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Search Results (298)

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Keywords = symmetrical uncertainty

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28 pages, 760 KB  
Article
Expanding the Fine-Kinney Methodology Using Fuzzy Logic: A Case Study in an Energy Linemen Workshop
by Chris Mitrakas, Alexandros Xanthopoulos and Dimitrios Koulouriotis
Safety 2025, 11(4), 94; https://doi.org/10.3390/safety11040094 - 2 Oct 2025
Abstract
This paper investigates the effectiveness and limitations of the traditional Fine-Kinney method for occupational risk assessment, emphasizing its shortcomings in addressing complex and dynamic work environments. To overcome these challenges, two advanced methodologies, Fine-Kinney10 (FK10) and Fuzzy Fine-Kinney10 (FFK10), are introduced. The FK10 [...] Read more.
This paper investigates the effectiveness and limitations of the traditional Fine-Kinney method for occupational risk assessment, emphasizing its shortcomings in addressing complex and dynamic work environments. To overcome these challenges, two advanced methodologies, Fine-Kinney10 (FK10) and Fuzzy Fine-Kinney10 (FFK10), are introduced. The FK10 employs a symmetric scaling system (1–10) for probability, frequency, and severity indicators, providing a more balanced quantification of risks. Meanwhile, FFK10 incorporates fuzzy logic to handle uncertainty and subjectivity in risk assessment, significantly enhancing the sensitivity and accuracy of risk evaluation. These methodologies were applied to a linemen workshop in an energy production and distribution company, analyzing various types of accidents such as falls from heights, exposure to electric currents, slips on surfaces, and more. The applications highlighted the practical benefits of these methods in effectively assessing and mitigating risks. A significant finding includes the identification of risks related to falls from heights of <2.5 m (SH1) and road traffic accidents (SH6), where all three methods yielded different verbal outcomes. Compared to the traditional Fine-Kinney method, FK10 and FFK10 demonstrated superior ability in distinguishing risk levels and guiding targeted safety measures. The study underscores that FK10 and FFK10 represent significant advancements in occupational risk management, offering robust frameworks adaptable across various industries. Full article
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43 pages, 1895 KB  
Article
Bi-Level Dependent-Chance Goal Programming for Paper Manufacturing Tactical Planning: A Reinforcement-Learning-Enhanced Approach
by Yassine Boutmir, Rachid Bannari, Abdelfettah Bannari, Naoufal Rouky, Othmane Benmoussa and Fayçal Fedouaki
Symmetry 2025, 17(10), 1624; https://doi.org/10.3390/sym17101624 - 1 Oct 2025
Abstract
Tactical production–distribution planning in paper manufacturing involves hierarchical decision-making under hybrid uncertainty, where aleatory randomness (demand fluctuations, machine variations) and epistemic uncertainty (expert judgments, market trends) simultaneously affect operations. Existing approaches fail to address the bi-level nature under hybrid uncertainty, treating production and [...] Read more.
Tactical production–distribution planning in paper manufacturing involves hierarchical decision-making under hybrid uncertainty, where aleatory randomness (demand fluctuations, machine variations) and epistemic uncertainty (expert judgments, market trends) simultaneously affect operations. Existing approaches fail to address the bi-level nature under hybrid uncertainty, treating production and distribution decisions independently or using single-paradigm uncertainty models. This research develops a bi-level dependent-chance goal programming framework based on uncertain random theory, where the upper level optimizes distribution decisions while the lower level handles production decisions. The framework exploits structural symmetries through machine interchangeability, symmetric transportation routes, and temporal symmetry, incorporating symmetry-breaking constraints to eliminate redundant solutions. A hybrid intelligent algorithm (HIA) integrates uncertain random simulation with a Reinforcement-Learning-enhanced Arithmetic Optimization Algorithm (RL-AOA) for bi-level coordination, where Q-learning enables adaptive parameter tuning. The RL component utilizes symmetric state representations to maintain solution quality across symmetric transformations. Computational experiments demonstrate HIA’s superiority over standard metaheuristics, achieving 3.2–7.8% solution quality improvement and 18.5% computational time reduction. Symmetry exploitation reduces search space by approximately 35%. The framework provides probability-based performance metrics with optimal confidence levels (0.82–0.87), offering 2.8–4.5% annual cost savings potential. Full article
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17 pages, 3603 KB  
Article
A Fault Diagnosis Method for the Train Communication Network Based on Active Learning and Stacked Consistent Autoencoder
by Yueyi Yang, Haiquan Wang, Xiaobo Nie, Shengjun Wen and Guolong Li
Symmetry 2025, 17(10), 1622; https://doi.org/10.3390/sym17101622 - 1 Oct 2025
Abstract
As a critical component of rail travel, the train communication network (TCN) is an integrated central platform that is used to realize the train control, condition monitoring, and data transmission, whose failure will disrupt the symmetry of TCN topology and endanger the security [...] Read more.
As a critical component of rail travel, the train communication network (TCN) is an integrated central platform that is used to realize the train control, condition monitoring, and data transmission, whose failure will disrupt the symmetry of TCN topology and endanger the security of rail trains. To enhance the reliability of TCN, an intelligent fault diagnosis method is proposed based on active learning (AL) and a stacked consistent autoencoder (SCAE), which is capable of building a competitive classifier with a limited amount of labeled training samples. SCAE can learn better feature presentations from electrical multifunction vehicle bus (MVB) signals by reconstructing the same raw input data layer by layer in the unsupervised feature learning phase. In the supervised fine-tuning phase, a deep AL-based fault diagnosis framework is proposed, and a dynamic fusion AL method is presented. The most valuable unlabeled samples are selected for labeling and training by considering uncertainty and similarity simultaneously, and the fusion weight is dynamically adjusted at the different training stages. A TCN experimental platform is constructed, and experimental results show that the proposed method achieves better performance under three different metrics with fewer labeled samples compared to the state-of-the-art methods; it is also symmetrically valid in class-imbalanced data. Full article
(This article belongs to the Special Issue Symmetry in Fault Detection and Diagnosis for Dynamic Systems)
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16 pages, 571 KB  
Article
Converting Entanglement into Ensemble Basis-Free Coherence
by Aleksei Kodukhov
Entropy 2025, 27(10), 1005; https://doi.org/10.3390/e27101005 - 26 Sep 2025
Abstract
The resource theory of coherence addresses the extent to which quantum properties are present in a given quantum system. While coherence has been extensively studied for individual quantum states, measures of coherence for ensembles of quantum states remain an area of active research. [...] Read more.
The resource theory of coherence addresses the extent to which quantum properties are present in a given quantum system. While coherence has been extensively studied for individual quantum states, measures of coherence for ensembles of quantum states remain an area of active research. The entanglement-based approach to ensemble coherence—arising from the measurement–ensemble duality principle and the Born rule—connects the ensemble coherence with both the entanglement resource and the measurement’s uncertainty. This paper presents two methods for generating ensemble coherence from a fixed amount of entanglement between two qubit systems. The first method involves applying a von Neumann measurement to one part of a non-maximally entangled bipartite state, resulting in a pair of non-orthogonal states whose coherence can equal the initial entanglement. The second method considers a class of symmetric observables capable of generating ensembles used in quantum key distribution (QKD) protocols such as B92, BB84, and three-state QKD. As a result, this work contributes to understanding how much ensemble coherence can be obtained from a given amount of entanglement. Full article
(This article belongs to the Special Issue Quantum Foundations: 100 Years of Born’s Rule)
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23 pages, 5145 KB  
Article
Parameter Estimation of General Uncertain Differential Equations via the Principle of Least Squares with Its Application in Economic Field
by Xiaoya Xu and Youde Dong
Symmetry 2025, 17(10), 1594; https://doi.org/10.3390/sym17101594 - 24 Sep 2025
Viewed by 56
Abstract
The parameter estimation problem is one of the research hotspots in the field of uncertain differential equations. However, most studies at present focus on parameter estimation based on residuals of uncertain differential equations, which relies strictly on the solvability of residuals. In view [...] Read more.
The parameter estimation problem is one of the research hotspots in the field of uncertain differential equations. However, most studies at present focus on parameter estimation based on residuals of uncertain differential equations, which relies strictly on the solvability of residuals. In view of this disadvantage, this paper derives a symmetrical statistical invariant, which is different from residuals based on the difference scheme, and proposes the least squares estimation of general uncertain differential equations based on the statistical invariant and the principle of least squares. In order to consider parameter estimation in more general cases, this paper also studies the least squares estimation of time-varying parameters in general uncertain differential equations and designs corresponding to numerical algorithms to calculate the numerical solutions of these least squares estimations. Finally, this paper also proposes two numerical examples and an empirical study to illustrate the above methods. Full article
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21 pages, 3628 KB  
Article
Uncertainty Propagation for Power-Law, Bingham, and Casson Fluids: A Comparative Stochastic Analysis of a Class of Non-Newtonian Fluids in Rectangular Ducts
by Eman Alruwaili and Osama Hussein Galal
Mathematics 2025, 13(18), 3030; https://doi.org/10.3390/math13183030 - 19 Sep 2025
Viewed by 149
Abstract
This study presents a novel framework for uncertainty propagation in power-law, Bingham, and Casson fluids through rectangular ducts under stochastic viscosity (Case I) and pressure gradient conditions (Case II). Using the computationally efficient Stochastic Finite Difference Method with Homogeneous Chaos (SFDHC), validated via [...] Read more.
This study presents a novel framework for uncertainty propagation in power-law, Bingham, and Casson fluids through rectangular ducts under stochastic viscosity (Case I) and pressure gradient conditions (Case II). Using the computationally efficient Stochastic Finite Difference Method with Homogeneous Chaos (SFDHC), validated via comparison with quasi-Monte Carlo simulations, we demonstrate significantly lower computational costs across varying Coefficients of Variation (COVs). For viscosity uncertainty (Case I), results show a 0.54–2.8% increase in mean maximum velocity with standard deviations reaching 75.3–82.5% of the COV, where the power-law model exhibits the greatest sensitivity (velocity variations spanning 71.2–177.3% of the mean at COV = 20%). Pressure gradient uncertainty (Case II) preserves mean velocities but produces narrower and symmetric distributions. We systematically evaluate the effects of aspect ratio, yield stress, and flow behavior index on the stochastic velocity response of each fluid. Moreover, our analysis pioneers a performance hierarchy: Herschel–Bulkley fluids show the highest mean and standard deviation of maximum velocity, followed by power-law, Robertson–Stiff, Bingham, and Casson models. A key finding is the extreme fluctuation of the Robertson–Stiff model, which exhibits the most drastic deviations, reaching up to 177% of the average velocity. The significance of fluid-specific stochastic analysis in duct system design is underscored by these results. This is especially critical for non-Newtonian flows, where system performance and reliability are greatly impacted by uncertainties in viscosity and pressure gradient, which reflect actual operational variations. Full article
(This article belongs to the Section E: Applied Mathematics)
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11 pages, 301 KB  
Article
Thermodynamics of Observations
by Arno Keppens and Jean-Christopher Lambert
Entropy 2025, 27(9), 968; https://doi.org/10.3390/e27090968 - 17 Sep 2025
Viewed by 204
Abstract
This work demonstrates that the four laws of classical thermodynamics apply to the statistics of symmetric observation distributions, and provides examples of how this can be exploited in uncertainty assessments. First, an expression for the partition function Z is derived. In contrast with [...] Read more.
This work demonstrates that the four laws of classical thermodynamics apply to the statistics of symmetric observation distributions, and provides examples of how this can be exploited in uncertainty assessments. First, an expression for the partition function Z is derived. In contrast with general classical thermodynamics, however, this can be performed without the need for variational calculus, while Z also equals the number of observations N directly. Apart from the partition function ZN as a scaling factor, three state variables m, n, and ϵ fully statistically characterize the observation distribution, corresponding to its expectation value, degrees of freedom, and random error, respectively. Each term in the first law of thermodynamics is then shown to be a variation on δm2=δ(nϵ)2 for both canonical (constant n and ϵ) and macro-canonical (constant ϵ) observation ensembles, while micro-canonical ensembles correspond to a single observation result bin having δm2=0. This view enables the improved fitting and combining of observation distributions, capturing both measurand variability and measurement precision. Full article
(This article belongs to the Section Multidisciplinary Applications)
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14 pages, 1603 KB  
Article
Adaptive Fault-Tolerant Sliding Mode Control Design for Robotic Manipulators with Uncertainties and Actuator Failures
by Yujuan Wang and Mingyu Wang
Symmetry 2025, 17(9), 1547; https://doi.org/10.3390/sym17091547 - 16 Sep 2025
Viewed by 297
Abstract
This research proposes a novel adaptive robust fault-tolerant controller for symmetrical robotic manipulators subject to model uncertainties and actuator failures. The key innovation lies in the design of a new sliding manifold that effectively integrates the advantages of a hyperbolic tangent function-based practical [...] Read more.
This research proposes a novel adaptive robust fault-tolerant controller for symmetrical robotic manipulators subject to model uncertainties and actuator failures. The key innovation lies in the design of a new sliding manifold that effectively integrates the advantages of a hyperbolic tangent function-based practical sliding manifold and a fast terminal sliding manifold. This structure not only eliminates the reaching phase and accelerates error convergence but also significantly enhances system robustness while mitigating chattering. Moreover, the proposed manifold ensures the global non-singularity of the equivalent control law, thereby improving overall stability. Another major contribution is an adjustable adaptive strategy that dynamically estimates the unknown bounds of fault information and external disturbances, reducing the reliance on prior knowledge. The stability and convergence of the robotic system under the proposed scheme are theoretically analyzed and guaranteed. Finally, simulation experiments demonstrate the superior performance of the proposed scheme. Full article
(This article belongs to the Section Engineering and Materials)
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18 pages, 1241 KB  
Article
Identifying AI-Driven Emerging Trends in Service Innovation and Digitalized Industries Using the Circular Picture Fuzzy WASPAS Approach
by Yingshan Xu and Dongdong Zhang
Symmetry 2025, 17(9), 1546; https://doi.org/10.3390/sym17091546 - 16 Sep 2025
Viewed by 253
Abstract
In the current digital era, as global industries transform due to technological advancements, tracking trends in emerging services has assumed increased significance. This study proposes an innovative model that integrates circular picture fuzzy sets (CPFSs) with the Weighted Aggregated Sum Product Assessment (WASPAS) [...] Read more.
In the current digital era, as global industries transform due to technological advancements, tracking trends in emerging services has assumed increased significance. This study proposes an innovative model that integrates circular picture fuzzy sets (CPFSs) with the Weighted Aggregated Sum Product Assessment (WASPAS) method to evaluate and rank various AI-driven trends within the service industry. The CPFS approach offers enhanced responses to uncertainty, symmetric information, indecision, and varying expert opinions, while the WASPAS method ensures a dependable system for ranking prominent trends. To facilitate the evaluation process, experts and relevant studies were consulted to establish criteria that address technological developments, organizational dynamics, and market fluctuations. A hybrid fuzzy Multi-Criteria Decision-Making (MCDM) framework enabled the analysis of several potential innovations related to AI and their prioritization in the context of digitalized sectors, including healthcare, finance, online shopping, retail, and logistics. This framework is a well-structured and flexible tool for professionals and policymakers seeking to navigate the challenges of identifying new trends within unpredictable digital environments. The findings indicate that the circular picture fuzzy WASPAS approach significantly enhances trend prioritization and fosters strategic thinking in digital innovation. Furthermore, the research provides valuable insights into the complexities of fuzzy decision-making and the promotion of AI-based innovation management. Full article
(This article belongs to the Section Mathematics)
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18 pages, 1082 KB  
Article
Strategic Sample Selection in Deep Learning: A Case Study on Violence Detection Using Confidence-Based Subsets
by Francisco Primero Primero, Daniel Cervantes Ambriz, Roberto Alejo Eleuterio, Everardo E. Granda Gutiérrez, Jorge Sánchez Jaime and Rosa M. Valdovinos Rosas
Symmetry 2025, 17(9), 1536; https://doi.org/10.3390/sym17091536 - 15 Sep 2025
Viewed by 293
Abstract
Automated violence detection in images presents a technical and scientific challenge that demands specialized methods to enhance classification systems. This study introduces an approach for automatically identifying relevant samples to improve the performance of neural network models, specifically DenseNet121, with a focus on [...] Read more.
Automated violence detection in images presents a technical and scientific challenge that demands specialized methods to enhance classification systems. This study introduces an approach for automatically identifying relevant samples to improve the performance of neural network models, specifically DenseNet121, with a focus on violence classification in images. The proposed methodology begins with an initial training phase using a balanced dataset (DS1, 6000 images). Based on the model’s output scores (outN), three confidence levels are defined: Safe (outN0.9+σ or outN0.1σ), Border (0.5σoutN0.5+σ), and Average (0.4σoutN0.6+σ). These levels correspond to scenarios with low, moderate, and high prediction error probabilities, respectively, where σ is an adjustable threshold. The Border subset exhibits symmetry around the decision boundary (outN=0.5), capturing maximally uncertain samples, while the Safe regions reflect functional asymmetries in high-confidence predictions. Subsequently, these thresholds are applied to a second dataset (DS2, 5600 images) to extract specialized subsets for retraining (DSSafe, DSBorder, and DSAverage). Finally, the model is evaluated using an independent test set (DStest, 4400 images), ensuring complete data isolation. The experimental results demonstrate that the confidence-based subsets offer competitive performance despite using significantly fewer samples. The Average subset achieved an F1-Score of 0.89 and a g-mean of 0.93 using only 20% of the data, making it a promising alternative for efficient training. These findings highlight that strategic sample selection based on confidence thresholds enables effective training with reduced data, offering a practical balance between performance and efficiency when symmetric uncertainty modeling is exploited. Full article
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30 pages, 18647 KB  
Article
Learning-Driven Intelligent Passivity Control Using Nonlinear State Observers for Induction Motors
by Belkacem Bekhiti, Kamel Hariche, Mohamed Roudane, Aleksey Kabanov and Vadim Kramar
Automation 2025, 6(3), 45; https://doi.org/10.3390/automation6030045 - 10 Sep 2025
Viewed by 257
Abstract
This paper proposes a learning-driven passivity-based control (PBC) strategy for sensorless induction motors, combining a nonlinear adaptive observer with recurrent neural networks (RNNs) to improve robustness and estimation accuracy under dynamic conditions. The main novelty is the integration of neural learning into the [...] Read more.
This paper proposes a learning-driven passivity-based control (PBC) strategy for sensorless induction motors, combining a nonlinear adaptive observer with recurrent neural networks (RNNs) to improve robustness and estimation accuracy under dynamic conditions. The main novelty is the integration of neural learning into the passivity framework, enabling real-time compensation for un-modeled dynamics and parameter uncertainties with only one gain adjustment across a broad speed range. Lyapunov-based analysis guarantees the global stability of the closed-loop system. Experiments on a 1.1 kW induction motor confirm the approach’s effectiveness over conventional observer-based and fuzzy-enhanced methods. Under torque reversal and flux variation, the proposed controller achieves a torque mean absolute error (MAE) of 0.18 Nm and flux MAE of 0.21 Wb, compared to 1.58 Nm and 0.85 Wb with classical PBC. When peak torque deviation drops from 42.52% to 30.85% of the nominal, torque symmetric mean absolute percentage error (SMAPE) improves by 7.6%, and settling time is reduced to 985 ms versus 1120 ms. These results validate the controller’s precision, adaptability, and robustness in real-world sensorless motor control. Full article
(This article belongs to the Section Control Theory and Methods)
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22 pages, 866 KB  
Article
Hybrid Interval Type-2 Fuzzy Set Methodology with Symmetric Membership Function for Application Selection in Precision Agriculture
by Radovan Dragić, Adis Puška, Branislav Dudić, Anđelka Štilić, Lazar Stošić, Miloš Josimović and Miroslav Nedeljković
Symmetry 2025, 17(9), 1504; https://doi.org/10.3390/sym17091504 - 10 Sep 2025
Viewed by 308
Abstract
The development of technology has influenced changes in agricultural production. Farmers are increasingly using modern devices and machinery that provide valuable information, and to manage this information effectively, it is necessary to use specialized applications. This research aims to evaluate various applications and [...] Read more.
The development of technology has influenced changes in agricultural production. Farmers are increasingly using modern devices and machinery that provide valuable information, and to manage this information effectively, it is necessary to use specialized applications. This research aims to evaluate various applications and determine which one is most suitable for small- and medium-sized farmers to adopt in precision agriculture. This research employed expert decision-making to determine the importance of criteria and evaluate applications using linguistic values. Due to the presence of uncertainty in decision-making, an interval type-2 fuzzy (IT2F) set was used, which addresses this problem through the support of a membership function. This approach allows for the display of uncertainty and imprecision using an interval rather than a single exact value. This enables a more flexible and realistic representation of ratings, leading to more confident decision-making. These membership functions are formed in such a way that there is symmetry around the central linguistic value. To use this approach, the SiWeC (simple weight calculation) and CORASO (compromise ranking from alternative solutions) methods were adapted. The results of the IT2F SiWeC method revealed that the most important criteria for experts are data accuracy, efficiency, and simplicity. The results of the IT2F CORASO method displayed that the A3 application delivers the best results, confirmed by additional analyses. This research has indicated that digital tools, in the form of applications, can be effectively used in small- and medium-scale precision agriculture production. Full article
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15 pages, 1249 KB  
Article
Investigation of the Variants of Independent Elastic Constants of Rigid Polyurethane Foams with Symmetry Elements
by Aivars Lagzdiņš, Ilze Beverte, Vilis Skruls and Jānis Andersons
Polymers 2025, 17(17), 2431; https://doi.org/10.3390/polym17172431 - 8 Sep 2025
Viewed by 351
Abstract
Rigid PU foams have wide practical applications, and their mathematical modelling would benefit from deeper knowledge about the variants of independent elastic constants of symmetric PU foams. Therefore, in this study, various symmetry elements of rigid PU foams were analysed in relation to [...] Read more.
Rigid PU foams have wide practical applications, and their mathematical modelling would benefit from deeper knowledge about the variants of independent elastic constants of symmetric PU foams. Therefore, in this study, various symmetry elements of rigid PU foams were analysed in relation to the characteristics of production moulds and technologies. The generalised Hooke’s law was considered together with additional relationships valid for certain types of symmetry. Variants of independent elastic constants were determined for orthotropic, orthotropic with a rotational symmetry, and isotropic PU foams. For transtropic PU foams, nine variants of independent elastic constants were identified and corresponding equations for the components of response strain tensor were derived. Then, in order to investigate the results provided by the 9 variants, 12 elastic constants were determined experimentally in compression and shear for free-rise, rigid, and quasi-transtropic PU foams with average densities of 34 kg/m3, 55 kg/m3, and 75 kg/m3. Based on the analysis of (a) measurement uncertainties and (b) satisfying of the transtropy equations, an assessment was made of the correspondence of the experimentally determined elastic constants to the constants of a perfectly transtropic material. This made it possible to identify variants of independent constants that ensure the best correspondence between the calculated strains and the set of average strains. Full article
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26 pages, 3998 KB  
Article
Graph-Symmetry Cognitive Learning for Multi-Scale Cloud Imaging: An Uncertainty-Quantified Geometric Paradigm via Hierarchical Graph Networks
by Qing Xu, Zichen Zhang, Guanfang Wang and Yunjie Chen
Symmetry 2025, 17(9), 1477; https://doi.org/10.3390/sym17091477 - 7 Sep 2025
Viewed by 379
Abstract
Cloud imagery analysis from terrestrial observation points represents a fundamental capability within contemporary atmospheric monitoring infrastructure, serving essential functions in meteorological prediction, climatic surveillance, and hazard alert systems. However, traditional ground-based cloud image segmentation methods have fundamental limitations, particularly their inability to effectively [...] Read more.
Cloud imagery analysis from terrestrial observation points represents a fundamental capability within contemporary atmospheric monitoring infrastructure, serving essential functions in meteorological prediction, climatic surveillance, and hazard alert systems. However, traditional ground-based cloud image segmentation methods have fundamental limitations, particularly their inability to effectively model the graph structure and symmetry in cloud data. To address this, we propose G-CLIP, a ground-based cloud image segmentation method based on graph symmetry. G-CLIP synergistically integrates four innovative modules. First, the Prototype-Driven Asymmetric Attention (PDAA) module is designed to reduce complexity and enhance feature learning by leveraging permutation invariance and graph symmetry principles. Second, the Symmetry-Adaptive Graph Convolution Layer (SAGCL) is constructed, modeling pixels as graph nodes, using cosine similarity to build a sparse discriminative structure, and ensuring stability through symmetry and degree normalization. Third, the Multi-Scale Directional Edge Optimizer (MSDER) is developed to explicitly model complex symmetric relationships in cloud features from a graph theory perspective. Finally, the Uncertainty-Driven Loss Optimizer (UDLO) is proposed to dynamically adjust weights to address foreground–background imbalance and provide uncertainty quantification. Extensive experiments on four benchmark datasets demonstrate that our method achieves state-of-the-art performance across all evaluation metrics. Our work provides a novel theoretical framework and practical solution for applying graph neural networks (GNNs) to meteorology, particularly by integrating graph properties with uncertainty and leveraging symmetries from graph theory for complex spatial modeling. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry Study in Graph Theory)
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28 pages, 6585 KB  
Article
Active Fault Tolerant Trajectory-Tracking Control of Autonomous Distributed-Drive Electric Vehicles Considering Steer-by-Wire Failure
by Xianjian Jin, Huaizhen Lv, Yinchen Tao, Jianning Lu, Jianbo Lv and Nonsly Valerienne Opinat Ikiela
Symmetry 2025, 17(9), 1471; https://doi.org/10.3390/sym17091471 - 6 Sep 2025
Viewed by 633
Abstract
In this paper, the concept of symmetry is utilized to design active fault tolerant trajectory-tracking control of autonomous distributed-drive electric vehicles—that is, the construction and the solution of active fault tolerant trajectory-tracking controllers are symmetrical. This paper presents a hierarchical fault tolerant control [...] Read more.
In this paper, the concept of symmetry is utilized to design active fault tolerant trajectory-tracking control of autonomous distributed-drive electric vehicles—that is, the construction and the solution of active fault tolerant trajectory-tracking controllers are symmetrical. This paper presents a hierarchical fault tolerant control strategy for improving the trajectory-tracking performance of autonomous distributed-drive electric vehicles (ADDEVs) under steer-by-wire (SBW) system failures. Since ADDEV trajectory dynamics are inherently affected by complex traffic conditions, various driving maneuvers, and other road environments, the main control objective is to deal with the ADDEV trajectory-tracking control challenges of system uncertainties, SBW failures, and external disturbance. First, the differential steering dynamics model incorporating a 3-DOF coupled system and stability criteria based on the phase–plane method is established to characterize autonomous vehicle motion during SBW failures. Then, by integrating cascade active disturbance rejection control (ADRC) with Karush–Kuhn–Tucker (KKT)-based torque allocation, the active fault tolerant control framework of trajectory tracking and lateral stability challenges caused by SBW actuator malfunctions and steering lockup is addressed. The upper-layer ADRC employs an extended state observer (ESO) to estimate and compensate against uncertainties and disturbances, while the lower-layer utilizes KKT conditions to optimize four-wheel torque distribution to compensate for SBW failures. Simulations validate the effectiveness of the controller with serpentine and double-lane-change maneuvers in the co-simulation platform MATLAB/Simulink-Carsim® (2019). Full article
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