Journal Description
Modelling
Modelling
is an international, peer-reviewed, open access journal on theory and applications of modelling and simulation in engineering science, published quarterly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within ESCI (Web of Science), Scopus, Ei Compendex, EBSCO and other databases.
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 18.9 days after submission; acceptance to publication is undertaken in 3.9 days (median values for papers published in this journal in the second half of 2024).
- Journal Rank: CiteScore - Q2 (Mathematics (miscellaneous))
- Recognition of Reviewers: APC discount vouchers, optional signed peer review and reviewer names are published annually in the journal.
Impact Factor:
1.3 (2023);
5-Year Impact Factor:
1.4 (2023)
Latest Articles
Machine Learning Models for Carbonation Depth Prediction in Reinforced Concrete Structures: A Comparative Study
Modelling 2025, 6(2), 46; https://doi.org/10.3390/modelling6020046 - 10 Jun 2025
Abstract
The durability of reinforced concrete (RC) structures is strongly influenced by carbonation, a phenomenon governed by material and environmental interactions. This study applied machine learning (ML) techniques—Random Forest (RF), Support Vector Regression (SVR), and Artificial Neural Networks (ANNs)—to predict carbonation depth using a
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The durability of reinforced concrete (RC) structures is strongly influenced by carbonation, a phenomenon governed by material and environmental interactions. This study applied machine learning (ML) techniques—Random Forest (RF), Support Vector Regression (SVR), and Artificial Neural Networks (ANNs)—to predict carbonation depth using a synthetic dataset of 20,000 instances generated from the validated Possan equation. Model performances were evaluated across multiple scenarios, with compressive strength and exposure time identified as the most influential features, while relative humidity and exposure conditions had intermediate effects. SVR consistently captured linear and nonlinear trends, the ANN achieved the highest R2 values but showed minor overestimations, and RF exhibited lower adaptability to feature variations. The results highlight the applicability of ML models for durability assessments, particularly under complex conditions where traditional approaches are limited. Moreover, this study reinforces the strategic value of synthetic datasets in developing predictive models when experimental data collection is time-consuming or impractical. The methodologies developed here can be extended beyond carbonation modeling to other deterioration processes, supporting data-driven strategies for maintenance planning and resilience design in RC structures.
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(This article belongs to the Section Modelling in Engineering Structures)
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Open AccessArticle
Thermodynamic, Economic, and Environmental Multi-Criteria Optimization of a Multi-Stage Rankine System for LNG Cold Energy Utilization
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Ruiqiang Ma, Yingxue Lu, Xiaohui Yu and Bin Yang
Modelling 2025, 6(2), 45; https://doi.org/10.3390/modelling6020045 - 9 Jun 2025
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Utilizing the considerable cold energy in liquefied natural gas (LNG) through the organic Rankine cycle is a highly important initiative. A multi-stage Rankine-based power generation system using LNG cold energy for waste heat utilization was proposed in this study. Moreover, a comprehensive assessment
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Utilizing the considerable cold energy in liquefied natural gas (LNG) through the organic Rankine cycle is a highly important initiative. A multi-stage Rankine-based power generation system using LNG cold energy for waste heat utilization was proposed in this study. Moreover, a comprehensive assessment method was used to select the working fluid for this proposed system. Not only were thermodynamic and economic indicators considered, but also the environmental impact of candidate working fluids was taken into account in the evaluation process. The optimal operating points of the system were determined using non-dominated sorting genetic algorithm II and TOPSIS methods, while employing Gray Relational Analysis was applied to compute the gray relational coefficients of candidate working fluids at the optimal operating points. In addition, four weighting methods were used to calculate the final gray correlation degree of the candidate working fluids by considering the weighting influence. The stability of the calculated gray correlation degree was observed by performing a standard deviation analysis. The results indicate that R245ca was chosen as the optimal working fluid due to its superior performance based on the entropy weighting method, the independent weighting coefficient method, and the mean weighting method. Simultaneously, R245ca exhibits the best specific net power output and levelized cost of energy values of 0.283 USD/kWh and 106.9 kWh/t, respectively, among all candidate working fluids. The gray correlation degree of R1233zd(E) is 0.948, exceeding that of R245ca under the coefficient of variation method. The gray correlation degree under the mean value method is the most stable, with a standard deviation of only 0.162, while the gray correlation degree under the coefficient of variation method exhibits the greatest fluctuation, with a standard deviation of 0.17, in the stability assessment.
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Open AccessArticle
PVkNN: A Publicly Verifiable and Privacy-Preserving Exact kNN Query Scheme for Cloud-Based Location Services
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Jingyi Li, Yuqi Song, Chengliang Tian and Weizhong Tian
Modelling 2025, 6(2), 44; https://doi.org/10.3390/modelling6020044 - 3 Jun 2025
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The k-nearest- neighbor (kNN) algorithm is crucial in data mining and machine learning, yet its deployment on large-scale datasets within cloud environments presents significant security and efficiency challenges. This paper is dedicated to advancing the resolution of these challenges and
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The k-nearest- neighbor (kNN) algorithm is crucial in data mining and machine learning, yet its deployment on large-scale datasets within cloud environments presents significant security and efficiency challenges. This paper is dedicated to advancing the resolution of these challenges and presents novel contributions to the development of efficient and secure exact kNN query schemes tailored for spatial datasets in cloud-based location services. Addressing existing limitations, our approach focuses on accelerating query processing while ensuring robust privacy preservation and public verifiability. Key contributions include the establishment of a formal framework underpinned by stringent security definitions, providing a solid groundwork for future advancements. Leveraging Paillier’s homomorphic cryptosystem and public-key signature techniques, our design achieves heightened security by safeguarding databases, query access patterns, and result integrity while enabling public verification. Additionally, our scheme enhances computational efficiency through optimized data-packing techniques and simplified Voronoi diagram-based ciphertext index construction, leading to substantial savings in computational and communication overheads. Rigorous and transparent theoretical analysis substantiates the correctness, security, and efficiency of our design, while comprehensive experimental evaluations confirm the effectiveness of our approach, showcasing its practical applicability and scalability across datasets of varying scales.
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Open AccessArticle
SAPEVO-H2 Multi-Criteria Modelling to Connect Decision-Makers at Different Levels of Responsibility: Evaluating Sustainability Projects in the Automobile Industry
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Miguel Ângelo Lellis Moreira, Maria Teresa Pereira, Igor Pinheiro de Araújo Costa, Carlos Francisco Simões Gomes and Marcos dos Santos
Modelling 2025, 6(2), 43; https://doi.org/10.3390/modelling6020043 - 3 Jun 2025
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Decision-making in complex environments, especially sustainable ones, requires flexible methodologies to handle multiple criteria and stakeholder perspectives. This study introduces the SAPEVO-H2 method (Simple Aggregation of Preferences Expressed by Ordinal Vectors—Hybrid and Hierarchical), an extensive model from the SAPEVO family, which offers
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Decision-making in complex environments, especially sustainable ones, requires flexible methodologies to handle multiple criteria and stakeholder perspectives. This study introduces the SAPEVO-H2 method (Simple Aggregation of Preferences Expressed by Ordinal Vectors—Hybrid and Hierarchical), an extensive model from the SAPEVO family, which offers multi-criteria analysis through a hierarchical structure of variables evaluated by groups partitioned into levels concerning their respective responsibilities. The proposal allows flexible analysis, considering inputs through ordinal and cardinal information. The validation of the methodology is demonstrated through a case study involving an automobile manufacturing company, which focuses on prioritizing sustainability projects based on multiple objectives aimed at minimizing polluting gas emissions. Within a hierarchical structure of five levels, the individual level results are presented. In addition, a sensitivity analysis is applied, exposing the most sensitive variables to changes concerning the highest levels. Then, we discuss the main contributions and limitations concerning the mathematical proposal and the conclusions and proposals for future work.
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Open AccessArticle
Modeling Skin Thermal Behavior with a Cutaneous Calorimeter: Local Parameters of Medical Interest
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Pedro Jesús Rodríguez de Rivera, Miriam Rodríguez de Rivera, Fabiola Socorro and Manuel Rodríguez de Rivera
Modelling 2025, 6(2), 42; https://doi.org/10.3390/modelling6020042 - 2 Jun 2025
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This study presents an advanced model of thermal Resistances and heat Capacities model approach (RC model), applied to a custom-built skin calorimeter for the in vivo characterization of localized thermal behavior of the skin. The device integrates a heat flux sensor and a
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This study presents an advanced model of thermal Resistances and heat Capacities model approach (RC model), applied to a custom-built skin calorimeter for the in vivo characterization of localized thermal behavior of the skin. The device integrates a heat flux sensor and a programmable thermostat, and is capable of measuring the heat flux, heat capacity, internal thermal resistance, and subcutaneous temperature of the skin, under both resting and exercising conditions. The model, refined through extensive experimental validation, incorporates the skin as part of the system and is adapted to three modes of operation: calibration base, ambient air, and direct skin contact. Simulations are used to analyze heat flux dynamics, optimize control parameters, and validate analytical expressions. Under resting conditions, the model enables the estimation of the skin’s heat capacity and thermal resistance. During exercise, it allows the determination of heat flux and internal temperature variations using simplified expressions. The system demonstrates high sensitivity (195.5 mV/W) and provides a robust, non-invasive method for extracting medically relevant thermal parameters from a 2 × 2 cm2 skin area.
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Open AccessArticle
The Effect of Impactor Geometry on the Damage Patterns Generated by Low-Velocity Impacts on Composite Pressure Vessels
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Shiva Rezaei Akbarieh, Dayou Ma, Claudio Sbarufatti and Andrea Manes
Modelling 2025, 6(2), 41; https://doi.org/10.3390/modelling6020041 - 28 May 2025
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Due to environmental concerns and increasing energy needs, hydrogen is increasingly seen as a promising alternative to fossil fuels. Its advantages include minimal greenhouse gas emissions (depending on origin), high efficiency, and widespread availability. Various storage methods have been developed, with high-pressure storage
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Due to environmental concerns and increasing energy needs, hydrogen is increasingly seen as a promising alternative to fossil fuels. Its advantages include minimal greenhouse gas emissions (depending on origin), high efficiency, and widespread availability. Various storage methods have been developed, with high-pressure storage being currently among the most common due to its cost-effectiveness and simplicity. Composite high-pressure vessels are categorized as type III or IV, with type III using an aluminum alloy liner and type IV utilizing a polymer liner. This paper investigates damage mechanisms in filament wound carbon fiber composite pressure vessels subjected to low-velocity impacts, focusing on two types of impactors (with different geometries) with varying impact energies. The initial section features experimental trials that capture various failure modes (e.g., matrix damage, delamination, and fiber breakage) and how different impactor geometries influence the damage mechanisms of composite vessels. A numerical model was developed and validated with experimental data to support the experimental findings, ensuring accurate damage mechanism simulation. The research then analyzes how the shape and size of impactors influence damage patterns in the curved vessel, aiming to establish a relationship between impactor geometry features and damage, which is crucial for the design and applications of carbon fiber composites in such an engineering application.
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Open AccessArticle
Natural Language Processing for Aviation Safety: Predicting Injury Levels from Incident Reports in Australia
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Aziida Nanyonga, Keith Joiner, Ugur Turhan and Graham Wild
Modelling 2025, 6(2), 40; https://doi.org/10.3390/modelling6020040 - 28 May 2025
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This study investigates the application of advanced deep learning models for the classification of aviation safety incidents, focusing on four models: Simple Recurrent Neural Network (sRNN), Gated Recurrent Unit (GRU), Bidirectional Long Short-Term Memory (BLSTM), and DistilBERT. The models were evaluated based on
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This study investigates the application of advanced deep learning models for the classification of aviation safety incidents, focusing on four models: Simple Recurrent Neural Network (sRNN), Gated Recurrent Unit (GRU), Bidirectional Long Short-Term Memory (BLSTM), and DistilBERT. The models were evaluated based on key performance metrics, including accuracy, precision, recall, and F1-score. DistilBERT achieved perfect performance with an accuracy of 1.00 across all metrics, while BLSTM demonstrated the highest performance among the deep learning models, with an accuracy of 0.9896, followed by GRU (0.9893) and sRNN (0.9887). Class-wise evaluations revealed that DistilBERT excelled across all injury categories, with BLSTM outperforming the other deep learning models, particularly in detecting fatal injuries, achieving a precision of 0.8684 and an F1-score of 0.7952. The study also addressed the challenges of class imbalance by applying class weighting, although the use of more sophisticated techniques, such as focal loss, is recommended for future work. This research highlights the potential of transformer-based models for aviation safety classification and provides a foundation for future research to improve model interpretability and generalizability across diverse datasets. These findings contribute to the growing body of research on applying deep learning techniques to aviation safety and underscore opportunities for further exploration.
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Open AccessArticle
Short-Term Highway Traffic Flow Prediction via Wavelet–Liquid Neural Network Model
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Yongjun Wu, Hongyun Kang, Weipin Wang, Shuli Zhao, Xuening He and Jingyao Chen
Modelling 2025, 6(2), 39; https://doi.org/10.3390/modelling6020039 - 14 May 2025
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Accurate, efficient, and reliable traffic flow prediction is pivotal for highway operation and management. However, traffic flow series present nonlinear, heterogeneous, and stochastic characteristics, posing significant challenges to precise prediction. To address this issue, this paper proposes a novel wavelet-LNN model, integrating the
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Accurate, efficient, and reliable traffic flow prediction is pivotal for highway operation and management. However, traffic flow series present nonlinear, heterogeneous, and stochastic characteristics, posing significant challenges to precise prediction. To address this issue, this paper proposes a novel wavelet-LNN model, integrating the strengths of wavelet decomposition and liquid neural networks (LNNs). Initially, multi-scale wavelet decomposition is applied to the original traffic flow data to yield approximation components and detailed components. Subsequently, each component is trained using the LNN. Ultimately, the predicted results of all components of the LNN models are aggregated to derive the final traffic flow prediction. The experiments conducted on four highway datasets demonstrate that the proposed wavelet-LNN model surpasses SVR, LSSVM, LSTM, TCN, and transformer models in prediction performance across R2, MSE, and MAE metrics. Notably, the wavelet-LNN model features the fewest parameters (<2% of typical deep learning models).
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Open AccessArticle
Morphological Background-Subtraction Modeling for Analyzing Traffic Flow
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Erik-Josué Moreno-Mejía, Daniel Canton-Enriquez, Ana-Marcela Herrera-Navarro and Hugo Jiménez-Hernández
Modelling 2025, 6(2), 38; https://doi.org/10.3390/modelling6020038 - 9 May 2025
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Automatic surveillance systems have become essential tools for urban centers. These technologies enable intelligent monitoring that is both versatile and non-intrusive. Today, these systems can analyze various aspects, such as urban traffic, citizen behavior, and the detection of unusual activities. Most intelligent systems
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Automatic surveillance systems have become essential tools for urban centers. These technologies enable intelligent monitoring that is both versatile and non-intrusive. Today, these systems can analyze various aspects, such as urban traffic, citizen behavior, and the detection of unusual activities. Most intelligent systems utilize photo sensors to gather information and assess situations. They analyze data sequences from these photo sensors over time to detect moving objects or other relevant information. In this context, background modeling approaches are crucial for efficiently detecting moving objects by differentiating between the foreground and background, which serves as the basis for further analysis. Although current methods are effective, the dynamic nature of outdoor environments can limit their performance due to numerous external variables that affect the collected information. This paper introduces a novel algorithm that uses mathematical morphology to create a background model by analyzing texture information in discrete spaces, leading to an efficient solution for the background subtraction task. The algorithm dynamically adjusts to global luminance conditions and effectively distinguishes texture information to label the foreground and background using morphological filters. A key advantage of this approach is its use of discrete working spaces, which enables faster implementation on standard hardware, making it suitable for a variety of devices. Finally, our proposal is tested against reference datasets of surveillance and common background subtraction algorithms, demonstrating that our method adapts better to outdoor conditions, making it more robust in detecting different moving objects.
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Open AccessArticle
Stochastic Finite Element Analysis for Static Bending Beams with a Two-Dimensional Random Field of Material Properties
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Dang Diem Nguyen, Sy Dan Dao, Xuan Tung Nguyen and Van Tan Giap
Modelling 2025, 6(2), 37; https://doi.org/10.3390/modelling6020037 - 6 May 2025
Abstract
This study presents the development and application of the stochastic finite element method (SFEM) to analyze the static response of beams with a two-dimensional (2D) spatially varying elastic modulus. A 2D stationary stochastic field is employed to model the elastic modulus, capturing the
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This study presents the development and application of the stochastic finite element method (SFEM) to analyze the static response of beams with a two-dimensional (2D) spatially varying elastic modulus. A 2D stationary stochastic field is employed to model the elastic modulus, capturing the material heterogeneity along both the longitudinal and vertical directions of the beam. The weighted integral method is applied to represent the random field as random variables and to compute the element stiffness matrices, while a first-order perturbation technique is utilized to estimate the statistical moments of the nodal displacement vector, including the mean and covariance matrix. This method enhances both computational efficiency and accuracy in capturing material heterogeneity compared to traditional approaches. The precision and effectiveness of the developed SFEM are evaluated through comparisons with Monte Carlo simulations (MCs), demonstrating strong agreement in the analysis of the coefficient of variation (COV) of displacement. A sensitivity analysis is conducted to examine the influence of the correlation length and dispersion of the stochastic field on the COV. The results indicate that the COV generally increases as these parameters grow, with the most significant variations occurring at small correlation lengths. As the correlation length becomes very large, the COV of displacement converges toward the standard deviation of the input stochastic field. Furthermore, the study reveals that the correlation length along the beam’s longitudinal axis has a more pronounced effect on the COV of displacement compared to the vertical correlation length.
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(This article belongs to the Section Modelling in Engineering Structures)
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Open AccessArticle
Evaluation of Neural Networks for Improved Computational Cost in Carbon Nanotubes Geometric Optimization
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Luis Josimar Vences-Reynoso, Daniel Villanueva-Vasquez, Roberto Alejo-Eleuterio, Federico Del Razo-López, Sonia Mireya Martínez-Gallegos and Everardo Efrén Granda-Gutiérrez
Modelling 2025, 6(2), 36; https://doi.org/10.3390/modelling6020036 - 2 May 2025
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Geometric optimization of carbon nanotubes (CNTs) is a fundamental step in computational simulations, enabling precise studies of their properties for various applications. However, this process becomes computationally expensive as the molecular structure grows in complexity and size. To address this challenge, this study
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Geometric optimization of carbon nanotubes (CNTs) is a fundamental step in computational simulations, enabling precise studies of their properties for various applications. However, this process becomes computationally expensive as the molecular structure grows in complexity and size. To address this challenge, this study utilized three deep-learning-based neural network architectures: Multi-Layer Perceptron (MLP), Bidirectional Long Short-Term Memory (BiLSTM), and 1D Convolutional Neural Networks (1D-CNNs). Simulations were performed using the CASTEP module in Material Studio to generate datasets for training the neural networks. While the final geometric optimization calculations were completed within Material Studio, the neural networks effectively generated preoptimized CNT structures that served as starting points, significantly reducing computational time. The results showed that the 1D-CNN architecture performed best for CNTs with 28, 52, 76, and 156 atoms, while the MLP outperformed others for CNTs with 84, 124, 148, and 196 atoms. Across all cases, computational time was reduced by 39.68% to 90.62%. Although the BiLSTM also achieved reductions, its performance was less effective than the other two architectures. This work highlights the potential of integrating deep learning techniques into materials science; it also offers a transformative approach to reducing computational costs in optimizing CNTs and presents a way for accelerated research in molecular systems.
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Open AccessSystematic Review
Advancement of Artificial Intelligence in Cost Estimation for Project Management Success: A Systematic Review of Machine Learning, Deep Learning, Regression, and Hybrid Models
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Md. Mahfuzul Islam Shamim, Abu Bakar bin Abdul Hamid, Tadiwa Elisha Nyamasvisva and Najmus Saqib Bin Rafi
Modelling 2025, 6(2), 35; https://doi.org/10.3390/modelling6020035 - 24 Apr 2025
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This systematic review investigates the integration of artificial intelligence (AI) in cost estimation within project management, focusing on its impact on accuracy and efficiency compared to traditional methods. This study synthesizes findings from 39 high-quality articles published between 2016 and 2024, evaluating various
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This systematic review investigates the integration of artificial intelligence (AI) in cost estimation within project management, focusing on its impact on accuracy and efficiency compared to traditional methods. This study synthesizes findings from 39 high-quality articles published between 2016 and 2024, evaluating various machine learning (ML), deep learning (DL), regression, and hybrid models in sectors such as construction, healthcare, manufacturing, and real estate. The results show that AI-powered approaches, particularly artificial neural networks (ANNs)—which constitute 26.33% of the studies—, enhance predictive accuracy and adaptability to complex, dynamic project environments. Key AI techniques, including support vector machines (SVMs) (7.90% of studies), decision trees, and gradient-boosting models, offer substantial improvements in cost prediction and resource optimization. ML models, including ANNs and deep learning models, represent approximately 70% of the reviewed studies, demonstrating a clear trend toward the adoption of advanced AI techniques. On average, deep learning models perform with 85–90% accuracy in cost estimation, making them highly effective for handling complex, nonlinear relationships and large datasets. Machine learning models achieve an average accuracy of 75–80%, providing strong performance, particularly in industries like road construction and healthcare. Regression models typically deliver 70–80% accuracy, being more suitable for simpler cost estimations where the relationships between variables are linear. Hybrid models combine the strengths of different algorithms, achieving 80–90% accuracy on average, and are particularly effective in complex, multi-faceted projects. Overall, deep learning and hybrid models offer the highest accuracy in cost estimation, while machine learning and regression models still provide reliable results for specific applications.
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Open AccessArticle
An Optimal Distillation Process for Turpentine Separation Using a Firefly Algorithm
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Gustavo Mendes Platt, Otávio Knevitz de Azevedo and Francisco Bruno Souza Oliveira
Modelling 2025, 6(2), 34; https://doi.org/10.3390/modelling6020034 - 22 Apr 2025
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The optimal design of distillation separation processes has become a fundamental tool in industries in order to minimize operating costs and investments. In many cases, the optimization stage has been carried out using metaheuristics, with the process simulation stage carried out externally to
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The optimal design of distillation separation processes has become a fundamental tool in industries in order to minimize operating costs and investments. In many cases, the optimization stage has been carried out using metaheuristics, with the process simulation stage carried out externally to the optimization. This paper presents an optimal design methodology for separating the components of turpentine, a raw material of natural origin, based on coupling a distillation process simulator with the Firefly metaheuristic as an optimizer. Results were obtained for a distillation process to obtain -pinene and -pinene (two of the main components of turpentine), meeting purity criteria in the top products of the equipment while minimizing a measure of the total annualized cost. The results show that the tool developed—together with the Firefly algorithm—is capable of obtaining optimized results (although there is no guarantee of a global optimum) from a small set of initial design configurations.
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Open AccessArticle
Human Action Recognition from Videos Using Motion History Mapping and Orientation Based Three-Dimensional Convolutional Neural Network Approach
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Ishita Arora and M. Gangadharappa
Modelling 2025, 6(2), 33; https://doi.org/10.3390/modelling6020033 - 18 Apr 2025
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Human Activity Recognition (HAR) has recently attracted the attention of researchers. Human behavior and human intention are driving the intensification of HAR research rapidly. This paper proposes a novel Motion History Mapping (MHI) and Orientation-based Convolutional Neural Network (CNN) framework for action recognition
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Human Activity Recognition (HAR) has recently attracted the attention of researchers. Human behavior and human intention are driving the intensification of HAR research rapidly. This paper proposes a novel Motion History Mapping (MHI) and Orientation-based Convolutional Neural Network (CNN) framework for action recognition and classification using Machine Learning. The proposed method extracts oriented rectangular patches over the entire human body to represent the human pose in an action sequence. This distribution is represented by a spatially oriented histogram. The frames were trained with a 3D Convolution Neural Network model, thus saving time and increasing the Classification Correction Rate (CCR). The K-Nearest Neighbor (KNN) algorithm is used for the classification of human actions. The uniqueness of our model lies in the combination of Motion History Mapping approach with an Orientation-based 3D CNN, thereby enhancing precision. The proposed method is demonstrated to be effective using four widely used and challenging datasets. A comparison of the proposed method’s performance with current state-of-the-art methods finds that its Classification Correction Rate is higher than that of the existing methods. Our model’s CCRs are 92.91%, 98.88%, 87.97.% and 87.77% which are remarkably higher than the existing techniques for KTH, Weizmann, UT-Tower and YouTube datasets, respectively. Thus, our model significantly outperforms the existing models in the literature.
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Open AccessArticle
Enhancing Accuracy in Hourly Passenger Flow Forecasting for Urban Transit Using TBATS Boosting
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Madhuri Patel, Samir B. Patel, Debabrata Swain and Rishikesh Mallagundla
Modelling 2025, 6(2), 32; https://doi.org/10.3390/modelling6020032 - 17 Apr 2025
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Passenger flow forecasting is crucial for optimizing urban transit operations, especially in developing countries such as India, where congestion, infrastructure constraints, and diverse commuter behaviors pose significant challenges. Despite its importance, limited research explored forecasting models for Indian urban transit systems, particularly incorporating
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Passenger flow forecasting is crucial for optimizing urban transit operations, especially in developing countries such as India, where congestion, infrastructure constraints, and diverse commuter behaviors pose significant challenges. Despite its importance, limited research explored forecasting models for Indian urban transit systems, particularly incorporating the effects of holidays and disruptions caused by the COVID-19 pandemic. To address this gap, we propose TBATS Boosting, a novel hybrid forecasting model that integrates the statistical strengths of trigonometric, Box–Cox, ARMA, trend, and seasonal (TBATS) with the predictive power of LightGBM. The model is trained on a five-year real-world dataset from e-ticketing machines (ETM) in Thane Municipal Transport (TMT), incorporating holiday and pandemic-related variations. While Route 12 serves as a primary evaluation route, different station pairs are analyzed to validate their scalability across varying passenger demand levels. To comprehensively evaluate the proposed framework, a rigorous performance assessment was conducted using MAE, RMSE, MAPE, and WMAPE across station pairs characterized by heterogeneous passenger flow patterns. Empirical results demonstrate that the TBATS Boosting approach consistently outperforms benchmark models, including standalone SARIMA, TBATS, XGBoost, and LightGBM. By effectively capturing complex temporal dependencies, multiple seasonalities, and nonlinear relationships, the proposed framework significantly enhances forecasting accuracy. These advancements provide transit authorities with a robust tool for optimizing resource allocation, improving service reliability, and enabling data-driven decision making across varied and dynamic urban transit environments.
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Open AccessArticle
Hydrodynamic Modeling of Unstretched Length Variations in Nonlinear Catenary Mooring Systems for Floating PV Installations in Small Indonesian Islands
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Mohammad Izzuddin Jifaturrohman, I Ketut Aria Pria Utama, Teguh Putranto, Dony Setyawan, I Ketut Suastika, Septia Hardy Sujiatanti, Dendy Satrio, Noorlaila Hayati and Luofeng Huang
Modelling 2025, 6(2), 31; https://doi.org/10.3390/modelling6020031 - 16 Apr 2025
Abstract
Floating photovoltaic (FPV) systems offer a promising renewable energy solution, particularly for coastal waters. This preliminary numerical study proposes a single-array pentamaran configuration designed to maximize panel installation and enhance stability by reducing rolling motion. The study investigates the effect of mooring length
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Floating photovoltaic (FPV) systems offer a promising renewable energy solution, particularly for coastal waters. This preliminary numerical study proposes a single-array pentamaran configuration designed to maximize panel installation and enhance stability by reducing rolling motion. The study investigates the effect of mooring length on the motion behavior of FPV systems and actual line tension using the Boundary Element Method (BEM) in both frequency and time domains under irregular wave conditions. The results demonstrate that the mooring system significantly reduces all horizontal motion displacements, with reductions exceeding 90%. Even with a reduction of up to 51% in the unstretched mooring length, from the original design (304.53 m) to the shortest alternative (154.53 m), the motion response shows minimal change. This is supported by RMSE values of only 0.01 m/m for surge, 0.02 m/m for sway, and 0.09 deg/m for yaw. In the time-domain response, the shortened mooring line demonstrates improved motion performance. This improvement comes with the consequence of stronger nonlinearity in restoring forces and stiffness, resulting in higher peak tensions of up to 15.79 kN. Despite this increase, all configurations remain within the allowable tension limit of 30.69 kN, indicating that the FPV’s system satisfies safety criteria.
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(This article belongs to the Section Modelling in Engineering Structures)
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Open AccessArticle
Numerical Study on Free Convection in an Inclined Wavy Porous Cavity with Localized Heating
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Sivasankaran Sivanandam, Huey Tyng Cheong and Aasaithambi Thangaraj
Modelling 2025, 6(2), 30; https://doi.org/10.3390/modelling6020030 - 5 Apr 2025
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The goal of the present investigation is to explore the heater position and tilting angle of geometry on a buoyant convective stream and energy transport in a tilted, curved porous cavity. This work can be utilized in the field of solar panel construction
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The goal of the present investigation is to explore the heater position and tilting angle of geometry on a buoyant convective stream and energy transport in a tilted, curved porous cavity. This work can be utilized in the field of solar panel construction and electrical equipment cooling. Since no study has explored the impact of the heater location in an inclined wavy porous chamber, three locations of the heater of finite length on the left sidewall, viz., the top, middle, and bottom, are explored. The stream through the porous material is explained by the Darcy model. The upper and lower walls, as well as the remaining area in the left wall, are covered with thermal insulation, while the curved right sidewall maintains the lower temperature. The governing equations and related boundary conditions are discretized by the finite difference approximations. The equations are then iteratively solved for different heater positions, inclinations, Darcy–Rayleigh number (RaD), and corrugation of the right walls. It is witnessed that the heater locations and cavity inclinations alter the stream and thermal fields within the curved porous domain. Furthermore, all heating zones benefit from improved heat conduction due to the right sidewall’s waviness and the tilted porous domain.
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Open AccessReview
A Review of Dynamic Operating Envelopes: Computation, Applications and Challenges
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Anjala Wickramasinghe, Mahinda Vilathgamuwa, Ghavameddin Nourbakhsh and Paul Corry
Modelling 2025, 6(2), 29; https://doi.org/10.3390/modelling6020029 - 3 Apr 2025
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The integration of Distributed Energy Resources (DERs) into power grids presents significant challenges to grid performance, requiring innovative solutions for effective operation. Dynamic Operating Envelopes (DOEs) offer a promising approach by optimizing the use of existing infrastructure while ensuring compliance with network constraints.
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The integration of Distributed Energy Resources (DERs) into power grids presents significant challenges to grid performance, requiring innovative solutions for effective operation. Dynamic Operating Envelopes (DOEs) offer a promising approach by optimizing the use of existing infrastructure while ensuring compliance with network constraints. This paper reviews various DOE calculation methodologies, focusing on Optimal Power Flow (OPF)-based methods. Key findings include the role of DOEs in optimizing import and export limits, with critical factors such as forecast accuracy, network modelling, and the effects of mutual phase coupling in unbalanced networks identified as influencing DOE performance. The paper also explores the integration of DOEs into smart grid frameworks, examining both centralized and decentralized control strategies, as well as their potential for providing ancillary services. Challenges in scaling DOEs are also discussed, particularly regarding the need for accurate forecasts, computational resources, communication infrastructure, and balancing efficiency and fairness in resource allocation. Lastly, future research directions are proposed, focusing on the practical application of DOEs to improve grid performance and support network operations, as well as the development of more robust DOE calculation methodologies. This review provides a comprehensive overview of current DOE research and identifies avenues for further exploration and advancement.
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Open AccessArticle
Aspects Concerning Validation of Theoretical Solution of Generalised Ladder Problem
by
Costica Lupascu, Stelian Alaci, Florina-Carmen Ciornei, Ionut-Cristian Romanu, Delia-Aurora Cerlinca and Carmen Bujoreanu
Modelling 2025, 6(2), 28; https://doi.org/10.3390/modelling6020028 - 29 Mar 2025
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One of the most well-known problems of dynamics is the “ladder problem”. In this paper, a theoretical model is proposed followed by the experimental validation of the predicted solution. The model refers to a rod of negligible thickness with the ends leaning frictionless
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One of the most well-known problems of dynamics is the “ladder problem”. In this paper, a theoretical model is proposed followed by the experimental validation of the predicted solution. The model refers to a rod of negligible thickness with the ends leaning frictionless on two walls. By approximating the rod as a segment, the problem is simplified, and the Lagrange equations can be applied. The experimental validation of the model had to address several challenges: the actual rod–wall contacts are singular points, friction cannot be neglected, and the rod’s motion must remain confined to the vertical plane. The physical “ladder” was designed as a cylindrical rod with two identical balls of well-controlled geometry, fixed at the ends. These spheres make contact with two half-cylinder grooves—one vertical and one horizontal—ensuring that the motion remains parallel to the vertical plane. The presence of dry friction in the sphere–groove contacts leads to a complex, strongly nonlinear differential equation of motion, requiring numerical methods of integration. A test-rig was designed and constructed for the experimental study of motion, and an aspect overlooked by the theoretical model was emphasised: the interruption of contact with the vertical wall. An excellent agreement was found between the experimental data and the theoretical results.
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Open AccessArticle
A Multi-Head Attention-Based Transformer Model for Predicting Causes in Aviation Incidents
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Aziida Nanyonga, Hassan Wasswa, Keith Joiner, Ugur Turhan and Graham Wild
Modelling 2025, 6(2), 27; https://doi.org/10.3390/modelling6020027 - 25 Mar 2025
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The timely identification of probable causes in aviation incidents is crucial for averting future tragedies and safeguarding passengers. Typically, investigators rely on flight data recorders; however, delays in data retrieval or damage to the devices can impede progress. In such instances, experts resort
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The timely identification of probable causes in aviation incidents is crucial for averting future tragedies and safeguarding passengers. Typically, investigators rely on flight data recorders; however, delays in data retrieval or damage to the devices can impede progress. In such instances, experts resort to supplementary sources like eyewitness testimonies and radar data to construct analytical narratives. Delays in this process have tangible consequences, as evidenced by the Boeing 737 MAX accidents involving Lion Air and Ethiopian Airlines, where the same design flaw resulted in catastrophic outcomes. To streamline investigations, scholars advocate for natural language processing (NLP) and topic modelling methodologies, which organize pertinent aviation terms for rapid analysis. However, existing techniques lack a direct mechanism for deducing probable causes. To bridge this gap, this study trains and evaluates the performance of a transformer-based model in predicting the likely causes of aviation incidents based on long-input raw text analysis narratives. Unlike traditional models that classify incidents into predefined categories such as human error, weather conditions, or maintenance issues, the trained model infers and generates the likely cause in a human-like narrative, providing a more interpretable and contextually rich explanation. By training the model on comprehensive aviation incident investigation reports like those from the National Transportation Safety Board (NTSB), the proposed approach exhibits promising performance across key evaluation metrics, including BERTScore with Precision: (M = 0.749, SD = 0.109), Recall: (M = 0.772, SD = 0.101), F1-score: (M = 0.758, SD = 0.097), Bilingual Evaluation Understudy (BLEU) with (M = 0.727, SD = 0.33), Latent Semantic Analysis (LSA similarity) with (M = 0.696, SD = 0.152), and Recall Oriented Understudy for Gisting Evaluation (ROUGE) with a precision, recall and F-measure scores of (M = 0.666, SD = 0.217), (M = 0.610, SD = 0.211), (M = 0.618, SD = 0.192) for rouge-1, (M = 0.488, SD = 0.264), (M = 0.448, SD = 0.257), M = 0.452, SD = 0.248) for rouge-2 and (M = 0.602, SD = 0.241), (M = 0.553, SD = 0.235), (M = 0.5560, SD = 0.220) for rouge-L, respectively. This demonstrates its potential to expedite investigations by promptly identifying probable causes from analysis narratives, thus bolstering aviation safety protocols.
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