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 19.5 days after submission; acceptance to publication is undertaken in 2.9 days (median values for papers published in this journal in the first half of 2025).
- Journal Rank: JCR - Q2 (Engineering, Multidisciplinary) / 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:
1.5 (2024);
5-Year Impact Factor:
1.5 (2024)
Latest Articles
An Analytical Thermal Model for Coaxial Magnetic Gears Considering Eddy Current Losses
Modelling 2025, 6(4), 114; https://doi.org/10.3390/modelling6040114 - 25 Sep 2025
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This work presents an analytical 2D model for estimating eddy current losses in the permanent magnets (PMs) of a coaxial magnetic gear (CMG), with a focus on loss minimization through magnet segmentation. The model is applied under various operating conditions, including different rotational
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This work presents an analytical 2D model for estimating eddy current losses in the permanent magnets (PMs) of a coaxial magnetic gear (CMG), with a focus on loss minimization through magnet segmentation. The model is applied under various operating conditions, including different rotational speeds, load levels, and segmentation configurations, to derive empirical expressions for eddy current losses in both the inner and outer rotors. A 1D lumped-parameter thermal model is then used to predict the steady-state temperature of the PMs, incorporating empirical correlations for the thermal convection coefficient. Both models are validated against finite element analysis (FEA) simulations. The analytical eddy current loss model exhibits excellent agreement, with a maximum error of 2%, while the thermal model shows good consistency, with a maximum temperature deviation of 5%. The results confirm that eddy current losses increase with rotational speed but can be significantly reduced through magnet segmentation. However, achieving an acceptable thermal performance at high speeds may require a large number of segments, particularly in the outer rotor, which could influence the manufacturing cost and complexity. The proposed models offer a fast and accurate tool for the design and thermal analysis of CMGs, enabling early-stage optimization with minimal computational effort.
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Open AccessArticle
Investigation of Aerodynamic Pressure Characteristics Inside and Outside a Metro Train Traversing a Tunnel in High-Altitude Regions
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Fei Wang, Haisheng Chen, Tianji Liu, Xingsen He, Chunjie Cheng, Lin Xu and Shengzhong Zhao
Modelling 2025, 6(4), 113; https://doi.org/10.3390/modelling6040113 - 24 Sep 2025
Abstract
The numerical method was employed to analyze the transient pressure characteristics of a metro train passing through a tunnel in high-altitude regions. The transient pressure evolution inside and outside the train under varying ambient pressures is analyzed and compared. The findings indicate that
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The numerical method was employed to analyze the transient pressure characteristics of a metro train passing through a tunnel in high-altitude regions. The transient pressure evolution inside and outside the train under varying ambient pressures is analyzed and compared. The findings indicate that while ambient pressure minimally impacts the waveform of the exterior transient pressure, it significantly influences the peak value. Specifically, as ambient pressure rises, the maximum transient pressure (P-max) and the peak-to-peak transient pressure (ΔP) on the train’s exterior surface increase linearly, whereas the minimum transient pressure (P-min) decreases linearly. Moreover, this study analyzed pressure changes within the metro train under varying ambient pressures to assess their impact on passengers’ ear comfort. The trend of pressure peak reduction and delay inside the metro train with a certain degree of airtightness remains well aligned for different ambient pressures. In areas of high altitude with low atmospheric pressure, the requirements for the tightness performance of the train are lower.
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(This article belongs to the Special Issue Recent Advances in Computational Fluid Mechanics)
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Open AccessArticle
Cloud-Edge Collaborative Inference-Based Smart Detection Method for Small Objects
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Cong Ye, Shengkun Li, Jianlei Wang, Hongru Li, Xiao Li and Sujie Shao
Modelling 2025, 6(4), 112; https://doi.org/10.3390/modelling6040112 - 24 Sep 2025
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Emerging technologies are revolutionizing power system operation and maintenance. Intelligent state perception is pivotal for stable grid operation, with small object detection technology being vital for identifying minor hazards in power facilities. However, challenges like small object size, low resolution, occlusion, and low
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Emerging technologies are revolutionizing power system operation and maintenance. Intelligent state perception is pivotal for stable grid operation, with small object detection technology being vital for identifying minor hazards in power facilities. However, challenges like small object size, low resolution, occlusion, and low confidence arise in small object detection for power operation and maintenance. This paper proposes PyraFAN, a feature fusion method designed for small object detection, and introduces a cloud-edge collaborative inference based smart detection method. This method boosts detection accuracy while ensuring real-time performance. Additionally, a graph-guided distillation method is developed for edge models. By quantifying model performance and task similarity, multi-model collaborative training is realized to improve detection accuracy. Experimental results show that compared with standalone edge models, the proposed method improves detection accuracy by 6.98% and reduces the false negative rate by 19.56%. The PyraFAN module can enhance edge model detection accuracy by approximately 12.2%. Updating edge models via cloud model distillation increases the mAP@0.5 of edge models by 2.7%. Compared to cloud models, the cloud-edge collaboration method reduces average inference latency by 0.8%. This research offers an effective solution for improving the accuracy of deep learning based small object detection in power operation and maintenance within cloud-edge computing environments.
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Open AccessArticle
Investigation of Mixing of Solid Particles in a Plowshare Mixer Using Discrete Element Method (DEM)
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Xi Luan, Wenzhao Li, Yibo Li and Junwei Zou
Modelling 2025, 6(3), 111; https://doi.org/10.3390/modelling6030111 - 22 Sep 2025
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The mixing process of powder materials determines the final quality of industrial products. This study employs the Discrete Element Method (DEM) to numerically characterize the effects of particle shape and mixer structure on mixing performance. Using the superquadratic equation, nine types of particles
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The mixing process of powder materials determines the final quality of industrial products. This study employs the Discrete Element Method (DEM) to numerically characterize the effects of particle shape and mixer structure on mixing performance. Using the superquadratic equation, nine types of particles with regular shape variations are constructed, and mixing models are further simulated. The feasibility of superquadratic-generated particles is validated through a classic drum calibration experiment. To investigate the intrinsic mechanisms of particle shape effects, the motion and contact behaviors of particles are quantified by the diffusion index, proportion of rotational kinetic energy, interparticle compressive force, and contact number. Meanwhile, to examine geometry effects, three supplementary mixing simulations are conducted by varying the plow angle and deactivating the choppers. The results show that Cubic particles exhibited poor mixing performance, while disk-shaped particles outperformed cylindrical ones; Increasing the plow blade inclination angle enhanced particle convection and diffusion, whereas excessively small angles may fail to achieve homogeneous mixing; The auxiliary shear of chopper blades promoted particle diffusion, effectively overcoming dead zones between plow blade intervals.
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Open AccessArticle
Finite Element-Based Multi-Objective Optimization of a New Inclined Oval Rolling Pass Geometry
by
Kairosh Nogayev, Aman Kamarov, Maxat Abishkenov, Zhassulan Ashkeyev, Nurbolat Sembayev and Saltanat Kydyrbayeva
Modelling 2025, 6(3), 110; https://doi.org/10.3390/modelling6030110 - 22 Sep 2025
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A novel rolling scheme incorporating an inclined oval-caliber configuration is proposed to enhance plastic deformation mechanisms in the traditional oval–round rolling sequence. Finite Element Method (FEM) simulations were performed using DEFORM-3D to evaluate and optimize this new scheme across multiple objectives: maximizing average
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A novel rolling scheme incorporating an inclined oval-caliber configuration is proposed to enhance plastic deformation mechanisms in the traditional oval–round rolling sequence. Finite Element Method (FEM) simulations were performed using DEFORM-3D to evaluate and optimize this new scheme across multiple objectives: maximizing average effective strain, minimizing strain non-uniformity (captured via the standard deviation of effective strain), and minimizing rolling force. Numerical modeling was conducted for calibration angles of γ = 0°, 25°, 35°, and 45°, from which Pareto-optimal solutions were identified based on classical non-dominance criteria. Pairwise 2D projections of the Pareto front enabled visualization of trade-offs and revealed γ = 35° as the Pareto knee-point, representing the most balanced compromise among high deformation intensity, increased uniformity, and reduced energy consumption. This optimal angle was further corroborated through a normalized weighted sum of the objective functions. The findings provide a validated reference for designing prototype deforming tools and support future experimental validation.
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Open AccessArticle
Modeling and Optimizing the Process of Identifying Energy-Saving Potential Scope (ESPS) in Municipalities: A Combinatorial Approach to ISO 50001 Implementation
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Ebagninin Séraphin Kouaho, Yao N’Guessan and Christophe Marvillet
Modelling 2025, 6(3), 109; https://doi.org/10.3390/modelling6030109 - 22 Sep 2025
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The energy consumption of buildings, the effectiveness of energy-saving measures, and the exploitation of energy-saving potential are strategic issues for improving the energy performance of public assets and limiting their environmental impact. However, small and medium municipalities (SMMs) encounter difficulties in identifying their
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The energy consumption of buildings, the effectiveness of energy-saving measures, and the exploitation of energy-saving potential are strategic issues for improving the energy performance of public assets and limiting their environmental impact. However, small and medium municipalities (SMMs) encounter difficulties in identifying their energy-intensive units, a process that is often lengthy (3 to 18 months), costly, and dependent on traditional methods such as the Real Estate and Energy Master Plan (REMP) promoted by ADEME or the Cit’ergie system. These approaches, although structured, rely on time-consuming manual analyses that require significant technical and human resources. This article proposes an innovative solution, PG2E, based on a combinatorial approach that quickly identifies Energy-Saving Potential Scope (ESPSs) from energy consumption data. Backed by a realistic–critical stance to assess the limitations of existing systems and a constructivist–pragmatic approach to designing a tool adapted to SMMs, the PG2E solution uses simple statistical criteria (average, upper quartile). This study, conducted in the town of Quesnoy-Sur-Deûle, shows that PG2E identifies ESPS with a success rate of 60% to 100% while reducing time and costs. It thus offers an accessible digital alternative for initiating an approach that complies with the ISO 50001 standard.
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Graphical abstract
Open AccessCommunication
Optimized Non-Linear Observer for a PMSM Speed Control System Integrating a Multi-Dimensional Taylor Network and Lyapunov Theory
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Chao Zhang, Ya-Qin Qiu and Zi-Ao Li
Modelling 2025, 6(3), 108; https://doi.org/10.3390/modelling6030108 - 19 Sep 2025
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Within the field of permanent magnet synchronous motor sensorless speed control systems, we present a novel scheme with a Multi-dimensional Taylor Network (MTN)-based nonlinear observer as the core, supplemented by two auxiliary MTN modules to realize closed-loop control: (1) MTN Model Identifier: Provides
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Within the field of permanent magnet synchronous motor sensorless speed control systems, we present a novel scheme with a Multi-dimensional Taylor Network (MTN)-based nonlinear observer as the core, supplemented by two auxiliary MTN modules to realize closed-loop control: (1) MTN Model Identifier: Provides real-time PMSM nonlinear dynamic feedback for the observer; (2) MTN Adaptive Inverse Controller: Compensates for load disturbances using the observer’s estimated states. The study focuses on optimizing the MTN observer to address key limitations of existing methods (high computational complexity, lack of stability guarantees, and low estimation accuracy). Compared with the neural network observer, this MTN-based scheme stands out due to its straightforward structure and significantly reduced approximately 40% computational complexity. Specifically, the intricate calculations and high resource consumption typically associated with neural network observers are circumvented. Subsequently, by leveraging Lyapunov theory, an adaptive learning rule for the MTN weights is meticulously devised, which seamlessly bridges the theoretical proof of the nonlinear observer’s stability. Simulation results demonstrate that the proposed MTN observer achieves rapid convergence of speed and position estimation errors (with steady-state errors within ±0.5% of the rated speed and ±0.02 rad for rotor position) after a transient period of less than 0.2 s. Even when stator resistance is increased by tenfold to simulate parameter variations, the observer maintains high estimation accuracy, with speed and position errors increasing by no more than 1.2% and 0.05 rad, respectively, showcasing strong robustness. These results collectively confirm the efficacy and practical value of the proposed scheme in PMSM sensorless speed control.
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Open AccessArticle
Fault Diagnosis Method Using CNN-Attention-LSTM for AC/DC Microgrid
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Qiangsheng Bu, Pengpeng Lyu, Ruihai Sun, Jiangping Jing, Zhan Lyu and Shixi Hou
Modelling 2025, 6(3), 107; https://doi.org/10.3390/modelling6030107 - 18 Sep 2025
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From the perspectives of theoretical design and practical application, the existing fault diagnosis methods with the complex identification process owing to manual feature extraction and the insufficient feature extraction for time series data and weak fault signal is not suitable for AC/DC microgrids.
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From the perspectives of theoretical design and practical application, the existing fault diagnosis methods with the complex identification process owing to manual feature extraction and the insufficient feature extraction for time series data and weak fault signal is not suitable for AC/DC microgrids. Thus, this paper proposes a fault diagnosis method that integrates a convolutional neural network (CNN) with a long short-term memory (LSTM) network and attention mechanisms. The method employs a multi-scale convolution-based weight layer (Weight Layer 1) to extract features of faults from different dimensions, performing feature fusion to enrich the fault characteristics of the AC/DC microgrid. Additionally, a hybrid attention block-based weight layer (Weight Layer 2) is designed to enable the model to adaptively focus on the most significant features, thereby improving the extraction and utilization of critical information, which enhances both classification accuracy and model generalization. By cascading LSTM layers, the model effectively captures temporal dependencies within the features, allowing the model to extract critical information from the temporal evolution of electrical signals, thus enhancing both classification accuracy and robustness. Simulation results indicate that the proposed method achieves a classification accuracy of up to 99.5%, with fault identification accuracy for noisy signals under 10 dB noise interference reaching 92.5%, demonstrating strong noise immunity.
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Open AccessArticle
Fuzzy Classifier Based on Mamdani Inference and Statistical Features of the Target Population
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Miguel Antonio Caraveo-Cacep, Rubén Vázquez-Medina and Antonio Hernández Zavala
Modelling 2025, 6(3), 106; https://doi.org/10.3390/modelling6030106 - 18 Sep 2025
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Classifying study objects into groups is facilitated by fuzzy classifiers based on a set of rules and membership functions. Typically, the characteristics of the study objects are used to establish the criteria for classification. This work arises from the need to design fuzzy
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Classifying study objects into groups is facilitated by fuzzy classifiers based on a set of rules and membership functions. Typically, the characteristics of the study objects are used to establish the criteria for classification. This work arises from the need to design fuzzy classifiers in contexts where real data is scarce or highly random, proposing a design based on statistics and chaotic maps that simplifies the design process. This study introduces the development of a fuzzy classifier, assuming that three features of the population to be classified are random variables. A Mamdani fuzzy inference system and three pseudorandom number generators based on one-dimensional chaotic maps are utilized to achieve this. The logistic, Bernoulli, and tent chaotic maps are implemented to emulate the random features of the target population, and their statistical distribution functions serve as input to the fuzzy inference system. Four experimental tests were conducted to demonstrate the functionality of the proposed classifier. The results show that it is possible to achieve a symmetric and robust classification through simple adjustments to membership functions, without the need for supervised training, which represents a significant methodological contribution, especially because this indicates that designers with minimal experience can build effective classifiers in just a few steps. Real applications of the proposed design may focus on the classification of biomedical signals (sEMG), network traffic, and personalized medical assistance systems, where data exhibits high variability and randomness.
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Open AccessArticle
Simulation-Guided Aerodynamic Design and Scaled Verification for High-Performance Sports Cars
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Noppakot Kuttasirisuk, Phet Munikanon, Nopdanai Ajavakom, Prabhath De Silva and Gridsada Phanomchoeng
Modelling 2025, 6(3), 105; https://doi.org/10.3390/modelling6030105 - 17 Sep 2025
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High-performance sports cars rely on aerodynamics for stability and speed, but developing aero packages is challenging when wind tunnel testing is limited. In this study, we employed a simulation-guided design loop to maximize downforce and minimize drag on a sports car using Computational
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High-performance sports cars rely on aerodynamics for stability and speed, but developing aero packages is challenging when wind tunnel testing is limited. In this study, we employed a simulation-guided design loop to maximize downforce and minimize drag on a sports car using Computational Fluid Dynamics (CFD). Thirteen aerodynamic modifications—including splitters, ducts, diffusers, and a Drag Reduction System (DRS)—were iteratively tested using CFD. To ensure numerical reliability, a mesh independence study and convergence analysis were performed, confirming stable aerodynamic predictions. The final configuration achieved an ~11× increase in downforce at 120 km/h (from about 320 N to 3588 N), meeting the design goal of roughly 2000 kg of downforce at 177 mph when scaled. This extreme downforce came with higher drag ( ≈ 0.83), so a dual-mode approach was developed: a DRS configuration provides moderate downforce with 50% less drag ( ≈ 0.41) for high-speed efficiency. A 1:12-scale wind tunnel test qualitatively supported the CFD predictions by visualizing wake narrowing and improved flow attachment. While quantitative force validation was not possible due to Reynolds mismatch and facility constraints, the qualitative results increased confidence in the CFD-based findings. Overall, the study demonstrates that substantial aerodynamic gains can be achieved under resource constraints, offering a practical framework for motorsport engineers and manufacturers to optimize aero kits when conventional full-scale testing is not accessible.
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Open AccessArticle
Dynamic Modelling and Simulation of a Permanent Magnet Synchronous Motor (PMSM) Applied in a Prototype Race Car and the Comparison of Its Performance with BLDC Motor
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Attila Szántó, Masuk Abdullah, Tibor Péter Kapusi and Szabolcs Sándor Diós
Modelling 2025, 6(3), 104; https://doi.org/10.3390/modelling6030104 - 16 Sep 2025
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Electric vehicles are playing an important role in transport, aided by rapid advances in battery technology. The Faculty of Engineering at the University of Debrecen is also engaged research and development in the field of electric vehicles. To support the development of electric
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Electric vehicles are playing an important role in transport, aided by rapid advances in battery technology. The Faculty of Engineering at the University of Debrecen is also engaged research and development in the field of electric vehicles. To support the development of electric vehicle prototypes, a vehicle dynamics simulation program has been designed. The study presents the modeling and simulation of a permanent magnet synchronous motor (PMSM) in MATLAB/Simulink, which has been integrated into the existing vehicle dynamics simulation framework. The methods used to determine the motor characteristics required for the simulation are described in detail. In addition, the performance of the PMSM is compared with that of a brushless DC (BLDC) motor within the vehicle dynamics simulation program. The developed method allows the selection of the appropriate motor type for the given competition tasks.
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Open AccessArticle
Evaluating Carsharing Fleet Management Strategies Using Discrete Event Simulation: A Case Study
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Alfred Chellanthara, Mohammad Khanahmadi and Anjali Awasthi
Modelling 2025, 6(3), 103; https://doi.org/10.3390/modelling6030103 - 15 Sep 2025
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In a carsharing organization, vehicle availability is considered as a measure of the quality of service. This paper presents a discrete event simulation model to evaluate the performance of round-trip (return to the same station) vs. one-way (return to any station) fleet management
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In a carsharing organization, vehicle availability is considered as a measure of the quality of service. This paper presents a discrete event simulation model to evaluate the performance of round-trip (return to the same station) vs. one-way (return to any station) fleet management strategies used by carsharing organizations. The proposed model evaluates the customer rejection rate for each fleet management strategy and recommends the one with the least number of rejections. A customer request is deemed to be rejected when a vehicle cannot be made available to the user at the requested time and location. A case study for the carsharing organization Communauto in Montreal is conducted. The simulation results show that the one-way model has a greater request rejection rate of 13%, compared to 8% for the round-trip model. Therefore, a round-trip strategy is recommended to Communauto for managing its current fleet operations.
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Open AccessArticle
A Novel Weak Fault Feature Extraction Method Based on Tensor Decomposition Model for Bearings
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Chengju Dong, Yue Wu and Huiming Jiang
Modelling 2025, 6(3), 102; https://doi.org/10.3390/modelling6030102 - 12 Sep 2025
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The problem of extracting bearing weak fault features under variable-speed conditions with strong background noise interference remains challenging due to the limitations of existing feature extraction methods. These methods, especially those that rely on manual parameter tuning and rigid regularization, often struggle with
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The problem of extracting bearing weak fault features under variable-speed conditions with strong background noise interference remains challenging due to the limitations of existing feature extraction methods. These methods, especially those that rely on manual parameter tuning and rigid regularization, often struggle with noise suppression and robustness optimization, resulting in inaccurate extraction of weak fault features. To overcome this drawback, this study proposes a novel weak fault feature extraction method based on tensor decomposition model for bearings. First, the time–frequency tensor is constructed based on the short-time Fourier transform. Then, two types of fault properties in tensor are explored and an improved tensor decomposition model is proposed to realize the accurate extraction of weak fault features under variable-speed conditions. In addition, the decomposed feature tensor is conducted by a multichannel global energy-weighted fusion strategy, which significantly improves the robustness in extracting multichannel weak fault features. The effectiveness and superiority of the proposed method are systematically investigated through both simulated and experimental case studies. The results demonstrate that the method effectively eliminates background noise interference in measurements while augmenting the resolution of fault features.
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Open AccessArticle
Optimal Configuration of Hydrogen Energy Storage Systems Considering the Operational Efficiency Characteristics of Multi-Stack Electrolyzers
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Jianlin Li, Zelin Shi, Ying Qiao and Xiaoxia Jiang
Modelling 2025, 6(3), 101; https://doi.org/10.3390/modelling6030101 - 12 Sep 2025
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Enhancing the economics of microgrid systems and achieving a balance between energy supply and demand are critical challenges in capacity allocation research. Existing studies often neglect the optimization of electrolyzer efficiency and multi-stack operation, leading to inaccurate assessments of system benefits. This paper
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Enhancing the economics of microgrid systems and achieving a balance between energy supply and demand are critical challenges in capacity allocation research. Existing studies often neglect the optimization of electrolyzer efficiency and multi-stack operation, leading to inaccurate assessments of system benefits. This paper proposes a capacity allocation model for wind-PV-hydrogen integrated microgrid systems that incorporates hydrogen production efficiency optimization. This paper analyzes the relationship between the operating efficiency of the electrolyzer and the output power, regulates power generation-load mismatches through a renewable energy optimization model, and establishes a double-layer optimal configuration framework. The inner layer optimizes electrolyzer power allocation across periods to maximize operational efficiency, while the outer layer determines configuration to maximize daily system revenue. Based on the data from a demonstration project in Jiangsu Province, China, a case study is conducted to verify that the proposed method can improve system benefits and reduce hydrogen production costs.
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Open AccessArticle
Joint Estimation of SOC and SOH Based on Kalman Filter Under Multi-Time Scale
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Hongyan Qin, Shilong Wang, Ke Li and Fachao Jiang
Modelling 2025, 6(3), 100; https://doi.org/10.3390/modelling6030100 - 9 Sep 2025
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Optimizing the accurate estimation algorithms for the State of Charge (SOC) and State of Health (SOH) of power batteries is crucial for improving the performance of electric vehicles. This paper takes lithium-ion batteries as the research object. The Singular Value Decomposition-Unscented Kalman Filter
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Optimizing the accurate estimation algorithms for the State of Charge (SOC) and State of Health (SOH) of power batteries is crucial for improving the performance of electric vehicles. This paper takes lithium-ion batteries as the research object. The Singular Value Decomposition-Unscented Kalman Filter (SVDUKF) at a micro-time scale is used to estimate the battery’s State of Charge, and the traditional Extended Kalman Filter (EKF) at a macro-time scale is used to estimate impedance parameters and capacity. The two filters operate alternately, with the output of one serving as the input for the other, thereby establishing a joint estimation method for SOC and SOH based on the SVDUKF-EKF under a multi-time scale. The joint estimation method is verified under the Dynamic Stress Test (DST) condition and Federal Urban Driving Schedule (FUDS) condition. The results show that the SOH estimation error is within 2% under the DST condition and within 1% under the FUDS condition. The method exhibits high estimation accuracy and stability under both conditions.
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Open AccessArticle
Dimensionless Modelling of Bond-Based Peridynamic Models and Strategies for Enhancing Numerical Accuracy
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Chaobin Hu and Xiaomiao Chen
Modelling 2025, 6(3), 99; https://doi.org/10.3390/modelling6030099 - 8 Sep 2025
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Peridynamics (PD) exhibits inherent advantages in solving solid mechanics problems involving strong discontinuities, such as crack propagation. However, the significant magnitude discrepancy between the micro-modulus and bond stretch in the nonlocal modelling, the extensive accumulation operations during nonlocal interaction integration, and the calculation
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Peridynamics (PD) exhibits inherent advantages in solving solid mechanics problems involving strong discontinuities, such as crack propagation. However, the significant magnitude discrepancy between the micro-modulus and bond stretch in the nonlocal modelling, the extensive accumulation operations during nonlocal interaction integration, and the calculation methods for surface-correction coefficients can all introduce or amplify numerical errors, thereby reducing the confidence in numerical results. To address these sources of error and enhance the numerical accuracy of the PD models, this study derived a dimensionless bond-based PD formulation and proposed computational strategies to mitigate numerical errors during model implementation. The correctness of the dimensionless bond-based PD model was validated through investigating an elastic-wave propagation problem and a crack-branching problem, and comparing the numerical results with that from the finite-element method and the referenced literature. The effectiveness of the dimensionless model and the numerical strategies in enhancing numerical accuracy was verified through comparing the numerical performance of the model while investigating symmetrical mechanical problems under extreme computational conditions and load conditions. This study provides an effective modelling framework and numerical processing strategies for accurate computations in PD.
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Open AccessArticle
Optuna-Optimized Ensemble and Neural Network Models for Static Characteristics Prediction of Active Bearings with Geometric Adjustments
by
Girish Hariharan, Ravindra Mallya, Nitesh Kumar, Deepak Doreswamy, Gowrishankar Mandya Chennegowda and Subraya Krishna Bhat
Modelling 2025, 6(3), 98; https://doi.org/10.3390/modelling6030098 - 5 Sep 2025
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Active vibration control designs for journal bearings have improved rotordynamic stability and led to advancements in adjustable bearing types that enable precise control of bearing geometry. In this study, optimized machine learning (ML) algorithms were modeled and implemented to accurately predict the static
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Active vibration control designs for journal bearings have improved rotordynamic stability and led to advancements in adjustable bearing types that enable precise control of bearing geometry. In this study, optimized machine learning (ML) algorithms were modeled and implemented to accurately predict the static performance envelope of a four-pad active journal bearing with features of controlling the radial and tilt positions of pads in real time. ML models developed for the adjustable bearing system help predict its behavior as a function of three key input parameters such as the eccentricity ratio and radial and tilt positions of pads. Four supervised regression models, such as Random Forest Regression (RFR), Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), and a feedforward Artificial Neural Network (ANN), were chosen for their demonstrated ability to capture complex nonlinear patterns and their robustness against overfitting in such tribological applications. Hyperparameter tuning for each model was performed using the Optuna framework, which applies Bayesian optimization to efficiently determine the best parameter settings. The Optuna-optimized ensemble and neural network models were used to identify the optimal combinations of input variables that maximize the static performance envelope of the active bearing system with geometric adjustments.
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Open AccessReview
Advancements in Active Journal Bearings: A Critical Review of Performance, Control, and Emerging Prospects
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Navaneeth Krishna Vernekar, Raghuvir Pai, Ganesha Aroor, Nitesh Kumar and Girish Hariharan
Modelling 2025, 6(3), 97; https://doi.org/10.3390/modelling6030097 - 5 Sep 2025
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The active or adjustable journal bearings are designed with unique mechanisms to reduce the rotor-bearing system lateral vibrations by adjusting their damping and stiffness. The article provides a comprehensive review of the literature, outlining the structure and findings of studies on active bearings.
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The active or adjustable journal bearings are designed with unique mechanisms to reduce the rotor-bearing system lateral vibrations by adjusting their damping and stiffness. The article provides a comprehensive review of the literature, outlining the structure and findings of studies on active bearings. Over the years, various kinds of adjustable bearing designs have been developed with unique operational mechanisms. Such bearing designs include adjustable pad sectors, externally adjustable pads, active oil injection through pad openings, and flexible deformable sleeves. These modifications enhance the turbine shaft line’s performance by increasing the system’s overall stability. The detailed review in this paper highlights the characteristics of bearings, along with the key advantages, limitations, and potential offered by active control across different bearing types. The efficiency of any rotor system can be greatly enhanced by optimally selecting the adjustable bearing parameters. These adjustable bearings have demonstrated a unique capability to modify the hydrodynamic operation within the bearing clearances. Experimental studies and simulation approaches were also utilized to optimize bearing geometries, lubrication regimes, and control mechanisms. The use of advanced controllers like PID, LQG, and Deep Q networks further refined the stability. The concluding section of the article explores potential avenues for the future development of active bearings.
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Open AccessCommunication
Directed Douglas–Rachford Splitting Method with Application to Feature Selection
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Yunda Dong and Miaomiao Chen
Modelling 2025, 6(3), 96; https://doi.org/10.3390/modelling6030096 - 3 Sep 2025
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In this article, we study a directed version of Douglas–Rachford splitting method in real Hilbert spaces. By using new, self-contained, and simplified techniques, we prove its weak convergence. The major innovation is that we exploit the firm non-expansiveness of the Douglas–Rachford operator for
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In this article, we study a directed version of Douglas–Rachford splitting method in real Hilbert spaces. By using new, self-contained, and simplified techniques, we prove its weak convergence. The major innovation is that we exploit the firm non-expansiveness of the Douglas–Rachford operator for the first time to derive the best possible upper bounds on direction factors, assuming that the involved factors remain constant. We give a new rare feature selection model equipped with the TripAdvisor hotel-review dataset. Numerical results confirm the user-friendliness and efficiency of directed Douglas–Rachford splitting in solving this model.
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Open AccessArticle
Numerical Investigation of Water Wave Impacting a Structure Using Fluid–Structure Interaction Simulation
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Yifei Peng, Jean-Marie Nianga, Zefeng Wang and Yunliang Jiang
Modelling 2025, 6(3), 95; https://doi.org/10.3390/modelling6030095 - 2 Sep 2025
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Unmanned surface vehicles (USVs) have great application prospects in defense, environmental surveillance and offshore energy due to their cost-effectiveness and long-duration mission ability. The structural safety issues induced by the prolonged cyclic wave loading on such small-sized marine structures, such as fatigue failure
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Unmanned surface vehicles (USVs) have great application prospects in defense, environmental surveillance and offshore energy due to their cost-effectiveness and long-duration mission ability. The structural safety issues induced by the prolonged cyclic wave loading on such small-sized marine structures, such as fatigue failure mechanism, represent an important research topic. In order to characterize the loading process, a piston-type numerical wave flume with wave absorption setting is constructed using the Arbitrary Lagrangian Eulerian (ALE) formulation, and the fluid–structure interaction (FSI) simulations are performed. Simulated wave profiles are measured and compared with corresponding analytical wave solutions to verify the accuracy of target waves. The wave absorption effect is verified by comparing the velocities of water particles in different water regions. Then, different impact scenarios are performed by applying a range of the applicable target waves. Simulated wave forms, impact scenes along with the computed wave load data are presented, and the impact process is analyzed. As a result, the FSI simulations demonstrate cyclic loading characteristics of small-sized floating structures subjected to wave impacts, and the constructed ALE numerical wave flume possesses the extensibility for the simulation of nonlinear water wave impact scenarios.
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