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22 pages, 876 KB  
Article
Large Autonomous Driving Overtaking Decision and Control System Based on Hierarchical Reinforcement Learning
by Chen-Ning Wang and Xiuhui Tang
Electronics 2026, 15(8), 1711; https://doi.org/10.3390/electronics15081711 - 17 Apr 2026
Abstract
To address the bottlenecks of low sample efficiency and poor control accuracy in traditional single-layer reinforcement learning during autonomous driving overtaking, this paper proposes an overtaking decision and control system based on hierarchical reinforcement learning to decouple complex tasks in spatial and temporal [...] Read more.
To address the bottlenecks of low sample efficiency and poor control accuracy in traditional single-layer reinforcement learning during autonomous driving overtaking, this paper proposes an overtaking decision and control system based on hierarchical reinforcement learning to decouple complex tasks in spatial and temporal dimensions. A heterogeneous two-layer architecture is constructed, where the upper layer adopts the Proximal Policy Optimization algorithm to generate macroscopic discrete decisions, while the lower layer employs Twin Delayed Deep Deterministic Policy Gradient combined with Long Short-Term Memory to achieve smooth continuous control of steering and acceleration by perceiving temporal features of dynamic obstacles. A composite reward mechanism, integrating hard safety constraints and soft efficiency incentives, is designed to balance safety, efficiency, and comfort. Experimental results in complex scenarios with multiple interfering vehicles and random lane-changing behaviors demonstrate that the proposed system improves the training convergence speed by approximately 30% within 500,000 steps compared to single-layer algorithms. In tests across varying traffic densities, the system achieves a 98.3% success rate in medium-density scenarios with a collision rate of only 0.6%. In high-density challenges, the success rate remains above 95%, with the collision rate reduced by about 80% compared to baseline models. Furthermore, the lateral control deviation is strictly limited to within 0.2 m, and the longitudinal safety distance remains stable above 5 m. This system provides a robust, high-efficiency paradigm for autonomous overtaking. Full article
33 pages, 1628 KB  
Article
A Reinforcement Learning and Unsupervised Clustering-Based Method for Automated Driving Cycle Construction for Fuel Cell Light-Duty Trucks
by Jinbiao Shi, Weibo Zheng, Ran Huo, Po Hong, Bing Li and Pingwen Ming
World Electr. Veh. J. 2026, 17(4), 213; https://doi.org/10.3390/wevj17040213 - 17 Apr 2026
Abstract
Addressing the lack of high-fidelity test cycles for fuel cell light-duty trucks, this paper proposes an automated driving cycle construction method that integrates unsupervised clustering and reinforcement learning. Firstly, based on large-sample real-world driving data, four libraries of typical driving pattern segments are [...] Read more.
Addressing the lack of high-fidelity test cycles for fuel cell light-duty trucks, this paper proposes an automated driving cycle construction method that integrates unsupervised clustering and reinforcement learning. Firstly, based on large-sample real-world driving data, four libraries of typical driving pattern segments are extracted through dimensionality reduction via Principal Component Analysis (PCA) and K-means clustering. Subsequently, the cycle construction process is formulated as a sequential decision-making problem, and a framework based on the Proximal Policy Optimization (PPO) algorithm, incorporating an action masking mechanism, is designed. This framework innovatively injects macro-level time budget allocation as a hard constraint into the agent’s policy space via action masking, while utilizing micro-level Markov transition probabilities as a soft guide. This dual approach drives the agent to learn an optimal segment concatenation strategy, thereby simultaneously ensuring both the macro-level statistical representativeness and the micro-level driving logic coherence of the synthesized cycle. Validation results demonstrate that the cycle constructed by the proposed method achieves an average relative error of only 7.53% in key characteristic parameters, and its joint speed-acceleration distribution exhibits a similarity as high as 0.9886 with the original data, significantly outperforming traditional methods such as the clustering method, the Markov chain method, and standard driving cycles. This study provides an effective tool for generating high-fidelity driving cycles and testing energy management strategies for fuel cell commercial vehicles. Full article
(This article belongs to the Section Vehicle and Transportation Systems)
27 pages, 1608 KB  
Article
Beyond Time to Collision: the Point of no Return as a Reliable Safety Indicator in Rear-End Vehicle Conflicts
by Adrian Soica
Appl. Sci. 2026, 16(8), 3869; https://doi.org/10.3390/app16083869 - 16 Apr 2026
Abstract
This paper introduces the concept of the Point of No Return as a physically grounded safety indicator for rear-end vehicle conflicts, addressing fundamental limitations of the widely used time-to-collision metric. Unlike purely kinematic approaches, the proposed formulation incorporates braking capability and reaction constraints, [...] Read more.
This paper introduces the concept of the Point of No Return as a physically grounded safety indicator for rear-end vehicle conflicts, addressing fundamental limitations of the widely used time-to-collision metric. Unlike purely kinematic approaches, the proposed formulation incorporates braking capability and reaction constraints, enabling a direct assessment of whether a collision can still be avoided. To illustrate the applicability of the concept, a vision-based framework using a single camera is developed based on dashcam data, combining YOLO-based object detection, Kalman-filter tracking, and geometric distance estimation derived from bounding-box features and camera projection models. The estimated distance is further processed to obtain relative motion, allowing a unified analysis of time to collision and the Point of No Return within the same evaluation pipeline. Experimental results on real-world driving sequences show that the Point of No Return consistently precedes critical conditions identified by time to collision and provides a more stable and physically interpretable characterization of the transition toward collision inevitability. The results also highlight the sensitivity of the proposed indicator to braking capability, while showing lower sensitivity to variations in relative speed. Overall, this study demonstrates the relevance of the Point of No Return as a complementary indicator for collision risk assessment, offering a physically meaningful basis for decision-making in driver assistance systems and improving the interpretation of critical traffic situations. The proposed approach supports sustainable urban mobility by enabling earlier and more reliable intervention strategies, contributing to improved traffic safety, smoother traffic flow, and reduced environmental impact. Full article
(This article belongs to the Special Issue Sustainable Urban Mobility: 2nd Edition)
15 pages, 2794 KB  
Article
Study on the Noise Reduction Characteristics of Porous Elastic Road Surface Based on Finite Element Analysis and Noise Field Tests
by Hongjin Liu, Zhendong Qian, Jinquan Zhang, Binfang Lan, Ke Zhong, Changhong Wang, Qi Wang and Xin Xu
Materials 2026, 19(8), 1593; https://doi.org/10.3390/ma19081593 - 15 Apr 2026
Abstract
In order to study the noise reduction performance of Porous Elastic Road Surface (PERS), the vibration noise and air pumping noise has been separated from the tire–road noise through the finite element numerical simulation method. The tire–road noise model among the tire, road [...] Read more.
In order to study the noise reduction performance of Porous Elastic Road Surface (PERS), the vibration noise and air pumping noise has been separated from the tire–road noise through the finite element numerical simulation method. The tire–road noise model among the tire, road and surface air has been constructed by coupling of acoustic waves. The characteristics of tire–road noise under the PERS, Porous Asphalt Concrete (PAC), and Asphalt Concrete (AC) pavements have been analyzed through the modelling. The tire–road noise has also been investigated through the noise field tests. The generating process, coupling characteristics, and noise reduction performance of the vibration noise and the pumping noise of PERS pavements has been revealed. The results show that the tire–road noise was mainly generated by the vibration noise under the vehicle speed below 80 km/h. The proportion of pumping noise gradually exceeds that of vibration noise under the vehicle speed greater than 90 km/h. And the pumping noise gradually played the major role in the tire–road noise, which also increased with the increasing of vehicle speed. Comparing with AC and PAC pavements, PERS pavement exhibited the obvious advantages in noise reduction. Additionally, the reliability of the tire–road noise model has been verified through the field noise tests. It is expected that this work will serve as a reference for future research on the mechanics of the generation of tire–road noise, and try to provided theoretical support for the application of PERS. Full article
(This article belongs to the Special Issue Artificial Intelligence in Materials Science and Engineering)
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23 pages, 464 KB  
Review
A Review of Intelligent Trajectory Planning and Optimization for Aerospace Vehicles
by Guanjie Hu, Linxin Li, Yingmin Yi, Lecheng Liang, Zongyi Guo, Jianguo Guo and Jing Chang
Aerospace 2026, 13(4), 371; https://doi.org/10.3390/aerospace13040371 - 15 Apr 2026
Abstract
Aerospace vehicles operate across a wide flight envelope, traversing dense atmospheric layers from near-space to low Earth orbit. Trajectory planning and optimization in a large spatial domain and wide speed range present severe challenges to traditional methods, including computational efficiency, model accuracy, and [...] Read more.
Aerospace vehicles operate across a wide flight envelope, traversing dense atmospheric layers from near-space to low Earth orbit. Trajectory planning and optimization in a large spatial domain and wide speed range present severe challenges to traditional methods, including computational efficiency, model accuracy, and constraint adaptability. Artificial intelligence provides an effective pathway to overcome these limitations and has become a key driver for advancing trajectory planning and optimization of aerospace vehicles. This paper presents a systematic review of the core characteristics of aerospace trajectory planning, including environment coupling, multi-constraint compliance, propulsion integration, and aerodynamic nonlinearity, as well as the limitations of traditional methods. The study focuses on the application of intelligent algorithms in both the ascent and reentry phases. For the ascent phase, three key issues are addressed: multistage hybrid optimization with continuous and discrete variables, propulsion multimodal–trajectory coupling, and trajectory reconfiguration under engine failure. For the reentry phase, discussions are focused on such technical difficulties as multi-constraint trajectory generation, no-fly zone avoidance, and multi-mission requirement optimization. Finally, future research directions in intelligent trajectory planning and optimization are discussed, providing theoretical support and methodological guidance for the autonomous and intelligent development of aerospace vehicle trajectory planning. Full article
(This article belongs to the Special Issue Guidance and Control Systems of Aerospace Vehicles)
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20 pages, 2345 KB  
Article
A Sharpness-Optimized Partitioned PSF Estimation Method for UAV TDI Push-Broom Image Deblurring
by Zhen Zhang and Min Xu
Sensors 2026, 26(8), 2414; https://doi.org/10.3390/s26082414 - 15 Apr 2026
Abstract
In uncrewed aerial vehicle (UAV)-based ground observation and detection missions involving high-speed moving targets or low-light conditions, Time Delay Integration (TDI) cameras enhance image brightness through multi-stage charge accumulation. However, the imaging quality is susceptible to motion blur induced by platform vibrations and [...] Read more.
In uncrewed aerial vehicle (UAV)-based ground observation and detection missions involving high-speed moving targets or low-light conditions, Time Delay Integration (TDI) cameras enhance image brightness through multi-stage charge accumulation. However, the imaging quality is susceptible to motion blur induced by platform vibrations and velocity mismatch. Based on TDI imaging technology, a TDI image degradation model for a UAV-based imaging platform is formulated. To address spatial blurring caused by platform vibration and velocity mismatch during TDI imaging, we propose a TDI image restoration algorithm based on sharpness-optimized partitioned Point Spread Function (PSF) estimation. The main innovation lies in the first application of partitioned PSF estimation combined with image sharpness optimization in TDI imaging. By formulating an accurate TDI image degradation model, spatial motion blur kernel estimation is transformed into an iterative search problem for partitioned optimal PSF. Solving for optimal sharpness yields the optimal PSF and corresponding local motion parameters, achieving image restoration. Simulation and experimental results demonstrate that the proposed algorithm in this paper effectively removes motion blur in TDI dynamic imaging, while suppressing artifacts and ringing, thus significantly enhancing image quality. Full article
(This article belongs to the Section Optical Sensors)
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24 pages, 6824 KB  
Article
Vibration Control and Micro-Forming Quality Guarantee of BMF-Based UHPC Wet Joints Under Traffic Loads Using Tuned Mass Dampers
by Zhenwei Wang, Lingkai Zhang, Chujia Zhou and Peng Wang
Materials 2026, 19(8), 1564; https://doi.org/10.3390/ma19081564 - 14 Apr 2026
Viewed by 173
Abstract
In bridge widening projects under uninterrupted traffic conditions, vehicular vibration easily leads to damage in the interfacial transition zone (ITZ) and microstructural degradation of early-age concrete in wet joints. Taking a typical hollow slab-low T-beam widening structure as the object, this study introduces [...] Read more.
In bridge widening projects under uninterrupted traffic conditions, vehicular vibration easily leads to damage in the interfacial transition zone (ITZ) and microstructural degradation of early-age concrete in wet joints. Taking a typical hollow slab-low T-beam widening structure as the object, this study introduces basalt micro fiber (BMF)-based ultra-high-performance concrete (UHPC) as the wet joint material and establishes a refined vehicle–bridge coupled dynamic model considering the time-varying stiffness of the joint material and road roughness excitation. The research indicates that although UHPC possesses excellent ultimate mechanical properties, its early-age setting process is extremely sensitive to vehicle-induced vibration. Numerical analysis reveals that while traditional temporary steel fixtures can effectively control the vertical relative displacement between the new and old girders within the critical value of 5.5 mm, the peak particle velocity (PPV) induced by heavy vehicles (buses and trucks) during the early pouring stage (<12 h) significantly exceeds the safety threshold of 3 mm/s, posing a severe threat to the directional distribution of steel fibers and interfacial bond strength. Therefore, this paper designs a single tuned mass damper (TMD) optimized based on Den Hartog’s fixed-point theory. Simulation results confirm that with the TMD configured, the vibration responses induced by buses across the entire speed range (≤120 km/h) are reduced below the safety limit; the vibration velocity induced by heavy trucks is also effectively controlled when combined with an 80 km/h speed limit. The collaborative strategy of “passive TMD vibration reduction + active traffic speed limit” proposed in this paper provides a theoretical basis for guaranteeing the early-age micro-forming quality of UHPC wet joints and overall traffic efficiency. Full article
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20 pages, 3200 KB  
Article
Experimental Wind Tunnel Study of Energy Consumption, Level Flight Speed, and Endurance of a Micro-Class UAV as a Function of Operating Weight
by Bartłomiej Dziewoński, Krzysztof Kaliszuk, Artur Kierzkowski, Jakub Jarecki and Kacper Lisowiec
Energies 2026, 19(8), 1892; https://doi.org/10.3390/en19081892 - 14 Apr 2026
Viewed by 248
Abstract
This paper presents an experimental investigation of the level flight speed and endurance characteristics of a micro-class unmanned aerial vehicle as a function of operating weight. Wind tunnel experiments were conducted to determine the aerodynamic performance and power requirements of the UAV over [...] Read more.
This paper presents an experimental investigation of the level flight speed and endurance characteristics of a micro-class unmanned aerial vehicle as a function of operating weight. Wind tunnel experiments were conducted to determine the aerodynamic performance and power requirements of the UAV over a range of operating weight configurations. The tested vehicle, a fixed-wing micro UAV, was examined under steady, level flight conditions, with particular emphasis on identifying variations in the minimum power required to sustain level flight. Measured aerodynamic forces and moments were used to derive drag polars and the corresponding power curves for each mass configuration. Based on these results, endurance estimates were obtained by coupling the experimentally derived power requirements with the characteristics of the onboard electric propulsion system. The study demonstrates a clear shift in flight speeds with increasing operating weight, as well as a reduction in achievable endurance, highlighting the sensitivity of micro-class UAV performance to mass variations, and therefore energy consumption. Full article
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17 pages, 1657 KB  
Article
HDAO: A Hierarchical Curiosity-Driven Reinforcement Learning Approach for AUV Dynamic Obstacle Avoidance
by Huazheng Du, Qian Liu, Xu Liu and Na Xia
J. Mar. Sci. Eng. 2026, 14(8), 720; https://doi.org/10.3390/jmse14080720 - 14 Apr 2026
Viewed by 225
Abstract
Autonomous obstacle avoidance is a critical capability for Autonomous Underwater Vehicles (AUVs) to operate safely in dynamic and uncertain marine environments. Traditional AUV control methods rely on precise physical modeling and preset rules, yet they struggle to adapt to multiple sources of uncertainty, [...] Read more.
Autonomous obstacle avoidance is a critical capability for Autonomous Underwater Vehicles (AUVs) to operate safely in dynamic and uncertain marine environments. Traditional AUV control methods rely on precise physical modeling and preset rules, yet they struggle to adapt to multiple sources of uncertainty, such as random initial states, dynamic obstacles, and varying currents. In recent years, deep reinforcement learning has provided a new avenue for data-driven adaptive policy learning. However, it remains insufficient for handling long-horizon tasks with sparse rewards. While hierarchical reinforcement learning can mitigate reward sparsity through temporal abstraction, it often faces challenges including exploration–exploitation imbalance, slow global convergence, and insufficient safety guarantees. Furthermore, most existing studies neglect dynamic environmental disturbances and task continuity, which further limits the practical application of these algorithms. To address these challenges, this paper proposes a hierarchical curiosity-driven AUV obstacle avoidance algorithm (HDAO), designed for autonomous obstacle avoidance in dynamic and uncertain underwater environments. The core design of HDAO incorporates several key innovations. Firstly, it introduces a Collision Threat Index for dynamic obstacles, which enables explicit risk perception and quantifies collision threats, thereby enhancing the policy’s generalization and robustness. Secondly, a task-decoupled hierarchical architecture is employed to synergistically optimize global path planning and local obstacle avoidance behaviors. This approach effectively manages long-horizon navigation tasks while alleviating high-dimensional training pressure. Finally, a novel reward mechanism is designed by integrating hierarchical active exploration with curiosity-driven passive exploration. This mechanism effectively incentivizes the agent to explore unvisited areas under sparse reward conditions and dynamically balances exploration and exploitation. Experimental results demonstrate that HDAO significantly outperforms existing methods in terms of obstacle avoidance success rate, training convergence speed and robustness against external disturbances. Full article
(This article belongs to the Special Issue Dynamics, Control, and Design of Bionic Underwater Vehicles)
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15 pages, 3451 KB  
Article
Synthesis and Drag Reduction Experimental Study of Superhydrophobic Surface Coatings for Underwater Vehicle Hulls
by Zhong Luo, Junbo Hu and Yao Li
Appl. Sci. 2026, 16(8), 3801; https://doi.org/10.3390/app16083801 - 13 Apr 2026
Viewed by 326
Abstract
To address the drag reduction requirements of superhydrophobic surface coatings for underwater vehicle hulls, this study designed a synthesis method based on resin substrate modification and filler modification according to superhydrophobic coating synthesis techniques. Three types of superhydrophobic microstructured surface coatings were prepared: [...] Read more.
To address the drag reduction requirements of superhydrophobic surface coatings for underwater vehicle hulls, this study designed a synthesis method based on resin substrate modification and filler modification according to superhydrophobic coating synthesis techniques. Three types of superhydrophobic microstructured surface coatings were prepared: polyurethane resin, silicone resin, and fluororesin. The coatings were fabricated by incorporating fluorine-modified SiO2 nanoparticles into the modified resin matrices to construct hierarchical micro/nanostructures. The main components and synthesis processes for each coating were determined. Performance tests were conducted to evaluate mechanical properties (thickness, hardness, adhesion, wear resistance), functional characteristics (surface morphology, static/dynamic hydrophobic angles), and environmental resistance (seawater immersion, salt spray stability, thermal stability). Five surface coating test plans for underwater vehicle hull models were proposed, and drag reduction experiments were carried out to compare total drag, drag coefficient, and drag reduction rate across coating plans. Experimental results indicated that the silicone resin superhydrophobic coating with F660 + 8% SiO2 exhibited the best comprehensive performance, while the PU + 6% SiO2 superhydrophobic coating achieved optimal drag reduction at speeds below 9 m/s, meeting the performance criteria for underwater vehicle hull applications. Full article
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19 pages, 13360 KB  
Article
Research on Coordinated Control Strategy of DHT Mode Switching Based on Multiple Power Sources
by Zhigang Zhang, Hao Yang, Xiaosong Wang, Zhige Chen, Hai Qing and Xiaolin Tang
Actuators 2026, 15(4), 217; https://doi.org/10.3390/act15040217 - 13 Apr 2026
Viewed by 223
Abstract
To suppress the severe output torque fluctuations caused by clutch engagement when a hybrid electric vehicle equipped with a dedicated hybrid transmission (DHT) switches from pure electric (E) drive mode to hybrid (H) drive mode, a coordinated control method for power source switching [...] Read more.
To suppress the severe output torque fluctuations caused by clutch engagement when a hybrid electric vehicle equipped with a dedicated hybrid transmission (DHT) switches from pure electric (E) drive mode to hybrid (H) drive mode, a coordinated control method for power source switching is proposed. First, an adaptive fuzzy proportional-integral (PI) controller regulates the engine speed based on the speed difference between the engine and the P2 motor. Second, an active disturbance rejection control (ADRC) controller is employed for trajectory tracking to eliminate the speed difference across the synchronizer’s friction surfaces. This compensates for clutch torque variations during engine startup and ensures rapid synchronizer engagement. Finally, the torque interruption caused by the decoupling of the engine and P2 motor from the driveline is compensated via feedforward control from the P3 motor. The proposed strategy was validated through MATLAB Simulink simulations and CANape calibration tests. The results indicate that applying the proposed method to E-H mode switching slightly extended the total duration by 0.02 s. However, compared with uncoordinated control, the maximum longitudinal jerk was reduced by 73.8%, and the clutch sliding work decreased by 38.6%. This significantly enhances switching smoothness and prolongs the clutch’s service life. Full article
(This article belongs to the Section Actuators for Surface Vehicles)
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34 pages, 6347 KB  
Article
Multi-Head Attention Deep Q-Network with Prioritized Experience Replay for UAV Path Planning in Dynamic Environments: A Bio-Inspired Approach
by Yang Li, Xinjie Qian, Jiexin Zhang, Xiao Yang and Chao Deng
Biomimetics 2026, 11(4), 268; https://doi.org/10.3390/biomimetics11040268 - 13 Apr 2026
Viewed by 164
Abstract
Unmanned Aerial Vehicles (UAVs) have become widely used tools for different applications including surveillance, search and rescue, and package delivery. However, autonomous path planning in dynamic environments with moving obstacles, wind disturbances, and energy constraints remains a significant challenge. This paper proposes a [...] Read more.
Unmanned Aerial Vehicles (UAVs) have become widely used tools for different applications including surveillance, search and rescue, and package delivery. However, autonomous path planning in dynamic environments with moving obstacles, wind disturbances, and energy constraints remains a significant challenge. This paper proposes a novel Multi-Head Attention Deep Q-Network with Prioritized Experience Replay (MA-DQN + PER) that integrates bio-inspired attention mechanisms with deep reinforcement learning for efficient UAV path planning. Our approach features a 46-dimensional state space that captures all environmental information, including static obstacles, wind conditions, and energy status. The proposed Attention-QNetwork architecture uses four specialized attention heads to selectively focus on different aspects of the environment, including obstacle avoidance, target tracking and energy management, and wind compensation. To improve sample efficiency and convergence speed, we incorporate Prioritized Experience Replay (PER) as well as Prioritized Experience Replay (PER) with a sum-tree data structure to improve sample efficiency and convergence speed. A curriculum learning strategy that includes 10 difficulty levels is designed to progressively enhance the agent’s capabilities. Extensive simulations demonstrate that our MA-DQN + PER approach reaches a 96% task success rate (defined as the percentage of episodes where the UAV successfully reaches the target without collision or battery depletion), while the convergence speed was 68% quicker than that of the baseline DQN. Our method demonstrates superior performance in path efficiency (+17%), energy consumption reduction (−26%), and collision avoidance compared to state-of-the-art algorithms. Full article
(This article belongs to the Section Bioinspired Sensorics, Information Processing and Control)
29 pages, 1369 KB  
Article
A Distribution-Free Neural Estimator for Mean Reversion, with Application to Energy Commodity Markets
by Carlo Mari and Emiliano Mari
Mathematics 2026, 14(8), 1302; https://doi.org/10.3390/math14081302 - 13 Apr 2026
Viewed by 112
Abstract
Accurate estimation of the mean-reversion speed α in the AR(1) process Xt+1=(1α)Xt+εt is central to energy-commodity modelling. Classical estimators such as GARCH, jump-diffusion, and regime-switching produce model-conditioned estimates by [...] Read more.
Accurate estimation of the mean-reversion speed α in the AR(1) process Xt+1=(1α)Xt+εt is central to energy-commodity modelling. Classical estimators such as GARCH, jump-diffusion, and regime-switching produce model-conditioned estimates by embedding α within distributional assumptions, so that different model choices yield different α^ values from the same series without a principled criterion to adjudicate. We propose a distribution-free neural estimator based on a Temporal Convolutional Network (TCN) trained on synthetic AR(1) series with Sinh-ArcSinh (SAS) innovations. Distribution-free here means that no parametric family is assumed for the innovation distribution at inference time: the estimator imposes no distributional hypothesis when processing a new series. The SAS family serves as a training vehicle—not a model for the real data—chosen for its ability to span a broad range of tail weights and asymmetry profiles. The theoretical foundation is spectral invariance: the Yule–Walker equations establish that the autocorrelation structure ρk=(1α)k depends on α alone, provided innovations are uncorrelated across lags—a condition satisfied not only by i.i.d. innovations but also by conditionally heteroscedastic processes such as GARCH. The TCN therefore generalises to volatility-clustering environments without modification, learning to extract α from temporal dependence alone, independently of the marginal innovation distribution and of the temporal variance structure. On held-out test series the estimator outperforms all classical competitors, with the advantage growing monotonically with non-Gaussianity. A robustness analysis on three out-of-distribution innovation families and on AR(1)-GARCH(1,1) processes empirically validates the spectral invariance guarantee across both marginal and temporal variance structure, including near-integrated GARCH processes where innovation kurtosis far exceeds the training range. The distribution-free α^ enables a two-stage pipeline in which α and the innovation distribution are characterised independently—a decoupling structurally impossible in classical likelihood-based approaches. Once trained, the TCN acts as a universal mean-reversion estimator applicable to any price series without re-fitting. Applied to four energy markets—Italian natural gas (PSV price), Italian electricity (PUN price), US Henry Hub, and US PJM West Hub—spanning log-return kurtosis from near-Gaussian to strongly heavy-tailed, the TCN yields robust, distribution-free estimates of mean-reversion speed. Full article
21 pages, 2662 KB  
Article
An Online Trajectory Optimization Method for the TAEM Phase Based on an Analytical Lateral Path and Equivalent Dynamic Decoupling
by Yankun Zhang, Changzhu Wei and Jialun Pu
Aerospace 2026, 13(4), 359; https://doi.org/10.3390/aerospace13040359 - 13 Apr 2026
Viewed by 191
Abstract
Rapid and robust trajectory planning for the Terminal Area Energy Management (TAEM) phase of horizontal-landing Reusable Launch Vehicles (RLVs) is critical but challenging due to large initial deviations, stringent terminal constraints, and strong model nonlinearities. To address the limitations of existing methods in [...] Read more.
Rapid and robust trajectory planning for the Terminal Area Energy Management (TAEM) phase of horizontal-landing Reusable Launch Vehicles (RLVs) is critical but challenging due to large initial deviations, stringent terminal constraints, and strong model nonlinearities. To address the limitations of existing methods in convergence reliability and computational speed, this paper proposes a novel online trajectory optimization framework based on analytical lateral planning and equivalent dynamic decoupling. First, a cubic Bézier curve is employed to parameterize the lateral ground track, enabling the rapid generation of analytical expressions for the lateral states that strictly satisfy boundary constraints. Leveraging these analytical solutions, the original six-degree-of-freedom dynamics are exactly decoupled and reduced to a lower-dimensional model governing only the longitudinal motion. To further mitigate nonlinearity, the third derivative of height with respect to range is introduced as a virtual control variable, transforming the problem into a smoother form. The resulting equivalent longitudinal optimization problem is then efficiently solved using the Gauss Pseudospectral Method. Numerical simulations demonstrate that the proposed method significantly outperforms traditional approaches in computational efficiency: it generates feasible trajectories satisfying all constraints within 0.26 s (3σ value). Furthermore, the method exhibits remarkable insensitivity to initial guesses, achieving stable convergence even with simple linear initialization. This approach provides a robust and real-time capable solution for complex TAEM trajectory optimization problems characterized by high nonlinearity and multiple constraints. Full article
(This article belongs to the Section Astronautics & Space Science)
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28 pages, 1616 KB  
Article
Influence of Turbulence Modeling on CFD-Based Prediction of Vehicle Hydroplaning Speed
by Thathsarani D. H. Herath Mudiyanselage, Manjriker Gunaratne and Andrés E. Tejada-Martínez
Appl. Mech. 2026, 7(2), 32; https://doi.org/10.3390/applmech7020032 - 11 Apr 2026
Viewed by 174
Abstract
Most computational studies of vehicle hydroplaning have emphasized structural realism through fluid–structure interaction, tire deformation, tread geometry, and pavement surface characterization. By contrast, the hydrodynamics governing the flow in the tire vicinity, particularly the role of turbulence, have received comparatively limited attention. In [...] Read more.
Most computational studies of vehicle hydroplaning have emphasized structural realism through fluid–structure interaction, tire deformation, tread geometry, and pavement surface characterization. By contrast, the hydrodynamics governing the flow in the tire vicinity, particularly the role of turbulence, have received comparatively limited attention. In a significant number of studies, the flow has been treated as laminar despite turbulent flow conditions, while in a few other studies turbulence modeling has been adopted without an explicit assessment of its impact on hydroplaning predictions. In this study, we present a simplified three-dimensional computational fluid dynamics (CFD) model designed to isolate the flow regimes governing hydroplaning and to quantify the mean effect of the turbulence modeling on the predicted hydroplaning speed. Using a finite-volume formulation with a volume-of-fluid representation of the air–water interface, the flow around and beneath a smooth 0.7 m-diameter tire sliding in locked-wheel mode over a flooded, nominally smooth pavement is simulated. The tire is represented as a rigid body with an idealized rectangular bottom patch whose area is determined from the tire load and inflation pressure, avoiding the need to prescribe a measured or assumed deformed footprint. Steady-state hydroplaning is modeled for a uniform upstream water film thickness of 7.62 mm with a 0.5 mm gap between the tire and the pavement, over tire inflation pressures ranging from approximately 100 to 300 kPa, and predictions are verified against the empirical NASA hydroplaning equation. For these conditions, simulations without turbulence closure exhibit a consistent, systematic underprediction of the hydroplaning speed of approximately 13.5% relative to the NASA relation. Incorporating turbulence effects through Reynolds-averaged closures substantially reduces this bias, with average deviations of about 6% for the realizable k–ε model and 2.4% for the shear stress transport (SST) k–ω model. An analysis of the results indicates that hydrodynamic lift is dominated by pressure buildup associated with stagnation at the lower leading edge of the tire, with a significant contribution from shear-dominated flow in the thin under-tire gap, and that turbulence acts to moderate the integrated lift from these pressure fields. These results demonstrate that explicitly accounting for turbulence in the tire vicinity is essential for reproducing empirical hydroplaning trends and for avoiding systematic bias in CFD-based hydroplaning predictions. Full article
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