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Keywords = four-dimensional trajectory optimization

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22 pages, 4864 KB  
Article
A K-Means Clustering Approach for Accelerated Path Planning in GMA-DED: The Fast Advanced-Pixel Strategy
by Rafael P. Ferreira, Vinicius Lemes Jorge, Emil Schubert and Américo Scotti
J. Manuf. Mater. Process. 2026, 10(2), 55; https://doi.org/10.3390/jmmp10020055 - 5 Feb 2026
Abstract
The performance of Gas Metal Arc-Directed Energy Deposition (GMA-DED) strongly depends on efficient path-planning strategies that balance trajectory quality and computational cost. With the purpose of developing a computationally faster and more scalable path-planning approach, this study introduces the Fast Advanced-Pixel strategy by [...] Read more.
The performance of Gas Metal Arc-Directed Energy Deposition (GMA-DED) strongly depends on efficient path-planning strategies that balance trajectory quality and computational cost. With the purpose of developing a computationally faster and more scalable path-planning approach, this study introduces the Fast Advanced-Pixel strategy by integrating the K-means clustering algorithm into to the Advanced Pixel strategy version to reduce the dimensionality of an optimization problem. Computational validation was conducted on four geometrically distinct parts using different clustering configurations. Statistical analysis (ANOVA) was applied to assess the significance of the results. The findings revealed that by increasing the number of clusters, computational time is substantially reduced, achieving up to a twenty-fold improvement compared with the former strategy, while maintaining consistent trajectory quality. Experimental validation using complex parts, such as a “Jaw Gripper” and a “C-frame” of a resistance spot welding gun, confirmed defect-free deposition and dimensional agreement with the CAD models. Accordingly, within the scope of GMA-DED technology and pixel-based path-planning strategies, the Fast Advanced-Pixel approach demonstrates a significant improvement in computational efficiency while preserving trajectory quality, enabling the accurate and reliable fabrication of geometrically complex metallic parts. Full article
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30 pages, 3944 KB  
Article
An Integrated Control Strategy for Trajectory Tracking of a Crane-Suspended Load
by Diankai Kong, Fenglin Yao, Chao Hu, Yuyan Guo and Wei Ye
Machines 2026, 14(1), 24; https://doi.org/10.3390/machines14010024 - 24 Dec 2025
Viewed by 367
Abstract
With the advancement of intelligent technologies, industrial production systems are being profoundly transformed by artificial intelligence algorithms. To address persistent challenges, such as cargo swing and low operational efficiency during the lifting processes of all-terrain cranes, this research investigates an intelligent control algorithm [...] Read more.
With the advancement of intelligent technologies, industrial production systems are being profoundly transformed by artificial intelligence algorithms. To address persistent challenges, such as cargo swing and low operational efficiency during the lifting processes of all-terrain cranes, this research investigates an intelligent control algorithm designed for swing suppression and high-stability payload trajectory control. Firstly, a nonlinear dynamic model of the crane system was derived using the Euler–Lagrange formulation based on a simplified three-dimensional representation. A linear time-varying model predictive control (LTV-MPC) strategy was then designed to incorporate real-time feedback during luffing and slewing motions to monitor the payload’s swing state. On this basis, the controller predicts the desired trajectory and applies negative feedback to adjust the control input, thereby steering the system toward the optimal trajectory and aligning it with the target path. Secondly, a comparative analysis was conducted among four scenarios: the natural swing state of the payload and three control strategies—LTV-MPC, sliding mode control (SMC), and PID control—under both single-input and dual-input conditions. Finally, an experimental platform was established, employing the YOLOv12 algorithm for real-time detection and trajectory tracking of the suspended payload. The experimental results validate the effectiveness of LTV-MPC in suppressing cargo swing. Under single-input control, LTV-MPC achieved the best performance in both stabilization time (3.05 s for luffing condition one and 1.15 s for luffing condition two) and steady-state error (0.003–0.007°). The swing angle, θ1, was reduced by 91.9%, 54.2%, and 59.3% compared to the natural swing state, SMC, and PID, respectively. In dual-input control, LTV-MPC attained a steady-state error of only 0.0008° under “luffing condition two,” while during slewing operations, it also outperformed SMC and PID in both settling time (26.05 s) and precision (0.008°). Full article
(This article belongs to the Section Machine Design and Theory)
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28 pages, 5515 KB  
Article
A Multivariable Mathematical Model of Conductivity, β-Amyloid and T-Protein Dynamics in Alzheimer’s Disease Progression
by Emmanouil Perakis and Panagiotis Vlamos
Mathematics 2025, 13(22), 3724; https://doi.org/10.3390/math13223724 - 20 Nov 2025
Viewed by 538
Abstract
Alzheimer’s disease (AD) affects over 55 million individuals worldwide, yet no transformative disease-modifying therapies exist. Mathematical modelling provides a powerful framework to elucidate complex disease mechanisms, predict therapeutic outcomes, and enable precision medicine—capabilities urgently needed where multiscale spatiotemporal processes defy experimental analysis alone. [...] Read more.
Alzheimer’s disease (AD) affects over 55 million individuals worldwide, yet no transformative disease-modifying therapies exist. Mathematical modelling provides a powerful framework to elucidate complex disease mechanisms, predict therapeutic outcomes, and enable precision medicine—capabilities urgently needed where multiscale spatiotemporal processes defy experimental analysis alone. We developed a mechanistic spatiotemporal model coupling four AD hallmarks: β-amyloid (Aβ) accumulation, T-protein (T-p) aggregation, neuroinflammation and electrical conductivity decline. Formulated as non-linear partial differential equations (p.d.es) on a 3-dimensional biological interpretation of non-linear terms (the ellipsoidal brain domain with biologically grounded parameters), the model was solved using eigenfunction expansion, Fourier analysis and numerical methods. Therapeutic interventions were simulated through mechanistically motivated parameter modifications and validated against longitudinal biomarker data from major cohort studies. Simulations reveal Aβ-initiated spatiotemporal cascades originating in the hippocampus and spreading radially at 0.15–0.20 cm/year, with T-pathology emerging after 2–3 years. Conductivity decline accelerates upon T-onset (year 5–7), reflecting the transition to symptomatic disease. Multimodal intervention at early symptomatic stages reduces peak Aβ by 36% and inflammation by 52% and preserves 41% more conductivity than untreated controls. Sensitivity analysis identifies Aβ production and inflammatory regulation as critical therapeutic targets, with dose–response curves demonstrating linear efficacy relationships. This biologically grounded framework explicitly links molecular pathology to functional decline, enabling patient-specific trajectory prediction through parameter calibration. The model establishes a foundation for precision medicine applications including individualized prognosis, optimal treatment timing and virtual clinical trial design, advancing quantitative systems biology of neurodegeneration. Full article
(This article belongs to the Section E3: Mathematical Biology)
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33 pages, 12683 KB  
Article
Analysis of Traffic Conflict Characteristics and Key Factors Influencing Severity in Expressway Interchange Diverging Areas: Insights from a Chinese Freeway Safety Study
by Feng Tang, Zhizhen Liu, Zhengwu Wang and Ning Li
Sustainability 2025, 17(18), 8419; https://doi.org/10.3390/su17188419 - 19 Sep 2025
Viewed by 1559
Abstract
Conflicts in freeway interchange diverging areas remain poorly understood, particularly their characteristics and severity determinants. To address this gap, we extracted over 20,000 vehicle trajectories from UAV footage at 16 interchange divergence zone across five multi-lane expressways using a YOLOX–DeepSORT method. From these [...] Read more.
Conflicts in freeway interchange diverging areas remain poorly understood, particularly their characteristics and severity determinants. To address this gap, we extracted over 20,000 vehicle trajectories from UAV footage at 16 interchange divergence zone across five multi-lane expressways using a YOLOX–DeepSORT method. From these trajectories, we identified longitudinal and lateral conflicts and classified their severity into minor, moderate, and severe levels using a two-dimensional extended time-to-collision metric. Subsequently, we incorporated 19 macroscopic traffic-flow and microscopic driver-behavior variables into four conflict-severity models–multivariate logistic regression, random forest, CatBoost, and XGBoost—and conducted to identify the key determinants of conflict severity based on the optimal models. The results indicate that lateral conflicts last longer and pose higher collision risks than longitudinal ones. Furthermore, moderate conflicts are most prevalent, whereas severe conflicts are concentrated within 300 m upstream of exit ramps. Specifically, for longitudinal conflicts, the most influential factors include speed difference, target-vehicle speed, truck involvement, traffic density, and exit behavior. In contrast, for lateral conflicts, the most critical factors include lane-change frequency, speed difference, target-vehicle speed, distance to the exit ramp, and truck proportion. Overall, these findings support the development of hazardous-driving warning systems and proactive safety management strategies in interchange diverging areas. Full article
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12 pages, 3923 KB  
Article
Quantitative Study on the Adsorption State of n-Octane in Kaolinite Slit-like Pores Based on Four Angular Parameters
by Fang Zeng, Shansi Tian, Zhentao Dong, Hongli Dong, Bo Liu, Valentina Erastova and Haiyang Liu
Molecules 2025, 30(18), 3739; https://doi.org/10.3390/molecules30183739 - 15 Sep 2025
Viewed by 636
Abstract
Shale oil extraction efficiency hinges on the interfacial interactions between oil molecules and reservoir clay minerals, such as kaolinite, whose slit-like pores serve as primary storage spaces for alkanes. This study introduces a novel multi-dimensional quantification method using four angular parameters—elevation angle (θ), [...] Read more.
Shale oil extraction efficiency hinges on the interfacial interactions between oil molecules and reservoir clay minerals, such as kaolinite, whose slit-like pores serve as primary storage spaces for alkanes. This study introduces a novel multi-dimensional quantification method using four angular parameters—elevation angle (θ), azimuth angle (φ), rotation angle (ω), and dihedral angle (τ)—to systematically investigate the adsorption configuration of n-octane in kaolinite slit pores ranging from 0.45 to 14.05 nm. Through molecular simulations and advanced trajectory analysis, we elucidate the impact of pore sizes on alkane adsorption density, layering, and molecular configurations. Results reveal that pore size regulates molecular behavior via steric hindrance and potential field superposition, while the four angular parameters can effectively capture subtle changes in. this molecular behavior: (1) the elevation angle (θ) around 0° indicates complete alignment parallel to surface, but is modulated at increasing distance from the surface into the pore-region highlighting a disordered state; (2) the azimuth angle (φ) is concentrated at 60° and 120° on the siloxane tetrahedral surface due to lattice regulation, but shows a disordered distribution on the hydroxyl octahedral surface; (3) the rotation angle (ω) is mainly concentrated at 0° and 90° indicating molecular plane being either parallel or perpendicular to the surface; (4) the dihedral angle (τ) remains at ~0°, indicating that the molecular chains are straight. In pores smaller than 4.26 nm, strong confinement yields ordered molecular arrangements (θ = 0°, φ at 60° or 120°, ω = 0°) with high adsorption density; for larger pores than 4.26 nm, disordered configurations and increased layering (up to eight layers) with stable density and adsorption capacity per unit area are observed. The proposed parameter system overcomes limitations of traditional qualitative approaches, offering a standardized, scalable tool for quantifying alkane-clay interactions. This framework enhances understanding of shale oil occurrence mechanisms and supports optimized extraction strategies, with broad applicability to other chain molecules and 2D materials in interface science. Full article
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33 pages, 22051 KB  
Article
Gradient-Guided Search for Autonomous Contingency Landing Planning
by Huseyin Emre Tekaslan and Ella M. Atkins
Drones 2025, 9(9), 642; https://doi.org/10.3390/drones9090642 - 13 Sep 2025
Cited by 1 | Viewed by 791
Abstract
The growing reliance on autonomy in uncrewed aircraft systems (UASs) necessitates a real-time solution for assured contingency landing management during in-flight emergencies. This paper presents a novel gradient-guided search algorithm for risk-aware emergency landing trajectory generation with a wing-lift UAS loss-of-thrust use case. [...] Read more.
The growing reliance on autonomy in uncrewed aircraft systems (UASs) necessitates a real-time solution for assured contingency landing management during in-flight emergencies. This paper presents a novel gradient-guided search algorithm for risk-aware emergency landing trajectory generation with a wing-lift UAS loss-of-thrust use case. This framework integrates a compact four-dimensional discrete search space with aircraft kinematic and ground-risk cost. A multi-objective cost function is employed, combining flight envelope feasibility, optimal descent, and overflown population risk terms. To ensure discrete search convergence, a constrained hypervolume definition is introduced around the destination. A holding pattern identification algorithm is defined to minimize risk during the necessary flight path angle-constrained descent to final approach. Planner effectiveness is validated through randomly generated case studies over a region of Long Island, NY, under steady wind conditions. Benchmark comparisons with a 3D Dubins solver demonstrate the approach’s improved risk mitigation and acceptable real-time computation overhead. Future development will focus on integrating collision avoidance into the discrete search-based landing planner. Full article
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14 pages, 2607 KB  
Article
Speed Climbing Analysis System Based on Spatial Positioning and Posture Recognition: Design and Effectiveness Assessment
by Pingao Huang, Tianzhan Huang, Zhihong Xu, Yuankang Zhang and Hui Wang
Appl. Sci. 2025, 15(16), 8959; https://doi.org/10.3390/app15168959 - 14 Aug 2025
Viewed by 1536
Abstract
The human body posture and trajectory are important parameters of the optimal path in speed climbing, and current researchers are focused on them. However, the performance of the newly developed analysis tools for synchronously and accurately analyzing climbing posture and trajectory is limited. [...] Read more.
The human body posture and trajectory are important parameters of the optimal path in speed climbing, and current researchers are focused on them. However, the performance of the newly developed analysis tools for synchronously and accurately analyzing climbing posture and trajectory is limited. This study develops an innovative speed climbing analysis system (SCAS) that integrates three-dimensional trajectory tracking using HTC Vive trackers and full-body posture capture with BlazePose. And the system is validated. Climbing trials were recorded from twelve professional athletes (speed climbers, eight males and four females; age 22 ± 2.2 years, all with ≥1 year of competitive experience) on a standard International Federation of Sport Climbing (IFSC) speed wall. The SCAS’s accuracy was analyzed by comparing its trajectory measurements to a video-based reference: the mean deviation was 0.061 ± 0.005 m (mean ± SD, 95% confidence interval [0.058, 0.064] m), indicating high precision. Trajectory metrics between genders were compared using independent-sample t-tests, revealing that male climbers had significantly shorter average path lengths (p < 0.05) and fewer movement inflections than female climbers. Finally, the group-optimal path derived from the data showed only slight deviations from the top-performing climbers’ paths. The proposed SCAS enables synchronous, millimeter-level tracking of climbing trajectory and posture, and can provide coaches with quantitative feedback for each athlete’s climbing strategy. Full article
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30 pages, 11317 KB  
Article
Real-Time Intelligent Recognition and Precise Drilling in Strongly Heterogeneous Formations Based on Multi-Parameter Logging While Drilling and Drilling Engineering
by Aosai Zhao, Yang Yu, Bin Wang, Yewen Liu, Jingyue Liu, Xubiao Fu, Wenhao Zheng and Fei Tian
Appl. Sci. 2025, 15(10), 5536; https://doi.org/10.3390/app15105536 - 15 May 2025
Cited by 2 | Viewed by 1725
Abstract
Facing engineering challenges of real-time and high-precision recognition of strongly heterogeneous formations during directional drilling, it is crucial to address the issues of sparse lithology geological labels and multi-source lithology identification from LWD data. This paper proposes a real-time intelligent recognition method for [...] Read more.
Facing engineering challenges of real-time and high-precision recognition of strongly heterogeneous formations during directional drilling, it is crucial to address the issues of sparse lithology geological labels and multi-source lithology identification from LWD data. This paper proposes a real-time intelligent recognition method for strongly heterogeneous formations based on multi-parameter logging while drilling and drilling engineering, which can effectively guide directional drilling operations. Traditional supervised learning methods rely heavily on extensive lithology labels and rich wireline logging data. However, in LWD applications, challenges such as limited sample sizes and stringent real-time requirements make it difficult to achieve the accuracy needed for effective geosteering in strongly heterogeneous reservoirs, thereby impacting the reservoir penetration rate. In this study, we comprehensively utilize LWD parameters (six types, including natural gamma and electrical resistivity, etc.) and drilling engineering parameters (four types, including drilling rate and weight on bit, etc.) from offset wells. The UMAP algorithm is employed for nonlinear dimensionality reduction, which not only integrates the dynamic response characteristics of drilling parameters but also preserves the sensitivity of logging data to lithological variations. The K-means clustering algorithm is employed to extract the deep geo-engineering characteristics from multi-source LWD data, thereby constructing a lithology label library and categorizing the training and testing datasets. The optimized CatBoost machine learning model is subsequently utilized for lithology classification, enabling real-time and high-precision geological evaluation during directional drilling. In the Hugin Formation of the Volve field in the Norwegian North Sea, the application of UMAP demonstrates superior data separability compared with PCA and t-SNE, effectively distinguishing thin reservoirs with strong heterogeneity. The CatBoost model achieves a balanced accuracy of 92.7% and an F1-score of 89.3% in six lithology classifications. This approach delivers high-precision geo-engineering decision support for the real-time control of horizontal well trajectories, which holds significant implications for the precision drilling of strongly heterogeneous reservoirs. Full article
(This article belongs to the Special Issue Advances in Reservoir Geology and Exploration and Exploitation)
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15 pages, 1272 KB  
Article
Design of an Immersive Basketball Tactical Training System Based on Digital Twins and Federated Learning
by Xiongce Lv, Ye Tao, Yifan Zhang and Yang Xue
Appl. Sci. 2025, 15(7), 3831; https://doi.org/10.3390/app15073831 - 31 Mar 2025
Cited by 2 | Viewed by 1968
Abstract
To address the challenges of dynamic adversarial scenario modeling distortion, insufficient cross-institutional data privacy protection, and simplistic evaluation systems in collegiate basketball tactical education, this study proposes and validates an immersive instructional system integrating digital twin and federated learning technologies. The four-tier architecture [...] Read more.
To address the challenges of dynamic adversarial scenario modeling distortion, insufficient cross-institutional data privacy protection, and simplistic evaluation systems in collegiate basketball tactical education, this study proposes and validates an immersive instructional system integrating digital twin and federated learning technologies. The four-tier architecture (sensing layer, digital twin layer, federated layer, and interaction layer) synthesizes multimodal data (motion trajectories and physiological signals) with Multi-Agent Reinforcement Learning (MARL) to enable virtual–physical integrated tactical simulation and real-time error correction. Experimental results demonstrate that the experimental group achieved 35.2% higher tactical execution accuracy (TEA) (p < 0.01), 1.8 s faster decision making (p < 0.05), and 47% improved team coordination efficiency compared to the controls. The hierarchical federated learning framework (trajectory ε = 0.8; physiology ε = 0.3) maintained model precision loss at 2.4% while optimizing communication efficiency by 23%, ensuring privacy preservation. A novel three-dimensional “Skill–Creativity–Load” evaluation system revealed a 22% increase in unconventional tactical applications (p = 0.013) through the Tactical Creativity Index (TCI). By implementing lightweight federated architecture with dynamic cognitive offloading mechanisms, the system enables resource-constrained institutions to achieve 87% of the pedagogical effectiveness observed in elite programs, offering an innovative solution to reconcile educational equity with technological ethics. Future research should focus on long-term skill transfer, multimodal adaptive learning, and ethical framework development to advance intelligent sports education from efficiency-oriented paradigms to competency-based transformation. Full article
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21 pages, 8622 KB  
Article
4D Track Prediction Based on BP Neural Network Optimized by Improved Sparrow Algorithm
by Hua Li, Yongkun Si, Qiang Zhang and Fei Yan
Electronics 2025, 14(6), 1097; https://doi.org/10.3390/electronics14061097 - 11 Mar 2025
Cited by 5 | Viewed by 1045
Abstract
The prediction accuracy of 4D (four-dimensional) trajectory is crucial for aviation safety and air traffic management. Firstly, the sine chaotic mapping is employed to enhance the sparrow search algorithm (Sine-SSA). This enhanced algorithm optimizes the threshold parameters of the BP (back propagation) neural [...] Read more.
The prediction accuracy of 4D (four-dimensional) trajectory is crucial for aviation safety and air traffic management. Firstly, the sine chaotic mapping is employed to enhance the sparrow search algorithm (Sine-SSA). This enhanced algorithm optimizes the threshold parameters of the BP (back propagation) neural network (Sine-SSA-BP), thereby improving the quality of the initial solution and enhancing global search capability. Secondly, the optimal weight thresholds obtained from the Sine-SSA algorithm are integrated into the BP neural network to boost its performance. Subsequently, the 4D trajectory data of the aircraft serve as input variables for the Sine-SSA-BP prediction model to conduct trajectory predictions. Finally, the prediction results from three models are compared against the actual aircraft trajectory. It is found that within the specified time series, the errors in longitude, latitude, and altitude for the Sine-SSA-BP prediction model are significantly smaller than those of the simple BP and SSA-BP models. This indicates that the Sine-SSA-BP model can achieve high-precision 4D trajectory prediction. The accuracy of trajectory prediction is notably improved by the sparrow search algorithm optimized with sine chaotic mapping, leading to faster convergence and better prediction outcomes, which better meet the requirements of aviation safety and control. Full article
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25 pages, 6074 KB  
Article
Cooperative Low-Carbon Trajectory Planning of Multi-Arrival Aircraft for Continuous Descent Operation
by Cun Feng, Chao Wang, Hanlu Chen, Chenyang Xu and Jinpeng Wang
Aerospace 2024, 11(12), 1024; https://doi.org/10.3390/aerospace11121024 - 15 Dec 2024
Cited by 3 | Viewed by 1682
Abstract
To address the technical challenges of implementing Continuous Descent Operations (CDO) in high-traffic-density terminal control areas, we propose a cooperative low-carbon trajectory planning method for multiple arriving aircraft. Firstly, this study analyzes the CDO phases of aircraft in the terminal area, establishes a [...] Read more.
To address the technical challenges of implementing Continuous Descent Operations (CDO) in high-traffic-density terminal control areas, we propose a cooperative low-carbon trajectory planning method for multiple arriving aircraft. Firstly, this study analyzes the CDO phases of aircraft in the terminal area, establishes a multi-phase optimal control model for the vertical profile, and introduces a novel vertical profile optimization method for CDO based on a genetic algorithm. Secondly, to tackle the challenges of CDO in busy terminal areas, a T-shaped arrival route structure is designed to provide alternative paths and to generate a set of four-dimensional (4D) alternative trajectories. A Mixed Integer Programming (MIP) model is constructed for the 4D trajectory planning of multiple aircraft, aiming to maximize the efficiency of arrival traffic flow while considering conflict constraints. The complex constrained MIP problem is transformed into an unconstrained problem using a penalty function method. Finally, experiments were conducted to evaluate the implementation of CDO in busy terminal areas. The results show that, compared to actual operations, the proposed optimization model significantly reduces the total aircraft operating time, fuel consumption, CO2 emissions, SO2 emissions, and NOx emissions. Specifically, with the optimization objective of minimizing total cost, the proposed method reduces the total operation time by 22.4%; fuel consumption, CO2 emissions, SO2 emissions by 22.9%, and NOx emissions by 23.7%. The method proposed in this paper not only produces efficient aircraft sequencing results, but also provides a feasible low-carbon trajectory for achieving optimal sequencing. Full article
(This article belongs to the Section Air Traffic and Transportation)
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19 pages, 16987 KB  
Article
Trajectory Planning Method in Time-Variant Wind Considering Heterogeneity of Segment Flight Time Distribution
by Man Xu, Jian Wang and Qiuqi Wu
Systems 2024, 12(12), 523; https://doi.org/10.3390/systems12120523 - 25 Nov 2024
Viewed by 1112
Abstract
The application of Trajectory-Based Operation (TBO) and Free-Route Airspace (FRA) can relieve air traffic congestion and reduce flight delays. However, this new operational framework has higher requirements for the reliability and efficiency of the trajectory, which will be significantly influenced if the analysis [...] Read more.
The application of Trajectory-Based Operation (TBO) and Free-Route Airspace (FRA) can relieve air traffic congestion and reduce flight delays. However, this new operational framework has higher requirements for the reliability and efficiency of the trajectory, which will be significantly influenced if the analysis of wind uncertainty during trajectory planning is insufficient. In the literature, trajectory planning models considering wind uncertainty are developed based on the time-invariant condition (i.e., three-dimensional), which may potentially lead to a significant discrepancy between the predicted flight time and the real flight time. To address this problem, this study proposes a trajectory planning model considering time-variant wind uncertainty (i.e., four-dimensional). This study aims to optimize a reliable and efficient trajectory by minimizing the Mean-Excess Flight Time (MEFT). This model formulates wind as a discrete variable, forming the foundation of the proposed time-variant predicted method that can calculate the segment flight time accurately. To avoid the homogeneous assumption of distributions, we specifically apply the first four moments (i.e., expectation, variance, skewness, and kurtosis) to describe the stochasticity of the distributions, rather than using the probability distribution function. We apply a two-stage algorithm to solve this problem and demonstrate its convergence in the time-variant network. The simulation results show that the optimal trajectory has 99.2% reliability and reduces flight time by approximately 9.2% compared to the current structured airspace trajectory. In addition, the solution time is only 2.3 min, which can satisfy the requirement of trajectory planning. Full article
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18 pages, 4085 KB  
Article
Population-Level Cell Trajectory Inference Based on Gaussian Distributions
by Xiang Chen, Yibing Ma, Yongle Shi, Yuhan Fu, Mengdi Nan, Qing Ren and Jie Gao
Biomolecules 2024, 14(11), 1396; https://doi.org/10.3390/biom14111396 - 1 Nov 2024
Viewed by 2311
Abstract
In the past decade, inferring developmental trajectories from single-cell data has become a significant challenge in bioinformatics. RNA velocity, with its incorporation of directional dynamics, has significantly advanced the study of single-cell trajectories. However, as single-cell RNA sequencing technology evolves, it generates complex, [...] Read more.
In the past decade, inferring developmental trajectories from single-cell data has become a significant challenge in bioinformatics. RNA velocity, with its incorporation of directional dynamics, has significantly advanced the study of single-cell trajectories. However, as single-cell RNA sequencing technology evolves, it generates complex, high-dimensional data with high noise levels. Existing trajectory inference methods, which overlook cell distribution characteristics, may perform inadequately under such conditions. To address this, we introduce CPvGTI, a Gaussian distribution-based trajectory inference method. CPvGTI utilizes a Gaussian mixture model, optimized by the Expectation–Maximization algorithm, to construct new cell populations in the original data space. By integrating RNA velocity, CPvGTI employs Gaussian Process Regression to analyze the differentiation trajectories of these cell populations. To evaluate the performance of CPvGTI, we assess CPvGTI’s performance against several state-of-the-art methods using four structurally diverse simulated datasets and four real datasets. The simulation studies indicate that CPvGTI excels in pseudo-time prediction and structural reconstruction compared to existing methods. Furthermore, the discovery of new branch trajectories in human forebrain and mouse hematopoiesis datasets confirms CPvGTI’s superior performance. Full article
(This article belongs to the Section Bioinformatics and Systems Biology)
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26 pages, 2649 KB  
Article
Multi-UAV Path Planning Based on Cooperative Co-Evolutionary Algorithms with Adaptive Decision Variable Selection
by Qicheng Meng, Qingjun Qu, Kai Chen and Taihe Yi
Drones 2024, 8(9), 435; https://doi.org/10.3390/drones8090435 - 26 Aug 2024
Cited by 20 | Viewed by 3342
Abstract
When dealing with UAV path planning problems, evolutionary algorithms demonstrate strong flexibility and global search capabilities. However, as the number of UAVs increases, the scale of the path planning problem grows exponentially, leading to a significant rise in computational complexity. The Cooperative Co-Evolutionary [...] Read more.
When dealing with UAV path planning problems, evolutionary algorithms demonstrate strong flexibility and global search capabilities. However, as the number of UAVs increases, the scale of the path planning problem grows exponentially, leading to a significant rise in computational complexity. The Cooperative Co-Evolutionary Algorithm (CCEA) effectively addresses this issue through its divide-and-conquer strategy. Nonetheless, the CCEA needs to find a balance between computational efficiency and algorithmic performance while also resolving convergence difficulties arising from the increased number of decision variables. Moreover, the complex interrelationships between the decision variables of each UAV add to the challenge of selecting appropriate decision variables. To tackle this problem, we propose a novel collaborative algorithm called CCEA-ADVS. This algorithm reduces the difficulty of the problem by decomposing high-dimensional variables into sub-variables for collaborative optimization. To improve the efficiency of decision variable selection in the collaborative algorithm and to accelerate the convergence speed, an adaptive decision variable selection strategy is introduced. This strategy selects decision variables according to the order of solving single-UAV constraints and multi-UAV constraints, reducing the cost of the optimization objective. Furthermore, to improve computational efficiency, a two-stage evolutionary optimization process from coarse to fine is adopted. Specifically, the Adaptive Differential Evolution with Optional External Archive algorithm (JADE) is first used to optimize the waypoints of the UAVs to generate a basic path, and then, the Dubins algorithm is combined to optimize the trajectory, yielding the final flight path. The experimental results show that in four different scenarios involving 40 UAVs, the CCEA-ADVS algorithm significantly outperforms the Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and JADE algorithms in terms of path performance, running time, computational efficiency, and convergence speed. In addition, in large-scale experiments involving 500 UAVs, the algorithm also demonstrates good adaptability, stability, and scalability. Full article
(This article belongs to the Section Drone Communications)
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23 pages, 9009 KB  
Article
Four-Dimensional Trajectory Optimization for CO2 Emission Benchmarking of Arrival Traffic Flow with Point Merge Topology
by Chao Wang, Chenyang Xu, Wenqing Li, Shanmei Li and Shilei Sun
Aerospace 2024, 11(8), 673; https://doi.org/10.3390/aerospace11080673 - 16 Aug 2024
Cited by 1 | Viewed by 1744
Abstract
The benchmarking of CO2 emissions serves as the foundation for the accurate assessment of the environmental impact of air traffic. To calculate the environmental benchmarks of arrival traffic flows with Point Merge System (PMS) patterns, this study proposes a 4D trajectory optimization [...] Read more.
The benchmarking of CO2 emissions serves as the foundation for the accurate assessment of the environmental impact of air traffic. To calculate the environmental benchmarks of arrival traffic flows with Point Merge System (PMS) patterns, this study proposes a 4D trajectory optimization method that combines data-driven and optimal control models. First, the predominant arrival routes of traffic flows are identified using the trajectory spectral clustering method, which provides the horizontal reference for 4D trajectory optimization. Second, an optimal control model for vertical profiles with point merging topology is established, with the objective of minimizing the fuel–time cost. Finally, considering the complex structure of the PMS, a flexible and adaptable genetic algorithm-based vertical profile nonlinear optimization model is created. The experimental results demonstrate that the proposed method is adaptable to variations in aircraft type and cost index parameters, enabling the generation of different 4D trajectories. The results also indicate an environmental efficiency gap of approximately 10% between the actual CO2 emissions of the arrival traffic flow example and the obtained benchmark. With this benchmark trajectory generation methodology, the environmental performance of PMSs and associated arrival aircraft scheduling designs can be assessed on the basis of reliable data. Full article
(This article belongs to the Section Aeronautics)
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