% higher stability than the traditional UKF; and (3) the joint scheme reduces the position RMSE, velocity RMSE, and ballistic-coefficient RMSE to 0.92 m, 0.256 m/s, and 0.023 m2/kg, respectively. These results indicate that the proposed method is effective for radar trajectory data processing under the adopted simulation conditions.

Modelling doi: 10.3390/modelling7030078

Authors: Masoud Ghaffari Mehdi Azhdary Moghaddam Gholamreza Aziziyan Mohsen Rashki

Cavitation damage poses a serious threat to the reliability of morning-glory spillways. This study aims to develop a reliability framework for predicting cavitation damage probability under uncertain operational conditions for the Haraz Dam spillway. Cavitation analysis in such structures exhibits inherent nonlinearity and uncertainty, complicating accurate damage prediction. This study incorporates model uncertainties to assess cavitation responses at multiple points on the Haraz Dam morning-glory spillway. Three-dimensional flow simulations were performed using Computational Fluid Dynamics (CFD) and validated against an experimental model from the Iran Water Research Institute, showing satisfactory agreement. Statistical parameters and probability density functions (PDFs) for key uncertainties were determined using the Shapiro–Wilk test. A total of 35 simulation runs, designed via the Central Composite Design (CCD) method, were conducted using Latin Hypercube Sampling (LHS). These simulations incorporated inter-uncertainty correlations and predicted cavitation damage responses at ten critical spillway locations through Response Surface Methodology (RSM). Both linear and second-order response functions were formulated based on interactions among model uncertainties. The results indicated a strong correlation (R2 > 0.95) between numerical model outputs and RSM predictions, with the maximum RSM errors remaining within acceptable thresholds. Among the uncertainty factors, the inflow velocity demonstrated the highest contribution (>50%) to cavitation damage responses. These outcomes advance the understanding of cavitation mechanisms and provide a reliable methodology for evaluating damage risks in morning-glory spillways under uncertain operational conditions.

Modelling doi: 10.3390/modelling7020077

Authors: Recep Kaş Mehmet Şen Seda Arık Hatipoğlu Mehmet Konar

Reliable short-term air traffic forecasts are important for operational planning in national airspace systems. This study develops a transparent forecasting framework for Türkiye’s monthly aircraft movements using publicly available data from the General Directorate of State Airports Authority (DHMİ) for 2018–2025. Because DHMİ releases may follow cumulative within-year reporting, month-specific increments are reconstructed through within-year differencing and checked through simple audit procedures. The empirical analysis compares seasonal naïve, ETS, and a constrained SARIMA family under leakage-free evaluation, combining a strict 2025 holdout with expanding-window rolling-origin validation. Forecast performance is assessed using standard accuracy metrics and complemented by Diebold–Mariano comparisons, which are interpreted cautiously, given the short holdout length. To examine instability around the pandemic period, this study also reports structural-break and stability diagnostics as supportive evidence rather than definitive identification. Uncertainty is evaluated through backtested 80% and 95% prediction intervals, comparing nominal SARIMA intervals, parametric bootstrap, split conformal prediction, and adaptive conformal inference (ACI). The results show that SARIMA provides the strongest point-forecast performance among the benchmarked models, while adaptive conformal calibration offers a useful balance between empirical coverage and interval width under changing conditions. Overall, this study provides a reproducible and operationally interpretable baseline for national air traffic forecasting in Türkiye and a clear benchmark for future multivariate extensions.

Modelling doi: 10.3390/modelling7020076

Authors: Yongliang Ma Zhenyu Yang Guoqing Lu

To precisely evaluate the fatigue hot-spot stress concentration factor (SCF) of welded tubular joints and verify the accuracy of existing methods, this research selects Y-type tubular joints as the research subject. The dihedral angle formula is re-derived, and the dihedral angles corresponding to each polar angle along the intersection line are calculated using MATLAB R2018a (MathWorks Inc., Natick, MA, USA). After determining the geometric parameters of the weld profile in accordance with AWS specifications, finite element models named “AWS-max” and “AWS-min” are established in ANSYS 2022 R1 (ANSYS Inc., Canonsburg, PA, USA). These models meet the maximum and minimum allowable weld sizes respectively, and a novel modeling approach is proposed. Tests on tubular joints under axial tension loading are conducted, and the SCF is obtained through the surface stress interpolation method. Comparative analyses are carried out among the SCF from the established “AWS-max” and “AWS-min” weld models, the non-weld model, and the test results of the tubular joints. The results indicate that the weld geometric size has a significant impact on SCF: a larger weld cross-section results in a lower SCF. For the AWS maximum weld model, the SCF of the chord ranges from 4.21 to 5.42, and that of the brace ranges from 1.71 to 5.33; for the AWS minimum weld model, the chord SCF is 4.41–5.73, and the brace SCF is 2.11–5.79. The numerical results are in good accordance with the experimental data, while the non-weld model produces obviously conservative results with inconsistent distribution laws. The calculated dihedral angles obtained by the proposed method are highly consistent with the AWS standard. The modeling method is characterized by reliable accuracy and strong engineering applicability, and can be extended to the SCF calculation and fatigue evaluation of various tubular joints.

Modelling doi: 10.3390/modelling7020075

Authors: Jianping Gao Wenju Liu Pan Liu Peiyi Bai Chengwei Xie

Trajectory planning in dynamic multi-vehicle interaction environments faces three critical challenges, including the difficulty of quantifying spatial risk distributions, the complexity of characterizing behavioral uncertainty arising from the multimodal maneuvers of surrounding vehicles, and the challenge of simultaneously optimizing multiple competing objectives such as safety, efficiency, comfort, and energy consumption. To address these challenges, this paper proposes an Improved Driving Risk Field-based Multi-objective Trajectory Optimization (IDRF-MTO) method. First, a joint spatiotemporal social attention mechanism achieves unified modeling of spatial interactions, temporal dependencies, and spatiotemporal coupling, combined with a lateral–longitudinal intent strategy for multimodal trajectory prediction. Second, an improved dynamic risk field model is constructed comprising three components: a vehicle risk field that incorporates spatial orientation and motion direction factors for anisotropic risk representation, along with a collision tendency factor that converts objective risk into effective risk; a predicted trajectory risk field that achieves anticipatory quantification of future risk from surrounding vehicles through confidence-weighted fusion; and a driving environment risk field that encapsulates road geometry, static obstacles, and environmental conditions. Finally, a multi-objective cost function embedding risk field gradients is formulated, and multi-objective coordinated optimization is realized through a three-dimensional spatiotemporal situation graph with adaptive safety sampling. Simulation results demonstrate that the proposed method enhances safety while simultaneously improving comfort and efficiency and reducing energy consumption, exhibiting excellent planning performance in complex dynamic environments.

Modelling doi: 10.3390/modelling7020074

Authors: Zhanchong Shi Kathrine Stemland Jinbao Xie Guomin Ji Max A. N. Hendriks Terje Kanstad

The condition assessment of alkali-silica reaction (ASR)-damaged concrete structures necessitates accurate reproduction of ASR expansion progression and its induced load effects across time and spatial dimensions. To address this challenge, a time-dependent free ASR expansion model was developed based on experimental measurements. A user subroutine incorporating stress-dependent behavior for restrained ASR expansion evolution was implemented on the ABAQUS platform and validated through simulation of ASR expansion in specimens under external loading and internal reinforcement restraint. Finite element analyses of the reinforced concrete specimens revealed distinct variations in ASR expansion between the surface and interior zones of concrete members. The assumption that surface ASR expansion strain equals steel rebar strain leads to significant overestimation of actual rebar stress and strain conditions. Additionally, based on the validated finite element model, the influence of elastic modulus, creep, stress-dependent function, steel plate thickness, and reinforcement ratio on the ASR expansion was investigated. For the reinforced concrete specimens, the stress variation over the cross-section is considerably reduced when creep is considered, while the concrete strain at the surface is only slightly influenced by creep.

Modelling doi: 10.3390/modelling7020073

Authors: Kasin Ransikarbum Naraphorn Paoprasert Pornthep Anussornnitisarn

Congestion in urban transportation is a significant challenge, often exacerbated by increasing private vehicle use and limitations in public transport. This study introduces a two-stage approach combining multi-criteria assessment and traffic simulation to examine current conditions and propose improvements. Initially, data on five primary and twenty-one secondary factors affecting public transport choice are assessed using the Best–Worst Method (BWM). The findings reveal that convenience is prioritized by working professionals, while travel cost is most important to students. A baseline simulation model is established using a case study at Kaset Intersection in Bangkok. Incorporating weighted preferences into the simulation aims to enhance public transport and encourage private car users to switch modes through potential traffic management policies. Additionally, a micro-simulation assesses the impacts of decreased traffic density, revealing that a reduction in traffic density can shorten overall travel time by about 2.04 s, based on regression analysis. The results suggest policies to improve public transport, reduce traffic density, and enhance urban transport system performance.

Modelling doi: 10.3390/modelling7020072

Authors: Herlindo Hernandez-Ramirez Jorge-Luis Perez-Ramos Daniel Canton-Enriquez Ana Marcela Herrera-Navarro Hugo Jimenez-Hernandez

The integration of automated learning and video analysis enables the development of intelligent systems that can operate effectively in uncertain scenarios. These systems can autonomously identify dominant motion dynamics, depending on the theoretical framework used for representation and the learning process used for pattern identification. Current literature offers a state-based approach to describe the key temporal and spatial relationships required to understand motion dynamics. An important aspect of this approach is determining when the number of positively learned rules from a given information source is sufficient to detect dominant motion in automatic surveillance scenarios. This is crucial, as it affects both the variability of movements that monitored subjects can exhibit within the camera’s field of view and the resources needed for effective implementation. This study addresses these gaps through a grammar-based sufficiency criterion, which posits that learning is complete when production rule growth stabilizes, under the assumption of system stationarity. The stability criterion evaluates whether the most probable rules are learned over time, and whenever a high-growth rule is added, it is used to update the criterion. We outline several benefits of having a formal criterion for determining when a symbolic surveillance system has a robust model that explains the observed motion dynamics. Our hypothesis is that a correct model can consistently account for the majority of motion dynamics over time in an automated learning process. The proposed approach is evaluated by modeling motion dynamics in several scenarios using the SEQUITUR algorithm as input and computing the probability of stability along the learning curve, which indicates when the model reaches a steady state of consistent learning. Experimental validation was conducted in real-world scenarios under varying acquisition conditions. The results show that the proposed method achieves robust modeling performance, with accuracy values ranging from 83.56% to 95.92% in dynamic environments.

Modelling doi: 10.3390/modelling7020071

Authors: Qiang Zeng Feilong Liang Xiang Liu Xiaofei Wang

To develop a refined traffic diversion scheme for expressway reconstruction and expansion, this study establishes generalized link impedance functions for cars and trucks, considering their differences in road travel time, time value, and toll costs. Subsequently, a traffic diversion model is constructed based on user equilibrium theory, taking the heterogeneity between cars and trucks into consideration. A path-based solution algorithm using the method of successive averages is designed to solve the model. To evaluate the environmental impact of the traffic diversion, a vehicle exhaust emission (including CO2, CO, HC, and NOx) estimation method based on the COPERT model is proposed. The results of a case study show that the optimized traffic diversion scheme significantly reduces the average V/C ratio while increasing the average velocity of both cars and trucks on the reconstructed links, without substantially compromising the traffic efficiency of other links. Additionally, the diversion scheme reduces the exhaust pollutant emissions, but increases the CO2 emissions within the network. The findings justify the effectiveness of the traffic diversion approach on alleviating the traffic congestion on the reconstructed expressway and its mixed impacts on the environment.

Modelling doi: 10.3390/modelling7020070

Authors: Shunsuke Arai Kentaro Mitsuma Takahiro Kawaguchi Keiichi Kaneko Seiji Hashimoto

In gasification-based waste treatment plants, continuous generation of combustible gas is essential for stable and efficient operation. To achieve this, multiple gasification furnaces are operated alternately; however, the internal states of the furnaces cannot be directly observed, making it difficult to assess the progress of gasification. Consequently, operation planning relies heavily on the experience of skilled operators. In this study, nonlinear system identification models based on deep learning are developed to predict the valve opening that controls the injection of gasification agents, which implicitly reflects the gasification state. Several modeling approaches, including linear finite impulse response (FIR) models, block-oriented Hammerstein–Wiener (HW) models, deep Hammerstein–Wiener models, and Transformer-based models, are investigated and compared. The models are trained and validated using actual operational data obtained from an industrial waste treatment plant. The results demonstrate that nonlinear models significantly outperform linear models, particularly for long-term prediction horizons. Among the examined approaches, the Transformer-based model shows stable and competitive performance across different prediction intervals. These findings indicate that deep learning-based nonlinear modeling is effective for predicting plant operation and has the potential to support automated operation planning, thereby reducing reliance on operator expertise.

Modelling doi: 10.3390/modelling7020069

Authors: Shuo Du Jianguo Xi Xianya Xu Jingyuan Li

In real-world operation, battery electric buses often encounter conditions with significant and rapid load variations. To improve regenerative braking energy recovery efficiency under such dynamic load conditions, this paper proposes a braking control strategy based on dynamic load estimation. First, a load estimation method based on a time-varying interactive multiple-model unscented Kalman filter (TVIMM-UKF) is developed by leveraging the vehicle longitudinal dynamics model and IMU sensor data, achieving high-accuracy online load estimation. Second, a multi-objective constrained optimization model is established, and an improved artificial bee colony algorithm is introduced to realize optimal brake force distribution under time-varying loads. Based on this, a regenerative braking control strategy is designed by incorporating motor characteristics and system-level operational constraints, enabling precise adjustment of braking torque across the full load range. Finally, simulation studies are conducted under two typical driving cycles, CHTC-B and C-WTVC, to verify the effectiveness of the proposed strategy. The results show that under dynamic load conditions, the proposed strategy can effectively improve braking energy recovery efficiency in both driving cycles.

Modelling doi: 10.3390/modelling7020068

Authors: Yury Ilyushin Alexander Vitalevich Martirosyan Mir-Amal Asadulagi Tatyana Kukharova

Modern oil refining is faced with the need to maximize raw material processing in the face of fierce competition and environmental requirements. Therefore, the fluid catalytic cracking (FCC) process, key to the production of high-octane gasoline, requires special attention to automation efficiency. Maintaining optimal reactor temperature is a complex scientific and technical challenge, the solution to which directly impacts the yield of target products and the service life of the catalyst. Existing automatic control systems often fail to cope with process transients, nonlinearities, and time delays, making the search for new control approaches highly relevant. The scientific significance of this study lies in the system analysis and quantitative comparison of the effectiveness of classical control laws (P, PI, PID) applied to a plant with a delay. For the first time, a rigorous comparative analysis of tuning methods—analytical (based on phase margin specifications) and automated (using the PID Tuner tool in MATLAB Simulink R2024b)—is performed for a plant characterized as a second-order system with time delay, formed by the series connection of two first-order lag elements with transport delay. The results contribute to automatic control theory by clearly demonstrating the limitations of the proportional controller and the insufficient speed of the integral controller, as well as confirming the hypothesis that a PID law is necessary to achieve a balance between accuracy and response speed under inertia conditions. The practical significance of the work is confirmed by the development of an optimized automatic temperature control system. Using the PID Tuner tool, we achieved critical industrial performance indicators: zero static error, minimal control time (44 s), and acceptable overshoot (9.6%). The system’s robustness (maintaining stability with changes in plant parameters by 30–40%) and its invariance to the main disturbance (catalyst temperature fluctuations), confirmed during simulation, guarantee the viability of the proposed solution under real-world production conditions. Implementation of such a controller will minimize deviations from the process conditions, leading to increased yield of light petroleum products and an extended service life of the expensive catalyst, providing direct economic benefits.

Modelling doi: 10.3390/modelling7020067

Authors: Akane Yamashita Hiroshi Yokoyama Yoichi Kageyama

For effective winter road management in snow-prone regions, timely snow removal that reflects weather and traffic conditions is required. In Akita City, Japan, city hall staff measure snow depth and dispatch contracted snow removal crews only when a predefined threshold is exceeded. Consequently, dispatch decisions depend heavily on staff experience. This study demonstrates objective, experience-independent dispatching based on predicting the number of snowplow dozers in operation, thereby reducing the municipal decision burden and improving contractor efficiency. The target variable is highly imbalanced, with long non-operational periods and wide variations in the number of deployed units during snowfall events. When trained directly on such data, models tend to regress toward near-median values and face difficulty capturing operational dynamics. To address this issue, we propose a two-stage framework: firstly, a classifier predicts whether snow removal operations will occur; secondly, a regressor estimates the number of operating dozers based on the operation. We further integrate multi-year datasets to enhance generalization across diverse snow conditions. Experiments showed that the proposed approach achieved an AUPRC of 0.84 for operation occurrence and an RMSE of 1.85 for dozer-count estimation, outperforming models trained on a single year.

Modelling doi: 10.3390/modelling7020066

Authors: Antoon Labib Bowen Zeng Carlos Cruz-Noguez Yong Li

Conventional concrete masonry construction consists of an assemblage of concrete blocks, mortar, grout, and steel reinforcement. While effective, this constructive method is constrained by its low productivity. In recent decades, advances in construction and manufacturing technologies now allow for the production of larger and more complex block typologies, enabling designers to reassess conventional designs to optimize structural performance and construction efficiency. As such, this study introduces the “mega-interlocking block”, a novel block that integrates the benefits of mega blocks (i.e., blocks with larger sizes) with a newly designed interlocking mechanism to enhance structural performance and expedite the construction of masonry walls in work sites where forklifts, scissor lifts and other smaller crane equipment are available. A numerical study was conducted to evaluate the in-plane (IP) and out-of-plane (OOP) behaviors of masonry walls constructed with mega-interlocking blocks, including both unreinforced masonry (URM) and reinforced masonry (RM) configurations, compared to standard block walls. A simplified micro-modeling approach was utilized to account for various possible failure modes associated with masonry structures. Results indicate that mega-interlocking blocks significantly improve wall stiffness and load-bearing capacity under IP loading, both with and without mortar, outperforming standard block walls. Under OOP loading, interlocking blocks provide moderate performance gains when mortar is present, though their effectiveness diminishes in mortarless configurations. For URM walls under IP loading, the implementation of mega-interlocking blocks yielded substantial improvements in stiffness and capacity, with the most notable benefits observed in walls with larger aspect ratios. Although the relative advantages in RM walls were less pronounced due to the homogenizing effects of grout and reinforcement, mega-interlocking blocks still demonstrated robust structural performance, making them a promising alternative to standard masonry units.

Modelling doi: 10.3390/modelling7020065

Authors: Jiahao Wang Xiaoqiang Dai Mingyu Zhang Kaikai You Jinxing Liu

Accurate and physically consistent state prediction is essential for shipboard power systems (SPS) operating under dynamic conditions. However, purely data-driven models often exhibit degraded robustness and physically inconsistent outputs when exposed to transient disturbances or limited data coverage. To address these limitations, this paper proposes a physics-constrained hybrid prediction model that integrates a convolutional neural network–bidirectional long short-term memory (CNN–BiLSTM) architecture with wide residual connections (WRC) and a physics-constrained loss (PCL). The proposed modeling approach combines real operational measurement data with high-resolution simulation data to enhance data diversity and improve generalization capability. The CNN–BiLSTM structure captures nonlinear temporal dependencies, while the WRC preserves critical low-level transient electrical features during deep temporal modeling. In addition, multiple physical constraints, including power balance, voltage conversion relationships, and battery state-of-charge (SOC) dynamics, are incorporated into the training process to enforce physically consistent predictions. The model is validated using charging and discharging experiments on a laboratory-scale SPS under both steady-state and transient conditions. Comparative results demonstrate that the proposed approach achieves higher prediction accuracy, improved dynamic stability, and faster recovery following disturbances compared with conventional data-driven models. These results indicate that physics-constrained deep learning provides an effective and interpretable modeling framework for SPS state prediction, supporting digital twin-oriented monitoring and real-time prediction applications.

Modelling doi: 10.3390/modelling7020064

Authors: Zouaoui R. Harrat Aida Achour Mohammed Chatbi Marijana Hadzima-Nyarko Ercan Işık

This study presents an analytical investigation of the dynamic behavior of concrete beams reinforced with different types of nano-clay (NC) particles and resting on a Winkler–Pasternak elastic foundation. The equivalent elastic properties of the nanocomposite were determined using an Eshelby-based homogenization model. An improved quasi-three-dimensional beam theory was applied to formulate the governing equations of motion, which were subsequently then analytically solved using Navier’s method. The analysis shows that NC reinforcement systematically elevates the natural frequencies of the beam, with the magnitude of improvement varying by particle type and concentration. Increasing the NC volume fraction to 30% leads to a significant rise in the fundamental frequency, reaching about 30% for hectorite (SHca-1) compared with the unreinforced beam, whereas montmorillonite (SWy-1) produces a more moderate increase of approximately 13%. This reinforcing effect remains consistent across different span-to-depth ratios, indicating that the influence of nano-clay content on the dynamic response is largely independent of beam slenderness. Furthermore, increasing the Winkler foundation stiffness results in an almost linear rise in frequency of approximately 18–22%, whereas the Pasternak shear parameter produces a stronger effect, reaching around 25% enhancement depending on the reinforcement type. These results indicate that incorporating nano-clay platelets can be an effective strategy for enhancing the vibrational stiffness of concrete beams and improving their dynamic performance when interacting with supporting soil media.

Modelling doi: 10.3390/modelling7020063

Authors: Joseph Jabbour Jalal Possik Adriano O. Solis Charles Yaacoub Sina Namaki Araghi Gregory Zacharewicz

The rising global incidence of kidney failure is increasing pressure on hemodialysis unit operations, with operational vulnerabilities further exposed by the COVID-19 pandemic. This scoping review mapped evidence on Lean management, discrete event simulation (DES), and virtual reality (VR) in hemodialysis units; compared reported outcome domains and performance indicators; identified barriers to Lean implementation; and assessed the empirical basis for a combined Lean–DES–VR framework. English-language peer-reviewed articles, conference papers, and book chapters addressing Lean, DES, VR, or their combination in dialysis settings were searched in Scopus, PubMed, SpringerLink, IEEE Xplore, ACM Digital Library, and Google Scholar to 30 June 2024; grey literature and opinion pieces were excluded. Structured data extraction and thematic narrative synthesis were applied. Twenty-seven studies were included (Lean n = 4, DES n = 9, VR n = 13, DES + VR n = 1). DES studies mainly reported operational outcomes, whereas VR studies focused predominantly on patient-centered rehabilitation and experience. Most studies examined methods in isolation, and integrated Lean–DES–VR applications were almost entirely absent. The literature suggests complementarity among these approaches but provides no robust empirical basis for a fully integrated framework. No protocol was prospectively registered.

Modelling doi: 10.3390/modelling7020062

Authors: Sharif H. Zein

Plastic waste gasification offers a dual-benefit pathway for hydrogen production and waste management in emerging economies. However, existing hydrogen infrastructure planning focuses predominantly on blue and green pathways, with limited integration of waste-derived hydrogen or spatially distributed waste availability constraints. This study determines optimal waste-to-hydrogen infrastructure deployment in Oman through 2040 using mixed-integer linear programming with verified techno-economic parameters. Results indicate that plastic waste can produce 21,997 tonnes H2 annually at a levelised cost of $2.88/kg, competitive with blue hydrogen ($1.80–2.50/kg) and significantly cheaper than current green hydrogen ($4–6/kg). The optimal network comprises four facilities at Muscat (500 TPD), Sohar (128 TPD), Salalah (192 TPD), and Nizwa (67 TPD), processing 275,000 tonnes of plastic waste whilst avoiding 137,000 tonnes of CO2-eq through landfill diversion. However, feedstock availability constrains production to 24% of base case demand (90,000 tonnes), positioning waste-to-H2 as a complementary pathway requiring integration with steam methane reforming for industrial hubs and electrolysis for the transport sector. Sensitivity analysis reveals hydrogen yield (±29% cost impact) and CAPEX (±20%) as critical parameters, with cost reduction pathways targeting $2.00–2.30/kg by 2035 through technology learning and co-benefit monetisation. Policy recommendations include extended producer responsibility schemes, government fleet procurement mandates, and regional waste trade agreements across the GCC. Waste-to-hydrogen demonstrates techno-economic viability as a guaranteed baseload contributor within diversified hydrogen strategies for Gulf economies.

Modelling doi: 10.3390/modelling7020061

Authors: D. A. P. Prabhakar Arun Kumar Shettigar Mervin A. Herbert Rashmi Laxmikant Malghan

A proposed study based on an artificial neural network (ANN) model will be used to predict microhardness (VHN) and tensile strength (TS) of Friction Stir Additive Manufacturing (FSAM) of AA8090 alloy. The process parameters taken into consideration were rotational speed (1000, 1500, 2000 rpm), traverse speed (45, 65, 85 mm/min) and tilt angle (0°, 1°, 2°). We performed 90 physical experiments (74 + 7 + 6 + 3), in which 74 experiments were generated with the help of the Central Composite Design of ANN modeling, seven independent experiments were used to validate the results, six repeat experiments were taken, and three mid-level interpolation experiments were performed. Out of 74 modeling runs, 60 samples were trained, 14 were internally tested, and seven separate modeling runs were exclusively tested externally. An ANN model was created based on the Adam optimizer, where the loss was taken to be Mean Squared Error (MSE). The level of model robustness was assessed employing 5-fold cross-validation and grouped validation (LOPCO, LOFLO-RPM, and LOFLO-TA). Under 5-fold cross-validation, the ANN had mean R2 values equal to 0.940 (VHN), 0.920 (TS). In normalized training, the model achieves MAE = 0.26 and R2 = 0.97, whereas testing in physical units has developed MAE values of 1.0 and 2.0, respectively (VHN and TS). These results correspond with the high predictive ability and generalization of the ANN model, as indicated by the uniform performance of the ANN model on training, cross-validation, internal testing, and independent validation. The importance analysis of features revealed that rotational speed was the most significant factor that influenced the tensile strength and microhardness. The constructed ANN model is a credible and sound system for optimizing and replicating processes from other friction-stir processing methods on AA8090 alloy.

Modelling doi: 10.3390/modelling7020060

Authors: Zhuofan Huang Shangkun Liu Jingli Huang Jie Huang

Driver fatigue detection (DFD) in low-light nighttime driving environments is crucial for road safety, but it remains challenging due to degraded image quality and computational constraints. This paper proposes a real-time three-stage framework specifically designed for nighttime driver fatigue detection, integrating low-light image enhancement, joint face and facial landmark detection, and geometry-based fatigue judgment. In the initial stage, the framework utilizes the Zero-Reference Deep Curve Estimation (Zero-DCE) algorithm to improve the visual quality of input images under low-light conditions. Subsequently, a novel lightweight single-stage detector, You Only Look Once for Joint Face and Facial Landmark Detection (YOLOJFF), is introduced for efficient joint localization. Finally, fatigue judgment is performed in real-time by calculating the Eye Aspect Ratio (EAR) and Mouth Aspect Ratio (MAR) from the detected landmarks and using a sliding time window strategy. Experimental results demonstrate that the enhancement module significantly improves detection performance. The YOLOJFF model achieves a favorable balance, with 90.9% precision, 87.6% mean Average Precision (mAP), and 5.2 Normalized Mean Error (NME), while requiring only 3.7 million (M) parameters and running at 107.5 FPS. The proposed framework provides a robust and efficient solution for real-time DFD in nighttime scenarios.

Modelling doi: 10.3390/modelling7020059

Authors: Xuan Qi Yifei Fang Xin Li Chao Zhai Hehong Zhang Wei Zhao

The environmental pressure simulation facility is crucial to the development and testing of high-performance aeroengines. During environmental pressure simulation tests of aeroengines, a large amount of uncertain high-temperature and low-pressure gas is discharged into the pressure regulation system, resulting in significant disturbances and complex coupling among compressor unites, valves and the main pipe. To analyze the surge mechanism and support controller design, a control-oriented dynamic model of pressure regulation system is established. By considering the dominant pressure dynamics of the main pipe and the dynamic characteristics of compressors and regulating valves, the original complex system is simplified into a nonlinear model suitable for control analysis and safety-oriented design. Based on the developed model, the safe operation problem of compressor units is transformed into a constrained control problem. A cooperative sliding mode control (Co-SMC) method is then proposed to ensure that the compressor pressure ratio remains within a safe range while mitigating the impact of exhaust disturbances on the pressure regulation process. The proposed method enhances the robustness of pressure regulation system and the grid-connected efficiency of compressor units while guaranteeing the stability of closed-loop system. Comparative simulations under complex operating conditions demonstrate that the proposed method significantly improves both the safety level and control performance of pressure regulation system.

Modelling doi: 10.3390/modelling7020058

Authors: Elias Heriberto Arias Nava Brendan Patrick Sullivan Luis A. Moncayo-Martinez

Mexico City’s Metro Line 7 is a critical north–south artery within one of the world’s largest metro systems, yet it suffers from persistent operational inefficiencies, including chronic overcrowding and extended passenger travel times. This research employed a data-driven discrete-event simulation model built in SIMIO to analyze the passenger dynamics of Line 7. The model was grounded in a comprehensive dataset of approximately 280,000 daily passengers over one year. Key innovations included modeling station-specific passenger arrivals as non-stationary Poisson processes with time-varying rates calculated at 15-min intervals and incorporating empirically derived walking times within stations. The simulation framework replicated the system’s operational logic, including train movements, passenger boarding and alighting, and complex transfer behaviors at interchange stations, while accounting for the influence of the broader metro network on Line 7’s passenger flows. The simulation results, derived from 100 replications, quantified severe systemic inefficiencies. The average total travel time for a passenger using Line 7 was 81.17 min. However, the ideal in-motion travel time was calculated to be only 53 min, revealing that passengers spend a disproportionate amount of time waiting. This yielded a travel time efficiency of just 65.3%. The model identified specific bottlenecks at key transfer stations like Tacubaya and San Pedro de Los Pinos, where platform utilization reaches full capacity, directly causing the excessive queuing times that degrade the overall passenger experience. This study demonstrated that the primary issue is not the speed of trains but the systemic inability to manage passenger flow during peak demand, leading to critical capacity shortfalls at specific stations. The simulation provides a quantitative tool for diagnosing these inefficiencies and offers a robust platform for prototyping and evaluating strategic interventions, such as optimized timetables and resource allocation, before costly real-world implementation.

Modelling doi: 10.3390/modelling7020057

Authors: Laila Taoufiq Omar Bamaarouf Abdelmajid Kadiri Rachid Marzoug

Traffic accidents at urban intersections represent a major road safety concern, particularly those caused by traffic signal violations. To analyze accident mechanisms and develop effective prevention strategies, this study employs a cellular automata model to investigate the relationship between accident probability Pac and traffic parameters at signalized intersections. Simulation results reveal a nonlinear relationship between Pac and traffic demand. The accident probability reaches a maximum under free-flow conditions and subsequently decreases as congestion increases, eventually stabilizing at a nearly constant level under highly congested traffic. Additionally, collision risk increases with lane-changing probability Pchg, especially upstream of the intersection. High traffic speeds significantly elevate both accident probability and severity. Finally, the results indicate that extending traffic signal cycle durations is not an effective strategy for reducing accident risk. Overall, the proposed model provides a useful framework for estimating accident risk under different traffic conditions and supporting traffic management, including control decisions aimed at improving road safety.

Modelling doi: 10.3390/modelling7020056

Authors: Tuo Zhang Qing-Yun Chen Seong-Jin Kwon Gee-Soo Lee

Overtaking maneuvers can induce significant changes in the airflow field between vehicles, potentially compromising the stability and safety of the overtaken vehicle. This study investigates the aerodynamic characteristics during overtaking in a platoon of vehicles using the 1:2.5 DrivAer fastback model as the subject of analysis. To simulate the external flow during overtaking within a vehicle platoon, the Reynolds-Averaged Navier–Stokes (RANS) equations are employed under steady-state, incompressible flow assumptions. A baseline simulation is first performed for a single vehicle, and the results are validated against experimental data to ensure the reliability of the numerical method. The simulation is subsequently extended to a two-vehicle platoon configuration with a longitudinal spacing of half a vehicle length. Under steady platoon driving conditions, no significant lateral aerodynamic disturbances are observed between adjacent vehicles, and a two-vehicle platoon is subjected to relatively small lateral forces. However, during the overtaking process, notable variations in aerodynamic forces and moments occur. In particular, the lateral force coefficient and yaw moment coefficient of two-vehicle platoons reach their peak values at about two vehicle lengths ahead of the critical overtaking position. Furthermore, during the overtaking maneuver, the aerodynamic characteristics of the overtaken vehicle exhibit continuous fluctuations. The resulting variations in the lateral force coefficient and cornering stiffness have a sustained impact on vehicle handling stability, providing crucial insights for enhancing vehicle maneuverability.

Modelling doi: 10.3390/modelling7020055

Authors: Jianqing Wu Jiaao Ren Hui Wang Fei Xie Shaohan Chen Mengjie Jiang

Accurate and reliable short-term traffic flow prediction is crucial for managing urban congestion but is challenged by the complex spatio-temporal dependencies inherent in traffic systems. Conventional single models, such as Long Short-Term Memory (LSTM) and Temporal Convolutional Network (TCN), often fail to capture these nonlinear dynamics. To address this, we propose a novel Bayesian-Optimized Mixture of Experts (BO-MoE) framework. This hybrid architecture utilizes a Mixture of Experts (MoE) to dynamically integrate multiple specialized deep learning models, allowing it to adapt to diverse and complex traffic patterns. Bayesian Optimization (BO) is further integrated to automate hyperparameter tuning, significantly enhancing predictive accuracy and model efficiency. We evaluated BO-MoE on three real-world traffic datasets. Empirical results demonstrate that our model consistently outperforms strong baselines, including TCN. Specifically, on PEMS04, it reduces MAE, RMSE, and MAPE by 1.97%, 1.19%, and 3.23%, respectively, while on PEMS08, the corresponding reductions reach 3.83%, 1.26%, and 5.49%. On the NZ dataset, BO-MoE also achieves superior performance, with improvements comparable to those on PEMS benchmarks.

Modelling doi: 10.3390/modelling7020054

Authors: Mukhtar Fatihu Hamza Auwalu Muhammad Abdullahi

For safe and efficient human–robot interaction, lower-limb exoskeletons used for assistance and rehabilitation need to be precisely and energy-efficiently controlled. By creating an adaptive neuro-fuzzy fractional-order PID (ANFIS-FOPID) controller, this project seeks to improve tracking accuracy, robustness, and energy efficiency in a two-degree-of-freedom hip–knee exoskeleton. The Euler–Lagrange formulation is used to derive a nonlinear dynamic model, and a Lyapunov-based stability analysis is used to show that the closed-loop system remains uniformly ultimately bounded under disturbances and parameter uncertainties. The suggested controller performs noticeably better than traditional PID and fixed-parameter FOPID controllers, according to numerical simulations conducted under both normal and perturbed conditions. The ANFIS FOPID achieves root mean square errors below 0.028 rad and lowers the integral absolute errors at the hip and knee joints to 0.1454 and 0.1480, as opposed to 0.3496–0.3712 for PID controllers. Under ±10% parameter uncertainty, the total control-energy proxy drops from 2870.0 (PID) to 936.25, a 67.4% decrease, and stays at 1587.93. Statistically significant variations in energy consumption are confirmed by one-way ANOVA (p < 10−176). Large effect sizes are found (η2 = 0.237–0.314). These results demonstrate the superior tracking performance, robustness, and energy efficiency of the ANFIS-FOPID controller. The results set a quantitative standard for future experimental validation and hardware-in-the-loop implementation, despite being based on high-fidelity simulations.

Modelling doi: 10.3390/modelling7020053

Authors: Satyaki Sinha Saumitra Bhate Tuhin Mukherjee

3D electrodeposition printing is an emerging process for fabricating metallic parts with controllable geometry, yet the coupled influences of electrochemical kinetics, ion transport, and tool motion on layer height remain difficult to interpret. This work presents a physics-based process model that links key process inputs, current density, electrolyte concentration, the inter-electrode gap, and tool scanning speed, to the resulting layer height in 3D electrodeposition printing of nickel-based structures. The model combines species transport in the inter-electrode gap with Butler–Volmer kinetics, under carefully stated assumptions regarding current efficiency, overpotential, and lateral spreading. Model predictions are validated against experimentally reported layer heights over a range of process conditions, yielding average errors (9–15%) and root-mean-square errors (0.13–0.28 µm) that demonstrate good agreement and highlight the impact of simplifying assumptions. Systematic parametric studies reveal how each process input monotonically influences layer height in ways consistent with Faraday’s law and diffusion-controlled growth, while also quantifying the relative sensitivity to different parameters. Building on these results, we introduce a dimensionless 3D Electrodeposition Printing Index that consolidates the key process and material parameters into a single scalar describing the geometric growth regime. The index enables construction of process maps that capture how combinations of current density, scan speed, concentration, and gap affect achievable layer height within the validated operating window. The scope and limitations of the proposed modeling framework and the index, particularly regarding other materials, more complex geometries, and pulsed or strongly convective regimes, are explicitly discussed, providing a basis for future model extensions and experimental validation.

Modelling doi: 10.3390/modelling7020052

Authors: Sergii Kroviakov Vitalii Kryzhanovskyi Pavlo Shymchenko Inna Aksyonova

This study investigates the properties of concrete incorporating recycled aggregates (RAs) for rigid pavement applications. A 15-point three-level experimental design was used to vary three composition factors: Portland cement substitution with fly ash (FA), and dosages of a superplasticizer (SP) and polypropylene fibers (PFs). A set of experimental–statistical models (ES models) was developed to predict the concrete strength, abrasion and frost resistance (FR), water absorption (WA), and global warming potential (GWP). This study aimed to develop a material that achieves both adequate mechanical performance for pavement applications and enhanced environmental sustainability by incorporating RAs and FA. The results demonstrate that replacing up to 13% of cement with FA does not compromise the splitting tensile strength or FR. For non-fibrous concrete, this substitution increases FR by approximately 50 freeze–thaw cycles. Application of PFs (2.4–3 kg/m3) enhances splitting tensile strength by 14–16% and improves FR by about 50 cycles. Using response surface methodology (RSM), optimal concrete compositions were identified that meet all target criteria: compressive strength ≥ 40 MPa, flexural strength ≥ 5 MPa, FR ≥ F200 (cycles), and abrasion resistance (AR) ≤ 0.5 g/cm2, while simultaneously minimizing GWP. An additional optimum composition was determined by imposing a constraint on splitting tensile strength of ≥4.5 MPa. This graphical optimization approach, utilizing two-factor interaction diagrams, provides an effective and visual methodology for practical concrete mixture design. The novelty of the method lies in the discretization of the factor space, which enables efficient identification of optimal concrete mixture compositions.

Modelling doi: 10.3390/modelling7020051

Authors: Sulistyo Wijanarko Rina Ristiana Anwar Muqorobin

PID (proportional integral derivative) control has been widely used in industry due to its simplicity in implementation and satisfactory performance. However, the controller tuning is very troublesome when used in complex and nonlinear systems. The full bridge boost converter (FBBC) is a nonlinear system, so the PID control application in this converter should be further explored. This paper introduces a control approach that integrates PID control with a Linear Quadratic Regulator (LQR) for FBBC. To enable linear control design, the FBBC is linearized around its steady state operating points. The control architecture is structured into four cases: Case 1: PI-LQR Output Feedback, Case 2: PI-LQR State Feedback, Case 3: PID-LQR Output Feedback, and Case 4: PID-LQR State Feedback. The analysis aims to identify the most reliable system performance under input voltage change and load variation. The simulation results indicate that under the input voltage and load changes, cases 2 and 4 produce faster settling times, each with a settling time of 0.025 s and 0.015 s, respectively. However, both controllers produce negligible steady state error (less than 1%). Overall, Case 4 (PID-LQR State Feedback) consistently delivers the best performance, characterized by faster settling time, negligible steady state error, optimal control signal, and significantly reduced oscillation in both the inductor current and output voltage.

Modelling doi: 10.3390/modelling7020050

Authors: Andrés Salas-Espinales Ricardo Vázquez-Martín Anthony Mandow

High-quality RGB–thermal infrared (RGB-T) semantic segmentation datasets are crucial for search-and-rescue (SAR) applications, yet their development is hindered by the scarcity of annotated ground-truth and by the challenges of thermal-camera calibration, which typically depends on heated targets with limited geometric definition. Recent approaches focus on using semantic segmentation annotation tools and transferring RGB masks to multi-spectral data, but they do not fully address the need for robust cross-modal geometric validation, quality control, or human-in-the-loop reliability assessment in RGB-T segmentation. To fill this gap, we propose a validated cross-modal annotation pipeline that combines deep correspondence matching, geometric transformation (affine or homography) of RGB-T pairs, and quantitative alignment validation. Our RGB-T pipeline integrates a semi-automatic annotation pipeline based on the Segment Anything Model 2 (SAM2) in Label Studio, with guided human refinement, and incorporates quantitative cost and quality control via inter-annotator agreement before being used in downstream model training. Results across three annotators show that the proposed approach reduces annotation time by 36% while achieving high annotation quality (mean IoU = 74.9%) and strong inter-annotator agreement (mean pixel accuracy = 74.3%, Cohen’s κ = 65%). The proposed RGB-T pipeline was annotated on a SAR-oriented RGB-T dataset comprising 306 image pairs and trained on two SOTA RGB-T. These findings demonstrate the practical value of the proposed methodology and establish a reproducible framework for generating reliable RGB-T semantic segmentation datasets, complementing and extending recent multispectral auto-labeling approaches.

Modelling doi: 10.3390/modelling7020049

Authors: Khushal Nitin Rajvansh Girish Hariharan Nitesh Kumar Chithirai Pon Selvan Ravindra Mallya Gowrishankar Mandya Chennegowda Subraya Krishna Bhat Vinyas

Multi-grooved water-lubricated bearings (MGWLBs) are widely used in marine stern tube applications, where hydrodynamic performance is strongly influenced by groove geometry and operating conditions. This study presents a combined experimental and computational investigation of water film lubrication characteristics in MGWLBs with different groove geometries. An experimental test setup redesigned to replicate the operational behavior of MGWLBs was employed to record the circumferential film pressure variations under varying rotational speeds and applied loads. Detailed experimental tests were performed on a MGWLBs with filleted V-shaped grooves, where the film pressures at the bearing midplane were measured using a flush-mounted diaphragm pressure sensor mounted on a hollow shaft. The experimental results revealed a transition from localized, non-uniform pressure generation at low speeds to stable and circumferentially continuous hydrodynamic pressure fields at higher speeds and loads. CFD simulations were also conducted to analyze the influence of groove geometry on pressure distribution and flow behavior. An increase in rotational speed was shown to significantly enhance pressure magnitude, circumferential continuity, and film stability under moderate to high loading conditions. Filleted V-shaped, semicircular, and short V-shaped groove models were analyzed for a speed range of 400 to 6000 RPM. Filleted V-shaped grooves produced smooth pressure development with moderate gradients, while semicircular grooves improved pressure and velocity uniformity by limiting localized intensification. In contrast, short V-shaped grooves generated higher peak pressures due to enhanced flow acceleration at groove–land interfaces. The findings provide design guidance for selecting groove geometry and operating conditions to enhance the hydrodynamic performance of marine water-lubricated bearings.

Modelling doi: 10.3390/modelling7020048

Authors: Haochu Cui Yan Sun

In this study, we propose a novel model based on multi-source spatio-temporal features and optimized ensemble learning for forecasting station- and line-level passenger flows of urban rail transit. First, we design a spatio-temporal feature engineering method to enhance the accuracy of forecasting using passenger flow features; the temporal features include periodic and lag effects and the spatial features cover spatio-temporal attention mechanisms, adjacency relationships in the network graph and station clustering features. Furthermore, an improved ensemble learning method based on Extra Randomized Trees (ExtraTrees) and Light Gradient Boosting Machine (LightGBM) is developed to forecast the station-level passenger flows using a weighted sum method in which a particle swarm optimization algorithm is adopted to determine the weights assigned to the forecasting results of the two models. Finally, ridge regression is adopted as the meta-learning model to forecast line-level passenger flows. We employed passenger flow data from three urban rail transit lines in Hangzhou to demonstrate the feasibility of the proposed model. The results indicate that it produces more accurate passenger flow forecasts at the station and line levels than benchmark models. Therefore, it can provide a solid support for optimizing the operations, management, and planning for both a single urban rail transit station and the entire network.

Modelling doi: 10.3390/modelling7020047

Authors: Domen Šeruga Lovro Novak Marko Nagode Jernej Klemenc

The study reports on the essential level of details in simulations during the development of structural components if reliability-based design is used to ensure their quality and operational safety. A general method, which is initially introduced, is then applied to an indicator spring of a fuse element during assembly and operation stages. First, it is proven that design of simulations based on orthogonal arrays which includes variations of form, material properties and operating conditions within expected scatter limits provides a comparable determination of the scale parameter for the two-parameter Weibull distribution as the experimental observations of the same process. The shape parameter of the distribution tends to be underestimated by the simulations resulting in a higher scatter of the expected properties than experimentally measured. Next, it is shown that the maximum likelihood method to determine representative parameters of the scatter of assembly and operation stages provides a better match with experimental data than the median rank regression. Finally, a high reliability of the indication has been calculated for the fuse element if both the scatter of the assembly and the operation conditions were considered.

Modelling doi: 10.3390/modelling7020046

Authors: Hongwu Li Bin Zhao Zhihong Yao Yangsheng Jiang

This paper addresses the optimization of electric vehicle (EV) charging facility configuration on highways by proposing a collaborative planning method that integrates driver anxiety psychology, mixed traffic flow dynamics, and service area queuing characteristics. By abstracting the road travel and service area replenishment processes into an integrated queuing network, a system analysis framework is constructed to characterize the coupling relationship of “facility supply, traffic assignment, and state feedback.” On this basis, a bi-level optimization model is established with the objective of minimizing the generalized total social cost. The upper level makes decisions on the coordinated quantities of fixed charging piles and mobile charging vehicles, while the lower level describes the stochastic user equilibrium behavior of drivers under the influence of real-time congestion and anxiety. To tackle the high-dimensional nonlinear nature of the model, an efficient solution algorithm based on simultaneous perturbation stochastic approximation (SPSA) is designed. A case study of the Nei-Yi Expressway demonstrates that compared with the traditional peak demand proportional allocation method, the proposed approach can better balance construction costs, operation and dispatching costs, and user travel experience under limited investment, significantly reducing waiting times and psychological anxiety costs. It provides theoretical methods and decision support for planning a resilient energy replenishment network that achieves “fixed facilities ensuring base load and mobile resources responding to peak demands.”

Modelling doi: 10.3390/modelling7020045

Authors: Patricia Rubio Herrero Belén Muñoz-Abella Inés Ivañez Lourdes Rubio

In recent decades, Artificial Neural Networks (ANNs) have become a robust tool for addressing complex engineering challenges. This paper implements an ANN-based methodology to determine the natural frequencies of rotating sandwich composite beams with core defects. The study focuses on the influence of rotation speed and defect characteristics (size and location) on a beam made of carbon fiber face-sheets and a honeycomb core, selected for its high strength-to-weight ratio in next-generation designs. The primary novelty lies in providing a simplified model that, through an ANN-based surrogate, establishes an automated and high-speed process for frequency prediction. This approach bypasses the prohibitive computational costs of 3D-FEM simulations, enabling near-instantaneous results essential for real-time Structural Health Monitoring (SHM) applications.

Modelling doi: 10.3390/modelling7020044

Authors: Kaiyi Xie Haotian He Yuzheng Li

This paper investigates an Organic Rankine Cycle (ORC) system for low-to-medium temperature heat recovery using comparative thermodynamic, exergoeconomic and economic modelling. A working-fluid study considering environmental and thermodynamic perspectives is conducted. A 20 kW ORC unit is tested and used as a feasibility and trend-consistency reference to support the modelling assumptions and practical operating bounds. A parametric study then examines the effects of evaporator pressure, condensation temperature, superheat, subcooling and heat-exchanger pinch-point temperature differences on net power output, first- and second-law efficiencies, total product cost and total capital investment under prescribed boundary conditions. Multi-objective optimization is applied to identify Pareto-optimal trade-offs and representative compromise solutions. Results show an intermediate evaporator pressure maximizes net power output, while lower condensation temperature generally improves efficiency; superheat has limited efficiency impact but should ensure safe operation, and a small subcooling margin (around 3 °C) mitigates cavitation risk. The best overall performance is obtained with an evaporator pinch of 3 °C and a condenser pinch of 5–9 °C; tightening pinch constraints increases required heat-transfer area and makes heat exchangers the main cost bottleneck for high-efficiency solutions.

Modelling doi: 10.3390/modelling7020043

Authors: Federico Casucci Enrico Tosoratti Mohamadreza Afrasiabi Pier Paolo Valentini

This study introduces a new synthesis algorithm for triply periodic minimal surfaces based on determining the equilibrium configuration of elastic membranes constrained at their boundaries. Beyond the methodology itself and its computational efficiency, the scientific relevance of this work lies in the 66 surfaces with these characteristics that it enabled to generate. Leveraging their continuous and highly regular geometry, these surfaces were used to define novel shell-based lattices, the mechanical behavior of which was investigated numerically and experimentally through both static and dynamic analyses. The computational models demonstrated high predictive accuracy, with numerical results deviating by less than 10% from the experimental data. Across the new geometries, the surface-area-to-volume ratio ranged from 1.8 to 4.8 cm−1. At infill coefficients of 10%, 20%, and 30%, the structures exhibited a wide range of stiffness and anisotropic behaviors, with equivalent elastic modulus spanning from 0.02% to 25% that of the base material and Zener indices from 4.67×10−2 to 11.8. Ultimately, the study revealed a clear influence of cell geometry on stress concentration and modal response.

Modelling doi: 10.3390/modelling7010042

Authors: Sajad Saberi Jaber A. Abu Qahouq

Reliable state-of-charge (SoC) estimation is crucial for safe and efficient battery management. However, it is challenging in practice. Terminal-voltage sensitivity becomes weak in open-circuit-voltage (OCV) plateau regions. Model uncertainty also persists at practical sampling periods. To tackle this issue, this paper proposes a discrete-time, model-based SoC estimation framework. This framework combines a dual-polarization equivalent-circuit model with a tuning-light sliding-mode observer. It is specifically designed for digitally sampled battery management systems. The modeling stage includes: (i) a discrete-time DP representation suitable for embedded use, (ii) a shape-preserving PCHIP reconstruction of the OCV–SoC curve and its derivative, and (iii) an effective-slope regularization mechanism that maintains non-vanishing output sensitivity even in flat OCV regions. On top of this structure, a boundary-layer SMO is developed with output-error shaping, model-driven gain scaling, and simple bias-compensation terms based on integral correction and leaky Coulomb counting. A discrete-time Lyapunov analysis is conducted directly on the surface dynamics. This analysis shows finite-time reaching to the boundary layer and a practical limit on the steady-state error that depends on the sampling period, disturbance level, and boundary-layer width. Numerical tests on a DP model identified from experimental data indicate that the proposed method achieves SoC accuracy similar to a switching-gain adaptive SMO. The results confirm the benefits of a model-centric design. The discrete-time formulation and convergence proof, which do not depend on high sampling rates, provide robustness advantages over traditional sliding-mode methods. The proposed method also performs better than a tuned EKF in plateau regions, requiring much less tuning effort.

Modelling doi: 10.3390/modelling7010041

Authors: Vivek M. Rao Jamieson Brechtl Corson L. Cramer Kashif Nawaz

Recently, there has been a heightened interest in using triply periodic minimal surfaces (TPMSs) in the design of compact process engineering components. The benefits of high surface area per unit volume, modular form, and inherent periodicity provide a holistic self-supporting network and flow-conducive features. Applications of importance include thermal power management, biomimetic scaffolds and structures, and feasibility of advanced manufacturing. This study presents a novel approach to the manipulation of the characteristic Schwarz-G, or gyroid TPMS, for thermal design in the context of advanced manufacturing. The study presents relationships between design parameters and resulting surface area as a target response using the characteristic equation of a gyroid. Through parametric control, the characteristic equation is manipulated to produce a 20-fold increase in achievable area over a baseline design characteristic of 25.4 mm through controlled combinations of design parameters. A second relationship is presented as a function of the maximum area achieved and manipulated design parameters. Through the analysis, the study presents a framework to identify and maximize the achievable area of TPMSs for advanced manufacturing and thermal management applications.

Modelling doi: 10.3390/modelling7010040

Authors: Junyi Zou Wu Huang Zhen Shi Kaili Wang Feng Wang

With the increasing demand for perception in complex road environments in intelligent driving, rapid and accurate identification of paved-road obstacles has become a critical prerequisite for driving safety and comfort. Various types of road obstacles can significantly affect vehicle stability and ride quality. To address this challenge, a lightweight and efficient vision-based obstacle detection framework, termed GroupScale-YOLO, is proposed, in which detection accuracy and computational efficiency are jointly enhanced through the collaborative design of multiple novel modules. First, a dedicated dataset targeting common paved-road obstacles is constructed, and six data augmentation strategies are employed to mitigate the adverse effects of road surface undulations and illumination variations on visual perception. Second, to overcome the limitations of YOLOv11n in paved-road obstacle detection tasks, targeted optimizations are introduced to the backbone network, convolutional blocks, and detection head. Experimental results indicate that GroupScale-YOLO achieves a 29.95% reduction in model parameters while simultaneously increasing mAP@0.5 by 0.6% on the self-built dataset, demonstrating its suitability for deployment in resource-constrained scenarios. Furthermore, real-vehicle road tests confirm that the proposed method maintains stable and accurate obstacle detection performance under practical driving conditions, offering a reliable solution for intelligent vehicle environmental perception.

Modelling doi: 10.3390/modelling7010039

Authors: Xin Pan Peng Chen Jianfeng Zhao

To address the limited dynamic voltage regulation performance of LLC resonant converters under wide input voltage and load variations, a reinforcement learning-based voltage control strategy is proposed in this paper. The twin delayed deep deterministic policy gradient (TD3) algorithm is adopted to learn the nonlinear mapping between system states and control actions, enabling adaptive adjustment of the converter operating parameters. Based on the established LLC resonant converter simulation model, the state space, action space, and reward function of the agent are designed to ensure rapid control response to abrupt changes in input voltage and load. Compared with the conventional PI control strategy, the proposed TD3-based strategy provides faster control actions during operating condition transitions, effectively suppressing output voltage overshoot and undershoot, and shortening the settling time. Simulation results verify that the proposed method achieves improved dynamic response performance under various operating conditions, demonstrating its effectiveness and superiority in LLC resonant converter voltage regulation.

Modelling doi: 10.3390/modelling7010038

Authors: Ali Juma Alnaqbi Ghazi G. Al-Khateeb Waleed Zeiada

Punchouts distress represents a major structural deficiency in Continuously Reinforced Concrete Pavements (CRCPs), contributing to premature deterioration, reduced ride quality, and increased maintenance demands. To improve the prediction of punchout occurrence, this study develops a hybrid data-driven modeling approach that combines Gradient Boosting Machines (GBMs) with Particle Swarm Optimization (PSO). The proposed framework utilizes 395 observations obtained from 33 CRCP sections in the Long-Term Pavement Performance (LTPP) database, incorporating structural, climatic, traffic, and performance-related variables. PSO was applied to systematically tune key GBM hyperparameters, including the number of boosting iterations, learning rate, and tree complexity, in order to enhance predictive accuracy. Model performance was evaluated using five-fold cross-validation, where the optimized PSO-GBM model achieved an average RMSE of 1.09 and an R2 value of 0.947, outperforming conventional GBM as well as Random Forest, Support Vector Regression, Artificial Neural Networks, and Linear Regression models. Variable importance and sensitivity analyses revealed that Layer 3 thickness, pavement age, annual average daily traffic, and precipitation play dominant roles in punchout development. The consistency of residual distributions and the stability of hyperparameter sensitivity trends further confirm the robustness of the proposed framework. Overall, the results demonstrate that integrating evolutionary optimization with ensemble learning provides an effective tool for modeling complex pavement distresses and offers practical support for proactive maintenance planning and long-term management of CRCP infrastructure.

Modelling doi: 10.3390/modelling7010037

Authors: Yulong Qiu Weimin Xu Wangqiang Niu

Addressing the challenge of balancing high-precision positioning with strict safety constraints for underactuated bridge cranes subject to model parameter mismatch and stochastic wind disturbances, an adaptive hybrid control framework is presented integrating a Safety-Aware Dynamic Gain Sliding Mode Controller (DG-SMC) with a TD3-based residual deep reinforcement learning network. By designing a gain scheduling mechanism based on swing angle amplitude, the proposed method physically limits trolley acceleration to strictly constrain the payload swing angle within a safe range (±7°). Simultaneously, a TD3 agent is introduced as a residual compensator to adaptively learn system dynamics through environmental interaction, generating real-time compensatory control forces to counteract unmodeled dynamics arising from system parameter deviations and continuous wind resistance. Numerical simulations demonstrate that, under conditions involving payload mass deviations of up to 25% and stochastic wind disturbances, the proposed control method effectively reduces steady-state positioning errors, suppresses payload swing during operation, and significantly enhances the system’s energy dissipation efficiency and global robustness in uncertain environments.

Modelling doi: 10.3390/modelling7010036

Authors: Stefan-Dan Pastrama

Many structures use stiffeners to improve their strength and stability and especially to stop the growth of cracks that can appear during the manufacturing process or in service. The most used stiffeners have rectangular cross-sections, other shapes being less used to strengthen mechanical structures. A numerical study of cracked aluminum plates reinforced with different types of stiffeners is presented in this paper to study the influence of different types of stringers on the structural integrity of the plates. Continuously attached stiffeners with rectangular, L- and T-shaped cross-sections are considered in two variants: with the stiffener broken and unbroken. A numerical model is developed and validated by comparing the obtained results with those calculated using the compounding method. It is shown that an important variation in the stress intensity factor occurs though the thickness of the plate and that stiffeners with the same area yield approximately the same average values of the stress intensity factor. However, the shape of the stiffeners influences the maximum stress intensity factors, which are responsible for the crack growth. Conclusions are drawn about the shape that provides a longer lifetime and higher critical stresses at which catastrophic failure may occur.

Modelling doi: 10.3390/modelling7010035

Authors: Gerardo Hurtado-Hurtado Tania Elizabeth Sandoval-Valencia Luis Morales-Velázquez Juan Carlos Jáuregui-Correa

Condition monitoring of railway track surfaces is crucial for ensuring the safety, operational efficiency, and effective maintenance of railway systems. This work presents a data-driven modelling and an experimental methodology for identifying and classifying contaminants on railway tracks using vibration analysis and artificial intelligence techniques. In this study, the railway dynamics were physically simulated using a 1:20 scaled test rig, where the rails were treated with various contaminants (oil, water, and sand), and the resulting vehicle vibrations were recorded by on-board accelerometers and gyroscopes. To construct the predictive model, a hybrid architecture was designed integrating Short-Time Fourier Transform (STFT) for time-frequency feature extraction and a multi-channel Convolutional Neural Network (CNN) for pattern recognition. Initial results indicate that accelerometer data, particularly from longitudinal and lateral vibrations, are more effective than gyroscope data for classifying certain contaminants. To enhance classification robustness, this work introduces a multi-channel CNN that simultaneously processes the most informative signals, leading to a significant improvement in detection accuracy across all tested contaminants. This study validates the effectiveness of the proposed methodology as a robust and reliable solution for contaminant detection, while also confirming the utility of the scaled testbed as a valuable platform for future research in railway dynamics.

Modelling doi: 10.3390/modelling7010034

Authors: Wenkui Xi Luyu Chen Wei Tian Xiongxiong Wang Shuqin Xiao Yanbin Li

A twin-screw multiphase pump is essential equipment for the transfer of gas-liquid multiphase mixtures in oil and gas operations. This work addresses rotor deformation in real applications by correcting the rotor profile using the arc transition approach, eliminating teeth tips, mitigating local stress concentration, and reducing the danger of rotor deformation. Simultaneously, in conjunction with the oil and gas mixed transportation requirements of the Changqing Oilfield, the MPC208-67 twin-screw mixed transportation pump was engineered, and the essential structural specifications were established. This paper employs the Mixture multiphase flow model and the SST k-ω turbulence model to simulate the internal flow field of the pump in Changqing Oilfield, aiming to examine the impact of high-gas-content conditions on the pump’s performance and ensure it aligns with design specifications. The modeling findings indicate that the pressure in the pump progressively rises along the axial direction and remains constant within the chamber. As the void fraction of the medium increases, the pressure differential between the inlet and exit of the rotor fluid domain progressively diminishes, resulting in high-velocity fluid emerging in the interstice between driving and driven rotors. The simultaneous increase in rotational speed elevates the overall fluid velocity while diminishing the pressure value. Under rated conditions, the output pressure and flow rate of the planned multiphase pump achieve 1.8 MPa and 300 m3/h, respectively, thereby fully satisfying the design specifications. This work employs the response surface approach to optimize multi-objective performance parameters, including leakage and pressurization capacity, to enhance the pump’s operational performance under high gas content situations. The optimization results indicate a 17.87% reduction in pump leakage, an 8.86% rise in pressurization capacity, and a substantial enhancement in pump performance.

Modelling doi: 10.3390/modelling7010033

Authors: Baoding Wang Qing Zhang Qingfen Ma Zhongye Wu Yilong Sun Jingru Li Hui Lu

The liquid oxygen subcooler is a key unit for the deep cooling, storage, and transportation of liquid oxygen. Its frequent start–stop operation under liquid nitrogen bath conditions introduces potential risks to service reliability. This study employs a thermo-structural sequential coupling approach to evaluate the stress behavior of ABS components in a flat plate-fin heat exchanger during the pre-cooling, heat-exchange, and recovery stages. Based on the maximum shear stress (Tresca) criterion, the evolution of principal stresses in the brazed layer under liquid nitrogen bath conditions was analyzed, and a conservative assessment of the material’s fatigue behavior was conducted. The results indicate that the equivalent stress is governed by the third principal stress, originating from the thermal compression effect induced by low-temperature constraint shrinkage. During the heat exchange phase (2700 s), the inlet equivalent stress reached 93.49 MPa, which is below the 258 MPa limit, falling within Region 1. Local stress concentration is primarily driven by thermal loading, with brazing layer thickness, curvature radius, and liquid oxygen pressure serving as key control variables. Under a safety factor of 1.15 (107 MPa), fatigue testing exceeding 1.5 million cycles has confirmed the static safety and operational reliability of the ABS.

Modelling doi: 10.3390/modelling7010032

Authors: Bomao Zhou Jin Tang Fan Guo

Laser Doppler vibrometer (LDV) has the characteristics of long-distance, non-contact, and high sensitivity, and plays an increasingly important role in industrial, military, and security fields. Remote speech acquisition technology based on LDV has progressed significantly in recent years. However, unlike microphone receivers, LDV-captured signals have severe signal distortion, which affects the quality of the LDV-captured speech. This paper proposes a nested U-network with gated temporal convolution (TCNUNet) to enhance monaural speech based on LDV. Specifically, the network is based on an encoder-decoder structure with skip connections and introduces nested U-Net (NUNet) in the encoder to better reconstruct speech signals. In addition, a temporal convolutional network with a gating mechanism is inserted between the encoder and decoder. The gating mechanism helps to control the information flow, while temporal convolution helps to model the long-range temporal dependencies. In a real-world environment, we designed an LDV monitoring system to collect and enhance voice signals remotely. Different datasets were collected from various target objects to fully validate the performance of the proposed network. Compared with baseline models, the proposed model achieves state-of-the-art performance. Finally, the results of the generalization experiment also indicate that the proposed model has a certain degree of generalization ability for different languages.

Modelling doi: 10.3390/modelling7010031

Authors: Chongming Wang Sujun Gu Bo Yang Yuan Cao

Urban sustainability heavily relies on efficient transportation systems, with dynamic bus lanes (DBL) being crucial components. However, traditional DBLs often face underutilization, leading to inefficient road usage. To this end, a novel IoT-Enabled Dynamic Bus Lane System (IoT-DBL) has been proposed, aimed at improving road utilization and reducing vehicle energy consumption. To assess the effectiveness of IoT-DBL, we developed a Markov chain-based queuing model and established a comprehensive evaluation framework through various performance metrics. Theoretical analysis reveals that the IoT-DBL system significantly improves intersection efficiency and reduces vehicle fuel consumption. Further optimization using a genetic algorithm (GA) identifies the optimal deployment length of IoT-DBLs to minimize fuel consumption. Numerical experiments demonstrate that the IoT-DBL strategy significantly outperforms traditional DBL methods, reducing queue lengths by 71.15%, vehicle delays by 69.48%, and fuel consumption by 70.42%, while increasing intersection efficiency by 100.11%. These results highlight that the IoT-DBL system can substantially improve traffic conditions, alleviate congestion, decrease fuel consumption, and enhance overall intersection efficiency, thereby providing a promising solution for sustainable urban transportation.

Modelling doi: 10.3390/modelling7010030

Authors: Elmira Nazirova Abdugani Nematov Gulstan Artikbaeva Shikhnazar Ismailov Marhabo Shukurova Asliddin R. Nematov Marks Matyakubov

This study introduces a mathematical framework for analyzing unsteady gas filtration in porous media with pressure-dependent porosity variations. The physical process is formulated as a nonlinear parabolic boundary value problem that captures the coupled interaction between pressure evolution and porosity changes during gas production. To solve the equation, a numerical strategy is developed by integrating the Alternating Direction Implicit (ADI) scheme with quasi-linearization iterations, employing finite difference discretization on a two-dimensional spatial grid. Extensive computational experiments are performed to investigate the influence of key reservoir parameters—including porosity coefficient, permeability, gas viscosity, and well production rate—on the spatiotemporal behavior of pressure and porosity during long-term extraction. The results indicate significant porosity variations near the wellbore driven by local pressure depletion, reflecting strong sensitivity of the system to formation properties. The validated numerical model provides valuable quantitative insights for optimizing reservoir management and improving production forecasting in gas field development. Overall, the proposed methodology serves as a practical tool for oil and gas engineers to assess long-term reservoir performance under diverse operational conditions and to design efficient extraction strategies that incorporate pressure-dependent formation property changes.

Modelling doi: 10.3390/modelling7010029

Authors: Liang Hong Haoran Song Lipu Zhang Xinyu Wang

In high-precision optical systems such as laser optics, astronomical observation, and semiconductor lithography, anti-reflection coatings are crucial for light transmittance, imaging quality, and stability, but traditional designs face modeling challenges in balancing ultralow reflectivity, high wavefront quality, and manufacturability amid multi-dimensional parameter coupling and multi-objective constraints. This study addresses these by proposing a unified mathematical modeling framework integrating a Symmetric five-layer high-low refractive index alternating structure (V-H-V-H-V) with dual-scale nanostructures, employing a constrained quasi-Newton optimization algorithm (L-BFGS-B) to minimize reflectivity, wavefront root-mean-square (RMS) error, and surface roughness root-mean-square (RMS) in a six-dimensional parameter space. The Sellmeier equation is adopted to calculate wavelength-dependent material refractive indices, the model uses the transfer matrix method for the Symmetric five-layer high-low refractive index alternating structure’s reflectivity, incorporates nano-surface height function gradient correction, sub-wavelength modulation, and radial optimization, applies Zernike polynomials for low-order aberration correction, quantifies surface roughness via curvature proxies, and optimizes via a weighted objective function prioritizing low reflectivity. Numerical results show the spatial average reflectivity at 632.8 nm reduced to 0.13%, the weighted average reflectivity across five representative wavelengths in the 550–720 nm range to 0.037%, the reflectivity uniformity to 10.7%, the post-correction wavefront RMS to 11.6 milliwavelengths, and the surface height standard deviation to 7.7 nm. This framework enhances design accuracy and efficiency, suits UV nanoimprinting and electron beam evaporation, and offers significant value for high-power lasers, lithography, and space-borne radars.

Modelling doi: 10.3390/modelling7010028

Authors: Paulino José García-Nieto Esperanza García-Gonzalo José Pablo Paredes-Sánchez Luis Alfonso Menéndez-García

In energy production systems, the higher heating value (HHV), also known as the gross calorific value, is a key parameter for identifying the primary energy source. In this study, a novel artificial intelligence model was developed using support vector machines (SVM) combined with the Differential Evolution (DE) optimizer to predict coal gross calorific value (the dependent variable). The model incorporated the elements from coal ultimate analysis—hydrogen (H), carbon (C), oxygen (O), sulfur (S), and nitrogen (N)—as input variables. For comparison, the experimental data were also fitted to previously reported empirical correlations, as well as Ridge, Lasso, and Elastic-Net regressions. The SVM-based model was first used to assess the influence of all independent variables on coal HHV and was subsequently found to be the most accurate predictor of coal gross calorific value. Specifically, the SVM regression (SVR) achieved a correlation coefficient (r) of 0.9861 and a coefficient of determination (R2) of 0.9575 for coal HHV prediction based on the test samples. The DE/SVM approach demonstrated strong performance, as evidenced by the close agreement between observed and predicted values. Finally, a summary of the results from these analyses is presented.

Modelling doi: 10.3390/modelling7010027

Authors: Changjun Zou Hui Luo

The Fluid Implicit Particle (FLIP) method is widely adopted in fluid simulation due to its computational efficiency and low dissipation. However, its high computational complexity makes it challenging for traditional CPU architectures to meet real-time requirements. To address this limitation, this work migrates the FLIP method to the GPU using the CUDA framework, achieving a transition from conventional CPU computation to large-scale GPU parallel computing. Furthermore, during particle-to-grid (P2G) mapping, the conventional scattering strategy suffers from significant performance bottlenecks due to frequent atomic operations. To overcome this challenge, we propose a GPU parallelization strategy based on spatial hashing indexing and thread block-level cooperation. This approach effectively avoids atomic contention and significantly enhances parallel efficiency. Through diverse fluid simulation experiments, the proposed GPU-parallelized strategy achieves a nearly 50× speedup ratio compared to the conventional CPU-FLIP method. Additionally, in the P2G stage, our method demonstrates over 30% performance improvement relative to the traditional GPU-based particle-thread scattering strategy, while the overall simulation efficiency gains exceeding 20%.

Modelling doi: 10.3390/modelling7010026

Authors: Thanrada Chaikajonwat Autcha Araveeporn

Accurate passenger traffic forecasting is vital for strategic planning in Thailand’s aviation industry. This study forecasts the monthly total number of passengers at Suvarnabhumi (BKK), Don Mueang (DMK), Chiang Mai (CNX), and Phuket (HKT) airports using data from 2017 to 2024. The dataset was partitioned into training (January 2017–December 2023) and testing (January–December 2024) sets. Six methods were compared: Single Exponential Smoothing, Holt’s, Holt’s with Events Adjustment, Holt–Winters Multiplicative, TBATS model, and Box–Jenkins. Performance was evaluated using Mean Absolute Percentage Error (MAPE) and Mean Absolute Error (MAE). The results indicate that the optimal forecasting method varies by airport characteristics. Holt’s Method with Events Adjustment, which incorporates major disruptions such as the COVID-19 pandemic, produced the most accurate forecasts for BKK and DMK by effectively capturing external shocks. In contrast, the Holt–Winters Multiplicative method performed best for CNX and HKT, reflecting strong seasonal patterns typically driven by tourism activities in these destinations.

Modelling doi: 10.3390/modelling7010025

Authors: Georgi Todorov Konstantin Kamberov Konstantin Dimitrov

The study is dedicated to the accuracy of engineering analyses of virtual prototypes. In particular, it aims to quantify the importance of material models and data consistent with physical tests. The focus is set on the stress–strain material characteristic that is the basis for correct simulation results, and the deviations of its parameters—elasticity module and yield stress—that are assessed. This is performed in three main steps: laboratory measurement of the material properties of a sample material (aluminum alloy), followed by an engineering analysis of a component produced from the same material, using the determined mechanical characteristics. The third step involves physical tests used to validate the virtual prototyping results by comparing them with the physical test results. The material properties used in the virtual prototype are subjected to a sensitivity analysis to determine their influence on the design’s elastic and plastic behavior. The main conclusions of the study are the importance of these material characteristics for achieving an adequate result. A general recommendation is formed that shows the importance of laboratory testing of material properties before virtual prototyping to avoid any influence of factors as production technology or geometry (specimen thickness).

Modelling doi: 10.3390/modelling7010024

Authors: Wenhao Fu Shenghan Luo Chi Cao Leyi Shi Juan Wang

Self-cleansing intrusion-tolerant systems mitigate attacker intrusions and control through periodic recovery, thereby enhancing both availability and security. However, vulnerabilities in the control link render these systems susceptible to request forgery attacks. Furthermore, existing research on the modeling and performance analysis of such systems remains insufficient. To address these issues, this paper introduces an authentication mechanism to fortify control link security and employs Generalized Stochastic Petri Nets for system evaluation. We constructed Petri net models for three distinct scenarios: a traditional system, a system compromised by forged controller requests, and a system fortified with authentication mechanism. Subsequently, isomorphic Continuous-Time Markov Chains were derived to facilitate theoretical analysis. Quantitative evaluations were performed by deriving steady-state probabilities and conducting simulations on the PIPE platform. To further assess practicality, we conduct scalability analysis under varying system scales and parameter settings, and implement a prototype in a virtualized testbed to experimentally validate the analytical findings. Evaluation results indicate that authentication mechanism ensures the reliable execution of cleansing strategies, thereby improving system availability, enhancing security, and mitigating data leakage risks.

Modelling doi: 10.3390/modelling7010023

Authors: Mingxuan Zhang Yituan Yu Shengkun Li Yan Liu Yingshuai Zhang Rui Zhang Sujie Shao

Software-defined (SD) honeypots, as dynamic cybersecurity technologies, enhance defense efficiency through flexible resource allocation. However, traditional SD honeypots face latency and jitter issues under network fluctuations, while balancing adjustment costs with defense benefits remains challenging. This paper proposes a DPU-accelerated SD honeypot security service deployment method, leveraging DPU hardware acceleration to optimize network traffic processing and protocol parsing, thereby significantly improving honeypot environment construction efficiency and response real-time performance. For dynamic attack–defense scenarios, we design an adaptive adjustment strategy combining Stackelberg game theory with deep reinforcement learning (AASGRL). By calculating the expected defense benefits and adjustment costs of optimal honeypot deployment strategies, the approach dynamically determines the timing and scope of honeypot adjustments. Simulation experiments demonstrate that the mechanism requires no adjustments in 80% of interaction rounds, while achieving enhanced defense benefits in 20% of rounds with controlled adjustment costs. Compared to traditional methods, the AASGRL mechanism maintains stable defense benefits in long-term interactions, verifying its effectiveness in balancing low costs and high benefits against dynamic attacks. This work provides critical technical support for building adaptive proactive network defense systems.

Modelling doi: 10.3390/modelling7010022

Authors: Changjun Zou Jia Yu

Fluid–structure coupling is a prominent and hot topic in computer graphics and virtual reality. The hybrid technique known as FLIP combines the benefits of grid-based and particle-based techniques. Nevertheless, a significant problem is figuring out how to accomplish fluid–structure coupling interaction based on the FLIP technique framework. We propose an immersed boundary approach to handle the problem of realistic fluid–structure coupling interaction under the FLIP framework. The benchmark test results demonstrate that, in addition to producing rich fluid–structure coupling interaction results, our novel technique also effectively reflects the effects of moving obstacle boundaries on the flow and pressure fields, thereby expanding the application area of the FLIP method.

Modelling doi: 10.3390/modelling7010021

Authors: Hu Yin Hongzhuo Yan Chunzhu Chen

Controlling bottom hole pressure (BHP) during tripping-out is a key challenge in ultra-deep well drilling. Under high-temperature and high-pressure (HTHP) conditions, ultra-deep wells feature long tripping-out cycles, where thermal effects are prone to causing BHP reduction and increasing kick risk. However, existing pressure control technologies struggle to adapt to the requirements of narrow safe density windows in deep formations. This study establishes a transient tripping-out temperature field model, taking the PS6 ultra-deep vertical well as a case study to calculate the variations in temperature, equivalent static density (ESD), and BHP during tripping-out at 2910 m and 9026 m. A weighted drilling fluid supplementation method is presented, with supplementary parameters designed and its feasibility verified. The results indicate that during the entire tripping-out process, the bottom hole temperature at 2910 m increases by 17.5 °C and BHP rises by 0.016 MPa; at 9026 m, the temperature increases by 72.6 °C and BHP decreases by 2.410 MPa. Compared with the traditional “heavy mud cap” technology, the presented method can control BHP within a smaller fluctuation range (within 0.339 MPa) during tripping-out, better adapting to the safe tripping requirements of narrow safe density windows in deep formations and effectively mitigating kick risk.

Modelling doi: 10.3390/modelling7010020

Authors: Shangming Mei Yihua Hu Mohammad Nasr Esfahani

Phased array speakers are often designed with uniform element spacing, which limits beam steering capability and sidelobe control under practical aperture and hardware constraints. This study presents an optimization-driven modelling framework for parametric array loudspeakers (PALs) that systematically links array layout synthesis with high-fidelity directivity prediction, by combining a frequency-domain convolution model with a finite element method (FEM) pipeline. We formulate array layout synthesis as a constrained optimization problem and employ particle swarm optimization (PSO) to determine non-uniform element positions that suppress sidelobes while preserving mainlobe integrity across steering angles. By integrating linear acoustic field simulation with far-field directivity prediction, the framework serves as a computationally efficient surrogate model suitable for iterative design under non-ideal spacing conditions. Simulation results and laboratory measurements demonstrate that the optimized non-uniform arrays achieve consistently lower sidelobe levels and more concentrated mainlobes than conventional uniform configurations. These results validate the proposed framework as a practical and reproducible solution for steering-capable PAL design when the conventional λ/2 spacing constraint cannot be satisfied and establish a foundation for subsequent robustness and sensitivity analyses.

Modelling doi: 10.3390/modelling7010019

Authors: Rui Wang Jiabin Dong Wenhao Dong

The accurate evaluation of the Joint Roughness Coefficient (JRC) is crucial for rock mechanics engineering. Existing JRC prediction models based on a single fractal parameter often face limitations in physical consistency and predictive accuracy. This study proposes a novel two-parameter JRC prediction method based on fractal topology theory. The core innovation of this method lies in extracting two distinct types of information from a roughness profile: the scale-invariant characteristics of its frequency distribution, quantified by the Hurst exponent (H), and the amplitude-dependent scale effects, quantified by the coefficient (C). By integrating these two complementary aspects of roughness, a comprehensive predictive model is established: JRC = 100.014H−1.5491C1.2681. The application of this model to Atomic Force Microscopy (AFM)-scanned coal rock surfaces indicates that JRC is primarily controlled macroscopically by amplitude-related information (reflected by C), while the scale-invariant frequency characteristics (reflected by H) significantly influence local prediction accuracy. By elucidating the distinct roles of scale-invariance and amplitude attributes in controlling JRC, this research provides a new theoretical framework and a practical analytical tool for the quantitative evaluation of JRC in engineering applications.

Modelling doi: 10.3390/modelling7010018

Authors: Zhenrong Liu Jiazhen Liu Zhuo Zeng Hong Shi

This study addresses the thermal management challenges of marine gas turbine enclosures by proposing an innovative optimization of the air intake design, enhancing thermal management capabilities without mechanical restructuring. Through Computational Fluid Dynamics (CFD), the research systematically optimizes key parameters including cooling air inlet pressure, positioning, and enclosure inlet diameter. The results demonstrate that elevating the cooling air inlet pressure to 300 Pa enhanced the entrainment ratio (η) by 9.55% and increased the pressure loss coefficient (PLC) by 2.06% compared to the baseline case (Pin = 0 Pa). An enclosure inlet diameter of 1100 mm optimizes entrainment efficiency (η = 0.331) and minimizes internal temperatures. The multi-objective optimization identifies the globally optimal configuration (D = 800 mm, Pin = 300 Pa, L = 1.6 m), which improves the entrainment ratio by 31.7% (η = 0.399) and reduces the average temperature at key monitoring points (T1–T5) by up to 14 K compared to the baseline, albeit with a marginal increase in PLC. This optimal configuration ensures that all local temperatures remain within the operational limit of 355 K. This research provides a theoretical foundation for enhancing marine power system performance and offers evidence-based guidance for engineering applications.

Modelling doi: 10.3390/modelling7010017

Authors: Manuel G. Satué Juana M. Martínez-Heredia José L. Mora

The Finite State Model Predictive Control (FSMPC) of variable speed drives is the subject of many works in the recent literature. Many variants of FSMPC exist, each aiming at an aspect such as the complexity of the cost function, switching frequency, current quality, etc. In the case of multiphase drives, two popular variants are the monovector and multivector techniques. Despite past efforts to compare different techniques, the field must still reach a consensus regarding the relative merits of each one. This paper presents a new method to compare two families of FSMPC. The method is based on a reduced set of figures of merit using the current modulation index as the variable. The comparison is made for the equal usage of the power converter in terms of commutations. The results point to better values for the figures of merit for the monovector that, in addition, portrays more flexibility and better DC link usage.

Modelling doi: 10.3390/modelling7010016

Authors: Yuguo Yu David Gardiner Jie Sun Kiru Pasupathy

Metakaolin (MK) obtained from calcined kaolinitic clay is a highly reactive pozzolanic ingredient for use as an emerging supplementary cementitious material (SCM) in modern sustainable binder productions. It provides elevated alumina to promote formations of Alumina Ferrite Monosulfate (AFm) and Calcium-Aluminium-Silicate-Hydrate (C-A-S-H) phases, enhancing the chloride binding capacity. However, due to inherent material uncertainty and lack of approach in quantifying hydration kinetics and chloride binding capacity across varied mixes, robustly assessing the chloride resistance of metakaolin-blended concrete remains challenging. In light of this, a machine learning-aided framework that encompasses physics-based material characterisation and ageing modelling is developed to bridge the knowledge gap. Through applying to laboratory experiments, the impacts of uncertainty on the phase assemblage of hydrated system and chloride penetration are quantified. Moreover, the novel Extended Support Vector Regression (XSVR) method is incorporated and verified against a crude Monte Carlo Simulation (MCS) to demonstrate the capability of achieving effective and efficient uncertainty-aware chloride resistance analyses. With the surrogate model established using XSVR, quality control of metakaolin towards durable design optimisation against chloride-laden environments is discussed. It is found that the fineness and purity of adopted metakaolin play important roles.

Modelling doi: 10.3390/modelling7010015

Authors: Ali Al-Darraji Christopher Lagat Ibukun Oluwoye

Accurate prediction of erosion rates in polymeric and composite materials is essential for their effective design and maintenance in diverse industrial environments. This study presents a predictive modelling framework developed using the JMP Pro machine learning integrated system to estimate erosion rates of polymers and polymer composites. For better model generalisation under various conditions, a curated dataset was compiled from peer-reviewed literature, standardised, and subjected to outliers and multivariate exploratory data analysis to identify dominant variables. The model utilises key input parameters, including impact angle, impact velocity, sand content, particle size, material type, and fluid medium, to predict the erosion rate as the target output variable. Six machine learning algorithms were evaluated through a systematic model comparison process, and two were selected. Model performance was assessed using robust error metrics, and the interpretability of erosion behaviour was validated through prediction profilers and variable importance analyses. Artificial Neural Network (ANN) and Extreme Gradient Boosting (XGBoost) demonstrated the best training and validation performance based on the evaluation metrics. While both models yielded high training performance, the ANN model demonstrated superior predictive accuracy and generalisation capability across a broad range of conditions. Beyond prediction, the model outputs also showed a meaningful representation of the influence of input variables on erosion rates.

Modelling doi: 10.3390/modelling7010014

Authors: Pieter Marx Henri Marais

Background: A patient’s lung condition can be estimated using mechanical ventilation waveform data. These procedures are often labour-intensive and error-prone, especially during large-scale health crises, leading to infrequent executions. Automated diagnostic techniques in healthcare are currently limited by the lack of large, labelled datasets required for effective machine learning applications. Analytical modelling of the mechanical ventilator-patient (MV-P) system is complex, and existing models fail to fully integrate adjustable parameters for patient, ventilation, and disease conditions. Methods: This article presents an expanded system model developed in MATLAB® Simulink®. The model accommodates adjustments to anthropometric parameters, ventilator settings for the three most common modes in ICU sedation, and disease progression simulations. Other uniquely combined aspects include the ability to perform an end-inspiratory hold manoeuvre and per-breath optimisation of PI control parameters. Results: The system has been validated against clinical techniques, compared to real-world data, and verified with accuracy within 3% and average normalised standard deviation of 3.4% for all adjustable parameters. Conclusions: Based on this model, which introduces high-fidelity disease progression modelling, a fully labelled synthetic dataset of nearly 2M breaths over a range of health conditions was generated. This addresses the critical shortage of labelled data needed for developing early proof-of-concept, resource-efficient diagnostic tools for automatically estimating lung conditions.

Modelling doi: 10.3390/modelling7010013

Authors: Ali Saberi Varzaneh Mahmood Naderi

Resistance against water penetration is one of the key indicators of concrete durability in humid and pressurized environments. An intelligent model based on the XGBoost machine-learning algorithm was developed to predict the water penetration depth, using 1512 independent experimental measurements. The influential variables included water pressure, pressure duration, thermal cycles, fiber content, curing, and compressive strength. The investigated concrete specimens and field-tested structures in this study were exposed to arid and hot climatic conditions, and the proposed model was developed within this environmental context. To accurately simulate the water transport behavior, a cylindrical-chamber test was employed, enabling non-destructive and in-situ evaluation of structures. Correlation analysis revealed that compressive strength had the strongest negative influence (r = −0.598), while free curing exhibited the strongest positive influence (r = +0.654) on penetration depth. After hyperparameter optimization, the XGBoost model achieved the best performance (R2 = 0.956, RMSE = 1.08 mm, MAE = 0.81 mm). Feature importance analysis indicated that penetration volume, pressure, and curing were the most significant predictors. According to the partial dependence analysis, both pressure and duration exhibited an approximately linear increase in penetration depth, while a W/C ratio below 0.45 and curing markedly reduced permeability. Microstructural interpretation using MIP, XRD, and SEM tests supported the physical interpretation of the trends identified by the machine-learning model. The results demonstrate that machine-learning-models can serve as fast and accurate tools for assessing durability and predicting permeability under severe environmental conditions. Finally, the permeability of several real structures was evaluated using the machine-learning approach, showing excellent prediction accuracy.

Modelling doi: 10.3390/modelling7010012

Authors: Yu Shen Xiaojue Xue Xinyi Chen Chaoliu Tong Shixiong Fang Kanjian Zhang Haikun Wei

Parametrization of photovoltaic (PV) modules makes an important foundation for monitoring and fault diagnosis. This work focus on the sensitivity of parameters for the single-diode model (SDM), which fills the gap in existing research. The sensitivity analysis in this work provides a fundamentally new perspective on understanding parameter robustness as well as the prior knowledge for the parameter identification method. Based on insights into the sensitivity analysis, a novel parameter identification method is proposed, which combines analytical expressions with the grid search algorithm. The proposed method reduces the relative error of the extracted parameters in the simulated dataset, and the quantitative improvement of the reverse saturation current is significant (12.6% average reduction). This method achieves the state-of-the-art overall performance in the measured dataset, and the Friedman test confirms that this improvement is statistically significant (p < 0.05). The transition capability of the proposed method is excellent under varying operating conditions, which implies that it has the potential to be applied to the intelligent operation and maintenance of photovoltaic systems.

Modelling doi: 10.3390/modelling7010011

Authors: Sampath Liyanarachchi Geoff Rideout

This paper presents a simulation-based artificial neural network (ANN) model to predict bit-rock interaction forces during drilling. Drill string vibration poses a significant challenge in the oil, gas, and geothermal industries, leading to non-productive time and substantial financial losses. This research addresses the challenge of modelling bit-rock interaction excitation forces, which is crucial for predicting vibration and component fatigue life. For a PDC bit with multiple cutters, the cutter tangential velocities at various drilling speeds are calculated, and individual cutter forces are predicted with a two-dimensional discrete element method simulation in which a single cutter moves in a straight line through rock modelled as bonded particles. This data is then used to train an ANN model that characterizes the bit-rock force time series in terms of frequency, amplitude, and distribution of force peaks. Once inserted into a dynamic simulation of the drill string, the algorithm reconstructs the expected bit-rock force time series. A case study using a rigid segment axial and torsional drill string model was used to show that the bit-rock model outputs lead to the expected bit-bounce and stick-slip under certain drilling conditions. Next, the model was implemented in a 3D deviated well drill string simulation with non-linear friction and contact, generating complex stress states with good computational efficiency.

Modelling doi: 10.3390/modelling7010010

Authors: Eduardo Conde López Jesús Flores Escribano Eduardo Salete Casino Antonio Vargas Ureña

This paper presents a finite element methodology for generating continuous digital elevation models (DEMs) from discrete terrain data using the Poisson equation under steady-state conditions. Unlike conventional DEM interpolation techniques, the proposed methodology formulates terrain reconstruction as a constrained harmonic problem, solved directly on scattered point sets using standard finite element procedures, without requiring structured grids or intermediate interpolation stages. The approach interprets the elevation field as a harmonic scalar function whose smoothness is enforced by the variational formulation of the Poisson problem. The governing equation is solved using standard finite element procedures with Dirichlet boundary conditions applied at the measurement points, ensuring that the reconstructed surface passes exactly through the known elevations. The isotropic conductivity coefficient is set to unity and the source term to zero, which simplifies the formulation and yields a harmonic interpolation independent of any physical parameters. The resulting surfaces exhibit continuous slopes and reduced sensitivity to irregular data distributions. Numerical tests comprising two analytical examples and a real terrain case show that, compared with thin-plate FEM and RBF–NURBS reconstructions, the proposed Poisson-based approach yields smoother and more stable surfaces, with global errors of the same order of magnitude and reduced computational cost.

Modelling doi: 10.3390/modelling7010009

Authors: Yajie Luo Jin Jin Kaiqiang Geng Lei Zhou Yu Qiao Yifan An Yajie Cui Xiaodong Wang

Under long-term dynamic water pressure, weld zones in vertical shaft pressure-bearing steel pipes are prone to cracking induced by welding residual stresses (WRSs), which may further propagate and threaten structural safety. This study investigates the effects of initial crack angle and position on crack tip stress and propagation path under the influence of WRSs. Using the XFEM combined with a DFLUX-based thermomechanical simulation, a numerical model of crack growth in vertical shaft steel pipes is developed. Results indicate that increasing the initial crack angle raises the stress intensity factor, while crack-tip residual stress initially increases and then decreases, reaching a maximum value of 457.9 MPa when the initial crack angle is 30°. When WRSs are considered, localized stress concentration at the crack tip intensifies, leading to higher stress, stress amplitude, and stress intensity factor, with the amplitude peaking at 365.49 MPa. Moreover, cracks located outside the weld exhibit higher stress intensity factors than those inside. Overall, WRS, crack angle, and crack location all contribute to crack propagation, with crack angle being the dominant factor. Cracks within welds and oriented between 15° and 45° exhibit a significantly higher likelihood of propagation. These findings aid in identifying hazardous crack scenarios and provide guidance for the operation and monitoring of pressure pipelines.

Modelling doi: 10.3390/modelling7010008

Authors: Mohammed Chatbi Silva Lozančić Zouaoui R. Harrat Marijana Hadzima-Nyarko

The integration of silica nanoparticles (NS) into cementitious composites has emerged as a promising strategy to refine the microstructure and enhance concrete performance. Beyond their chemical role in accelerating hydration and promoting additional C–S–H gel formation, silica nanoparticles act as physical fillers, reducing porosity and improving interfacial bonding within the matrix. These dual effects result in a denser and more resilient composite, whose mechanical and dynamic responses differ from those of conventional concrete. However, studies addressing the vibrational and modal behavior of nano-reinforced concretes, particularly under elastic and viscoelastic foundation conditions, remain limited. This study investigates the dynamic response of NS-reinforced concrete slabs using a refined quasi-3D plate deformation theory with five (05) unknowns. Different foundation configurations are considered to represent various soil interactions and assess structural integrity under diverse supports. The effective elastic properties of the nanocomposite are obtained through Eshelby’s homogenization model, while Hamilton’s principle is used to derive the governing equations of motion. Navier’s analytical solutions are applied to simply supported slabs. Quantitative results show that adding 30 wt% NS increases the Young’s modulus of concrete by about 26% with only ~1% change in density; for simply supported slender slabs, this results in geometry-dependent increases of up to 18% in the fundamental natural frequency. While the Winkler and Pasternak foundation parameters reduce this frequency, the damping parameter of the viscoelastic foundation enhances the dynamic response, yielding frequency increases of up to 28%, depending on slab geometry.

Modelling doi: 10.3390/modelling7010007

Authors: Huifang Lan Xiaoying Hui Jiangbo Du Shuai Tang Linxiu Du

A semi-analytical mixed-control model based on the Non-Partitioned Local Equilibrium (NPLE) assumption was developed to simulate the austenite phase transformation kinetics during heating and isothermal processes. The model was validated by comparing the simulation results with experimental data, showing excellent agreement. The effects of various model parameters and process conditions on the phase transformation kinetics was investigated. The results indicate that higher heating rates lead to an increase in the austenite volume fraction at the start of the isothermal hold, accelerating the transformation and resulting in a more complete phase transformation. The transformation during the isothermal stage was found to follow a mixed control mode at all investigated heating rates. Increasing the mobility coefficient enhances interface migration, thereby accelerating the transformation kinetics, while decreasing the grain size promotes nucleation, further accelerating the phase transformation. Modifying the diffusion coefficient had a minor effect on transformation kinetics. Additionally, raising the isothermal temperature increased both the austenite volume fraction at the beginning and end of the isothermal process and the interface migration velocity, suggesting that temperature dominates the phase transformation rather than time. The phase transformation mode under different process conditions was also investigated. For both 5 °C/s and 100 °C/s heating rates, the phase transformation during the isothermal process was predominantly interface-controlled, as indicated by the mixed-mode parameter approaching 1, with a rapid increase followed by a decrease.

Modelling doi: 10.3390/modelling7010006

Authors: Wei-Chin Chang Masjudin

ANSYS-Fluent was applied to simulate diffusion combustion flame in a two-dimensional (2D) industrial burner to determine the contours of the mass fraction of gas emissions, velocity, and combustion temperature. The effects of the boundary conditions, including momentum, thermal, and species (inlet air, inlet fuel, and outlet pressure) on combustion temperature and mass fraction (gas emissions) were analyzed in the designed burner. The present study focused on using and analyzing the volumetric reaction and the turbulence-chemistry interaction of the eddy dissipation model for the diffusion flame model. The simulation used the discrete ordinate model and p1 for radiation and the k-ε model for turbulence with enhanced wall treatment. Based on the results, the magnitude velocities of air and fuel, inlet temperature, and mass fractions of oxygen and inert gas can influence the parameters of flame temperature and gas emissions in the industrial burner. The flame shape for all the cases of inlet velocity was predominantly symmetric about the x = 0 mm for all the axial distances towards the outlet. The radial velocity contour at 0.01 m/s (300 K) gave better results with an area of 1.31 m/s to 4.08 m/s, which was wider than that of the case at 0.01 m/s (700 K). By varying the inlet temperature and oxygen mass fraction, the flame configurations on temperature, CO2, and H2O formed a symmetric flame structure. The temperature distribution resulted in the centerline being hotter than other radial positions for all of the inlet temperatures. The emissions of CO2 and H2O generally increased with the addition of the oxygen mass fraction.

Modelling doi: 10.3390/modelling7010005

Authors: Georgi Venelinov Valchev Stoyan Dimitrov Slavov

This paper presents a novel approach using machine learning methods for the automated segmentation of acceleration signals measured during ball burnishing (BB) operations performed on a computer numerical controlled (CNC) milling machine. The study addresses the challenge of accurately finding actual feedrates in that finishing operation, which often deviate from programmed values due to various dynamic reasons. The method involves a two-stage process: first, an automatic signal segmentation algorithm employing Gaussian Mixture Modeling (GMM) and K-means clustering is applied to the ball burnishing (BB) process and acceleration data. Second, a Taguchi L9 experimental design is used to assess the influence of some regime parameters on the actual feedrate and the BB’s cycle duration. Results show successful segmentation of the toolpaths based on X-axis accelerations and deforming force data, with the Calinski–Harabasz Index confirming good cluster separability. Programmed feedrate and the number of toolpath points were identified as the most significant factors affecting the percentage delay between programmed and obtained feedrates. The main contribution is the development and testing of a new method for segmenting different toolpath states in ball burnishing operations, based on measured accelerations and momentary deforming force magnitudes. The present work offers valuable insights into autonomous monitoring and control in BB operations.

Modelling doi: 10.3390/modelling7010004

Authors: Zhidan Liu Xuqing Luo Jiaqiang Yang Zhenhua Zhang Fan Yang Pengyong Miao

Cracks serve as a critical indicator of tunnel structural degradation. Manual inspections are difficult to meet engineering requirements due to their time-consuming and labor-intensive nature, high subjectivity, and significant error rates, while traditional image processing methods exhibit poor performance under complex backgrounds and irregular crack morphologies. To address these limitations, this study developed a high-quality dataset of tunnel crack images and proposed an improved lightweight semantic segmentation network, LiteSqueezeSeg, to enable precise crack identification and quantification. The model was systematically trained and optimized using a dataset comprising 10,000 high-resolution images. Experimental results demonstrate that the proposed model achieves an overall accuracy of 95.15% in crack detection. Validation on real-world tunnel surface images indicates that the method effectively suppresses background noise interference and enables high-precision quantification of crack length, average width, and maximum width, with all relative errors maintained within 5%. Furthermore, an integrated intelligent detection system was developed based on the MATLAB (R2023b) platform, facilitating automated crack feature extraction and standardized defect grading. This system supports routine tunnel maintenance and safety assessment, substantially enhancing both inspection efficiency and evaluation accuracy. Through synergistic innovations in lightweight network architecture, accurate quantitative analysis, and standardized assessment protocols, this research establishes a comprehensive technical framework for tunnel crack detection and structural health evaluation, offering an efficient and reliable intelligent solution for tunnel condition monitoring.

Modelling doi: 10.3390/modelling7010003

Authors: Michal Hrubý Petr Čermák

Chemical emergencies in transport are rare but operationally demanding. This study presents a framework that converts the timeline of a real intervention involving a cyclohexylamine leak after a tanker truck overturned into a Petri net and subsequently into an absorbing Markov model. This provides decision-oriented indicators for the intervention phases and enables what-if analysis. Application to a case study shows that the capacity of the decontamination line has a significant impact on the duration of the incident resolution, while introducing a small probability of returning from technical measures to decontamination slightly prolongs the course while leaving the certainty of successful completion unchanged. Mapping between activities, Petri net locations, and aggregated states promotes transparency and the repeatability of procedures and highlights activities with a high number of repeat visits. The outputs are useful for decision making related to personnel and material resources, post-review analyses, and exercise planning. The limitations lie in calibration to a single incident, the partial use of expertly estimated parameters, and the approximate conversion of “steps” to time. Future work will focus on multiple cases, finer-grained time handling, and explicit capacity modelling.

Modelling doi: 10.3390/modelling7010002

Authors: Xiaofei Zhang Zhengwei Yang Zhiqiang Xin

When operating in the marine environment, floating offshore wind turbines (FOWTs) are subjected to various inflow conditions such as wind, waves, and currents. To investigate the effects of complex inflow conditions on offshore wind farms, an integrated fluid-structure interaction computational and coupled dynamic analysis method for FOWTs is employed. An aero-hydro-servo-elastic coupled analysis model of the NREL 5 MW semi-submersible wind turbine array based on the OC4-DeepCwind platform is established. The study examines the variations in power generation, platform motion, structural loads, and flow field distribution of the FOWT array under different wave incident angles and yaw angles of the first column turbines. The results indicate that the changes in power generation, platform motion, and flow field distribution of the wind farm are significantly influenced by the yaw angle. The maximum tower top yaw bearing torque and the tower base Y-direction bending moment of the wind turbines undergo significant changes with the increase in the angle between wind and wave directions. The study reveals the mechanism of power generation and load variation during yaw control of the FOWT array under misaligned wind and wave conditions, providing a theoretical basis for the future development of offshore floating wind farms.

Modelling doi: 10.3390/modelling7010001

Authors: Jing Mao Lianming Sun Jie Chen

To address the limitations of traditional non-local mean (NLM) denoising algorithms in terms of neighborhood similarity metrics, weight calculation, and computational efficiency, this paper proposed a structural-tensor-driven and dynamic window-based fast non-local mean denoising algorithm with dual kernel weighting. First, a Gaussian–Tukey dual-kernel weighting function was designed to optimize similarity metrics. Then, spatial neighborhood features were adopted. By measuring both grayscale similarity and spatial correlation, the weight distribution rationality was further enhanced. Second, structural tensor eigenvalues were used to quantify regional structural properties. A dynamic window allocation function was designed to adaptively match search window sizes to different image regions. Finally, an integral image acceleration mechanism was proposed, significantly improving algorithm execution efficiency. Experimental results demonstrated that the proposed algorithm achieved both excellent denoising performance and edge/texture preservation capabilities. In high-noise environments, its Peak Signal-to-Noise Ratio (PSNR) outperformed the Gauss kernel non-local mean algorithm by an average of 1.96 dB, while Structural Similarity (SSIM) improved by an average of 5.7%. Moreover, the algorithm’s execution efficiency increased by approximately 7–11 times, indicating strong potential for real-time application in digital image processing.

Modelling doi: 10.3390/modelling6040166

Authors: María Cruz Navarro Damián Castaño Henar Herrero

In this study, we numerically investigate the influence of thermal gradients on the growth and intensification of vortices formed within a rotating cylinder subjected to inhomogeneous cooling at the top or inhomogeneous heating at the bottom. The presence of horizontal thermal inhomogeneities at the upper and lower boundaries determines whether the vortex originates near the top or the bottom of the domain. Moreover, the magnitude of both horizontal and vertical thermal gradients plays a critical role in the vortex’s intensification, vertical stretching, and overall development. The observed phenomena are interpreted through a force balance analysis. Increasing the ambient rotation rate leads to the emergence of periodic structures, such as tilted or double vortices, which also undergo intensification and stretching as thermal gradients increase. These findings highlight the importance of thermal boundary conditions in shaping vortical structures and may contribute to a deeper understanding of the genesis, morphology, and intensification mechanisms of thermoconvective vortices.

Modelling doi: 10.3390/modelling6040165

Authors: Riko Luša Damir Pintar Mihaela Vranić

Graph learning is well suited to modeling relationships among communicating entities in network intrusion detection. However, the resulting models are frequently difficult to interpret, in contrast to many classical approaches that offer more transparent reasoning. This work integrates SHapley Additive exPlanations with temporal, edge-aware GNN based on GraphSAGE architecture to deliver an explainable, inductive intrusion detection model for NetFlow data named TE-G-SAGE. Using the NF-UNSW-NB15-v3 dataset, flow data are transformed into temporal communication graphs where flows are directed edges and endpoints are nodes. The model learns relational patterns across two-hop neighborhoods and achieves strong recall under chronological evaluation, outperforming a GCN baseline and recovering more attacks than a tuned XGBoost model. SHAP is adapted to graph inputs through a feature attribution on the two-hop computational subgraph, producing global and local explanations that align with analyst reasoning. The resulting attributions identify key discriminative features while revealing shared indicators that explain cross-class confusion. The research shows that temporal validation, inductive graph modeling, and Shapley-based attribution can be combined into a transparent, reproducible intrusion detection framework suited for operational use.

Modelling doi: 10.3390/modelling6040164

Authors: Xiangdong Li Kailin Yin Yuxin Gu

Eye tracking scanpaths encode the temporal sequence and spatial distribution of eye movements, offering insights into visual attention and aesthetic perception. However, analysing scanpaths still requires substantial manual effort and specialised expertise, which limits scalability and constrains objectivity of eye tracking methods. This paper examines whether and how multimodal large language models (MLLMs) can provide objective, expert-level scanpath interpretations. We used GPT-4o as a case study to develop eye tracking scanpath analysis (ETSA) approach which integrates (1) structural information extraction to parse scanpath events, (2) knowledge base of visual-behaviour expertise, and (3) least-to-most and few-shot chain-of-thought prompt engineering to guide reasoning. We conducted two studies to evaluate the reliability and effectiveness of the approach, as well as an ablation analysis to quantify the contribution of the knowledge base and a cross-model evaluation to assess generalisability across different MLLMs. The results of repeated-measures experiment show high semantic similarity of 0.884, moderate feature-level agreement with expert scanpath interpretations (F1 = 0.476) and no significant differences from expert annotations based on the exact McNemar test (p = 0.545). Together with the ablation and cross-model findings, this study contributes a generalisable and reliable pipeline for MLLM-based scanpath interpretation, supporting efficient analysis of complex eye tracking data.

Modelling doi: 10.3390/modelling6040163

Authors: Menghui Ding Youfeng Zhang Guangyu Han Yinling Wang Wenzhu Zhang

Titanium alloys such as Ti-6Al-4V are widely used in aerospace and biomedical fields, but their poor wear resistance and high friction coefficient limit service performance. In this study, laser cladding with La2O3 addition was employed to enhance the surface properties of Ti-6Al-4V, and the underlying mechanisms were systematically investigated by combining experimental characterization with multiphysics simulations. XRD and SEM analyses revealed that La2O3 addition refined grains and promoted uniform phase distribution throughout the coating thickness, leading to good metallurgical bonding. The hardness was 2–3 times higher than that of the titanium alloy substrate when the content of 2–3 wt.% was of added La2O3, while the wear loss ratio was reduced to 0.021% and the average friction coefficient decreased to 0.421. These improvements were strongly supported by simulations: temperature field calculations demonstrated steep thermal gradients conducive to rapid solidification; velocity field analysis and recoil-pressure-driven flow revealed vigorous melt pool convection, which homogenized solute distribution and enhanced coating densification; phase evolution simulations confirmed the role of La2O3 in heterogeneous nucleation and dispersion strengthening. In summary, the combined results establish a mechanistic framework where thermal cycling, melt pool dynamics, and La2O3-induced nucleation act synergistically to optimize coating microstructure, hardness, and wear resistance. This integrated experimental–numerical approach provides not only quantitative improvements but also a generalizable strategy for tailoring surface performance in laser-based manufacturing.

Modelling doi: 10.3390/modelling6040162

Authors: Yufan Wang Yinxiao Hu Yuchen Li Hongjuan Ge

Common cause failure (CCF) is concealed and harmful. With the increase in the number of redundant systems in aircraft, quantifying the impact of CCF is crucial for accurately calculating system failure probabilities. However, the diverse and complex redundancy configurations prevalent in modern aircraft systems often limit the applicability and analytical efficiency of existing CCF quantification methods. To address these challenges, the applicability of three CCF modeling approaches, namely the β-factor model, the α-factor model, and the square root model is analyzed. Furthermore, a failure probability correction model is constructed to quantify CCF impacts across systems with varying redundancy levels and configurations. The effectiveness and versatility are then validated on three typical aircraft system failure cases. Further, a software for correcting the failure probability of complex systems considering CCF is developed, which is highly applicable and efficient in calculation. This study not only enriches the methodologies for system safety analysis but also significantly enhances the efficiency and accuracy of CCF quantification in aerospace engineering.

Modelling doi: 10.3390/modelling6040161

Authors: Zhixin Suo Jingyang Zhou Yukai Chen Zihao Zhang Liang Zhao Shanshan Bai Pengyu Wang Kangli Liu

The modern power system is becoming increasingly complex, and the uncertainty in the operation of each link has intensified the possibility of risks emerging. Therefore, efficient risk prediction is of great significance for maintaining the reliable operation of the entire system. In this paper, to address the uncertainty and spatiotemporal coupling in local power grids with renewable integration, an integrated “state prediction–risk assessment–early warning” framework is proposed. A spatiotemporal graph neural network is used to predict node voltage, power, and phase angles under topological constraints, where physics-aware graph attention, disturbance-enhanced temporal modeling, and prediction-smoothing constraints are jointly incorporated to improve sensitivity to renewable fluctuations and ensure stable multi-step forecasting. Furthermore, voltage deviation, power fluctuation, and phase-angle variation are quantified to compute a composite risk index via normalized softmax weighting, with factor contributions enhancing interpretability. Test results on the IEEE 33-bus system under diverse disturbances show improved accuracy and stability over baselines, showing consistently lower MAE/RMSE than three baselines across all disturbance scenarios while pinpointing high-risk nodes and causes, highlighting good engineering potential.

Modelling doi: 10.3390/modelling6040160

Authors: Yu Lin Feng Wang Yu Wu Hao Xu Jun Zhou Junfei Yang Xunjia Zhang Guodong Zheng

In natural gas gathering and transportation projects, efficient gas-liquid separation equipment is crucial to ensuring the stable operation of subsequent processes. Conventional separation units often have problems such as low efficiency, high energy consumption and poor resistance to load fluctuations when dealing with foam-containing gas-liquid mixtures. For this purpose, numerical simulation and structural optimization of multi-stage foam separation units were carried out in this study. Based on FLUENT software fluid analysis software, a three-dimensional, multi-physics coupled model incorporating cyclonic defoaming components and axial-flow separation tubes was developed. The volume of fluid (VOF) multiphase flow model was used to capture the dynamic characteristics of the gas-liquid interface, and the population balance model was used to simulate the coalescence and fragmentation of the foam. The results show that in the non-working fluid stage, the optimal operating pressure is 5.0–5.5 MPa, and the droplet concentration should be maintained below 50 × 10−5. The system performance during the working fluid stage is significantly influenced by foam size. The efficiency of millimeter-sized foams is stable above 88% in the 5.0–6.0 MPa range, while the efficiency of micrometer-sized foams is optimal in the 5.3–5.7 MPa range. It is recommended to control the foam proportion below 35% and add a pre-defoaming unit to improve overall performance.

Modelling doi: 10.3390/modelling6040159

Authors: Jifei Ye Guanghong Wang Hua Li Zhiquan Song Peng Fu

The current contact of pyro-breakers must rapidly interrupt current when the superconducting magnet loses its superconductivity. To enhance the microsecond-scale current-breaking capability of pyro-breakers in nuclear fusion devices, this study investigates the impact of current contact notch structures on dynamic fracture behavior. Through multi-physics field modeling and controlled explosive testing, it is revealed for the first time that the rectangular-notch structure demonstrates enhanced fracture performance relative to the V-notch configuration under explosive impact loading conditions, achieving a 27.3% reduction in fracture initiation time alongside a 47.5% increase in crack propagation width. These findings provide a robust theoretical basis for designing pyro-breakers with enhanced fast-break capabilities in fusion devices.

Modelling doi: 10.3390/modelling6040158

Authors: Enbin Liu Xinxi He Dianpeng Lian

Accurate short-term (10–20 days) natural gas load forecasting is crucial for the “tactical planning” of gas utilities, yet it faces significant challenges from high volatility, strong noise, and the high-dimensional multicollinearity of influencing factors. To address these issues, this paper proposes a novel hybrid forecasting framework: PCCA-ISSA-GRU. The framework first employs Principal Component Correlation Analysis (PCCA), which improves upon traditional PCA by incorporating correlation analysis to effectively select orthogonal features most relevant to the load, resolving multicollinearity. Concurrently, an Improved Singular Spectrum Analysis utilizes statistical criteria (skewness and kurtosis) to adaptively separate signals from Gaussian noise, denoising the historical load sequence. Finally, the dually optimized data is fed into a Gated Recurrent Unit (GRU) neural network for prediction. Validated on real-world data from a large city in Northern China, the PCCA-ISSA-GRU model demonstrated superior performance. For a 20-day forecast horizon, it achieved a Mean Absolute Percentage Error (MAPE) of 6.09%. Results show its accuracy is not only significantly better than single models (BPNN, LSTM, GRU) and classic hybrids (ARIMA-ANN), but also outperforms the state-of-the-art (SOTA) model, Informer, within the 10–20 days tactical window. This superiority was confirmed to be statistically significant by the Diebold–Mariano test (p < 0.05). More importantly, the model exhibited exceptional robustness, with its error increase during extreme weather scenarios (e.g., cold waves, rapid temperature changes) being substantially lower (+56.7%) than that of Informer (+109.2%). The PCCA-ISSA-GRU framework provides a high-precision, highly robust, and cost-effective solution for urban gas short-term load forecasting, offering significant practical value for critical operational decisions and high-risk scenarios.

Modelling doi: 10.3390/modelling6040157

Authors: Alejandro Jimenez-Flores Pablo A. Tellez-Belkotosky Edmundo Javier Ollervides-Vazquez Luis Arturo Reyes-Osorio Luis Amezquita-Brooks Octavio Garcia-Salazar

The translational and rotational dynamics of quadrotor UAVs are commonly described by mathematical modeling where aerodynamic and inertial parameters are involved. Therefore, the importance of having accurate parameters in the model is critical for the correct performance of the UAV. In this paper, Artificial Neural Networks (ANNs) are used to estimate the aerodynamic and inertial parameters corresponding to the mathematical model of a quadrotor. Thrust and torque coefficients from the rotor models and the quadrotor inertia matrix are estimated by proposing and training two different ANN models implementing the back-propagation algorithm, using both experimental and simulation data. The estimated parameters are then compared with the reference parameters by means of quadrotor attitude simulations, showing high accuracy in their behavior. The results have shown that the proposed ANN models can accurately estimate both the aerodynamic and inertial parameters of a quadrotor UAV model using both experimental and simulation data, thus contributing to increasing the tools available for parameter estimation.

Modelling doi: 10.3390/modelling6040156

Authors: Ahmad Eid

This study investigates the optimal operation of distribution systems incorporating Photovoltaic (PV) units, Electric Vehicle Charging Stations (EVCSs), and DSTATCOM devices using the Starfish Optimization Algorithm (SFOA). The main goal of the SFOA is to minimize a combined function that encompasses three key objectives: reducing system losses, increasing PV capacity, and enhancing EVCS power. By applying the SFOA within a multi-objective optimization framework, the optimal locations and sizes of PV units, EVCSs, and DSTATCOMs are identified to meet these objectives. This study analyzes and compares several case studies with different numbers of EVCSs, focusing on the operation of a modified 51-bus distribution system over 24 h. Results show that PV hosting energy increases to 21.73, 23.83, and 29.22 MWh for cases with 1, 2, and 3 EVCSs, respectively. EVCS energy also rises to 12.41, 19.50, and 37.23 MWh for the same cases. The corresponding optimized DSTATCOM reactive powers are 11.02, 12.02, and 13.74 MVarh. Throughout all cases, system constraints—such as voltage limits, utility current, and power flow equations—remain within acceptable ranges. The findings demonstrate the SFOA’s effectiveness in optimizing distribution systems with various devices, ensuring efficient operation and meeting all key objectives while adhering to system constraints.

Modelling doi: 10.3390/modelling6040155

Authors: Xiaohui Yu Qing Xu Bin Yang Shuo Ma

High-space industrial facilities often store substantial quantities of flammable volatile organic compounds (VOCs), posing significant fire and explosion hazards. This study employed computational fluid dynamics (CFD) to investigate the migration and diffusion characteristics of VOCs in a semi-enclosed, high-space wood chip fuel storage shed. A three-dimensional transient numerical model was developed based on a real-scale industrial prototype, incorporating the Realizable k−ε turbulence model with species transport equations. Validation using experimental data demonstrated good agreement between the model and experimental results, with a maximum relative error of 5.0%. A systematic assessment of key parameters was conducted, including time, ambient temperature, relative humidity, wood chip stack height, and VOCs type. Evaluation metrics comprised the surface-average mass fraction and the proportion of areas exceeding 5% of the lower explosive limit (LEL). The results show that peak concentrations occurred at 25~27 min. The system reaches quasi-steady state after 60 min. At 300~304 K, the lowest peak mass fractions are observed (0.31% and 0.43% at 19 m), yet the area exceeding 5% LEL was the largest. Moderate humidity (40~60%) reduces peaks by 0.06~0.11%. A stacking height of 7.5 m reduces peak values to 0.21% (left) and 0.28% (right), while a 10 m height increases the hazardous area to 48.87%. Low-polarity VOCs (C10H16) spread widely (34.10% exceeding 5% LEL area), whereas polar VOCs (C15H26O) accumulated locally (4.48%). These findings provide theoretical guidance for VOC hazard control and ventilation optimization in high-space biomass fuel storage facilities.

Modelling doi: 10.3390/modelling6040154

Authors: Xingsheng Deng Xu Zhu Zhongan Tang

A series of machine learning models have been proposed in the past decades, but it remains undetermined which is optimal for specific applications. Establishing mathematical prediction models for dam deformation and structural health monitoring based on environmental factors is crucial to dam safety assessment. This paper takes Zhexi Dam, a concrete gravity-type dam in China, as an example to conduct a comparative study on the performance of deformation prediction models. The physical factors that cause dam deformation include the air temperature, reservoir water temperature, reservoir water level, and dam aging. The correlations between environmental factors and dam deformation are evaluated by maximum information coefficient (MIC) and Pearson, Kendall, and Spearman correlation coefficients. The monitoring data reveal that the deformation has a high correlation with environmental factors. A number of the most representative monitoring points from hundreds of monitoring points are selected for modeling. For comparison, seven modeling methods, i.e., multiple linear regression (MLR), gradient boosting decision tree (GBDT), random forest (RF), support vector machine (SVM), and long short-term memory network (LSTM), weighted average model (WAM) of the above five algorithms, and Transformer-based neural network, are introduced to establish dam deformation prediction models. The experimental results indicate that both the weighted average model and the Transformer-based neural network achieve consistently high accuracy, showing strong agreement with the monitoring data generally. However, in scenarios involving small sample sizes, the SVM model demonstrates relatively superior predictive performance compared to the other models.