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Keywords = improved kriging

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32 pages, 5102 KB  
Article
Quantifying Uncertainty in Permeability Estimation Using Deep Learning and Generative Models
by Oriyomi Raheem, Misael M. Morales, Michael Pyrcz, Carlos Torres-Verdín, Wen Pan, Yuanjun Li, Xiaohui Xiao, Rafael Centeno, Jay Chen and Pandu Devarakota
Geosciences 2026, 16(7), 275; https://doi.org/10.3390/geosciences16070275 - 6 Jul 2026
Abstract
Uncertainty quantification of well-log interpretation is essential to derisking subsurface exploration and development decision-making by providing possible scenarios for reservoir property distribution, fluid flow behaviors, and hydrocarbon potential. Well-log interpretation offers crucial insights into permeability variations, reservoir compartmentalization, mineral composition, and fluid mobility. [...] Read more.
Uncertainty quantification of well-log interpretation is essential to derisking subsurface exploration and development decision-making by providing possible scenarios for reservoir property distribution, fluid flow behaviors, and hydrocarbon potential. Well-log interpretation offers crucial insights into permeability variations, reservoir compartmentalization, mineral composition, and fluid mobility. Inherent uncertainties, such as those arising from geological heterogeneity, limited sampling, and non-uniform distribution of rock properties, can lead to inaccuracies that compromise petrophysical interpretation and formation evaluation. However, traditional data-driven well-log interpretation methods, which map well logs to formation properties based on core measurements, are primarily deterministic and fail to quantify uncertainty accurately. By leveraging deep learning and generative models, we introduce a probabilistic approach that significantly improves permeability estimation and uncertainty quantification. Our methodology integrates co-kriging techniques with Conditional Generative Adversarial Networks (cGANs) and Conditional Variational Autoencoders (cVAEs), establishing a quantitative relationship between kriged core, well-log data and permeability. Our approach enhances petrophysical property uncertainty estimations based on geostatistics by establishing a quantitative relationship between kriged estimates and flow-related properties. Training features are constructed using collocated co-kriging, capturing the cross-correlation between well logs (input features) and core data (output formation properties). Core bulk density, calculated from grain density, is kriged to well-log resolution to enable porosity estimation, while permeability is similarly kriged. A low-pass filter is then applied to smooth the kriged core bulk density, permeability, and estimated porosity, ensuring more accurate interpretations. The results reveal that cGANs and cVAEs consistently produce lower uncertainty estimates compared to traditional machine learning models. High-permeability zones exhibit lower uncertainty (approximately 3–5%), while low-permeability zones show higher uncertainty (10–15%). Traditional deep learning models tend to overestimate uncertainty, whereas generative models provide more reliable estimates. Additionally, applying kriged permeability data improves uncertainty estimations, further reducing uncertainty to 3% in high-permeability zones and 10% in low-permeability zones. To ensure broad applicability, the methods were tested on datasets from both carbonate and clastic reservoirs. In carbonate formations, prior classification steps are necessary to achieve accurate permeability predictions. The interpretation workflow improves permeability estimation accuracy and enhances uncertainty quantification across conventional and unconventional reservoirs. Additionally, this method is adaptable for CO2 injection and H2 storage wells, demonstrating versatility across various reservoir types. Full article
15 pages, 4393 KB  
Article
Spatiotemporal Analysis and Deep Learning-Based Prediction of Air Pollution in China, 2015–2024
by Kai Tan, Qianjun Ren, Yiting Huo, Lu Ran, Xiaofang Xu, Li Cao, Qianying Xiang, Huirong Duan, Shuhan Wang, Jisheng Nie and Xiujuan Yang
Atmosphere 2026, 17(7), 659; https://doi.org/10.3390/atmos17070659 - 30 Jun 2026
Viewed by 153
Abstract
Air quality in China has markedly improved over the past decade, yet pollution levels remain high and continue to threaten public health. This study analyzed the spatiotemporal variations in six air pollutants (PM2.5, PM10, SO2, NO2 [...] Read more.
Air quality in China has markedly improved over the past decade, yet pollution levels remain high and continue to threaten public health. This study analyzed the spatiotemporal variations in six air pollutants (PM2.5, PM10, SO2, NO2, O3, CO) across seven regions in China (2015–2024) using Kriging interpolation. The performance of Recurrent Neural Network (RNN), Long Short-term Memory (LSTM), and Convolutional Neural Network-Long Short-term Memory (CNN-LSTM) models was assessed using the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of Determination (R2) metrics. Results showed that all pollutants exhibited overall declining trends, with SO2 depicting the largest reduction (69.53%), while O3 displayed intermittent increases from 2017 to 2024. North China recorded both the highest concentrations and the greatest reductions in PM2.5, SO2, and CO, whereas Southwest and South China maintained the lowest overall levels. Among the predictive models, LSTM achieved the highest overall accuracy (mean RMSE = 1.802, mean MAE = 0.915, R2 > 0.99). These findings provide a comprehensive depiction of China’s air pollution evolution and highlight the potential of deep learning for region-specific air quality prediction and policy design. The results offer a quantitative foundation for optimizing differentiated control strategies and advancing precision air quality management. Full article
(This article belongs to the Section Air Quality)
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26 pages, 6355 KB  
Article
Structural Optimization Design of a Skateboard Chassis Based on Universal Kriging–NSGA-II–TOPSIS
by Jianshe Zhang, Guohui Zhang and Minggang Shen
World Electr. Veh. J. 2026, 17(7), 334; https://doi.org/10.3390/wevj17070334 - 28 Jun 2026
Viewed by 227
Abstract
To achieve coordinated optimization of lightweighting and static–dynamic performance for a skateboard chassis, this paper proposes a multi-objective optimization method based on Universal Kriging, NSGA-II, and TOPSIS. A three-dimensional parametric model of the skateboard chassis structure for electric commercial vehicles was established based [...] Read more.
To achieve coordinated optimization of lightweighting and static–dynamic performance for a skateboard chassis, this paper proposes a multi-objective optimization method based on Universal Kriging, NSGA-II, and TOPSIS. A three-dimensional parametric model of the skateboard chassis structure for electric commercial vehicles was established based on a modular design philosophy, and modal and static analyses under four typical operating conditions were conducted. Six key variables were identified through parameter sensitivity analysis, and a surrogate model was constructed using the optimal Latin hypercube sampling method and the Universal Kriging model. The NSGA-II algorithm was used to solve the multi-objective optimization model and obtain a set of Pareto optimal solutions, from which the optimal compromise solution was selected using the entropy-weighted TOPSIS multi-criteria decision-making method. The optimized design achieved the objectives of reducing the skateboard chassis mass by 2.02%, decreasing the maximum deformation under bending conditions by 19.16%, and increasing the first-order natural frequency by 2.24%, thereby effectively improving lightweight, stiffness, and dynamic response performance of the skateboard chassis. This method integrates modular design with multi-objective optimization, providing a theoretical framework and technical pathway for the structural optimization design of a skateboard chassis. Full article
(This article belongs to the Section Power Electronics Components)
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17 pages, 3702 KB  
Article
A Spatiotemporal Interpolation Method for Regional Precipitation Data Based on a Spatiotemporal Decay Graph Model
by Li Liu, Chuhan Lu, Julong Huang, Feng Zhang, Guangyu Qu, Lu Guo and Runze Luo
Climate 2026, 14(7), 136; https://doi.org/10.3390/cli14070136 - 24 Jun 2026
Viewed by 295
Abstract
Traditional meteorological data spatial interpolation methods often rely on linear or static assumptions, which are inadequate for complex terrain and fail to exploit continuous spatiotemporal variation information. This paper proposes a Spatiotemporal Graph Network with Adaptive Temporal Decay (DG) that integrates a learnable [...] Read more.
Traditional meteorological data spatial interpolation methods often rely on linear or static assumptions, which are inadequate for complex terrain and fail to exploit continuous spatiotemporal variation information. This paper proposes a Spatiotemporal Graph Network with Adaptive Temporal Decay (DG) that integrates a learnable graph convolution module and a temporal attenuation mechanism, enabling accurate precipitation estimation for target stations or regions at consecutive time steps. The method is evaluated using daily precipitation data from nine stations in Longnan City, Gansu Province, China, along with ERA5 (0.25°) and GPCP (0.5°) gridded reanalysis products. In the station-to-station interpolation scenario, DG significantly outperforms ordinary Kriging (OK), reducing the average RMSE from 1.4 mm/day to 1.2 mm/day, with a 28.6% improvement at mountainous stations. The DG model also exhibits superior performance in grid-to-station interpolation, achieving an average RMSE of 1.9 mm/day (OK: 2.5 mm/day). On heavy precipitation days (≥20 mm/day), DG reduces the RMSE nearly by half (11.7 mm/day) compared to OK (23.2 mm/day). A temporal-only LSTM baseline and three ablation variants (spatial-only OSI, temporal-only OTI and dgcn-only OD) are also compared, and DG consistently outperforms them, confirming the essential role of spatiotemporal integration. Additional baselines including IDW and Co-Kriging further validate the superiority of DG. The proposed method offers a promising new approach for high-precision spatiotemporal interpolation of meteorological elements in complex terrain. Full article
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24 pages, 7098 KB  
Article
Reliability-Based Design Optimization of an Interior Permanent Magnet Synchronous Motor Water-Cooling System for Pressure-Drop Reliability
by Eunsoo Kim, Jun Hur, Cheonha Park, Dai Duc Mai and Chang-Wan Kim
Mathematics 2026, 14(12), 2123; https://doi.org/10.3390/math14122123 - 14 Jun 2026
Viewed by 185
Abstract
In electric vehicle thermal management systems, direct measurement of the internal motor temperature is difficult. Therefore, the coolant pressure drop is an important indicator for estimating the motor thermal state. However, manufacturing and operating uncertainties in water-cooled interior permanent magnet synchronous motors (IPMSMs) [...] Read more.
In electric vehicle thermal management systems, direct measurement of the internal motor temperature is difficult. Therefore, the coolant pressure drop is an important indicator for estimating the motor thermal state. However, manufacturing and operating uncertainties in water-cooled interior permanent magnet synchronous motors (IPMSMs) can cause variability in cooling performance and pressure drop, requiring a reliability-based design approach. In this study, reliability-based design optimization (RBDO) is performed by considering manufacturing tolerances in the cooling channels and uncertainty in the inlet coolant flow rate. Based on coupled electromagnetic–thermal–fluid analysis and Kriging surrogate models, RBDO is applied to minimize the maximum temperature while satisfying the allowable pressure-drop limit at a target reliability level. The proposed RBDO improves the probability of satisfying the pressure-drop constraint from 54.1% in the baseline design to 99.9%, while increasing the mean maximum temperature by only 0.17 K. These results indicate that RBDO can improve the reliability of the pressure-drop constraint in IPMSM water-cooling systems under practical manufacturing and operating uncertainties, with only a limited change in thermal performance. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics with Applications)
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26 pages, 27672 KB  
Article
Predicting High-Resolution Gridded Sea Ice Concentration by Integrating LightGBM and Kriging Algorithms
by Wuliu Tian, Chi Zhang, Shanshan Fu, Fangyang Zhu and Haofan Hu
J. Mar. Sci. Eng. 2026, 14(12), 1092; https://doi.org/10.3390/jmse14121092 - 12 Jun 2026
Viewed by 195
Abstract
High-resolution spatiotemporal sea ice concentration (SIC) estimates are essential for Arctic navigation and ice analysis, but existing observational products are often too coarse, and physics-based models are computationally expensive. This study proposes a data-driven framework that couples Light Gradient Boosting Machine (LightGBM) temporal [...] Read more.
High-resolution spatiotemporal sea ice concentration (SIC) estimates are essential for Arctic navigation and ice analysis, but existing observational products are often too coarse, and physics-based models are computationally expensive. This study proposes a data-driven framework that couples Light Gradient Boosting Machine (LightGBM) temporal prediction with Kriging-based spatial interpolation to reconstruct SIC fields over the Northern Sea Route sector. LightGBM is trained on a grid-based SIC time series with engineered features representing persistence, seasonality, and short-term variability, enabling multi-horizon forecasting across large spatial grids. The predicted SIC fields are then refined using Ordinary Kriging (OK) and Co-Kriging (CK) with Gaussian and spherical semi-variogram models. Prediction performance is evaluated using root mean square error, and interpolation accuracy is assessed through cross-validation. Results show that, for high-latitude regions and resolutions finer than 0.25° × 0.25°, OK with a spherical semi-variogram achieves lower interpolation errors than CK and Gaussian-based alternatives. By sequentially coupling temporal learning and spatial refinement, the proposed framework improves temporal continuity, spatial structure, and error quantification, providing high-resolution SIC information suitable for large-scale Arctic ice analysis and navigation support. Full article
(This article belongs to the Special Issue AI-Driven Optimization of Ship Performance and Navigation Safety)
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23 pages, 6831 KB  
Article
Study of the Performance/Cost Bi-Objective Optimization Problem for Solid Rocket Motors
by Wei Zhou, Jing Zhou, Yulong Zhang, Peiyang Ma, Zhigao Xu, Shan Li and Qiuyan Wang
Aerospace 2026, 13(6), 543; https://doi.org/10.3390/aerospace13060543 - 10 Jun 2026
Viewed by 245
Abstract
Historically, in the initial stages of solid rocket motor (SRM) development, performance parameters, such as specific impulse, total impulse, mass, and thrust, have been prioritized, with cost considerations often treated as secondary. Consequently, SRM performance optimization under cost constraints has emerged as a [...] Read more.
Historically, in the initial stages of solid rocket motor (SRM) development, performance parameters, such as specific impulse, total impulse, mass, and thrust, have been prioritized, with cost considerations often treated as secondary. Consequently, SRM performance optimization under cost constraints has emerged as a central objective in aerospace propulsion. To address this gap, this study establishes a cost–performance evaluation model for SRMs. A Kriging surrogate model, the Non-dominated Sorting Genetic Algorithm II (NSGA-II), and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) are leveraged to minimize the manufacturing cost and maximize the terminal velocity of SRM engines, subject to constraints associated with the maximum operating pressure of the combustion chamber and burn time. First, a cost–performance calculation model for an SRM is developed and validated. Subsequently, Pearson correlation analysis and Sobol-based global sensitivity analysis are combined to reduce the dimensionality of the design parameters, and optimal Latin hypercube sampling is used to generate the training samples. Building on this foundation, a Kriging surrogate model is constructed. The cost–performance model of the SRM is subjected to multi-objective optimization using NSGA-II and TOPSIS to support decision-making. The results indicate that the proposed cost–performance calculation model achieves an error below 5%, demonstrating high accuracy. Among the design parameters, the combustion chamber length, nozzle outlet area, and expansion ratio significantly influence the cost and performance of SRMs. The surrogate models exhibit strong predictive accuracy, with coefficients of determination exceeding 0.9. The optimized TOPSIS scheme yields a performance improvement of 10.94% with a cost increase of 4.15% compared with the reference scheme. In summary, the cost–performance evaluation and optimization framework established in this work provides quantitative decision support for SRM design under cost constraints, and the integrated methodology can be extended to other aerospace propulsion systems or complex engineering equipment. This contributes to achieving synergistic optimization of performance and cost under resource limitations, and offers practical guidance for advancing affordability-driven design in propulsion engineering. Full article
(This article belongs to the Section Astronautics & Space Science)
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21 pages, 53560 KB  
Article
Research on the Preparation Technology of Geomagnetic Reference Map Based on Improved Artificial Bee Colony Optimization for Random Forest
by Jiazheng Liu, Xiaolin Ji, Binfeng Yang, Jiaojiao Guo, Yukun Li and Hanbing Wang
Geomatics 2026, 6(3), 68; https://doi.org/10.3390/geomatics6030068 - 9 Jun 2026
Viewed by 195
Abstract
High-precision geomagnetic reference maps are essential for reliable geomagnetic field modeling and accurate geomagnetic matching navigation, especially in regions with sparse observations and complex magnetic anomaly variations. However, conventional map construction methods often exhibit limited precision and robustness, particularly when geomagnetic observations are [...] Read more.
High-precision geomagnetic reference maps are essential for reliable geomagnetic field modeling and accurate geomagnetic matching navigation, especially in regions with sparse observations and complex magnetic anomaly variations. However, conventional map construction methods often exhibit limited precision and robustness, particularly when geomagnetic observations are sparse or spatial variations are complex. To address these challenges, this study proposes an improved artificial bee colony-optimized random forest model (IABC-RF) for reconstructing geomagnetic reference maps using magnetic anomaly data. The proposed method integrates an enhanced artificial bee colony strategy to optimize the hyperparameters of the random forest model, improving its predictive accuracy and stability in nonlinear geomagnetic environments. The experiments conducted on geomagnetic anomaly data from the South China Sea region, specifically between 5–25′ N and 100–120′ E, derived from the World Digital Magnetic Anomaly Map, show that the IABC-RF method outperforms traditional approaches. The IABC-RF method achieves the lowest root mean square error (RMSE) of 1.46 nT and the smallest standard deviation of 1.58 nT, while also maintaining a competitive computational time of 3.4 s. In comparison, Kriging interpolation produces an RMSE of 2.47 nT, inverse distance weighting (IDW) results in an RMSE of 14.45 nT, and improved Shepard interpolation gives an RMSE of 11.68 nT. The IABC-RF method excels at preserving global geomagnetic trends and accurately recovering localized anomaly details, offering enhanced robustness to outliers. Further evaluation of the IABC-RF method under noisy conditions (5% and 10% noise) revealed that although all methods experienced a decrease in performance due to the added noise, the IABC-RF method continued to show superior robustness. These findings demonstrate that the IABC-RF method provides a highly effective and reliable solution for constructing high-precision geomagnetic reference maps, with strong performance even in noisy environments. The method is particularly valuable for improving geomagnetic matching navigation in complex operational settings. Full article
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24 pages, 5032 KB  
Article
Distribution Network Hosting Capacity Assessment Method of Electric Vehicle Charging Stations Based on Multi-Zone Load Profiling
by Ning Guo, Jinming Chen, Xing Zhang, Ye Chen, Jian Liu and Zhijun Zhou
Symmetry 2026, 18(6), 990; https://doi.org/10.3390/sym18060990 - 9 Jun 2026
Viewed by 270
Abstract
Fast growth in electric vehicle (EV) charging stations is changing the way regional distribution networks are loaded. The difficulty is not only the size of the added demand, but also the fact that charging appears at different places, at different times, and under [...] Read more.
Fast growth in electric vehicle (EV) charging stations is changing the way regional distribution networks are loaded. The difficulty is not only the size of the added demand, but also the fact that charging appears at different places, at different times, and under different voltage constraints. This paper considers the common planning situation in which station-level charging records are incomplete and only transformer-side aggregate measurements are available. A data-driven hosting capacity (HC) assessment method is developed for this setting. The method first constructs zone-specific daily load profiles and then separates EV charging components from mixed transformer curves through an improved ISODATA clustering method and an improved genetic algorithm (IGA). For planned electric vehicle charging stations (EVCSs) without historical measurements, Ordinary Kriging (OK) is used to infer charging profiles from nearby observed stations in the same functional zone. The calculated HC is then checked successively at the 10 kV, 35 kV, and 110 kV levels. When an upstream constraint is violated, an improved Entropy-weight TOPSIS (EW-TOPSIS) model reallocates the available capacity according to both network constraints and zone priority. The case study indicates that the method can identify upstream bottlenecks that are hidden in local assessments, preserve residential charging demand, and provide zone-specific guidance for EVCS expansion. Full article
(This article belongs to the Special Issue Symmetry with Power Systems: Control and Optimization)
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22 pages, 4372 KB  
Article
Multi-Objective Optimization of Nozzle Layout for UAV-Based Liquid Anti-Riot Agent Dispersion Using Kriging Surrogate Model and NSGA-II
by Ye Tian, Xiaoping Cui, Jinyu Qian, Weishi Peng and Xudan Dong
Drones 2026, 10(6), 436; https://doi.org/10.3390/drones10060436 - 3 Jun 2026
Viewed by 226
Abstract
The surging need for public security risk mitigation has placed stricter demands on the modernization of emergency response capacities. Unmanned aircraft systems (UASs) offer a promising solution for liquid anti-riot agent dispersion, yet the complex interaction between rotor-induced downwash and droplet trajectories makes [...] Read more.
The surging need for public security risk mitigation has placed stricter demands on the modernization of emergency response capacities. Unmanned aircraft systems (UASs) offer a promising solution for liquid anti-riot agent dispersion, yet the complex interaction between rotor-induced downwash and droplet trajectories makes nozzle layout optimization a significant challenge. To address the prohibitive computational costs of traditional Computational Fluid Dynamics (CFD) and the limitations of single-objective optimization, this study proposes an integrated “simulation–modeling–optimization–decision” framework. First, a linear nozzle layout was identified as superior to the traditional circular arrangement, achieving a 44.8% increase in deposition rate. Subsequently, Optimal Latin Hypercube Sampling (OLHS) and CFD simulations were combined to construct high-precision Kriging surrogate models for three key indicators: deposition rate, uniformity, and coverage rate. The NSGA-II algorithm was then employed to solve the multi-objective trade-off, followed by the entropy-weighted TOPSIS method to identify the optimal engineering solution. Results indicate that nozzle count is the dominant system-level variable under the constant per-nozzle flow-rate condition, showing strong positive correlations with all performance indicators. The identified optimal configuration (6 nozzles with a 1.88 m boom length) achieved a 66.1% increase in deposition rate and an 18.7% increase in coverage rate compared to the original circular layout. Furthermore, the surrogate-based framework improved optimization efficiency to 296% compared to full factorial methods. This study provides a scientific theoretical basis and a highly efficient technical pathway for the structural design of high-performance UAV spray systems. Full article
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29 pages, 6516 KB  
Article
Numerical and Experimental Investigation of Hydraulic Optimization and Internal Flow Mechanisms in a Low-Specific-Speed Pump as Turbine
by Yin Luo and Bo Jiang
Water 2026, 18(11), 1343; https://doi.org/10.3390/w18111343 - 1 Jun 2026
Viewed by 322
Abstract
Pump-as-turbine (PAT) units have been widely used for energy recovery in water-supply networks, petrochemical systems, and small hydropower applications; however, their turbine-mode performance is often limited because most commercial pumps are originally designed for pumping conditions. To improve the hydraulic performance of a [...] Read more.
Pump-as-turbine (PAT) units have been widely used for energy recovery in water-supply networks, petrochemical systems, and small hydropower applications; however, their turbine-mode performance is often limited because most commercial pumps are originally designed for pumping conditions. To improve the hydraulic performance of a low-specific-speed PAT, this study developed a surrogate-assisted multi-objective optimization framework combining three-dimensional computational fluid dynamics (CFD), design of experiments, a Kriging surrogate model, and a multi-objective genetic algorithm. Five key impeller geometric parameters, including blade inlet angles, blade wrap angles, and impeller outlet diameter, were selected as design variables, and turbine-mode efficiency was maximized under a head constraint of H ≥ 24 m at the rated condition of 1450 r/min. The results showed that the optimized design increased efficiency from 72.34% to 84.42% while satisfying the head requirement. Comparative analyses of pressure and velocity fields in the impeller and volute further revealed that the performance improvement was mainly associated with enhanced flow-field uniformity and reduced local hydraulic losses. A dedicated PAT test rig was finally established to experimentally validate the optimized design. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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9 pages, 4438 KB  
Proceeding Paper
Visual Analytics Framework for Multi-Objective Optimisation of Aircraft Design
by Shubham Shubham, Andrea Spinelli and Timoleon Kipouros
Eng. Proc. 2026, 133(1), 167; https://doi.org/10.3390/engproc2026133167 - 22 May 2026
Viewed by 388
Abstract
This paper presents a web-based visual analytics framework for robust multi-objective aircraft wing design. Aerodynamic and structural simulation data are generated for a redesigned CRM wing, with aspect ratio and skin root thickness as key variables. Ordinary Kriging surrogates are coupled with NSGA-III [...] Read more.
This paper presents a web-based visual analytics framework for robust multi-objective aircraft wing design. Aerodynamic and structural simulation data are generated for a redesigned CRM wing, with aspect ratio and skin root thickness as key variables. Ordinary Kriging surrogates are coupled with NSGA-III to explore trade-offs among lift-to-drag ratio, wing mass, and range. Input design uncertainties are propagated using Monte Carlo Simulation with Halton sampling, enabling low-cost robustness assessment. An interactive HTML–Python dashboard provides contour plots, sampled design points, and Pareto fronts, allowing engineers to perform what-if analyses and rapidly identify robust Pareto-optimal designs. Results show that a higher aspect ratio with lower skin thickness improves aerodynamic efficiency and range, while structural constraints and uncertainty bounds define feasible regions. The Kriging surrogate achieves a Surrogate Speed-Up Index (SSI) of O(103), offering comparable insight into wing mass, range, and L/D at roughly three-orders-of-magnitude-lower computational cost than direct mid-fidelity simulations. Full article
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22 pages, 4257 KB  
Article
Coordinated Stator–Rotor Structural Optimization of an Automotive IPMSM for Improved Torque Performance
by Chunyan Gao, Yimeng Han, Kunfeng Liang, Min Li, Shiman Su and Yun Zhu
World Electr. Veh. J. 2026, 17(5), 272; https://doi.org/10.3390/wevj17050272 - 18 May 2026
Viewed by 800
Abstract
Traditional optimization methods for interior permanent magnet synchronous motors (IPMSMs) often treat the stator and rotor as independent design domains, which limits the potential for suppressing torque fluctuations due to the neglected electromagnetic coupling between these components. This paper proposes a synergistic optimization [...] Read more.
Traditional optimization methods for interior permanent magnet synchronous motors (IPMSMs) often treat the stator and rotor as independent design domains, which limits the potential for suppressing torque fluctuations due to the neglected electromagnetic coupling between these components. This paper proposes a synergistic optimization strategy for a 120 kW IPMSM, aiming to overcome the inherent limitations of conventional unilateral optimization in design space exploration and achieve global performance enhancement through cross-domain collaboration. By establishing a unified surrogate model incorporating both stator slot geometries and rotor pole topologies, the collaborative effect of seven high-sensitivity design variables is systematically analyzed. The NSGA-II algorithm, coupled with a Kriging surrogate model, is employed to navigate the complex trade-offs among average torque, torque ripple, and cogging torque. Results demonstrate that the synergistic approach achieves a 28.1% reduction in torque ripple while maintaining high average torque, demonstrating superior improvement over conventional stator-only or rotor-only optimization schemes. Analysis based on Maxwell stress tensors and air-gap permeance functions reveals that the proposed method achieves simultaneous suppression of cogging torque and torque ripple by effectively harmonizing the 24th and 48th spatial harmonics. This study provides an efficient synergistic design methodology for the comprehensive performance enhancement of traction motors, offering practical reference value for the engineering development of high-performance electric vehicles. Full article
(This article belongs to the Section Propulsion Systems and Components)
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26 pages, 4509 KB  
Article
Integrated Design and Dynamic Performance Optimisation of Hybrid Electric Propulsion Systems for Coastal Cargo Vessels Under Real-World Operational Profiles
by Junchi Du, Yongxin Song, Zhenhang Xu, Bozhen Liu and Baoshan Ma
Appl. Sci. 2026, 16(10), 4940; https://doi.org/10.3390/app16104940 - 15 May 2026
Viewed by 232
Abstract
International and regional decarbonisation policies are accelerating the deployment of hybrid electric propulsion systems (HEPSs) in short-sea and coastal trades, yet most existing design studies focus on ferries or tugs, rely on stylised duty cycles, and treat battery degradation only superficially. This paper [...] Read more.
International and regional decarbonisation policies are accelerating the deployment of hybrid electric propulsion systems (HEPSs) in short-sea and coastal trades, yet most existing design studies focus on ferries or tugs, rely on stylised duty cycles, and treat battery degradation only superficially. This paper proposes an integrated, data-driven framework for the design and dynamic performance optimisation of a diesel–battery HEPS for a coastal general cargo vessel operating on short-sea routes. A multi-year automatic identification system (AIS) and logbook data are processed to derive route-specific, time-resolved operating profiles, which drive a DC-based hybrid propulsion model comprising diesel generator sets, propulsion motors and a lithium-ion battery energy storage system (ESS). A degradation-aware ESS model is embedded in a life-cycle cost (LCC) formulation that explicitly accounts for battery replacement timing and residual value. The hybrid design problem is cast as a bi-level optimisation: an upper level determines engine rating and ESS capacity to minimise LCC, while fuel savings and emissions are evaluated as key parallel performance indicators, while a lower level uses dynamic programming to compute optimal power split trajectories under state-of-charge, C-rate and power constraints. A surrogate-assisted global search with Kriging and Expected Improvement is employed to manage the computational burden of repeated lower-level optimisations. Case-study results for representative coastal routes show that the optimised hybrid configurations achieve fuel savings of 16–21%, CO2 reductions of 17–20%, and LCC reductions of 8–14% relative to a conventional mechanical baseline, outperforming a rule-based hybrid design. Sensitivity analyses with varying fuel prices and ESS costs confirm the robustness of the proposed framework and highlight the importance of explicitly coupling degradation-aware ESS. Full article
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23 pages, 4385 KB  
Article
Aerodynamic Optimization of the Archimedes Spiral Wind Turbine Blade Based on the Kriging Surrogate Model and Differential Evolution
by Mengyao Li, Zhi Li and Shuhui Xu
Energies 2026, 19(10), 2298; https://doi.org/10.3390/en19102298 - 10 May 2026
Viewed by 441
Abstract
The Archimedes Spiral Wind Turbine (ASWT) is a novel horizontal axis wind turbine for urban low-wind-speed applications. To improve the wind energy capture efficiency of the ASWT, this study adopted a multivariable global optimization strategy. A differential evolution–Kriging surrogate model method was employed [...] Read more.
The Archimedes Spiral Wind Turbine (ASWT) is a novel horizontal axis wind turbine for urban low-wind-speed applications. To improve the wind energy capture efficiency of the ASWT, this study adopted a multivariable global optimization strategy. A differential evolution–Kriging surrogate model method was employed for blade structural optimization. The blade geometry was parametrically modeled, and three design variables were selected: spiral pitch, opening angle, and spiral rotation number (SRN). Latin hypercube sampling was used to generate sample points in the design space. The power coefficients (Cp) of all design samples were calculated by Computational Fluid Dynamics (CFD) simulations. A Kriging surrogate model was constructed to map the nonlinear relationship between the design variables and Cp. The optimal blade geometry was obtained by solving the surrogate model with differential evolution (DE) and validated by CFD. The results showed that at the design condition of a wind speed of 8 m/s and a tip speed ratio (TSR) of 1.875, the relative error between Kriging model predictions and CFD simulations was only 0.27%. The optimized blade achieved a Cp of 0.3085, representing a 4.78% improvement over the best sample blade, with both achieving their peak power coefficients at TSR = 1.875. Full article
(This article belongs to the Section A3: Wind, Wave and Tidal Energy)
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