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Modelling, Volume 7, Issue 2 (April 2026) – 29 articles

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17 pages, 7715 KB  
Article
A Traffic Diversion Approach for Expressway Reconstruction and Expansion Considering Highway Toll and Heterogeneity Between Cars and Trucks
by Qiang Zeng, Feilong Liang, Xiang Liu and Xiaofei Wang
Modelling 2026, 7(2), 71; https://doi.org/10.3390/modelling7020071 - 2 Apr 2026
Viewed by 177
Abstract
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 [...] Read more.
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. Full article
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21 pages, 1385 KB  
Article
Operation Prediction of a Gasification-Based Waste Treatment Plant Using Deep Learning
by Shunsuke Arai, Kentaro Mitsuma, Takahiro Kawaguchi, Keiichi Kaneko and Seiji Hashimoto
Modelling 2026, 7(2), 70; https://doi.org/10.3390/modelling7020070 - 1 Apr 2026
Viewed by 192
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Modelling)
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23 pages, 6200 KB  
Article
Braking Control Strategy for Battery Electric Buses Based on Dynamic Load Estimation
by Shuo Du, Jianguo Xi, Xianya Xu and Jingyuan Li
Modelling 2026, 7(2), 69; https://doi.org/10.3390/modelling7020069 - 30 Mar 2026
Viewed by 177
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Topic Dynamics, Control and Simulation of Electric Vehicles)
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30 pages, 3234 KB  
Article
Modeling and Optimization of an Automatic Temperature Control System for the Catalytic Cracking Process
by Yury Ilyushin, Alexander Vitalevich Martirosyan, Mir-Amal Asadulagi and Tatyana Kukharova
Modelling 2026, 7(2), 68; https://doi.org/10.3390/modelling7020068 - 30 Mar 2026
Viewed by 261
Abstract
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 [...] Read more.
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. Full article
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20 pages, 2671 KB  
Article
Two-Stage Prediction of Snowplow Dozer Operation Counts from GPS Data: A Case Study of Akita City, Japan
by Akane Yamashita, Hiroshi Yokoyama and Yoichi Kageyama
Modelling 2026, 7(2), 67; https://doi.org/10.3390/modelling7020067 - 29 Mar 2026
Viewed by 210
Abstract
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, [...] Read more.
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. Full article
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26 pages, 9769 KB  
Article
Numerical Investigation of Masonry Walls Using Mega-Interlocking Concrete Blocks
by Antoon Labib, Bowen Zeng, Carlos Cruz-Noguez and Yong Li
Modelling 2026, 7(2), 66; https://doi.org/10.3390/modelling7020066 - 29 Mar 2026
Viewed by 233
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Section Modelling in Engineering Structures)
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24 pages, 4367 KB  
Article
A Physics-Constrained Hybrid Deep Learning Model for State Prediction in Shipboard Power Systems
by Jiahao Wang, Xiaoqiang Dai, Mingyu Zhang, Kaikai You and Jinxing Liu
Modelling 2026, 7(2), 65; https://doi.org/10.3390/modelling7020065 - 26 Mar 2026
Viewed by 299
Abstract
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 [...] Read more.
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. Full article
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21 pages, 6457 KB  
Article
Modelling the Dynamic Response of Clay Nanoparticle-Modified Concrete Beams Resting on Two-Parameter Elastic Foundations
by Zouaoui R. Harrat, Aida Achour, Mohammed Chatbi, Marijana Hadzima-Nyarko and Ercan Işık
Modelling 2026, 7(2), 64; https://doi.org/10.3390/modelling7020064 - 25 Mar 2026
Viewed by 242
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Section Modelling in Engineering Structures)
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32 pages, 1111 KB  
Review
Lean Management, Discrete Event Simulation, and Virtual Reality in Hemodialysis Units: A Scoping Literature Review and Evidence Gap Analysis
by Joseph Jabbour, Jalal Possik, Adriano O. Solis, Charles Yaacoub, Sina Namaki Araghi and Gregory Zacharewicz
Modelling 2026, 7(2), 63; https://doi.org/10.3390/modelling7020063 - 25 Mar 2026
Viewed by 299
Abstract
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 [...] Read more.
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. Full article
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28 pages, 1397 KB  
Article
Evaluation of Waste-to-Hydrogen Infrastructure in Oman: A Mixed-Integer Programming Approach for Circular Economy Integration
by Sharif H. Zein
Modelling 2026, 7(2), 62; https://doi.org/10.3390/modelling7020062 - 24 Mar 2026
Viewed by 207
Abstract
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 [...] Read more.
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. Full article
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21 pages, 5024 KB  
Article
Predictive Modeling of Microhardness and Tensile Strength for Friction Stir Additive Manufacturing of AA8090 Alloy Using Artificial Neural Network
by D. A. P. Prabhakar, Arun Kumar Shettigar, Mervin A. Herbert and Rashmi Laxmikant Malghan
Modelling 2026, 7(2), 61; https://doi.org/10.3390/modelling7020061 - 24 Mar 2026
Viewed by 189
Abstract
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 [...] Read more.
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. Full article
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21 pages, 22338 KB  
Article
Nighttime Driver Fatigue Detection Based on Real-Time Joint Face and Facial Landmarks Detection
by Zhuofan Huang, Shangkun Liu, Jingli Huang and Jie Huang
Modelling 2026, 7(2), 60; https://doi.org/10.3390/modelling7020060 - 21 Mar 2026
Viewed by 271
Abstract
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 [...] Read more.
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. Full article
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22 pages, 19775 KB  
Article
Decentralized Optimization Approach for Modeling and Cooperative Control of Pressure Regulation System in Environmental Simulation Facility
by Xuan Qi, Yifei Fang, Xin Li, Chao Zhai, Hehong Zhang and Wei Zhao
Modelling 2026, 7(2), 59; https://doi.org/10.3390/modelling7020059 - 18 Mar 2026
Viewed by 196
Abstract
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 [...] Read more.
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. Full article
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20 pages, 1006 KB  
Article
A Data-Driven Discrete-Event Simulation for Assessing Passenger Dynamics and Bottlenecks in Mexico City Metro Line 7
by Elias Heriberto Arias Nava, Brendan Patrick Sullivan and Luis A. Moncayo-Martinez
Modelling 2026, 7(2), 58; https://doi.org/10.3390/modelling7020058 - 17 Mar 2026
Viewed by 288
Abstract
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 [...] Read more.
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. Full article
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14 pages, 418 KB  
Article
Traffic Accident Risk Assessment at Urban Signalized Intersections Using Cellular Automata Modeling
by Laila Taoufiq, Omar Bamaarouf, Abdelmajid Kadiri and Rachid Marzoug
Modelling 2026, 7(2), 57; https://doi.org/10.3390/modelling7020057 - 17 Mar 2026
Viewed by 242
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Advanced Modelling Techniques in Transportation Engineering)
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19 pages, 3784 KB  
Article
Analysis of Aerodynamic Behavior in Overtaking Maneuvers Within Vehicle Platooning
by Tuo Zhang, Qing-Yun Chen, Seong-Jin Kwon and Gee-Soo Lee
Modelling 2026, 7(2), 56; https://doi.org/10.3390/modelling7020056 - 16 Mar 2026
Viewed by 242
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Section Modelling in Mechanics)
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12 pages, 765 KB  
Article
A Bayesian-Optimized Mixture of Experts Framework for Short-Term Traffic Flow Prediction
by Jianqing Wu, Jiaao Ren, Hui Wang, Fei Xie, Shaohan Chen and Mengjie Jiang
Modelling 2026, 7(2), 55; https://doi.org/10.3390/modelling7020055 - 16 Mar 2026
Viewed by 314
Abstract
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 [...] Read more.
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. Full article
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26 pages, 4174 KB  
Article
An Adaptive Neuro-Fuzzy Fractional-Order PID Controller for Energy-Efficient Tracking of a 2-DOF Hip–Knee Lower-Limb Exoskeleton
by Mukhtar Fatihu Hamza and Auwalu Muhammad Abdullahi
Modelling 2026, 7(2), 54; https://doi.org/10.3390/modelling7020054 - 12 Mar 2026
Viewed by 284
Abstract
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 [...] Read more.
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. Full article
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25 pages, 2978 KB  
Article
Process Modeling of 3D Electrodeposition Printing of Metallic Materials
by Satyaki Sinha, Saumitra Bhate and Tuhin Mukherjee
Modelling 2026, 7(2), 53; https://doi.org/10.3390/modelling7020053 - 11 Mar 2026
Viewed by 560
Abstract
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 [...] Read more.
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. Full article
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19 pages, 5783 KB  
Article
Multi-Objective Optimization of Rigid Pavement Concrete Using Industrial By-Products and Polypropylene Fibers
by Sergii Kroviakov, Vitalii Kryzhanovskyi, Pavlo Shymchenko and Inna Aksyonova
Modelling 2026, 7(2), 52; https://doi.org/10.3390/modelling7020052 - 9 Mar 2026
Viewed by 309
Abstract
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 [...] Read more.
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. Full article
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26 pages, 4189 KB  
Article
A Novel PID-LQR Controller Scheme to Enhance the Performance of Full-Bridge Boost Converter
by Sulistyo Wijanarko, Rina Ristiana and Anwar Muqorobin
Modelling 2026, 7(2), 51; https://doi.org/10.3390/modelling7020051 - 6 Mar 2026
Viewed by 349
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Modelling of Nonlinear Dynamical Systems)
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18 pages, 9422 KB  
Article
A SAM2-Driven RGB-T Annotation Pipeline with Thermal-Guided Refinement for Semantic Segmentation in Search-and-Rescue Scenes
by Andrés Salas-Espinales, Ricardo Vázquez-Martín and Anthony Mandow
Modelling 2026, 7(2), 50; https://doi.org/10.3390/modelling7020050 - 4 Mar 2026
Viewed by 535
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Section Modelling in Artificial Intelligence)
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36 pages, 26044 KB  
Article
Design, Development and Performance Evaluation of Water-Lubricated Bearings with Diverse Groove Patterns: A CFD and Experimental Investigation
by Khushal Nitin Rajvansh, Girish Hariharan, Nitesh Kumar, Chithirai Pon Selvan, Ravindra Mallya, Gowrishankar Mandya Chennegowda, Subraya Krishna Bhat and Vinyas
Modelling 2026, 7(2), 49; https://doi.org/10.3390/modelling7020049 - 3 Mar 2026
Viewed by 445
Abstract
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 [...] Read more.
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. Full article
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32 pages, 6608 KB  
Article
A Forecasting Model for Passenger Flows of Urban Rail Transit Based on Multi-Source Spatio-Temporal Features and Optimized Ensemble Learning
by Haochu Cui and Yan Sun
Modelling 2026, 7(2), 48; https://doi.org/10.3390/modelling7020048 - 28 Feb 2026
Viewed by 619
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence in Modelling)
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16 pages, 8985 KB  
Article
Practical Significance of Reliability-Based Structural Design: Application to Electro-Mechanical Components
by Domen Šeruga, Lovro Novak, Marko Nagode and Jernej Klemenc
Modelling 2026, 7(2), 47; https://doi.org/10.3390/modelling7020047 - 27 Feb 2026
Viewed by 248
Abstract
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 [...] Read more.
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. Full article
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26 pages, 1121 KB  
Article
A Queuing-Network-Based Optimization Model for EV Charging Station Configuration in Highway Service Areas
by Hongwu Li, Bin Zhao, Zhihong Yao and Yangsheng Jiang
Modelling 2026, 7(2), 46; https://doi.org/10.3390/modelling7020046 - 27 Feb 2026
Viewed by 661
Abstract
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 [...] Read more.
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.” Full article
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17 pages, 4317 KB  
Article
Neural Approach to Study the Vibration Behavior of Damaged Composite Rotating Beams
by Patricia Rubio Herrero, Belén Muñoz-Abella, Inés Ivañez and Lourdes Rubio
Modelling 2026, 7(2), 45; https://doi.org/10.3390/modelling7020045 - 27 Feb 2026
Viewed by 215
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Topic Numerical Simulation of Composite Material Performance)
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27 pages, 7990 KB  
Article
A Comparative Study and Experimental Investigation of Multi-Objective Optimization for Geothermal-Driven Organic Rankine Cycle
by Kaiyi Xie, Haotian He and Yuzheng Li
Modelling 2026, 7(2), 44; https://doi.org/10.3390/modelling7020044 - 25 Feb 2026
Viewed by 428
Abstract
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 [...] Read more.
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. Full article
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43 pages, 41959 KB  
Article
Synthesis, Static and Dynamic Characterization of Novel Triply Periodic Minimal Surface Lattices
by Federico Casucci, Enrico Tosoratti, Mohamadreza Afrasiabi and Pier Paolo Valentini
Modelling 2026, 7(2), 43; https://doi.org/10.3390/modelling7020043 - 24 Feb 2026
Viewed by 566
Abstract
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 [...] Read more.
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 4.67×102 to 11.8. Ultimately, the study revealed a clear influence of cell geometry on stress concentration and modal response. Full article
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