Modelling doi: 10.3390/modelling7040168

Authors: Rafat Al-Waked Asher Ahmed Malik Mohammad Shakir Nasif

Fire-induced domino effects in tank farms can be catastrophic, particularly under wind conditions. However, due to multiple evolutionary stages, Computational Fluid Dynamics (CFD)-based modelling of wind-influenced, fire-induced domino effects and tank farm Time to Failure (TTF) calculation remain computationally expensive. This study addresses this gap by using Fire Dynamics Simulator (FDS) to model fire-induced domino effects in a tank farm and perform detailed tank farm TTF calculations across multiple wind speeds and primary pool fire scenarios. The FDS results showed that increasing wind speed from 0 to 8 m/s altered domino escalation, increasing incident heat flux on the downwind in-line tank by more than sevenfold (a 35% reduction in tank farm TTF). A new perturbation-based analytical formulation was then proposed for rapid determination of tank farm TTF under wind effects, without requiring complete CFD simulations of pool fire escalation. The formulation updates tank farm TTF under the no-wind baseline solution with wind-influenced perturbative correction terms. The proposed formulation agreed with the detailed CFD modelling-based calculation, with a mean relative error of 2.8% across all primary fire scenarios and wind conditions. This formulation provides a practical basis for rapid assessment of domino effects due to pool fire under wind conditions. However, it is calibrated for one specific six-tank configuration and crosswind directions and is not yet general.

Modelling doi: 10.3390/modelling7040167

Authors: László Gyarmati Csaba Mihálykó Éva Orbán-Mihálykó

Paired comparison models are examined from the perspective of the placement of objects within specific comparison structures. For both pairwise comparison matrix-based models and stochastic models, previous studies have examined which comparison structures maximize the amount of information that can be recovered from incomplete comparisons. In this paper, we investigate how the amount of extracted information can be increased in stochastic paired comparison models—primarily the Bradley–Terry model—by way of exploiting prior information about the ranking of the objects, if such information is available. We examine several comparison structures to identify the optimal placement of objects within each structure with respect to information recovery and evaluability. The investigated structures are the star graph, the union of two star graphs, and the union of two edge-disjoint spanning trees. Parameters are estimated using the maximum likelihood method. The applied evaluation metrics are the Euclidean distance, Pearson, Spearman, and Kendall correlations, called similarity metrics. Moreover, the rate of evaluable datasets and an inconsistency index is also computed. We found that, in almost all cases, all four similarity metrics identified the same placement as optimal. Our results show that, for the star graph, placing an object of medium strength at the center and comparing all other object to it maximizes the amount of information recovered from the comparisons. For the union of two star graphs, placing objects that occupy middle positions in the ranking at the centers also outperforms the commonly used best–worst centered placement. However, the union of two edge-disjoint spanning trees provides, on average, even better information recovery based on all investigated metrics. We also examined the proportion of evaluable datasets and found it to be higher when medium-strength objects were placed at the centers. Finally, we compared the findings obtained from the stochastic models with those from pairwise comparison matrix-based models and observed strong agreement between the two approaches.

Modelling doi: 10.3390/modelling7040166

Authors: Guang Yang Haoyue Yang Yongjun Wu

Non-uniform illumination in tunnel environments severely degrades image quality, posing substantial challenges to visual monitoring and intelligent transportation systems. While histogram equalization (HE) remains prevalent due to its computational simplicity, its non-linear pixel transformations frequently induce over-enhancement, artifacts, and structural distortions. This paper proposes Prior-Guided Histogram Equalization (PGHE), a lightweight enhancement framework that integrates conventional HE with Retinex-based illumination priors. Within the Retinex decomposition paradigm, PGHE constructs a contrast illumination map from the ratio between the HE-enhanced image and the original input. A Prior Correction Module (PCM) subsequently refines this map via relative total variation regularization, thereby restoring spatial coherence and alleviating local discontinuities introduced by HE. The corrected map is then applied to the original image to obtain the final enhanced result. Extensive evaluation on the LOL low-light benchmarks and a proprietary tunnel dataset comprising 247 real-world frames shows that PGHE offers favorable trade-offs among contrast enhancement, structural fidelity, and brightness preservation: it is particularly strong in brightness preservation and Entropy, while its PSNR/SSIM on LOL and its NIQE on the tunnel dataset are comparable to, but not always the best among, the compared methods. Furthermore, the proposed PCM functions as a plug-in module that improves existing HE variants with measurable gains in Structural Similarity and perceived naturalness at a modest cost in Absolute Mean Brightness Error.

Modelling doi: 10.3390/modelling7040165

Authors: Rahil Miten Doshi Matthias Markl

Constitutive models define how physical properties depend on evolving state variables, and consequently have a strong influence on computational simulations. However, material descriptions are commonly embedded within solver implementations, limiting their reusability and exchangeability. We introduce a declarative material layer that separates state-dependent material descriptions from numerical solvers and that integrates material behavior into the generated solver code. Material properties are represented symbolically, allowing constitutive relations to be defined independently of discretization methods and reused across different simulation frameworks without solver-specific modifications. A reference implementation demonstrates the compile-time integration of this approach into code-generated solvers for one reference code generation backend. Flow and thermal diffusion benchmarks show that identical constitutive descriptions can be applied consistently across different numerical methods while preserving physical behavior. Performance measurements reveal that the computational impact depends on the interaction between constitutive model complexity and solver characteristics. The proposed declarative material layer opens up the possibility of reusable and solver-independent integration of state-dependent constitutive models into high-performance simulation workflows.

Modelling doi: 10.3390/modelling7040164

Authors: Xiaole Guan Xin Jin Zhijing Zhang

Assembly-oriented geometric models of aero-engine casings require the spatial distribution of deviations at mating interfaces. Conventional scalar descriptors, including flatness, axial runout, and radial runout, cannot retain this information. This study proposes a measurement-driven integrated modelling method based on measured point clouds. After boundary completion, gross-error removal, and Gaussian filtering, the interface morphology is reconstructed as a tensor-product cubic B-spline surface in unit-weight non-uniform rational B-spline (NURBS) form. The reconstructed surface is then integrated with the nominal computer-aided design (CAD) model. Validation was performed using two cuboidal specimens and three representative casing flange surfaces. The relative differences between the reconstructed and measured flatness values of the cuboidal specimens were −8.58% and −1.04%. At the withheld verification points of the casing flange surfaces, the mean absolute reconstruction errors were 0.0022 mm, 0.0017 mm, and 0.0049 mm. These results show that measured interface morphology can be transferred into a CAD-compatible component model while retaining its spatial characteristics. The present study provides a geometric basis for subsequent assembly analysis.

Modelling doi: 10.3390/modelling7040163

Authors: Raheemat O. Yussuf Omar S. Asfour Ahmed Abd El Fattah Muhammad Asif

Roofing systems strongly influence the energy performance and environmental footprint of buildings, particularly in hot–arid climates such as Saudi Arabia, where cooling dominates electricity demand; however, the comparative lifecycle environmental performance of alternative roofing strategies remains underexplored in this specific climatic and market context. This study therefore aims to evaluate and compare the environmental performance of four sustainable roofing strategies against a conventional flat roof (FR) baseline in order to provide evidence-based guidance for climate-specific roofing selection in Saudi Arabia. This study conducts a comparative cradle-to-grave lifecycle assessment (LCA) of four sustainable roofing strategies considering the hot–arid climate of Saudi Arabia. Green roof (GR), cool roof (CR), solar photovoltaic roof (SPV), and roof canopy (RC) were assessed using the ReCiPe 2016 method in the SimaPro software. The environmental impacts of these strategies were assessed across product, construction, use, and end-of-life stages relative to conventional flat roofs (FRs). The results indicate that the production stage consistently contributes the highest environmental impacts, with increases ranging from 30 to 3000% for GR, CR, and RC and exceeding 10,000% for SPV. On the other hand, the use stage offers the greatest reductions ranging from 10 to 200%, particularly for SPV and CR, due to operational energy savings and electricity generation. Overall, CR demonstrates the most balanced environmental performance, combining high impact reductions with minimal trade-offs, while SPV provides significant climate and fossil resource benefits but increases mineral resource use. These findings highlight the importance of climate-specific and resource-conscious selection of roofing strategies in Saudi Arabia and provide a transferable comparative LCA framework that can inform sustainable roofing decisions in other hot–arid and hot–humid regions, in support of the Kingdom’s Vision 2030 objectives for sustainable urban development.

Modelling doi: 10.3390/modelling7040162

Authors: Juchen Hong Xue Feng Zhengyun Ren

In the wet-process stage of lithium-ion battery manufacturing, double-sided coating combined with air-flotation drying can reduce repeated drying operations, thereby helping improve production throughput. However, the requirements of air-flotation drying for equipment stability, together with the coupling among process parameters such as temperature, air velocity, and tension, substantially increase the difficulty of process-parameter calibration. As critical components degrade over time, deviations arise between nominal process parameters and actual operating conditions, introducing non-negligible uncertainty and further complicating parameter recalibration. This paper proposes a collaborative robust multi-objective optimization algorithm to obtain stable and reliable process-parameter combinations under limited computational resources. Specifically, multi-objective optimization models are first established. Then, the operating condition of new equipment is approximately formulated as an undisturbed auxiliary optimization problem, whereas the operating condition of aged equipment with parameter perturbations is formulated as a robust optimization problem; surrogate models are constructed for both problems. Finally, search information from the auxiliary problem is used to guide the evolution of the robust optimization problem, thereby improving its optimization efficiency. Experimental results demonstrate that the proposed algorithm can obtain robust Pareto solutions with favorable convergence and diversity while consuming fewer resources, providing engineers with reliable references for selecting suitable process parameters.

Modelling doi: 10.3390/modelling7040161

Authors: Guo-Kang Er Chang Tian Haofan Wu

Accurate probabilistic analysis of wind-induced structural vibration is essential for accurately analyzing structural safety and serviceability. Though the FPK equation offers a tool for analysis, its application is challenged by the noise characteristics of wind spectra, such as the Davenport and Kaimal spectra. Using the conventional second-order linear filter model to fit Davenport and Kaimal spectra tends to underestimate their spectral energy in the mid-to-high-frequency range. To address this limitation, this paper proposes an improved second-order filter model that enhances fidelity without increasing filter dimensionality. This model is complemented by an optimization strategy based on the idea that the frequency range is partitioned, which generates three models specifically for low-, mid-, and high-frequency ranges. These models can better fit Davenport and Kaimal spectra in a much larger frequency range compared to the conventional model. The effectiveness of the proposed models is validated through numerically analyzing a linear SDOF stochastic oscillator and a nonlinear stochastic SDOF oscillator in various cases. The results demonstrate that the proposed models maintain exceptional accuracy across a wide range of structural natural frequencies.

Modelling doi: 10.3390/modelling7040160

Authors: Shuichi Sakamoto Hiroaki Soeta Yosuke Kubo Okuda Taichi Odashima Takeomi

A powder layer was treated as a one-dimensional beam undergoing longitudinal vibration, and the loss factor was derived from the damping ratio based on Rayleigh damping, thereby introducing frequency dependence into the complex modulus. The transfer matrix of the powder layer was subsequently formulated based on the complex modulus, and the validity and effectiveness of the proposed model were evaluated by comparing the calculated and measured values of transmission loss and sound-absorption coefficient. A loss correction was introduced to account for energy dissipation associated with viscous boundary-layer effects and other dissipative mechanisms. A parametric study of the loss correction was conducted, and the correction was quantitatively incorporated through curve fitting based on the root mean square error (RMSE). Comparison of theoretical and experimental transmission loss values revealed that the increasing trend in transmission loss at high frequencies was captured by the proposed model. In the comparison between the experimental and theoretical sound absorption coefficients, this evaluation approach places greater emphasis on the average degree of agreement across the full measurement frequency range rather than at specific frequency points. Consequently, the loss correction yielding the minimum error across the entire frequency range was selected, which occasionally resulted in differences in peak values near the first-order peak frequency.

Modelling doi: 10.3390/modelling7040159

Authors: Krishnaraj Vilasraj Bhat Ignacio Martínez-Terés Pablo Pflueger Tejero Juan García-Martínez Francisco J. Montans

Mechanical metamaterials (MMMs) are periodic architectures engineered to achieve extraordinary macroscopic mechanical properties. A primary objective in their design is wave propagation isolation, achieved through the generation of phononic bandgaps. These bandgaps are highly sensitive to the geometric features of the underlying unit cell, which is frequently based on a lattice topology. While additive manufacturing has become the predominant approach for fabricating these MMMs, a persistent challenge remains: standard finite element (FE) models based on nominal designs may differ from both the manufactured geometry and its numerical representation. In this context, manufacturing-induced geometric deviations and FE modelling discrepancies can both lead to dispersion characteristics that diverge from the intended behaviour. The present work focuses on the latter through a controlled numerical sensitivity study. This work assesses the impact of these FE modelling errors on the dynamic response of lattice metastructures by simulating structural deviations through conditional node addition and relocation. Specifically, we investigate the influence of two distinct scenarios that lead to significantly different outcomes: nodes subjected to Floquet–Bloch periodic boundary conditions, and interior nodes unaffected by these boundary constraints. Finally, a quantitative threshold for the maximum permissible modeling error is established for each case.

Modelling doi: 10.3390/modelling7040158

Authors: Valérie N’Guessan Gboulouhonon Komenan N’dri Kacoutchy Jean Ayikpa Pierre Gouton Vincent Oria

Band selection is a crucial step in hyperspectral imaging to reduce spectral redundancy and processing costs whilst retaining information useful for classification. Most existing approaches require the number of bands to be retained to be set manually or rely on parameters that are difficult to adjust. This work proposes the Clustering-Unified Schur complement for Diversity with Hierarchical Clustering (CUSD-HC). This fully unsupervised band selection method combines Ward’s hierarchical clustering with a greedy selection based on the Schur complement. Bands are grouped by spectral similarity, and then a representative band is chosen from each group to preserve diversity and informational content. The number of bands is determined automatically using a multi-detector k-fold criterion combined with an intrinsic dimension threshold estimated via PCA. Evaluated on six benchmark datasets using four classifiers (SVM-RBF, Random Forest, XGBoost, LightGBM), CUSD-HC achieves an average rank of between 2.7 and 3.3 among nine compared methods, placing it consistently among the leading group. The Nemenyi test shows no statistically significant difference between CUSD-HC and the top-ranked competitors, while CUSD-HC significantly outperforms the weakest baselines (p < 0.05); unlike the best-ranked alternatives, it reaches this level of performance without any manual selection of the number of bands, which is determined automatically from the data. An inter-scene transferability experiment on the WHU-Hi datasets shows a maximum degradation of 3.9 points in overall accuracy (OA), and the transferred bands even outperform the native selection in three cases out of six. Furthermore, the selected bands naturally cover the main spectral regions (visible, near-infrared, and SWIR), which facilitates the interpretation of results for applications such as precision agriculture and environmental monitoring.

Modelling doi: 10.3390/modelling7040157

Authors: Yuzhuo Zhang Jialin Liang Ziqiong Yuan Zanzan Dai Yaozheng Kang

Traffic states evolve on irregular sensor graphs and vary with calendar context, yet the original ASTGCN does not explicitly model how the contribution of different graph receptive fields changes across traffic periods. This paper proposes CD-MRFG, a context-gated extension of ASTGCN that encodes hour-of-day, day-of-week and weekend information and uses the resulting representation to weight Chebyshev graph-convolution orders in each spatio-temporal block. Under a common 12-step forecasting protocol, CD-MRFG reduced the overall MAE and RMSE of the reproduced ASTGCN baseline from 18.66 and 31.05 to 16.98 and 28.59 on PEMS03, from 22.79 and 35.02 to 20.82 and 32.77 on PEMS04, and from 18.88 and 28.83 to 17.24 and 26.84 on PEMS08. Three-seed experiments confirmed lower mean MAEs on PEMS04 (p = 0.028) and PEMS08 (p = 0.042), although the corresponding RMSE differences did not reach the 0.05 significance threshold. Ablation, gate-weight, sensitivity, complexity and convergence analyses showed that temporal context was the main source of the improvement and that the gate provided a model-internal view of order selection with moderate overhead. CD-MRFG remains less accurate than several stronger recent baselines, so its value is a bounded and interpretable extension of ASTGCN rather than a universal state-of-the-art replacement.

Modelling doi: 10.3390/modelling7040156

Authors: Ksenija Mladenović Ivan Milovanović Zoran Stanković Olivera Pronić Rančić Nebojša Dončov

This paper presents an efficient framework for surrogate modeling and rapid optimization of a dual-band circular patch antenna with a C-shaped slot (DB-CPAC) using multilayer perceptron (MLP) neural networks. Although highly accurate, traditional full-wave electromagnetic simulations are computationally expensive for geometric optimization due to complex slot-induced surface current perturbations. To address this limitation, a hybrid optimization framework based on Latin Hypercube Sampling (LHS) is proposed, combining the developed MLP model with a Method-of-Moments (MoM) simulator. The surrogate model uses an advanced modular architecture consisting of an ensemble of MLP neural networks for regressing center frequencies and classification MLP modules with a softmax output layer to estimate the probabilities of achieving bandwidth and gain targets. All networks are trained using the Levenberg–Marquardt algorithm with early stopping on data generated by a dedicated DB-CPAC_MoM_Sim software package. The proposed LHS-based optimizer employs the surrogate model for rapid global search and targeted local optimization before final MoM verification. Results show that this hybrid approach achieves an order-of-magnitude acceleration of the optimization process compared to conventional MoM methods while maintaining high accuracy.

Modelling doi: 10.3390/modelling7040155

Authors: Chenyao Wan Zheng Li Xiaoqian Ma Yongshou Liu Wei Sun

The roller–raceway contact response is a key factor affecting stress concentration, fatigue initiation, and raceway spalling in spherical roller thrust bearings. Uncertainty analysis of this response is therefore important for revealing how practical parameter fluctuations affect bearing contact behavior and for supporting robust bearing design and operating-condition optimization. In this paper, a multibody dynamic model of a spherical roller thrust bearing is established by explicitly considering the main internal contact pairs, including roller–raceway, roller–flange, roller–cage, and cage–guide interactions. The model is used to obtain the transient roller–raceway contact loads under coupled axial loading and rotational motion. The resulting contact loads are introduced into a finite element contact model to evaluate the dynamic contact stress response of the inner raceway. To assess the effects of random uncertainties on this response, an improved deep neural network (DNN) surrogate model is developed. An attention mechanism deep neural network (AM-DNN) is improved by incorporating feature importance information from random forest (RF) into its attention mechanism, and the resulting model is denoted by RF-AM-DNN. Validation on the generated dataset demonstrates that the proposed RF-AM-DNN outperforms conventional surrogate models in prediction accuracy. Finally, the RF-AM-DNN is used to investigate the uncertainty characteristics of dynamic contact stress in spherical roller thrust bearings under multiple uncertainty factors.

Modelling doi: 10.3390/modelling7040154

Authors: Omid Hassanshahi Nima Azimi Mohammad Bakhshi Diāna Bajāre Shaghayegh Karimzadeh

The integration of bio-based constituents into cementitious materials requires robust predictive models capable of describing mechanical degradation while supporting sustainability-driven material design. This study presents a macro-constitutive damage modelling framework for biomass-modified cement mortars subjected to monotonic compressive loading, combining experimental characterisation, continuum damage mechanics (CDM), and life-cycle assessment (LCA). The calibrated parameters are interpreted in terms of meso-scale mechanisms, but the study does not constitute a direct imaging-based multiscale characterisation. Mortars containing 0–10% dried microalgal biomass as a partial replacement for binder mass were investigated through their complete compressive stress–strain response. A scalar damage variable was employed to model stiffness degradation and progressive microcrack evolution, enabling the identification of elastic-modulus reduction, damage-initiation thresholds, softening behaviour, and residual load-bearing capacity. A thermodynamically consistent Mazars-type damage model was calibrated against the measured envelopes and internally verified by reproducing the same pre-peak and post-peak responses, with coefficients of determination ranging from 0.979 to 0.996. Increasing biomass content reduced the 28-day compressive strength from 47.8 to 23.7 MPa and the elastic modulus from 27.5 to 14.9 GPa, while increasing the damage level at peak load from 0.26 to 0.46 and promoting a more gradual post-peak softening response. The calibrated law provides a compact constitutive representation within the tested replacement range; independent external validation is still required before extrapolation to other biomass types, mixture proportions, or curing regimes. In parallel, a cradle-to-gate LCA quantified global warming, acidification, eutrophication, ozone depletion, and abiotic depletion potentials. An integrated carbon-efficiency index was used to relate mechanical performance to environmental impact. Biomass replacement reduced global warming potential by up to 7.7% but increased eutrophication potential, highlighting a clear performance–environment trade-off. Despite the reduction in mechanical properties, all mixtures satisfied masonry-unit strength requirements, supporting the application of biomass-modified mortars in low-carbon concrete masonry units. The proposed framework demonstrates how experimentally calibrated damage models can support the structural assessment and sustainable development of emerging bio-based cementitious materials.

Modelling doi: 10.3390/modelling7040153

Authors: Gustavo de Mello Ricardo Rodrigues Magalhães Fernando Elias de Melo Borges

The discrete element method (DEM) has become an important numerical tool for investigating the interactions between agricultural machinery and granular agricultural materials. By enabling the analysis of particle-scale dynamics and macroscopic system behavior, the DEM provides valuable support for the design, optimization, and performance evaluation of agricultural equipment. This paper presents a comprehensive review of advances in the application of the DEM in agricultural machinery, with particular emphasis on material modeling, parameter calibration strategies, and the simulation of machine operational processes. First, the establishment of DEM models for major agricultural materials, including soil, seeds, and plant residues, is analyzed, highlighting commonly adopted contact models and calibration methodologies. Second, the application of the DEM in the simulation of key agricultural operations, such as soil tillage, material conveying, and harvesting processes, is examined to identify current capabilities and limitations. Finally, the main technical challenges and future research directions are discussed, focusing on improving model accuracy, validation practices, and integration with experimental and industrial workflows. Among the studies analyzed, the results showed varying performance when comparing experimental and simulated values, with the best results exhibiting a relative difference of less than 1%. However, persistent challenges regarding transferability and computational cost limit industrial-scale adoption. This review aims to provide an organized framework to guide future developments and promote the effective use of the DEM in the design and optimization of agricultural machinery.

Modelling doi: 10.3390/modelling7040152

Authors: Chutong Hao Qingwei Xu Kaili Xu Tianwei Shi Bingjun Li Yaping Zhu Wanjun Niu

This study develops an integrated risk assessment framework to trace the evolution from multi-factor coupling to systemic failure, using coal mine rock burst as a case study. First, a fault tree containing 56 basic events is established from statistical analysis of accident cases from 2010 to 2024. Expert judgment is then combined with fuzzy theory to assign probabilities to basic events, which are further analyzed through a Bayesian Network. Next, differentiated importance measures, including Birnbaum Importance and Fussell–Vesely Importance, are calculated at multiple levels, and gray relational analysis is used to identify the most critical basic events. Results show that management-related factors, particularly insufficient monitoring and inadequate hazard identification, play dominant roles in risk propagation. The Bow-Tie model is subsequently applied to examine inadequate hazard identification in greater depth and to propose targeted preventive measures. Finally, by integrating the comprehensive accident model with chaos theory across the four dimensions of human, machine, environment, and management, the study reveals the internal mechanism of disaster evolution under multi-factor coupling. Validation against objective data confirms the reliability of both probability assignment and critical-event identification.

Modelling doi: 10.3390/modelling7040151

Authors: Zixuan Zhang Beirong Han Xilong Zhou

Dynamic atomic force microscopy (AFM) is a key technique for nanoscale characterization and mechanical property measurement, where the geometric shape of the probe tip critically determines imaging quality and measurement accuracy. This study proposes a tip shape classification framework based on the dynamic response of the AFM microcantilever. First, a dimensionless dynamic model of the microcantilever is established, and its vibrational response is solved using a finite-difference scheme. For conical, spherical, and flat tip geometries, interaction force models are provided under both non-contact and tapping-mode AFM. Based on these formulations, multidimensional dynamic feature parameters, including amplitude, phase, virial, and root-mean-square force, are extracted. On this basis, an XGBoost-based classifier is constructed for tip shape identification, and the model’s decision-making mechanism is further interpreted through a SHAP-based explainability framework combined with dimensionality reduction and visualization techniques. Results show that, under non-contact conditions, the overall classification accuracy on the test set reaches 96.7%, with a 100% recognition rate for conical tips. Under tapping-mode conditions, the classification accuracies for conical, spherical, and flat tips are 100%, 85.5%, and 98.3%, respectively. The results demonstrate the feasibility of identifying tip shapes from dynamic responses using simulated data, thereby establishing a theoretical and methodological basis for future experimental validation and the development of tip diagnostic techniques.

Modelling doi: 10.3390/modelling7040150

Authors: Yi Zang Yuan Ding

Diesel generator sets are key frequency-supporting units in islanded microgrids and shipboard power systems, where rapid speed recovery under abrupt load variations is essential for maintaining power quality. However, conventional linear active disturbance rejection control (LADRC) is limited by the disturbance-estimation and noise-amplification trade-off of a single observer, while fixed parameters restrict its adaptability under varying operating conditions. To address these limitations, this paper proposes an RBF neural-network-optimized cascaded LADRC method, termed RBF-CLADRC. A mechanism-based torque balance model is first established, with uncertain mechanical coupling, friction losses, and load variations lumped into the total disturbance. A residual-disturbance cascaded observer is then constructed, in which the first linear extended state observer estimates the total disturbance and the second further reconstructs the residual estimation error. Unlike conventional ML-based ADRC methods that directly tune multiple gains, the proposed RBFNN adjusts only a common controller bandwidth within a prescribed interval, while all observer and feedback gains are generated through predefined analytical relationships. This low-dimensional adaptation preserves coordinated gain variation, reduces online computational complexity, and facilitates real-time implementation. Lyapunov analysis shows that the observer and tracking errors are uniformly ultimately bounded under bounded disturbance rates and converge exponentially for constant disturbances. Finally, comparative simulations in MATLAB/Simulink demonstrate that the proposed method achieves better dynamic response and disturbance-rejection performance than conventional LADRC and other benchmark controllers.

Modelling doi: 10.3390/modelling7040149

Authors: Yicheng Wang Wanzhong Li Jianning Xu Yapeng Li Liaobo Li

Stable drainage of coalbed methane wells is essential for reducing reservoir pressure and promoting methane desorption. However, coal fines carried by produced water tend to accumulate and deposit within the standing valves of drainage pumps. To address this common problem, this study investigates the transport characteristics of coal fines within the standing valve during the liquid-dominated water-pumping stage of the plunger upstroke, with the standing valve fully open. Theoretical calculations, numerical simulations, and settling experiments were conducted for three coal fines size fractions of 60–100, 100–200, and 200–400 mesh to validate the model’s predictive capability for coal fines motion. The results show that the RNG k–ε model has the lowest mean absolute relative error, at 14.50%. A solid–liquid two-phase flow model was employed to comparatively analyze five valve seat cone angles ranging from 105° to 165° and representative inlet velocities of 0.1–0.4 m/s. The results indicate that the mixture within the standing valve accelerates markedly while passing through the narrow clearance between the valve ball and the valve seat and then decelerates in the region above the valve ball. The region above the valve ball and the valve seat transition region are the primary locations of instantaneous coal fines enrichment. Increasing the inlet velocity generally enhances coal fines transport capacity and reduces the local maximum solid-phase volume fraction. Larger coal fines particles exhibit more pronounced inertial deviation and a higher degree of local enrichment, whereas smaller particles show stronger flow-following behavior and a more dispersed spatial distribution. The results further indicate that, within the investigated structural range, the 150° valve seat cone angle provides the best overall balance between coal fines transport capacity and hydraulic resistance. Ultimately, the findings provide a theoretical foundation and methodological reference for understanding the anti-clogging mechanisms of CBM pump standing valves, optimizing structural parameters, and guiding the blockage-resistant design of downhole flow components.

Modelling doi: 10.3390/modelling7040148

Authors: Longxing Jin Luemou Ju Xu Zhang Zhengfei Lu Tinghuang Wang Jingyang Zhou Kangli Liu

To address the challenges in remote monitoring of power system secondary equipment, including dispersed multi-source heterogeneous corpora, inconsistent terminology, non-standardized expressions, unstable knowledge granularity, and fragmented evidence retrieval, a knowledge-organized and retrieval-augmented intelligent decision-making model is proposed in this paper. First, heterogeneous textual resources, including defect records, standards and operating procedures, maintenance logs, typical cases, and abnormal operation reports, are transformed into retrievable, reusable, and traceable knowledge units through text cleaning, terminology normalization, semantic chunking, and metadata annotation. Monitoring issues are then uniformly represented and modeled as structured retrieval requests. A hybrid retrieval scheme is further developed by integrating keyword retrieval, vector retrieval, hierarchical index backtracking, and unified re-ranking. On this basis, an evidence-constrained retrieval-augmented output mechanism is introduced to generate structured results containing anomaly assessment, evidence-based interpretation, handling recommendations, and source traceability, thereby forming an intelligent auxiliary analysis workflow with expert-system-oriented support for duty-operation scenarios. Results show that the proposed model improves evidence retrieval over baseline retrieval settings and achieves better assisted-analysis performance than direct LLM output and conventional RAG. It effectively improves evidence matching accuracy, completeness of evidence organization, and stability of source traceability, indicating its scenario-level feasibility for intelligent auxiliary analysis and decision-support tasks in remote monitoring of power system secondary equipment.

Modelling doi: 10.3390/modelling7040147

Authors: Jing Xu Zhengming Liao Xiaoying Ren Tianyang Liu Zongmin Liang

Understanding wind load characteristics of greenhouse clusters in valley terrain is essential for ensuring structural safety in high-altitude agricultural regions. This study investigates the wind pressure coefficient distribution of plastic greenhouse clusters located in a representative high-altitude valley region (Case sourced from Tibet, China) using computational fluid dynamics simulations. Numerical models incorporating realistic topographic features and representative cluster layouts (2 × 3, 3 × 3, and 3 × 5) were established to evaluate surface wind pressure coefficient distribution and wind load shape factors. The results indicate that valley terrain modifies the incoming wind field through terrain-induced acceleration and possible flow separation. Compared with flat-terrain assumptions, wind load shape factors show noticeable deviations, particularly in windward, roof, and leeward regions. First-row and peripheral greenhouses consistently experience the largest wind loads due to direct wind exposure, while interior greenhouses are significantly influenced by aerodynamic shielding effects from upstream structures. As cluster density increases, shielding effects reduce wind pressure magnitude and result in a more stable pressure distribution within the interior region of the cluster. The correction coefficient derived in this study should be regarded as site-specific indicators for the selected valley terrain, greenhouse layout, and wind direction, rather than as generally applicable design coefficients.

Modelling doi: 10.3390/modelling7040146

Authors: Chang-Yong Song

This study presents a structural design sensitivity analysis and metamodeling framework for a 30-ft class modular pontoon boat utilizing High-Density Polyethylene (HDPE) and an aluminum alloy (Al-5083) frame. Finite element analysis (FEA) was performed under the design load conditions specified by the Korean Register (KR) rules for high-speed light craft. Based on the FEA simulation results, a design sensitivity analysis was conducted using an L81(311) orthogonal array design matrix (OADM) to identify the quantitative influence of structural thicknesses on the hull weight and maximum stresses. The best design combination among the OADM experiments successfully achieved a 31.9% weight reduction while strictly satisfying the allowable stress criteria. Furthermore, Kriging metamodels with four different correlation functions (Gaussian, Exponential, Matérn linear, and Matérn cubic) were constructed to predict the structural responses efficiently. A comparative analysis of the approximation accuracy revealed that the Matérn linear function provided the most robust predictive performance, yielding the highest average cross-validation coefficient of determination (R2) of 0.971 across all performance metrics. The predictive accuracy of the selected metamodel was further verified by leave-one-out cross-validation in terms of root mean square error (RMSE) and mean absolute error (MAE). The findings confirm that the Kriging metamodel employing the Matérn linear correlation function is highly suitable for capturing the complex structural behavior of hybrid-material marine structures.

Modelling doi: 10.3390/modelling7040145

Authors: Hamid Reza Soltani Motlagh A. M. Amer Nourhan I. Ghoneim Ahmed M. Megahed Amr M. Abdallah Seyed Behbood Issa-Zadeh

This research presents a physics-informed deep learning framework for investigating the magnetohydrodynamic flow of a dissipative non-Newtonian micropolar nanofluid induced by a stretching sheet, incorporating Stefan blowing, internal heat generation, and the zero nanoparticle mass flux condition. The physical model consists of the interplay between the microrotation dynamics, resistance of porosity on the microrotation, Brownian diffusion, and thermophoretic transport phenomenon. The numerical solutions for the nonlinear yielded equations that result from the above interaction are obtained by employing a PINN that considers the laws of physics and boundary conditions. With this technique, the flow behavior, temperature, concentration, and microrotation fields can be predicted accurately without requiring huge datasets. This shows the ability of PINNs to numerically treat highly-coupled nonlinear transport equations in a very efficient manner compared to other traditional methods. The important discoveries from this study include that the porous and magnetic factors increased the skin friction coefficient, but the magnetic effect and viscous dissipation decreased the rate of heat transfer, and the thermophoresis effect decreased the rate of mass transfer while the Brownian effect increased it. The precision of the PINN algorithm is confirmed by comparison of the results with the earlier findings, which proves very high accuracy and hence the robustness of the current computing framework. Results of this research are useful for the development of some thermal management systems, energy converters, cooling methods, chemical reaction processes, fuel cell technology, porous media reactors, and ocean engineering involving the transport of complicated non-Newtonian nanofluids.

Modelling doi: 10.3390/modelling7040144

Authors: Yajuan Wang Yuehong Wang Gao Zhang Junde Guo Xiyao Liu

To enhance the thermal performance of a Stirling air conditioner, this study applies Schmidt-based dimensionless analysis to systematically investigate the influence of key structural parameters on its cooling and heating characteristics. A dimensionless thermodynamic framework is established under the ideal isothermal assumptions of the Schmidt model to investigate the effects of temperature ratio, swept volume ratio, dead volume ratio, and phase angle on a Stirling system. The results indicate that increasing the temperature ratio enhances the thermodynamic driving potential; however, excessive temperature ratios introduce stronger irreversibilities, resulting in saturation or even degradation of effective cooling performance. The dimensionless cooling capacity increases significantly with phase angle, rising from 0.25 at α = 50° to 0.65 at α = 120°, while heating capacity peaks at α ≈ 71.6° with εe = 0.18. The p–v diagram analysis reveals optimal work output at α ≈ 75°, where the cycle area reaches 20.8, representing a 44.4% increase from the value at 15°. Performance saturation occurs at τ > 3 and κ > 6 for cooling and beyond κ > 4 for heating. Within the assumptions of the ideal Schmidt model, the results suggest that medium-to-high temperature ratios (τ ≈ 3–4) combined with moderate swept volume ratios (κ ≈ 6–8) provide the optimal balance between thermodynamic performance and structural compactness; these parameter combinations should be regarded as theoretical design references for ideal operating conditions rather than directly applicable engineering optimization guidelines.

Modelling doi: 10.3390/modelling7040143

Authors: Naveed Ashraf Ghulam Abbas Umar Farooq Jason Gu

Three-port DC-to-DC converters based on the SEPIC-boost circuit have gained remarkable attraction in standalone applications such as DC micro grids having PV panels as roof-tops in electric boats, electric and hybrid vehicles, LED driving circuits, telecommunication systems, and medical and industrial electronics devices. Such a combination of SEPIC-boost in a single converter eliminates the use of three separate DC-to-DC converters to charge the batteries and to supply power from the PV module or batteries to the load. All such modes of operation in a single package make the converter compact by reducing the number of solid-state devices and passive components. It also enables the reduction in conversion losses and hence improves the system’s overall conversion efficiency. The control of a single circuit becomes simple and effective in terms of power management by detecting the solar irradiation and state of charge (SOC) of the battery. It enables the continuous flow of power to the load from PV modules or batteries, which is determined by the SOC of the battery and the available level of solar irradiation. This article develops the dynamic or state-space modeling of the combined operation of the SEPIC-boost-based DC-to-DC converter, which has not yet been developed in the literature. The development of systems based on separate dynamic SEPIC or boost modeling cannot meet the requirements of all operating modes. A state-space model of the combined operation of the SEPIC-boost converter enables evaluating the performance of such an energy management system during its various operating modes effectively. The validity of the developed model is recognized with results gained from MATLAB/Simulink and electronics-based Multisim computer software.

Modelling doi: 10.3390/modelling7040142

Authors: Tatiana Kin Aleksey Budnikov Yury Gamin Anna Khakimova Ivan Soloviev

This study conducts a preliminary FE simulation of screw piercing and screw rolling processes for producing bimetallic pipes with variable inner and outer positioning and thickness of the corrosion-resistant steel CL (13Cr and 18Cr10Ni grades) as a rational first step before experimental testing. The results demonstrate that a favorable stress–strain state is formed in both processes under the selected deformation parameters (there are no high tensile stresses in the area of high strains and low temperatures). Shape change analysis confirmed that the pipe geometric dimensions according to simulation are sufficiently close to the target values, with only minor deviations in wall thickness and ovality. The change in CL thickness during piercing ranges from 34% to 51% and increases with the elongation ratio. In the rolling process, it reaches approximately 55–56%. The CL position, its thickness and the material choice significantly influence the deformation heating intensity within the bonding of base and clad materials, as well as the magnitude of the forces acting on the tool in contact with the CL. The obtained results can serve as a methodology that lays the groundwork for experimental verification and the further technology implementation, while minimizing risks and costs.

Modelling doi: 10.3390/modelling7040141

Authors: Guoyuan Wang Wenbo Fan Yinhe Sun Bowen Hu Liyuan Yu Zhaoyang Song

Fractures exert a significant influence on rock mass deformation and seepage pathways, thereby posing a serious challenge to the safe and efficient extraction of deep mines. This problem is particularly evident in deep mines located near the sea, where fractures are extensively developed. For such mines, the overlying seawater represents a considerable potential risk to mining safety. Therefore, investigating the distribution characteristics of deep fractures and clarifying the coupling relationships among the fracture, stress, seepage, and temperature fields are important for ensuring safe and efficient production in deep mines near the sea. Taking the auxiliary shaft of the Sanshandao Gold Mine as the engineering case, this study uses extensive measured fracture data, determines fracture locations by their centroids, and adopts kernel density estimation to non-parametrically characterize the fracture spatial distribution. Fourier convolution is then employed to rapidly reconstruct fracture positions in the discrete fracture network (DFN) model. The results demonstrate that the proposed kernel density estimation method can effectively identify the spatial distribution characteristics of fractures. Subsequently, the fracture field of the underground rock mass is reconstructed by the Monte Carlo method, and a thermal–hydro–mechanical multi-field coupling model incorporating the fracture field is established. The numerical results indicate that fluid flow is primarily concentrated along fractures, and that heat transfer within fractures is markedly faster than that in the rock matrix. The presence of fractures significantly affects the stress field of the underground rock mass, and their influence on the stress distribution increases as fracture length becomes greater. Accordingly, the effects of fractures should not be neglected in numerical analyses. The findings provide reliable support for mine stability calculations and safety evaluations.

Modelling doi: 10.3390/modelling7040140

Authors: Fabien Beaumont Guillaume Polidori Mohammed Lachi

Despite growing interest in sustainable construction materials, unfired clay bricks still exhibit limited thermal insulation performance. This study investigates the enhancement of perforated raw earth bricks through the integration of a bio-based phase change material (PCM) derived from coconut oil to improve thermal damping and heat storage capacity. A numerical analysis was conducted on several configurations, including a solid reference brick, a hollow brick with air-filled cavities, and bricks incorporating one, two, or three rows of PCM encapsulated in polylactic acid (PLA) tubes. Results show a progressive improvement in thermal performance with increasing PCM content showing that the three-row PCM configuration achieved the best dynamic thermal behavior. Thermal gradient and enthalpy analyses revealed the combined effects of the thermal conductivity of PLA and raw earth and the latent heat storage capacity of the PCM. Replacing 17 PCM tubes with a single container of equivalent volume further improved performance while reducing system complexity and cost, decreasing the decrement factor by nearly 50% compared with the three-row configuration. These findings demonstrate the potential of PCM-enhanced raw earth bricks for passive thermal regulation in sustainable buildings, although experimental validation remains necessary.

Modelling doi: 10.3390/modelling7040139

Authors: Oscar H. Sierra-Herrera Mario Eduardo González Niño Carlos E. Pinto-Salamanca Wilman Alonso Pineda Muñoz Jersson X. Leon-Medina

Wind turbines are critical components in renewable energy systems, where early fault detection is essential to ensure reliable operation and reduce maintenance costs. Vibration-based monitoring using multichannel signals provides rich information about the dynamic behavior of the system, although it also introduces challenges related to high dimensionality and feature redundancy. This paper proposes a machine learning-based methodology for fault classification that combines Discrete Wavelet Transform (DWT) for time–frequency feature extraction with Linear Discriminant Analysis (LDA) for dimensionality reduction within a structured processing pipeline. The approach incorporates a Group K-Fold cross-validation strategy to prevent data leakage and ensure a reliable evaluation when working with segmented signals. Experimental results show that the proposed framework achieves high classification performance, reaching a mean accuracy of 98.84±1.16% and a weighted F1-score of 0.9905±0.0089 using a Support Vector Machine (SVM) classifier over five Group K-Fold splits. The results also indicate that dimensionality reduction plays a critical role in improving class separability, having a greater impact than the specific choice of wavelet transform. Findings demonstrate that the proposed DWT–LDA-based approach provides an effective solution for rotor imbalance detection in the laboratory-scale wind turbine evaluated in this study.

Modelling doi: 10.3390/modelling7040138

Authors: Carolina Lima da Silva Luiz Carlos Lobato dos Santos George Simonelli

Accurate prediction of natural gas thermophysical properties is essential for applications in production and transportation engineering, including reservoir simulation and flow modeling. Although machine learning (ML) techniques have been widely used, most studies focus on the estimation of these properties, with limited integration into practical applications. In this study, we propose a supervised model based on a Backpropagation Neural Network for simultaneous estimation of four interdependent properties: compressibility factor (Z), viscosity (μ), density (ρ) and gas formation volume factor (Bg). The multi-output model was trained on 58,165 data points generated from thermodynamic correlations, using pressure, temperature, composition (mole fractions of N2, CO2 and H2S), and gas specific gravity as inputs. The results yielded RMSE values of 5.56 × 10−4, 3.24 × 10−5, 3.01 × 10−2, and 6.33 × 10−4 for Z, μ, ρ and Bg, respectively, with R2 coefficients close to unity. The model’s applicability was evaluated by integrating the Z-factor into pressure drop calculations in pipelines using the Cullender and Smith method, resulting in a mean percentage error of 3.78%, close to the traditional method (3.83%). The results indicate that the model is an efficient and consistent alternative, highlighting the potential for integrating ML with classical hydraulic models.

Modelling doi: 10.3390/modelling7040137

Authors: Mohammed Mawlana Amin Hammad

Simulation optimization has been used to analyze construction operations and support planning decisions under uncertainty. It enables the identification of effective planning strategies throughout a project’s lifecycle. However, the use of stochastic simulation to evaluate alternative strategies results in higher computational demands and the generation of inferior solutions within the resulting optimal solutions. This study examines the feasibility of overcoming these issues by implementing variance reduction techniques into a discrete-event simulation optimization framework. Three variance reduction techniques are evaluated in a case study: Common Random Numbers, Antithetic Variates, and a combined application of both. While these techniques are well established in simulation, their impact on the optimization performance of construction problems has not been fully explored. The results show that VRT not only reduces the computational effort required to evaluate planning strategies but also provides better planning strategies. Among the evaluated techniques, the combined approach demonstrates the best improvements. Overall, the study highlights that variance reduction techniques can make simulation optimization frameworks more practical and reliable for complex construction projects.

Modelling doi: 10.3390/modelling7040136

Authors: Laura Paola Villalobos-Baquero Juan Camilo Mosquera-Jiménez Oscar Danilo Montoya

This paper introduces a methodology for evaluating the voltage stability margin in high-voltage direct-current (HVDC) systems, which analyzes the singularity of the power flow Jacobian matrix—computed via the Newton—Raphson method—and identifies saddle-node bifurcations. The continuation power flow method is employed to model progressive load increases, enabling the continuous tracking of power flow solutions and the determination of voltage collapse points. Within this framework, the system’s behavior is analyzed under contingency conditions, particularly transmission line outages, assessing its capability to maintain secure operating conditions under increasing demand scenarios. The main objective is to identify the most critical line in the system, defined as that which leads to the greatest reduction in loadability when unavailable, prior to voltage collapse. This approach allows for the early identification of structural vulnerabilities, supporting decision-making processes aimed at risk mitigation and operating cost optimization. The proposed methodology is validated using two systems: the six-terminal CIGRE-B4 HVDC system and an 11-node HVDC test feeder.

Modelling doi: 10.3390/modelling7040135

Authors: Nikola Mirkov Milada Pezo Rastko Jovanović Martina Balać Ognjen Peković

This study presents the analysis of global dynamics and stability (e.g., coexisting attractors, Hopf bifurcation boundary) for a nonlinear rotor system with an automatic ball balancer (ABB). The presence of nonlinearity, anisotropy and non-ideal dynamics makes this system not fully understood. The Lagrangian is written explicitly in terms of the displacement of the rotor centre and the angular positions of the balls (x,y,ψ,φj). The kinetic energy separates into structural, unbalance coupling, and ball coupling blocks, and the Rayleigh dissipation function covers both support damping and race drag. The three families of equations of motion (translational, spin, ball) are compacted into the matrix form and solved numerically. Non-dimensionalisation introduces the seven groups (Ω,μun,μb,ε,β^,D^,Δ) with Δ being the anisotropy parameter. The results document bistability between the clustered and balanced ball configurations depending solely on ball initial conditions rather than rotor displacement, together with a basin of attraction analysis in which the balanced basin occupies only approximately 20% of ball initial-condition space. A three-dimensional stability map reveals a previously unreported phenomenon: narrow islands of stability at very low race damping, suggesting that effective balancing may not always require dissipation, alongside a two-lobe Hopf bifurcation boundary with a disconnected instability pocket. Anisotropy study uncovers that the rotor’s response is dominated by quasi-periodic torus attractor across almost the entire (93.5%) parameter space rather than the simple periodic balancing usually assumed, with a clean analytical rule identifying exactly when support asymmetry will resonantly amplify vibration. Together these findings point to design principles on ball seeding, damping selection, and permissible anisotropy.

Modelling doi: 10.3390/modelling7040134

Authors: Kumari Gamage Buddhika Weerasinghe Shasha Wang Sabrina Fawzia

In-plane curved steel beams with circular hollow sections (CHSs) are widely gaining appeal in bridges. Strengthening such elements for increased demand or decreased strength due to environmental effects or fatigue, without affecting the usage of structure, is a timely need. Carbon fiber-reinforced polymer (CFRP) materials have been a promising solution for such situations. This paper investigates the flexural behavior of CFRP-strengthened vertically curved steel beams with CHSs. Sixteen such beams, each with a span of 1200 mm and having four different radii of curvature, i.e., 0 m, 2000 mm, 4000 mm, and 6000 mm, and retrofitted with a range of CFRP bond lengths, are considered. Numerical models of these beams are developed and validated using the results of tests performed by the authors, and the validated models were used to simulate bond characteristics and structural performance. Optimum performance was noted in the specimens strengthened with CFRP fibers attached in the axial direction of the members, irrespective of their curvature. On average, strength enhancements of 21% and 14% were obtained in CFRP-strengthened straight and curved beams, respectively. Detailed bond characteristics presented in this paper under transverse loads yield important data for researchers, designers and material developers to strengthen in-plane curved steel members.

Modelling doi: 10.3390/modelling7040133

Authors: Fangqian Wu Xueping Song Lin Yuan Shanglei Jiang Yuwen Sun

Due to the low stiffness characteristics, thin-walled parts are prone to force-induced deformation during the peripheral milling process, which severely restricts machining accuracy and efficiency. In existing studies, for curved thin-walled parts, the Finite Element Method (FEM) is usually adopted for deformation prediction. However, the traditional FEM usually requires a considerable amount of computing time, owing to the high model complexity and batch parameter evaluations. Therefore, this study proposes a method of constructing a surrogate model based on a small amount of FEM simulation data. Firstly, a peripheral milling cutting force model is established to obtain the instantaneous milling force. Secondly, a finite element model considering the material removal effect is constructed, and an iterative solution strategy is introduced to calculate the force-induced deformation. Finally, an Enhanced Latin Hypercube Sampling (ELHS) method is used to generate training samples, and the Elliptic Basis Function Neural Network (EBFNN) is selected as the surrogate model to establish a nonlinear mapping relationship between machining parameter combinations and force-induced deformation. This method enables rapid prediction of deformation at any machining position on curved thin-walled parts, reducing the computation time from hours to seconds while maintaining prediction accuracy.

Modelling doi: 10.3390/modelling7040132

Authors: Shuichi Sakamoto Yoshiaki Kojima Kenta Saito Zulhafiz Syazmi Bin Roslan Shui Miyata Ryuki Kiuchi

Rice straw, a byproduct of global rice production (~530 million tons annually), is generated at 80–100 million tons per year, yet a significant portion is incinerated or discarded, causing environmental problems. This study investigated the sound absorption properties of straw from IR8, a high-yielding long-grain rice variety. The normal incidence sound absorption coefficient was measured at three bulk densities (0.140, 0.150, and 0.160 g/cm3) for bundled rice straw structures. Cross-sectional images obtained using a micro-computed tomography (CT) scanner were then used to theoretically estimate the sound absorption coefficient. Each CT cross-section, oriented perpendicular to the incident sound wave direction, was modeled as a clearance between two parallel planes. The characteristic impedance and propagation constant were calculated from this model, and the normal incidence sound absorption coefficient was determined using the transfer matrix method with measured tortuosity incorporated. The experimental and theoretical absorption peaks showed similar trends across bulk densities. A parameter study was also conducted by scaling cross-sectional images according to the diameter ratios of Koshihikari short-grain rice straw and Yumekaori wheat straw relative to IR8. Additionally, reducing the number of CT images to as few as ten adequately approximated the full dataset for a 20 mm thick sample.

Modelling doi: 10.3390/modelling7040130

Authors: Shang Wang Yajuan Zhang Linjie Li

The Traveling Salesman Problem (TSP) is a fundamental NP-hard combinatorial optimization problem with broad applications in logistics, scheduling, and satellite mission planning. While Ant Colony Optimization (ACO) offers distributed search and positive feedback, conventional variants suffer from premature convergence and quadratic construction costs that limit scalability. We propose the Globally Adaptive Ant Colony System (GACS), which integrates three synergistic mechanisms: (1) K-nearest neighbor candidate-list pruning that reduces per-step construction complexity from O(n) to O(K); (2) a globally adaptive pheromone weighting scheme that dynamically calibrates reinforcement intensity as the search matures; and (3) an adaptive stagnation recovery mechanism that applies pheromone smoothing to escape local optima. Numerical experiments demonstrate that GACS consistently outperforms four traditional ACO baselines under an equivalent time budget. On a large benchmark set from TSPLIB, GACS achieves highly competitive results against various state-of-the-art metaheuristics, with non-parametric statistical tests confirming its significant superiority in both solution quality and convergence rank. Ablation and sensitivity analyses verify that all three mechanisms are individually indispensable and that the framework is robust to parameter perturbation. Specifically, the evaporation rate and stagnation threshold are identified as the most critical parameters affecting performance, while the smoothing and adaptive range parameters exhibit low sensitivity. These results establish GACS as a lightweight, scalable, and adaptable framework for the TSP.

Modelling doi: 10.3390/modelling7040131

Authors: Ying Huang Zhiqiang Xin Zhiming Cai Songyang Liu Yanming Xu

Recognizing that efficient and high-fidelity simulation of wind farms in mountainous terrain remains a significant challenge, this study adopted an integrated Large Eddy Simulation (LES) and Dynamic Wake Meandering (DWM) approach to conduct medium-fidelity fluid–structure interaction analysis of a wind farm situated on multiple-hill terrain. Furthermore, a comparative investigation with a flat wind farm was conducted to elucidate the coupled effects of turbine layout and terrain conditions on wake characteristics and structural loads. Results show that the terrain-induced vortical structures in the mountainous wind farm significantly enhance the wake meandering amplitude and expansion rate, leading to higher overall turbulence intensity compared to the flat wind farm. Due to the higher wake recovery rate in the mountainous wind farm, the power gain from lateral offset is more limited. Both wind farms reach their maximum power output at a lateral offset of one turbine rotor diameter (1D) under the present setup, beyond which no further increase is observed. The streamwise decay of the terrain-induced flow acceleration effect is identified as the primary cause of power differences among front-row turbines located on distinct hills within the mountainous wind farm. Furthermore, the terrain-induced vortices create more non-uniform inflow conditions in the mountainous wind farm, causing certain turbines to exhibit peak short-term equivalent fatigue loads with a distribution pattern distinct from the flat wind farm. Due to the generally higher turbulence intensity, all turbines in the mountainous wind farm experience increased fatigue loads compared to the flat wind farm.

Modelling doi: 10.3390/modelling7040129

Authors: Tuo Zhou

In this paper, a class of distributed event-triggered (ET) control strategy is proposed to address the average consensus problem for multi-agent systems (MAS). Compared with the existing ET control methods with fixed connected communication links, underlying topology considered here is jointly connected, which is more adaptable to the needs of practicality. In order to save communication energy resources among agents, an improved integral-type event-triggered (ITET) strategy is chosen to guarantee that the entire system reaches an agreement on the desired state and no Zeno behavior occurs. Finally, two simulation examples are given to investigate the effectiveness of the proposed control strategy.

Modelling doi: 10.3390/modelling7040128

Authors: Ahmed Y. Zakariya Ahmed F. Tayel Shehab Ahmed

Energy-efficient operation of railway systems is of great importance for both environmental and economic reasons. Minimizing net energy consumption helps to achieve such energy-efficient operation. In this paper, the train’s speed profile and headway between trains are controlled to achieve lower traction energy consumption and higher train synchronization for better regenerative braking energy utilization. Eventually, the net energy consumption, defined as the difference between the traction energy consumption and the utilization of regenerative braking energy, is minimized. Two optimization problems are defined to solve the problem efficiently. The first main problem is to find the optimal speeds at each segment of the railway track. The second sub-problem’s objective is to find the optimal values of travel time, dwell time, and headway for every suggested solution to the main problem. Both problems are solved using the genetic algorithm. Numerical results are based on the actual operation data of the Beijing Metro Yizhuang Line in China. In the numerical results, the proposed strategy of dividing the problem into two problems and the use of variable headway shows an enhancement in reducing net energy consumption by 7.5% compared to other strategies in the literature.

Modelling doi: 10.3390/modelling7040127

Authors: Ismail Ekmekci Faruk Oral Cemil Koyunoğlu

Accurate characterization of wind-speed distributions is essential for preliminary wind-resource assessment, vertical wind-profile evaluation, and energy-yield estimation. This study presents a CFD-assisted reconstruction and validation framework that integrates two-parameter Weibull statistics with class-conditioned OpenFOAM v13 simulations to reconstruct wind-speed distributions at different measurement heights. Hourly wind-speed records measured at 10 m and 30 m at the Sakarya–Esentepe station during the period of 2009–2010 were used. The 2009 dataset was employed to estimate the Weibull shape and scale parameters by maximum likelihood estimation, while the 2010 dataset was reserved for independent validation. To ensure methodological consistency between statistical wind characterization and steady CFD modeling, the fitted Weibull distribution was discretized into representative wind-speed classes. For each class, a steady Reynolds-averaged Navier–Stokes simulation was performed in OpenFOAM under neutral atmospheric boundary-layer assumptions using the standard k–ε turbulence model, a logarithmic inlet velocity profile, and rough-wall boundary treatment. The class-wise CFD velocity responses extracted at 10 m and 30 m were then weighted by the corresponding Weibull class probabilities to reconstruct height-specific wind-speed probability distributions. The reconstructed distributions showed good agreement with the measured and fitted Weibull references. The RMSE values obtained by CFD for measurements at heights of 10 m and 30 m on the measurement mast were 0.45 m s−1 and 0.52 m s−1, respectively, and the Pearson correlation coefficients were 0.97 and 0.96, respectively; these values indicate that the CFD analyses are reliable. For the Lilliefors-adjusted Kolmogorov–Smirnov statistics, there is no value higher than 0.06. The differences between the reference and CFD-reconstructed AEP estimates were +0.40% at 10 m and −1.97% at 30 m. These findings indicate that the proposed Weibull–OpenFOAM framework provides a reproducible engineering approach for CFD-assisted wind-speed distribution reconstruction and height-specific consistency assessment. However, the method should be interpreted as a class-conditioned reconstruction framework rather than a stand-alone transient atmospheric wind prediction model.

Modelling doi: 10.3390/modelling7040126

Authors: Chen Xu Yang Yang Xiaojiang Gu Yijun Mao

The snapshot proper orthogonal decomposition (POD) method relies on synchronously sampled datasets, significantly limiting its utility for analyzing asynchronous measurements in unsteady flow studies. This paper proposes a frequency-domain proper orthogonal decomposition (FDPOD) method tailored for mode extraction and flow field reconstruction from asynchronously sampled data. The FDPOD framework integrates three key components: frequency-domain transformation to decouple phase discrepancies inherent in asynchronous sampling, power spectral density (PSD) analysis combined with segmented ensemble averaging to suppress spectral leakage errors, and eigenvalue decomposition of energy-ranked frequency components to identify dominant coherent structures. Validated through numerical simulations of a subsonic jet and experimental measurements from a low-speed mixed-flow fan, the method demonstrates exceptional performance under asynchronous conditions: cumulative energy errors are reduced to 0.3% across the first 50 modes, while flow field reconstruction achieves 99.5% accuracy. Dominant mode structures exhibit remarkable consistency with those derived from synchronous conditions, with hot-wire measurement errors remaining below 0.03% for both asynchronous and temporally shuffled datasets. These results position FDPOD as a robust and practical tool for analyzing complex unsteady flows where synchronous data acquisition proves impractical, particularly in large-scale or spatially distributed measurement systems.

Modelling doi: 10.3390/modelling7040125

Authors: Juraj Kováč Peter Malega Pavlo Vaulin

Virtual reality can support the preparation and rehearsal of assembly tasks by providing a safe and repeatable digital representation of workstations. This study presents the development and laboratory feasibility validation of a geometry- and procedure-oriented VR simulation model for the assembly and disassembly of end-effectors on an industrial robot. The workflow was implemented using the Almega AX-V6 robotic workstation as a case study and included geometric acquisition of the real robot, CAD modelling in SolidWorks, redesign of the original end-effector connection using a quick-change flange concept, creation of two alternative end-effector models, modelling of the laboratory workspace in SketchUp, and scene enhancement in Twinmotion. The resulting robot and environment models were integrated in Pixyz Review and deployed through an Oculus Rift-based VR setup. Compared with the original flange concept, which required twelve screws, the redesigned training concept used two screws and two nuts, reducing the number of fastening elements by 66.7% and the number of screw positions by 83.3%. The VR implementation supported visual inspection, controller-based placement and alignment, and symbolic confirmation of fastening steps; it did not include force feedback, threaded fastening physics, automatic error scoring, or quantified transfer-of-training evaluation. Laboratory feasibility validation confirmed correct asset integration, spatial correspondence with the physical workplace, and functional executability of the target exchange sequence. The results show that the workflow is useful as a case-study pipeline for CAD-to-VR modelling and assembly rehearsal, while controlled user studies are still required before claims about training effectiveness can be made.

Modelling doi: 10.3390/modelling7040124

Authors: Steven D. Harris Christopher D. Gill Roger D. Chamberlain

Orchestration of Asymmetric Multiprocessing Platforms (AMPs), such as ARM big.LITTLE, frequently relies on the heuristic assumption of cluster independence, wherein high-performance (“Big”) and high-efficiency (“Little”) cores operate as computationally orthogonal resources. These cores are partitioned into “islands” of separate power/performance clusters, operating on independent/voltage frequency rails. However, these platforms share resources, including Last-Level Cache (LLC), main memory, and interconnects across all cores. Therefore, we assume that islands interact, operating in a functionally “coupled state.” To conduct a measure-theoretic evaluation of this assumption, we apply the Boltzmann uniqueness theorem, recently demonstrated to be the singular method to determine the veracity of this assumption. Mathematically, we define an “uncoupled” system as one whose joint resource measurement is strictly the convolution of its subsystem measures. We evaluate two distinct AMP topologies—Orange Pi 5 and Cubie A7A under controlled saturation—and demonstrate a systemic failure of convolution commutativity. We subsequently expand this investigation to high-performance x86 hybrid architectures via the Intel i7-12800H platform. Our findings, characterized by significant negative power correlations and the failure of predictive convolution models, constitute a counterexample for cluster independence. We identify shared architectural resources, specifically the LLC and shared power rails, as the likely physical mechanisms of “architectural entanglement,” rendering traditional additive performance models underspecified.

Modelling doi: 10.3390/modelling7040123

Authors: Shunzuo Qiu Qin Liu Yan Yang Qianqi Xiao Yan Jiang

To solve the problem that the theory of in situ separation and sand removal of marine hydrate is not perfect enough, the formulas of fluid tangential velocity and particle radial migration were derived based on the separation theory of rotating fluid and equilibrium orbit. Under certain assumptions, theoretical prediction models of fluid tangential velocity, particle radial migration and separated particle size under different operation and physical parameters were established. Then the theoretical results were compared with the numerical simulation results. The results show that the key factors affecting the tangential velocity are the inlet spiral pitch, the number of spiral blades, the diameter of the overflow pipe, the thickness of the spiral blades, and the main diameter of the desander. The tangential velocity is proportional to the flow rate. When the particle diameter is fixed, the radial migration velocity of the particle decreases with the increase in the rotation radius. When the rotation radius is fixed, the radial migration velocity of particles increases with the increase in particle diameter. The larger the hydrate particle size, the shorter the time to reach the center, and the larger the sand particle size, the shorter the time to reach the wall. The particle size is inversely proportional to the tangential velocity of the fluid in the equilibrium orbit. The determination of fluid velocity, liquid–solid density difference and particle size is the key factor affecting particle equilibrium trajectory and particle size separation. The numerical simulation results are basically consistent with the theoretical values. The obtained results enrich the theoretical model of hydrate in situ sand removal.

Modelling doi: 10.3390/modelling7030122

Authors: Jiaren Sun Yating Jiang Shuai Teng Zongchao Liu Nuo Chen

Accurate detection of field insect pests remains a significant challenge for precision agriculture due to the elongated and variable morphology of the target organisms, their frequent resemblance to complex background textures, and the long-tail distribution of species in natural datasets. While deep convolutional neural networks (CNNs) have advanced the field, they are often constrained by a limited effective receptive field and the entanglement of semantic and spatial features, which can lead to elevated false-positive rates and missed detections for low-contrast or rare targets. This paper introduces a novel detection framework that integrates state space modeling with multi-stream feature disentanglement to address these limitations. First, a visual state space module is employed as the backbone feature extractor, enabling the establishment of a global receptive field with linear computational complexity and thereby improving the perception of long-range morphological structures. Second, a Topological Feature Disentanglement Pyramid Network is proposed. This architecture explicitly separates feature representations into semantic and spatial streams and recombines them through graph convolutional interactions, which serves to suppress background interference and enhance localization precision. A meta-auxiliary detection head, active only during training, is introduced to amplify supervision signals for hard, low-contrast samples via adversarial gradient modulation. Furthermore, an implicit neural radiance field augmentation pipeline is used to generate physically consistent synthetic views of underrepresented pest classes, mitigating the negative effects of long-tail data distributions. Experimental evaluations on the public BAU-Insectv2 benchmark demonstrate that the proposed method achieves a mean average precision (mAP@0.5) of 81.8%, representing a 4.4-percentage-point improvement over a comparable baseline, while maintaining a compact parameter count of 2.33 M and an inference speed of 178.6 FPS. The framework exhibits particular efficacy in detecting elongated, minute, and rare pests, suggesting a promising technical approach for real-time, field-based pest surveillance in precision agriculture.

Modelling doi: 10.3390/modelling7030121

Authors: Ming-Lei Ma Cheng-Da Yu Ji-Long Chai Guo-Wen Xu Biao Wu Jing-Zhong Tong Qing-Hua Li

To address the deterioration issues of wet joints in prefabricated steel–UHPC composite bridge decks caused by inadequate interfacial performance, an orthotropic steel–UHPC composite bridge deck system under hogging moments was investigated. A numerical study on the cracking resistance of wet joints was conducted using a cohesive zone model based on the traction–separation law to characterize the interfacial mechanical behavior. The numerical model was validated against experimental results, showing good agreement in terms of crack development and structural response. Subsequently, a parametric analysis was carried out to evaluate the influence of different reinforcement details, UHPC thickness and stud spacing. The results indicated that the adopted cohesive model was capable of accurately simulating the cracking behavior at the wet joint interface. In addition, the cracking resistance of UHPC wet joints could be significantly improved by providing additional reinforcement and reducing the longitudinal stud spacing. Moreover, the results revealed that joint reinforcement primarily enhanced local crack control performance, while having a limited effect on the global load–deflection response of the structure. These findings provide a reliable basis for the design and optimization of wet joint configurations in prefabricated steel–UHPC composite bridge decks.

Modelling doi: 10.3390/modelling7030120

Authors: Rogério F. F. Lopes Christian J. Silva Rodrigo R. Menéres Pedro J. S. C. P. Sousa Pedro M. G. P. Moreira João S. Silva Rodrigo S. Andrade

The design of a railway coach must meet strict certification requirements, especially in crashworthiness analysis under the European standard EN 15227. Performing this analysis with full-scale FEM models is highly demanding in terms of time, computational power and engineering resources, even with large server clusters. To improve efficiency, it is useful to simplify regions of the structure that are less influenced by external loads. In this approach, less critical parts are replaced with flexible one-dimensional elements, reducing the number of degrees of freedom while preserving the vehicle’s main dynamic behaviour. By concentrating on a specific mid-span section, the model becomes more robust and easier to manage. Calibrated elements are introduced to accurately reproduce the mass and stiffness of the removed structural components. The methodology also integrates mass and stiffness elements to capture structural response over a broader frequency range. An iterative non-gradient calibration procedure is then applied to adjust the equivalent stiffness and mass distribution so that the simplified model reproduces the response of the full-scale reference model. The results show that this strategy is effective, achieving a 77.6% reduction in simulation time while maintaining reliable accuracy. However, the process is still labour-intensive, and its performance may decline under large deformation conditions.

Modelling doi: 10.3390/modelling7030119

Authors: Shuichi Sakamoto Kenta Saito Yoshiaki Kojima Ryuki Kiuchi Shui Miyata

This study aims to establish a simple theoretical method for estimating the sound absorption characteristics of randomly packed granular materials. Using insights gained from existing mathematical models for regular packing and methods utilizing CT images, we propose the “single-clearance” model, a theoretical model that estimates the sound absorption coefficient. It calculates the volume of voids and the surface area of spheres in a granular material based on the material particle size and packing density; the volume and surface area are then used to simplify the packing structure of the granular material to a clearance between two planes. The model is then validated by comparing its obtained theoretical sound absorption coefficients with experimental values and theoretical values derived from CT images. In random packing structures with small variations in porosity relative to the direction of sound propagation, the effect of accounting for this variation on the sound absorption coefficient is negligible. In the single-clearance model, the sound absorption coefficient calculated using a packing density of 0.65 for the random packing structure generally agrees with that derived from CT images at all particle sizes. Thus, the sound absorption coefficient can be estimated simply using particle size and packing density.

Modelling doi: 10.3390/modelling7030118

Authors: Dianchao Wang

Accelerated carbonation of cement-based materials offers a promising route for CO2 sequestration driven by waste heat co-emitted from cement and power plants; however, existing kinetic models typically describe the low-temperature gas–liquid–solid regime near 100 °C and the high-temperature gas–solid regime near 600 °C in isolation, limiting their applicability to plant-scale reactor design. This study proposes a unified dual-regime kinetic framework spanning 20–700 °C. The low-temperature branch couples Henry’s-law CO2 solubility, a sigmoidal water-film stability function, and an Arrhenius ionic reaction term, whereas the high-temperature branch integrates shrinking-core surface reaction and product-layer diffusion with an attenuation term near the CaCO3 decomposition onset. Seven parameters were calibrated by bounded least squares against a 51-point temperature dataset compiled from the author’s previously published carbonation experiments. The calibrated model reproduced the bimodal temperature dependence of the carbonation degree (R2 = 0.62; RMSE = 0.083), with peaks near 100 °C and 640 °C, and predicted reactor volumes of order-of-magnitude 150–200 m3 for a 1 Mt/y cement plant under three waste-heat operating points. The framework bridges particle-scale kinetic and plant-scale design, and identifies mixing as the dominant operational sensitivity at the clinker-cooler condition.

Modelling doi: 10.3390/modelling7030117

Authors: Haoran Song Lipu Zhang

The evolution of 193 nm deep-ultraviolet (DUV) lithography toward high numerical aperture (NA > 1.35) presents challenges approaching physical limits for antireflective (AR) coatings on strongly curved lens elements. In this study, a full-stack multi-objective optimization framework is developed by coupling the Non-dominated Sorting Genetic Algorithm II (NSGA-II) with the Transfer Matrix Method (TMM) to optimize a 7-layer LaF3/MgF2 system on strongly curved substrates (R=150 mm). The model integrates material dispersion, thermo-optic effects, deposition flux deviations, and manufacturing thickness constraints. Following 1500 generations of optimization and TOPSIS-based decision-making, the selected Pareto optimal solution achieves a full-aperture average reflectance of 1.3633% and a radial uniformity of 9.5037%. The design further exhibits high environmental robustness with a thermal drift of 0.0019% and a residual stress of 39.23 MPa. These results demonstrate that the proposed method overcomes the critical process bottleneck of achieving full-aperture uniformity below 10% on strongly curved optics. This framework provides a general paradigm for the robust design of next-generation ultra-precision DUV optical systems, effectively balancing theoretical depth with engineering feasibility.

Modelling doi: 10.3390/modelling7030116

Authors: Jinzhao Fan Bixiao Zhang Jiazhen Liu Yufei Cai Hong Shi

With the rising integration of high-performance GPUs, localized hotspots induced by discrete heat sources present severe thermal challenges. Traditional single-inlet–single-outlet liquid cold plates can scarcely meet the heat dissipation requirements of inhomogeneous high heat fluxes. This study systematically investigates the effects of nine multiple-inlet–multiple-outlet (MIMO) configurations, ranging from single-inlet–single-outlet to three-inlet–three-outlet, on cold plate hydrothermal performance. An innovative stepwise optimization strategy, topology optimization (TO)-driven channel layout combined with fin-enhancement (FE)-based fine regulation, is proposed and verified to precisely regulate surface temperature distribution of discrete heat sources. The results show that the three-inlet–three-outlet configuration C-3 exhibits the optimal comprehensive performance among the nine configurations. Compared with the worst configuration A-2, C-3 reduces the pressure drop by 58.37% to only 147.18 Pa and yields the highest PEC, striking the optimum trade-off between heat transfer enhancement and fluid flow resistance. Through multi-inlet flow distribution and multi-outlet heat extraction, C-3 accurately suppresses heat accumulation in high heat flux regions, limiting the maximum temperature to merely 29.82 °C and drastically narrowing the substrate temperature difference from 8.69 °C to 2.12 °C. In comparison with the traditional cold plate (TCP), the optimized cold plate (OCP) realizes a 17.42% increase in performance evaluation criterion (PEC). Furthermore, the fin-enhanced optimized cold plate (FEOCP) reduces the temperature standard deviation by 54.15% relative to TCP, significantly enhancing temperature uniformity with only an additional pressure drop penalty of 5.43%. This study reveals the regulation mechanism of MIMO configurations on the flow field distribution of liquid cold plates and verifies the effectiveness of the TO-FE optimization framework, thus providing highly valuable engineering solutions for the high-efficiency, uniform-temperature and low-resistance heat dissipation of high-power electronic devices.

Modelling doi: 10.3390/modelling7030115

Authors: Yi Guo Chun Li Yang Lv Liuxiao Li Yangfan Lu Kai Wen

Heated crude oil pipelines transporting high-pour-point, high-viscosity, and high-wax-content crude oil are increasingly operated under small-batch and multi-condition scenarios. Under such conditions, fixed-parameter models and experience-based operating strategies may fail to accurately describe the evolving thermo-hydraulic state, resulting in inaccurate temperature-safety assessment and conservative energy use. To address this problem, this study develops a hybrid modelling and simulation framework for the energy-efficient operation of heated crude oil pipelines. The framework integrates operating-state perception, online parameter inversion, transient thermo-hydraulic simulation, data assimilation, and rolling optimization. First, an online parameter inversion method based on inverse problem solving is established to dynamically identify the overall heat-transfer coefficient and friction correction factor from Supervisory Control and Data Acquisition (SCADA) measurements. Second, a transient thermo-hydraulic simulation and data-assimilation model is constructed to predict pressure, temperature, and safety margins under changing boundary conditions. Third, a constraint-aware rolling optimization strategy is introduced to coordinate heating and pumping operations while satisfying temperature and pressure constraints. The proposed framework is validated using a practical crude oil pipeline. Under a representative low-flow-rate condition, online parameter inversion corrects the overestimation of the thermo-hydraulic state by the fixed-parameter model: the total temperature drop along the pipeline is revised from 33.12 °C to 35.65 °C, and the minimum station-inlet oil temperature is revised from 24.77 °C to 21.61 °C. After optimization is introduced, the total operating energy consumption decreases from 11,715.65 kW to 11,287.43 kW, corresponding to a reduction of 3.66%, while all temperature and pressure constraints remain satisfied. Under time-varying boundary conditions, the rolling optimization strategy further adjusts heating-furnace operation according to variations in inlet flow rate, inlet oil temperature, and ambient temperature, thereby reducing cumulative heating energy consumption while maintaining safe operation. The results demonstrate that the proposed framework provides an implementable modelling and simulation approach for online state assessment, transient prediction, and energy-efficient operation of heated crude oil pipelines under variable operating conditions.

Modelling doi: 10.3390/modelling7030114

Authors: Tianxue Yang Dongpo Zhao

To address the issues of pronounced resonance, limited control bandwidth, and insufficient trajectory tracking accuracy in piezoelectric-driven elliptical vibration-assisted cutting (EVC) systems under high-frequency vibration, this paper proposes a trajectory tracking control strategy combining damping control with frequency-domain shaping. First, a damping-control strategy is integrated into the control system to refine the plant’s inherent dynamic properties, suppressing the resonance peak and elevating the system’s stability margin. Second, to enhance the system bandwidth and dynamic response, a high-gain PID controller is designed via frequency shaping. Additionally, given that the nominal model becomes high-order after implementing the damping controller, proportional gain is used for approximate equivalence with the system transfer function, lowering the model order and streamlining controller design. Next, a disturbance observer (DOB) is introduced to estimate and compensate for the unmodeled dynamics in the feedforward path in real time, further improving the trajectory tracking accuracy. Finally, taking the designed piezoelectric-driven EVC device as the controlled plant, the system frequency response is obtained through sweep excitation experiments, based on which the nominal model is identified, and the controller parameters are determined. The experimental results demonstrate that the proposed control strategy effectively suppresses resonance effects, increases system bandwidth, and reduces the trajectory tracking error. In the complex harmonic superposition trajectory tracking experiment, the steady-state tracking error is maintained within ±0.09 μm. These results demonstrate that the proposed approach markedly improves the system’s dynamic response and trajectory tracking performance, thereby providing technical support for high-precision fabrication of micro/nano-structured surfaces.

Modelling doi: 10.3390/modelling7030113

Authors: Olivier Plé Anna Lushnikova Xiaohui Jia

Carbon nanotubes (CNTs) are commonly used to reinforce and functionalize cement matrices, thereby imparting new properties. To facilitate the introduction of CNTs into inorganic matrices such as cement, the use of a master batch is advantageous. In this approach, the CNTs are premixed with a carboxymethyl cellulose (CMC) to form this master batch, which enables homogeneous dispersion and simplifies the mixing of all components (cement, CNTs, CMC, and water). The system, a CNT–CMC–cement mixture, is modeled here by using a molecular dynamics simulation. Three models were constructed for comparative analysis: pristine tobermorite 11Å (T11) for hydrated cement paste, T11 with embedded CNT (T11 + CNT), and T11 with both CNT and CMC (T11 + CNT + CMC). All models were first equilibrated to obtain stable and low-energy configurations. Subsequently, three types of loading conditions were applied to investigate mechanical and physical properties: tension, compression, and heating. Under mechanical loading, both the stress–strain response and the resulting piezoelectric effect were analyzed. Under thermal loading, the focus was on thermally induced polarization. The simulation was used to elucidate the role of CNTs and polymer modification (CMC) at the atomistic scale.

Modelling doi: 10.3390/modelling7030112

Authors: Amrita Bhadoriya Manish R. Betheja Mrudul Y. Jani Vivek Panwar Vishal Pradhan

This study develops an inventory model for deteriorating products within a dual-warehouse system under carbon tax regulation. The framework is motivated by supply chains for perishable goods where storage constraints, product deterioration, environmental costs, and financing decisions arise simultaneously. The model considers an owned warehouse and a rented warehouse with higher holding cost, where the rented facility is utilized first. To capture realistic operational conditions, the model integrates time-dependent holding costs, trend-based demand, preservation technology investment to reduce deterioration, and a two-tier trade credit scheme. Carbon tax is incorporated as an environmental cost component, while preservation technology directly influences the deterioration rate, creating a trade-off between investment and waste reduction. The proposed model is examined through numerical analysis based on parameter settings representative of perishable products such as organic dairy items. The objective is to determine the optimal replenishment cycle time, preservation investment, and order quantity that minimize the total cost within the dual-warehouse system. Numerical results indicate an average optimal cycle time of approximately 0.57 years, preservation investment of about 1.32 dollars, and order quantity near 459 units. The average total cost is around 1056 dollars, with a minimum observed cost of approximately 964 dollars. The findings highlight the significant impact of preservation technology and carbon taxation on profitability and sustainability.

Modelling doi: 10.3390/modelling7030111

Authors: D. M. Li Zhi-Yan Zhong Liu Yang Bi-He Yuan Ying Zhang

This paper focuses on the characterization of the micro-leakage channel geometry in the flange-gasket rough contact interface of hazardous chemicals transport vehicles. This work represents the first step in a multi-physics simulation framework for optical-fiber-based micro-leakage monitoring. Directly establishing a full-scale contact model from micron-scale rough peaks and valleys to the decimeter-scale flange structure would lead to extremely high computational costs; a nonlinear contact model based on quasi-representative volume element (quasi-RVE) and quasi-periodic boundary condition (quasi-PBC) is proposed in this paper. Quasi-RVE refers to a local region selected from the overall rough surface. Unlike a traditional RVE that requires strict geometric periodicity, the quasi-RVE is only approximately consistent with the overall surface with respect to key morphological parameters and volume parameters. Quasi-PBC only imposes in-plane displacement compatibility constraint on the relative side boundary without imposing periodic constraints in the peak-valley height direction. In this paper, the average interface gap and its distribution are selected as the geometric descriptors of the micro-leakage channel, and the reliability of the contact model is verified by comparing with the existing experimental and numerical results. On this basis, the influences of surface roughness, gasket material and loading conditions on the geometric characteristics of the micro-leakage channel are further analyzed. The results show that the lower stiffness gasket is easier to fit with the rough flange surface under the same load conditions, so as to obtain a larger contact area and a smaller average gap. The quasi-RVE contact model established in this paper can effectively reduce the computational scale of contact analysis of the rough sealing interface, and provide reliable channel geometric information for subsequent micro-leakage fluid simulation and optical fiber signal response simulation.

Modelling doi: 10.3390/modelling7030110

Authors: Zhihao Zhao Xiran Wang Leyi Shi Juan Wang

As an active defense paradigm, cyber deception technology effectively misleads attackers by constructing deceptive network environments, thereby increasing the cost of attack operations and introducing uncertainty into their decision-making, while providing defenders with critical response time. However, existing deception strategies are mostly based on predefined static rules derived from expert knowledge and lack the ability to adapt to dynamic attack scenarios autonomously and intelligently. This limitation results in poor adaptability and suboptimal performance of the strategy. To solve these issues, this paper proposes an Adaptive Cyber Deception Defense System (ACDDS). Different from off-the-shelf MDP/DQN frameworks in existing adaptive defense, the core innovation of ACDDS is a scenario-customized Trigger-based Adaptive Deception Strategy evolution method using Deep Q-Networks (TADS-DQN). We specifically formulate the dynamic deception strategy optimization as a cyber-deception-tailored Markov Decision Process (MDP). In this model, the state of the system is represented as a state matrix, and the attack behavior defines the environment for agent interaction. The TADS-DQN method employs a trigger-based mechanism: when a threat to real services is detected, a Deep Q-Network agent is activated. This agent takes the current system state as input and outputs the optimal reconfiguration action. The simulation results indicate that, compared to the baseline methods, TADS-DQN provides more stable defense performance, as evidenced by a smaller fluctuation range and a lower standard deviation of the attack success rate. At the same time, it achieves a reduction in the hit rate against real services that is competitive with the baseline methods.

Modelling doi: 10.3390/modelling7030109

Authors: Luca Vaccino Alana K. Lund Shirley J. Dyke Mohsen Azimi Ethan Vallerga

Establishing long-term human settlements in deep space presents significant challenges. Environmental conditions, such as extreme temperature fluctuations, micrometeorite impacts, seismic activity, and exposure to solar and cosmic radiation, pose obstacles to the design and operation of habitat systems. Prolonged mission duration and vast distances from Earth introduce further complications in the form of delayed communication and limited resources, making Earth independence through appropriate autonomous management systems especially desirable. Enabling the modeling and simulation of the consequences of disruptions and faults, and their propagation through the various habitat subsystems, is critically needed for the development of resilience-based design frameworks and methods for autonomous operation. While existing simulation tools can assist in modeling isolated aspects of damage, the integration of damage propagation and the capacity to enable detection and repair are rarely considered in a computational model. This paper introduces and demonstrates an architecture designed specifically to enable the modeling and integration of faults and damage, as well as their cascading effects. By combining physics-based and phenomenological models, our approach balances computational efficiency with model fidelity. After describing the modeling approach and corresponding architecture, we demonstrate its application within HabSim, a system-level space habitat model developed by the NASA-funded Resilient Extraterrestrial Habitat Institute (RETHi), as a simulation-based design aid suited to early-phase trade studies. Fire hazard propagation within a lunar habitat is used as an illustrative example of how the architecture supports modeling of disruption consequences, propagation, detection, and repair, and of how HabSim can be leveraged for stochastic simulations to support resilience assessment. Resilience-focused studies that apply this architecture can quantify and compare design alternatives.

Modelling doi: 10.3390/modelling7030108

Authors: Douglas M. Rieger Alisson L. Daga Ervin K. Lenzi Marcelo K. Lenzi

This study investigates the inverse estimation of the effective thermal diffusivity of a polytetrafluoroethylene (PTFE) plate subjected to oscillatory heating from a hot plate with on–off control. Transient temperature measurements at four internal positions were used to evaluate three modeling strategies: a constant-diffusivity formulation with a prescribed Dirichlet boundary condition, a position-dependent effective diffusivity formulation, (x), and a constant-diffusivity model with a Robin boundary condition to account for thermal contact resistance. The constant-diffusivity Dirichlet model, when fitted to all data simultaneously, was unable to reproduce the experimental thermal response satisfactorily. When fitted separately at each thermocouple position, the estimated effective diffusivity increased systematically with position change, indicating that the experimental response could not be represented by a single scalar parameter under the adopted Dirichlet formulation. Variable-(x) models improved the fit, especially the exponential and rational expressions, which reproduced the apparent saturating spatial trend more effectively. However, these functions should be interpreted as empirical effective representations rather than intrinsic constitutive laws for PTFE. The Robin-boundary model with constant diffusivity also provided a comparable fit, suggesting that interfacial thermal resistance at the PTFE–hot plate contact may explain part of the apparent spatial variation inferred by the Dirichlet models. These results indicate that internal temperature measurements under realistic transient heating are not sufficient to uniquely distinguish between distributed effective diffusivity and boundary-contact resistance effects. Therefore, the estimated diffusivity values should be interpreted as model-dependent effective parameters rather than direct measurements of intrinsic PTFE thermal diffusivity.

Modelling doi: 10.3390/modelling7030107

Authors: Bin Cai Sri Sritharan Eugene S. Takle Chris Milliren

While conventional wind towers operate at heights of 80 to 90 m across many regions, including the United States, emerging tower technologies enable higher hub heights that are expected to reduce the levelized cost of energy (LCOE) and increase profit margins. This paper investigates whether increased hub heights, as well as different turbine technologies, deliver measurable economic and performance benefits in wind-rich regions using measured and simulated wind data. First, a model for estimating hourly and monthly energy production is validated with data from a site in Minnesota. To evaluate the advantages of tall towers, the model is extended to estimate the annual energy production (AEP) at various hub heights across multiple sites using different wind datasets. The results confirm that simulated data can be effectively used for predicting AEP and capacity factors in wind-rich regions. Next, it is demonstrated that increasing the hub height by 20 m yielded an average 11% increase in AEP and an 18% reduction in LCOE. Finally, the integration of advanced turbine technologies with taller towers shows the potential to reduce the LCOE of wind power by 23% while increasing profit margins by over 40%.

Modelling doi: 10.3390/modelling7030106

Authors: Jenny Vanessa Rojas-Báez María Fernanda Laverde-Rojas Oscar Danilo Montoya

Voltage stability under transmission line contingencies is a critical concern in modern power systems, as the growing electricity demand and the large-scale integration of renewable energy sources increasingly challenge the security of network operation. This paper addresses the problem of estimating the voltage stability margin under N−1 transmission line contingencies through three solution methodologies: a nonlinear programming formulation solved via an interior-point algorithm (IPOPT) with a multi-start strategy, a recursive heuristic approach based on successive Newton–Raphson power flow solutions with progressive load scaling, and a convex second-order cone programming relaxation. The proposed methods are validated on the IEEE 9-, 14-, 30-, and 57-bus test systems, thereby covering networks of varying topological complexity and redundancy. A comparative analysis evaluates the accuracy of each approach against a nonlinear programming reference, as well as their computational efficiency under a comprehensive set of contingency scenarios. The results indicate that the heuristic method achieves higher precision, while the convex formulation offers a substantially faster solution, with both approaches demonstrating robustness in cases where the nonlinear programming method fails to converge.

Modelling doi: 10.3390/modelling7030105

Authors: Yifei Wang Jiatian Gan Jun Yang Ning Zhang Jingang Wang Xingyu Zhang Pengcheng Zhao

Aiming at the problem that the degradation mechanism of lithium-ion batteries is complex during aging and that a single feature is difficult to fully characterize the battery state of health (SOH), this paper proposes an SOH prediction method for lithium-ion batteries based on multidimensional HF weighted fusion. First, health features (HF) are extracted from the battery charge–discharge data, and the Pearson correlation coefficient is used to analyze the correlation between each HF and SOH. Based on this, a weighted fused feature matrix is constructed. Then, through the collaborative modeling of a convolutional neural network (CNN) and a bidirectional long short-term memory (BiLSTM), the joint extraction of local features and temporal features from multidimensional HF is realized. Meanwhile, manta ray foraging optimization (MRFO) is introduced to optimize key hyperparameters. Finally, experiments are conducted based on the CALCE dataset, and the prediction performance of the proposed method is evaluated through comparisons with different prediction models and an ablation experiment on HF fusion strategies. The results show that the proposed method achieves good prediction results on the CS2-35, CS2-36, and CS2-37 test batteries, with the lowest MAE of 1.134% and the highest R2 of 0.963.

Modelling doi: 10.3390/modelling7030104

Authors: Hexing Zheng Jinguo Liu Haitao Gu Fang Shi Kexin Zhang

Magnetic anomaly detection (MAD) is a passive technique for detecting ferromagnetic targets, but weak magnetic anomaly signals are often submerged in background noise. Existing stochastic resonance (SR)-based MAD methods mainly focus on target detection and generally provide limited capability for waveform and amplitude reconstruction. To address this problem, this paper proposes a weak magnetic anomaly signal enhancement method based on an adaptive variable-structure stochastic resonance (AVSSR) system. A potential function capable of switching among monostable, bistable, and multistable structures is designed to improve the adaptability of SR processing under different noise conditions. The noisy vector magnetic signals are processed by the AVSSR system, and the normalized sliding-window standard deviation is combined with a scaling factor to reconstruct the magnetic anomaly signal’s waveform and amplitude. The system parameters are optimized using the differential evolution algorithm. Simulation results show that the proposed method can effectively reconstruct magnetic anomaly signals under Gaussian white noise and colored 1/fα noise, even at an input SNR of −15 dB. Comparisons with the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method and an adaptive multistable SR method demonstrate better waveform preservation and more stable amplitude reconstruction. Experimental results using measured Bt signals further verify its practical applicability.

Modelling doi: 10.3390/modelling7030102

Authors: Hualong Li Yong Mei Yunhou Sun Zixun Wu Shengyi Cong Shaojun Cao

To examine the dynamic response of tunnel floor slabs subjected to blasting under varying stress conditions, a numerical model was developed to simulate blasting effects at different tunnel depths. This model integrated Hopkinson bar experiments conducted under confining pressure with the Riedel–Hiermaier–Thoma (RHT) constitutive framework. The study subsequently investigated the effects of geostress fields, tunnel depth and tunnel inclination on the propagation characteristics of stress waves. Additionally, the mechanisms stress wave transmission and the damage evolution within the rock mass were analyzed. Results from the numerical simulations reveal that increasing the charge depth diminishes the dissipation of post-blasting stress waves toward the free surface, thereby concentrating stress wave propagation within the rock mass and substantially amplifying shock wave intensity and impact loading. Moreover, elevated stress levels in the surrounding rock increase the peak stress wave amplitude, constrain damage propagation on the tunnel’s upper side, and redirect more stress waves toward deeper regions of the model. Increasing tunnel inclination was also found to intensify stress concentration and augment stress wave intensity. Notably, at a tunnel inclination of 5°, stress wave intensity attains its maximum; beyond this angle, the development of stress waves exhibits irregular patterns.

Modelling doi: 10.3390/modelling7030103

Authors: Yusuf Fatihu Hamza Mukhtar Fatihu Hamza

The Loop subdivision scheme is one of the most widely used approximation subdivision methods for generating smooth surfaces. However, the limiting surface of the Loop subdivision scheme does not interpolate the vertices of the original mesh and may exhibit shrinkage in certain cases. To overcome this limitation, we propose the Successive Overrelaxation–Progressive Iterative Approximation (SOR-PIA) method, which adjusts the positions of the original vertices so that the corresponding limit surface of the Loop subdivision scheme can interpolate the vertices of the given mesh. The optimal relaxation parameter for the SOR-PIA method is also provided. Compared to classical PIA, Weighted PIA (W-PIA), Hermitian and skew-Hermitian PIA (HSS-PIA), and Weighted Hermitian and skew-Hermitian PIA (WHSS-PIA), the proposed method converges faster while maintaining accuracy, as demonstrated by numerical examples.

Modelling doi: 10.3390/modelling7030101

Authors: Qianxu Yang Guangda Lu Xiaozhou Xia

An explicit dynamic framework based on the Nonlocal Macro-Meso-scale Consistent Damage (NMMD) model is proposed to simulate complex multiple-crack evolution in quasi-brittle materials subjected to blast loading. Three numerical examples—a single-edge-notched half-plate, a thick ring, and a hollow mortar cylinder containing a small borehole—are analyzed. The results show that crack initiation, propagation, branching, and coalescence can be naturally captured by the proposed framework without remeshing. Reliable predictions are obtained only when sufficient mesh resolution is used to resolve nonlocal interactions and the time step satisfies the explicit stability criterion. Comparisons indicate that fewer but more dominant crack paths are predicted by the model, suggesting a conservative tendency in estimating the number of fragments. Crack-path selection is significantly influenced by material heterogeneity, which enables secondary cracks to evolve into dominant crack paths. Crack multiplication and network connectivity are promoted by increased blast pressure, whereas crack complexity and spatial extent are reduced by higher damping coefficients.

Modelling doi: 10.3390/modelling7030100

Authors: Oleg Lyashuk Dmytro Mironov Pavlo Maruschak Volodymyr Dzyura Viktor Shevchuk

Although PI and PID controllers are mature control laws, their effect on energy-related variables is rarely isolated in a complete electric vehicle traction model when the plant, controller tuning basis and driving conditions are kept unchanged. A full-system MATLAB/Simulink model was developed, comprising a DC motor with PWM H-bridge, reduction gear, vehicle dynamics and a lithium-ion battery with SOC monitoring. Fixed-gain PI and PID configurations were compared under FTP75, with US06 added as a dynamic-cycle assessment. Speed tracking was evaluated using RMSE, MAE, IAE and ITAE, while energy behavior was assessed through SOC depletion, battery voltage, current and braking-command signals. Under FTP75, both controllers achieved nearly identical tracking accuracy, with an overall RMSE of 0.1525 km/h across the active intervals. Despite this kinematic equivalence, PID reduced SOC depletion by 0.980 percentage points over 4.963 km and produced a less intense but more distributed braking command. The additional 600 s US06 simulation did not confirm a general PID advantage: both controllers reached the same maximum speed and showed practically identical tracking accuracy, while PID did not reduce SOC depletion. The results show that the derivative channel changes the control-command pattern, but it does not automatically improve kinematic or energy performance under fixed-gain tuning.

Modelling doi: 10.3390/modelling7030099

Authors: Minhao Wang Zhenjia Wang Gangping Chen Jun Zhou Jian Luo Fang Qin Yue Wu Pan Zhou Chuqi Lin

Virtual flow metering (VFM) serves as an effective alternative to traditional physical flow meters, significantly reducing gas-field metering costs and operational complexity. However, conventional VFM typically employs a single-modeling approach, failing to address metering requirements across varying production conditions and data types. Focusing on wellhead choke equipment, four mechanistic models (MModels) based on choke-flow dynamics are constructed using piecewise linear regression, alongside six machine learning models. Hyperparameters are optimized via grid search and cross-validation, establishing a hybrid mechanistic and data-driven multi-model VFM method for gas wells. Systematic testing utilizes field data from gas wells in the Southwest Oil and Gas Field, with the Shapley additive explanations (SHAP) method quantifying feature contributions. MModel results indicate superior overall performance by the temperature-difference piecewise linear model, yielding a training R2 of 0.91 and a mean test error of 4.59%. Under different valve-position conditions, the downstream-temperature piecewise linear model demonstrates better predictive capability when the valve position is equal to 100, whereas the valve-position piecewise linear model achieves higher accuracy when the valve position is less than 100. MLModel results reveal that among ten feature parameters, “Date” and “Valve Position Indication” contribute most significantly to prediction accuracy, accounting for over 50% of cumulative contribution in GBoost (extreme gradient boosting) and CatBoost (categorical boosting) models. Notably, the XGBoost model exhibits optimal predictive performance, achieving a training R2 of 0.979 and a mean test error of merely 0.13%. Random sampling results show coefficient of variation values below 0.1 for all metrics, demonstrating exceptional robustness, providing an effective technical solution and solid theoretical support for gas-field VFM.

Modelling doi: 10.3390/modelling7030098

Authors: He Jiang Tianhui Shi Qingzheng Li Xinyu Wang

The development of renewable energy is vital for addressing future climate change and environmental degradation. Nevertheless, the irregular and fluctuating essential features of wind power presents a considerable barrier to grid operational stability. Hence, precise prediction of wind energy output is crucial for improving power system management, boosting the reliability of the supply, and minimizing reserve expenditure. This study presents a predictive model designed for predicting short-term wind speeds using a stacking ensemble approach, which is based on an enhanced Multi-Feature Zebra Optimization Algorithm (IZOA-Stacking). In the data preprocessing phase, to minimize computational costs and prevent overfitting, a module tailored to the various features affecting wind power is developed for the IZOA-Stacking model. Grey relational analysis and Pearson correlation analysis are employed to determine and filter feature correlations. Critically, the preprocessing module demonstrates strong robustness: the One-Class Support Vector Machine (OneSVM) model is applied to identify and replace 100% of anomalous wind speed data, which leads to a substantial and measurable increase in feature correlation and overall model performance. For instance, when retaining wind speed features, the One-Class Support Vector Machine (OneSVM) model is employed to eliminate anomalous wind speed data. During model construction, a stacking ensemble learning strategy integrates multiple prediction models, including Long Short-Term Memory (LSTM) net-works, Extreme Gradient Boosting (XGBoost), ridge regression (RR), and Residual Networks (ResNets). This integration leverages the predictive strengths of each model. Additionally, the improved Zebra Optimization Algorithm (ZOA) optimizes the hyperparameters of each constituent model, further enhancing forecasting accuracy. The findings suggest that the proposed model demonstrates better performance than reference competitor models with regard to predictive accuracy.

Modelling doi: 10.3390/modelling7030097

Authors: Irfan Ullah Ahmed Farid Khaled Ksaibati

Road intersection crashes remain a major contributor to injuries due to complex conflict patterns and multimodal interactions. Among the factors influencing intersection safety, inadequate intersection sight distance (ISD) attributed to roadside sight obstructions can limit drivers’ ability to respond to conflicting movements, potentially affecting crash injury outcomes. Despite its importance, visual obstruction has rarely been examined as a distinct context in traffic crash injury severity modeling. This study investigates crash injury severity at visually obstructed intersections using an ordinal probit modeling framework applied to 951 intersection crashes documented with sight obstruction as a contributing factor in Wyoming over the period 2014 through 2023. Crash data were analyzed to identify the effects of driver behavior, vehicle characteristics, roadway geometry, environmental conditions, and traffic control on ordered injury severity outcomes ranging from property damage only (PDO) to fatal and serious injury. Nonparametric bootstrap resampling with 1000 iterations was employed to assess parameter stability and construct empirical confidence intervals. Average marginal effects were estimated to quantify the change in probability of each injury severity level associated with key predictors. The results indicate that alcohol involvement produces the largest severity shift, reducing the probability of PDO outcomes by 51.2 percentage points while increasing the probability of fatal and serious injury by 34.2 percentage points. Hillcrest grade locations increase fatal and serious injury risk by 14.4 percentage points, while adverse road surface conditions, including snowy, icy, and wet pavements, consistently reduce fatal and serious injury probability by 12.5 to 15.1 percentage points, reflecting behavioral adaptation to visually salient hazard cues. Bootstrap validation confirms strong parameter stability across all estimates, with 94% of parameters showing bootstrap standard errors within 25% of their asymptotic counterparts. By formally establishing visually obstructed intersections as a dedicated severity modeling context and integrating systematic bootstrap validation, this study contributes both substantive and methodological insights to support evidence-based prioritization of intersection safety improvements.

Modelling doi: 10.3390/modelling7030096

Authors: Changjun Zou Zhihua Shi

Fluid–structure interaction (FSI) research is crucial for applications in fields such as naval engineering, geological hazards, and biomechanics. Traditional grid-based methods (such as CFD) often face challenges in simulating large-deformation flow fields and complex boundary conditions, where mesh distortion can compromise simulation accuracy. Building upon the DualSPHysics5.2 framework, this study leverages the strengths of weakly compressible SPH (WCSPH) in modeling free surface flows and large-deformation fluids, as well as the discrete element method (DEM), for accurately describing particle collisions and fragmentation behaviors. We propose an improved MSPH-DEM coupling algorithm that incorporates moving least squares (MLS) correction for kernel function gradient optimization. This algorithm utilizes MLS-based gradient correction to achieve smoother fluid surfaces as well as bidirectional coupling between fluids and particles. Experimental validation demonstrates that in dam break simulations, this method reduces pressure errors. In the dam break impacting a cube experiment, it enhances accuracy, while in the dam break impacting a baffle experiment, the horizontal displacement of marker points closely aligns with the experimental values from Liao et al. This approach effectively improves the accuracy of the simulations of FSI problems, offering a more reliable numerical simulation methodology for engineering applications such as geological hazard prevention.

Modelling doi: 10.3390/modelling7030095

Authors: Wei Xu Yi-Fan Li Yong-Ou Zhang

This study selects five numerical methods: the explicit Leap-Frog scheme, the implicit Crank–Nicolson scheme, the explicit second-order Runge–Kutta scheme, the implicit Newmark-β scheme, and the implicit Bathe scheme. These methods are compared through representative dynamic cases in terms of solution accuracy and computational efficiency. The results demonstrate that implicit schemes maintain numerical convergence even with relatively large time steps. The findings also indicate that, although the actual convergence accuracy of the given schemes varies slightly among motion models of different dimensions, it remains close to the theoretical second-order accuracy. Different time integration schemes exhibit distinct numerical accuracies when applied to multi-dimensional motion problems. Overall, under identical time step sizes, the Bathe time integration scheme demonstrates slightly superior computational accuracy and error stability compared to other schemes considered. The numerical efficiency of time integration schemes also varies across dimensions and problem types. The actual computational time does not scale linearly with the time step size and is partially influenced by the complexity of the solution algorithm employed. In general, when solution accuracy is comparable, the Leap-Frog scheme shows marginally higher efficiency in explicit simulations, whereas the Crank–Nicolson scheme proves more efficient in implicit simulations.

Modelling doi: 10.3390/modelling7030094

Authors: Ivica Smojver Darko Ivančević Fran Ušurić Moritz Kuhtz Andreas Hornig

This study investigates the mechanical behaviour of continuous carbon-fibre-reinforced additively manufactured composite structures aimed at applications in aeronautical structures, through a combination of experimental testing and numerical simulation. Tensile, compressive, and shear tests established stiffness and failure characteristics, while finite element analyses were used for a preliminary calibration-based reproduction of the measured coupon response, with an emphasis on the initial elastic part of the impact event. The integration of measured data with structural modelling provides a clearer understanding of load transfer and damage initiation in continuous-fibre AM, supporting more accurate simulation-based design of additively manufactured composite components. Experimental results show pronounced anisotropy, and a stable, rate-dependent impact response. The preliminary numerical model based on CT-derived homogenized properties accurately reproduces the initial part of the measured quasi-static and dynamic responses.

Modelling doi: 10.3390/modelling7030093

Authors: Yong Chen Ping Xiong Ding Yang

To address the issues associated with traditional multi-point surveying processes in the dead-end cutting for oil and gas pipelines—such as cumbersome procedures, high error rates, lengthy emergency repair cycles, and difficulties in ensuring welding precision—an infrared line drawing device has been developed that enables rapid positioning, long-distance high-precision alignment, and accurate marking of cutting locations. This paper establishes mathematical models for the centering deflection mechanism and the marking mechanism, and derives theoretical solutions for key structural parameters. Thirteen finite element models were constructed using Abaqus to simulate operating conditions involving different pipe diameters and link lengths. A variance-based uniformity metric was employed to quantify structural stress stability, and optimal parameters were determined based on the principle that smaller variance indicates more uniform stress distribution and closer to ideal component service life. The results indicate that the optimal length of the three mounting bolts is 85 mm, with a maximum deflection angle of 9.25°, which meets the requirements. A spring extension of 5 mm for the marking pen can accommodate the compensation needs for marking on DN300 to DN500 pipes. An optimal set of connecting rod parameters across pipe diameters has been determined, with a 240 mm connecting rod capable of covering more than 75% of operating conditions. This device and its parameters are expected to contribute to first-pass compliance and reduce downtime, providing efficient and precise technical support for the maintenance and emergency repair of oil and gas pipelines.

Modelling doi: 10.3390/modelling7030092

Authors: Andrew Eno Daniel Patton Germán H. Alférez Benjamin L. Clausen

Magmatic–hydrothermal systems transport heat through coupled conduction and buoyancy-driven fluid flow in porous rock, behavior conventionally modeled with grid-based finite-difference simulators such as HYDROTHERM. We demonstrate that a physics-informed neural network (PINN), built on the NVIDIA PhysicsNeMo framework using automatic differentiation and mesh-free collocation, can produce a stable two-dimensional time-dependent solution for a magma-chamber configuration based on the Rio Pisco pluton in the Peruvian Coastal Batholith. Boundary conditions and material parameters are taken from a prior HYDROTHERM study of the same pluton, and 28 temperature samples digitized from that study are used as a supervised constraint. The PINN couples Fourier conduction, advective heat transport, Darcy flow with a temperature-dependent permeability law, and a mass-conservation formulation; the mass-conservation equation is written in two-phase form, but in the regime studied here, the simulation remains below the boiling curve, so the steam-phase saturation stays at zero and the formulation reduces to its single-phase liquid–water limit. The network reproduces the conductive temperature gradient and a directionally consistent buoyancy-driven flow field, with weaker and less organized circulation than the reference simulation, and a cooling time of approximately 1.6×105 years, comparable to the ∼175,000 years reported for the matching k=10−16m2 HYDROTHERM reference scenario from which the supervised training data was digitized. We discuss the conditions under which the mesh-free, automatically differentiable PINN approach offers a useful alternative to grid-based solvers.

Modelling doi: 10.3390/modelling7030091

Authors: Mina Golzar Mohammad Kazem Moayyedi Faranak Fotouhi-Ghazvini Maryam Vahabi Hossein Fotouhi

Modelling plays a critical role in many engineering applications. Partial differential equations (PDEs) are ubiquitous, describing various physical phenomena such as fluid flow, electromagnetism, and quantum mechanics. Although some of these equations have analytical solutions, many require high-fidelity simulations of parametric PDEs. In general, high-fidelity simulations are computationally expensive and often infeasible for real-time or multi-query applications. This challenge has led to the development of reduced-order models (ROMs). Over the past few decades, ROMs have emerged as a practical solution for simulating, controlling, and optimizing large-scale and complex dynamical systems. This paper introduces a novel Calibrated Intrusive Reduced-Order Modelling (CIROM) approach for the efficient and accurate simulation of the one-dimensional Burgers’ equation, employed as a canonical benchmark because it is a simplified fundamental partial differential equation that captures the behaviour of many real-world phenomena. The proposed method, combining the strengths of proper orthogonal decomposition (POD) and long short-term memory (LSTM) networks, effectively reduces computational complexity while addressing inherent instabilities in classical reduced-order models. Unlike traditional POD-ROMs, which often suffer from error accumulation and instability at high Reynolds numbers, the CIROM employs an iterative LSTM-based error correction mechanism to learn and compensate for truncation and projection errors. This study is benchmark-oriented and does not aim to provide a general PDE solver. The performance of the proposed method is rigorously evaluated across a broad range of Reynolds numbers, including interpolation and extrapolation scenarios, demonstrating robust extrapolation within moderate ranges. Comprehensive numerical experiments confirm that the CIROM outperforms both pure intrusive ROMs and purely data-driven LSTM models in terms of prediction accuracy, stability, and computational cost.

Modelling doi: 10.3390/modelling7030090

Authors: Yong Zhang Chunsen Wan Jiajie Yang Juan Zhai

Lithology identification is a key task in petroleum geological exploration and development, essential for evaluating sweet spots and characterizing reservoirs. A significant challenge in lithology identification is the insufficient accuracy of traditional machine learning methods due to the uneven distribution of geological data categories. To address this, we propose a novel lithology identification framework combining a denoising diffusion model with auxiliary classification, a neural network with channel attention mechanisms, and a bidirectional Gated Recurrent Unit (GRU). The proposed framework first employs the Auxiliary Classification Denoising Diffusion Probabilistic Model (A-CDPM) to generate high-quality well log data, effectively balancing the data classes. Secondly, it utilizes a multi-scale convolutional model with channel attention mechanisms and a Bidirectional GRU classification model, which automatically adjusts feature weights and effectively integrates information from different well log data. Experimental results demonstrate that our method significantly improves lithology identification accuracy, achieving 86.66% on datasets from the Hugoton and Panoma fields in Kansas, USA. Compared to traditional methods, this framework substantially enhances recognition precision, providing a novel and effective solution for lithology identification in petroleum geological exploration.

Modelling doi: 10.3390/modelling7030089

Authors: Ke Hao Wang Hwi Gyu Lee Seon Min Yoo In Soo Lee

Reliable fault detection in brushless DC motors is challenging owing to environmental complexity and high equipment costs. To address these challenges, we propose an effective and cost-effective approach using an optimized end-to-end one-dimensional convolutional neural network. Specifically, a real experimental platform simulating bearing and eccentricity faults was developed. Statistical t-tests indicated that three-axis accelerometer signals from a low-cost inertial measurement unit provided sufficient fault information for the present diagnosis task. Unlike traditional methods such as support vector machines, multilayer neural networks, and random forests, which rely on manual feature extraction, our model learns directly from raw waveforms and can handle signal drift. Under the present controlled experimental setting and the leave-one-day-out evaluation protocol, the model achieved 100.00% average window-level classification accuracy, considerably outperforming traditional methods, the performances of which declined to 67.95–71.37% under environmental shifts. Moreover, with an inference time of only 0.96 ms, 32 times faster than that of random forests, this approach is well suited for real-time embedded monitoring. The proposed method demonstrates strong potential for cost-efficient and robust fault diagnosis under the present experimental setting.

Modelling doi: 10.3390/modelling7030088

Authors: Clayton Valenko Fernandes Padmaraj N H Thara Reshma I V Chethan K N Divya D Shetty Laxmikant G Keni

This study presents a comparative computational fluid dynamics (CFD) investigation of the aerodynamic performance of four simplified crossover/sports utility vehicle (SUV)-type vehicle body configurations. The models were developed with systematic geometric variations, including front face inclination, roof spoiler length, roof spoiler slotting, and rear underbody diffuser integration. Steady-state Reynolds-averaged Navier–Stokes (RANS) simulations using the k–ω SST turbulence model were conducted in ANSYS Fluent to evaluate key aerodynamic parameters, including the drag coefficient, drag force, pressure distribution, velocity field, and modeled turbulence kinetic energy. The results indicate that the baseline configuration exhibits the highest drag due to early flow separation and poor rear pressure recovery. Progressive geometric modifications led to improved aerodynamic performance, with the configuration incorporating a slotted roof spoiler and rear diffuser achieving the lowest drag coefficient, corresponding to an approximate 13% reduction compared to the baseline model. The findings demonstrate that coordinated front- and rear-end design modifications play a critical role in reducing wake intensity and enhancing aerodynamic efficiency. This study provides insight into effective drag reduction strategies for crossover-type vehicles and highlights the importance of integrated aerodynamic design approaches.

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.