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16 pages, 1554 KB  
Review
Explainable and Trustworthy Artificial Intelligence in Cardiology: A Narrative Review of Clinical Applications, Operational Integration, and Future Directions
by Mateusz Lucki, Ewa Lucka, Jacek Żak, Przemysław Mitkowski and Maciej Lesiak
J. Clin. Med. 2026, 15(13), 4885; https://doi.org/10.3390/jcm15134885 (registering DOI) - 23 Jun 2026
Abstract
Background/Objectives: Artificial intelligence (AI) is increasingly transforming cardiology through advanced analytical tools capable of identifying complex patterns across cardiovascular imaging, electrophysiology, and clinical datasets. Machine learning (ML) and deep learning (DL) algorithms are being integrated into echocardiography, cardiac computed tomography (CT), cardiac magnetic [...] Read more.
Background/Objectives: Artificial intelligence (AI) is increasingly transforming cardiology through advanced analytical tools capable of identifying complex patterns across cardiovascular imaging, electrophysiology, and clinical datasets. Machine learning (ML) and deep learning (DL) algorithms are being integrated into echocardiography, cardiac computed tomography (CT), cardiac magnetic resonance imaging (MRI), and electrocardiography (ECG), enabling earlier diagnosis and more personalized cardiovascular care. This narrative review summarizes current clinical and organizational applications of AI in cardiology and discusses emerging concepts related to explainable and trustworthy AI. Methods: A narrative review was conducted according to SANRA recommendations using the PubMed, MEDLINE, Web of Science, and Scopus databases, including peer-reviewed publications from 2015 to 2026 addressing clinical, organizational, and ethical applications of AI in cardiology, with particular emphasis on cardiovascular imaging, electrocardiography, heart failure, digital health, and explainable AI frameworks. Results: Substantial evidence demonstrates that AI-based tools can achieve expert-level performance in cardiovascular imaging interpretation, automated electrocardiographic analysis, and clinical risk prediction. Across multiple cardiovascular settings, AI has been associated with improved diagnostic accuracy, enhanced workflow efficiency, and earlier detection of cardiovascular disease. Predictive models support risk stratification in heart failure and ischemic heart disease, while chatbots and digital health platforms may facilitate patient engagement, remote monitoring, and continuity of care. Despite these advances, important challenges remain, including algorithmic bias, limited transparency, insufficient external validation, data heterogeneity, and barriers to routine clinical implementation. Emerging explainable AI approaches may improve model interpretability, clinician confidence, and the safe adoption of AI-driven decision support systems. Conclusions: Artificial intelligence is rapidly evolving from a research-oriented technology into a clinically relevant component of cardiovascular care. Current evidence indicates that AI can enhance diagnostic performance, improve risk prediction, streamline clinical workflows, and facilitate more personalized management across multiple cardiovascular domains. However, the successful translation of AI into routine practice will depend on robust external validation, transparent decision-making mechanisms, regulatory oversight, and clinician acceptance. The development of explainable and trustworthy AI frameworks represents a critical step toward the safe, ethical, and sustainable integration of AI into modern cardiology. Full article
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20 pages, 1953 KB  
Article
Improved African Vulture Optimization Algorithm for Trajectory Optimization in Autonomous Aircraft Terminal Area Energy Management Phase
by Shupeng Fang, Senlin Chen, Yiyun Zhao and Sijie Yao
Algorithms 2026, 19(7), 503; https://doi.org/10.3390/a19070503 (registering DOI) - 23 Jun 2026
Abstract
Trajectory optimization during the terminal area energy management (TAEM) phase is pivotal for achieving accurate runway alignment and enhancing landing safety in autonomous aircraft operations. In the presence of initial state uncertainties in TAEM phase, conventional pseudo-spectral methods still suffer from robustness limitations [...] Read more.
Trajectory optimization during the terminal area energy management (TAEM) phase is pivotal for achieving accurate runway alignment and enhancing landing safety in autonomous aircraft operations. In the presence of initial state uncertainties in TAEM phase, conventional pseudo-spectral methods still suffer from robustness limitations and exhibit a strong dependence on the quality of the initial guess. Therefore, this paper proposes the composite African vulture optimization algorithm (CAVOA), a meta-heuristic framework designed to automate trajectory optimization. An in-depth examination of the heading alignment cone (HAC) trajectory model enables effective heading adjustments prior to landing, augmented by a tailored dynamic pressure profile to ensure safe touchdown velocities. By incorporating dynamic opposition learning, intelligent boundary processing, and composite exploration, CAVOA enhances global search efficiency. These enhancements are substantiated through comparisons with benchmark function optimization, Wilcoxon rank sum tests, and convergence analysis. Numerical simulations validate that CAVOA reliably directs autonomous aircraft to predefined touchdown states, demonstrating superior performance in complex aerial environments. Full article
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46 pages, 1440 KB  
Article
A Bidirectional Gas Continuation Method for Steady-State Loadability Analysis in Gas Transmission Networks
by Victor J. Gutierrez-Martinez, Vicente Torres-Garcia, Hector J. Estrada-Garcia, Ivan A. Hernandez-Robles and Jonatan Pena Ramirez
Energies 2026, 19(13), 2959; https://doi.org/10.3390/en19132959 (registering DOI) - 23 Jun 2026
Abstract
This article proposes a gas-only continuation framework for steady-state loadability analysis in natural gas transmission networks based on a direction-free reformulation of the General Flow Equation (GFE). The proposed formulation introduces signed pipe flows directly as state variables, thereby representing bidirectionality intrinsically. As [...] Read more.
This article proposes a gas-only continuation framework for steady-state loadability analysis in natural gas transmission networks based on a direction-free reformulation of the General Flow Equation (GFE). The proposed formulation introduces signed pipe flows directly as state variables, thereby representing bidirectionality intrinsically. As a result, flow reversals are handled without switching logic, while the branch geometry and criticality mechanism of the underlying gas-network equilibrium map are preserved. On this basis, a Gas Continuation Method (GCM) is developed to trace equilibrium branches directly in native gas-load space under specified gas-load stress. The method distinguishes the last admissible operating point from the mathematical critical point and incorporates a formal diagnosis to determine whether the detected limiting condition is consistent with a Saddle-Node Bifurcation (SNB). The proposed framework is validated on a three-node benchmark, a realistic Belgian gas transmission network, and a 40-node test system. The results show accurate agreement with Newton–Raphson (NR) solutions in the regular operating regime, robust branch tracing near limiting conditions where standalone NR loses convergence, and consistent handling of signed pipe flows under load-induced flow reversal and under algebraic orientations assigned a priori opposite to the solved physical flow. The Belgian and 40-node cases further show that the operational admissibility limit may precede the mathematical critical point, so pressure-based feasibility and branch-level criticality emerge as related but distinct notions. These features make the proposed methodology a rigorous and practical tool for identifying admissibility limits, interpreting critical behavior, and assessing loadability margins in gas transmission networks. Full article
34 pages, 40975 KB  
Article
Comparative Study of Machine Learning Models for Instantaneous Wave-Height Estimation Using Three-Degree-of-Freedom Ship Motion Responses
by Yuyao Ni, Xiaopeng Gao, Qing Ye, Ruomo Xin and Yongpeng Ou
J. Mar. Sci. Eng. 2026, 14(13), 1158; https://doi.org/10.3390/jmse14131158 (registering DOI) - 23 Jun 2026
Abstract
To address the high deployment cost, insufficient local coverage, and limited timeliness of conventional wave-observation methods in onboard real-time applications, this study conducts a comparative investigation of centre-of-gravity-equivalent instantaneous wave-height estimation models based on three-degree-of-freedom ship motion responses under the framework of the [...] Read more.
To address the high deployment cost, insufficient local coverage, and limited timeliness of conventional wave-observation methods in onboard real-time applications, this study conducts a comparative investigation of centre-of-gravity-equivalent instantaneous wave-height estimation models based on three-degree-of-freedom ship motion responses under the framework of the wave buoy analogy (WBA). The heave, roll, and pitch responses of a 1:2 scaled Series 62 4667-1 planing craft model in regular head seas are used as inputs, while the synchronous instantaneous wave-height signal measured by a wave probe near the centre of gravity is used as the label. A unified protocol is established with consistent inputs, labels, window construction, data partitioning, and evaluation metrics. Six models, namely SVR, TCN, LSTM, CNN-LSTM, Transformer, and LSTM-MHA, are compared and validated using STAR-CCM+ numerical simulation data and towing-tank experimental data. The results indicate that, in the simulated case of H = 0.10 m and T = 1.5 s, LSTM-MHA achieves the highest estimation accuracy, with RMSE and R² values of 0.001231 and 0.997848, respectively, but it also has the largest model size and computational cost. In comparison, TCN achieves near-optimal accuracy with a smaller parameter count and lower inference latency, and shows stable performance across multiple conditions. The towing-tank experimental results further show that both LSTM-MHA and TCN clearly outperform the SVR baseline. Overall, accuracy in the simulation domain, robustness in the towing-tank experimental domain, and cross-domain generalisation capability are not fully consistent. Therefore, the selection of onboard instantaneous wave-height estimation models should jointly consider estimation error, model complexity, computational latency, window length, and practical deployment requirements. Full article
16 pages, 695 KB  
Article
Association Between Pediatric Obesity and Ocular Structural Parameters: A Cross-Sectional Study
by Alev Koçkar, Ahmet Oran, Ayşe Nurcan Cebeci and Elvan Alper Şengül
Children 2026, 13(7), 847; https://doi.org/10.3390/children13070847 (registering DOI) - 23 Jun 2026
Abstract
Background/Objectives: To explore potential associations between pediatric obesity and retinal and anterior segment ocular structures using OCT and ocular biometry. This study was designed as an exploratory, hypothesis-generating analysis without a pre-specified primary endpoint; all findings should be interpreted accordingly. Methods: This retrospective [...] Read more.
Background/Objectives: To explore potential associations between pediatric obesity and retinal and anterior segment ocular structures using OCT and ocular biometry. This study was designed as an exploratory, hypothesis-generating analysis without a pre-specified primary endpoint; all findings should be interpreted accordingly. Methods: This retrospective cross-sectional study included 52 children (104 eyes): 27 obese children (body mass index (BMI) percentile ≥95%) and 25 healthy controls (BMI percentile 5–85%). Optical coherence tomography (OCT) and ocular biometry were used to assess retinal nerve fiber layer (RNFL), ganglion cell complex (GCC), focal loss volume (FLV), global loss volume (GLV), Early Treatment Macular Map 5 (EMM5), corneal parameters, axial length (AL), anterior chamber depth (ACD), and white-to-white corneal diameter (WTOW). Group comparisons and cluster-robust bootstrap regression adjusted for inter-eye dependency, age, and sex; Bonferroni correction was applied. Results: Obese children showed nominally higher GCC average thickness, RNFL, and EMM5 values and shallower ACD; however, no parameter survived Bonferroni correction. ACD showed the most internally consistent exploratory pattern (unadjusted p = 0.006; adjusted p = 0.018; Bonferroni p = 0.249); however, this finding did not survive Bonferroni correction and should not be interpreted as a confirmed association. Other corneal and biometric parameters were not significantly different. Conclusions: Pediatric obesity may be associated with subtle ocular structural variations, but all findings are exploratory and hypothesis-generating. Larger prospective, pre-registered studies are needed to determine whether pediatric obesity is associated with structural ocular changes. Full article
(This article belongs to the Section Global Pediatric Health)
22 pages, 1833 KB  
Article
Kinematic Modeling of a Novel (31)-Degree-of-Freedom Planar Parallel Manipulator Using Screw Theory+
by Jaime Gallardo-Alvarado, Alvaro Sanchez-Rodriguez, Horacio Orozco-Mendoza, Ramon Rodriguez-Castro and Luis A. Alcaraz-Caracheo
Algorithms 2026, 19(7), 502; https://doi.org/10.3390/a19070502 (registering DOI) - 23 Jun 2026
Abstract
This work presents the kinematic analysis of a redundant planar parallel manipulator within the framework of screw theory. The main contribution of this work is the introduction and kinematic modeling of a novel redundant planar parallel manipulator topology composed exclusively of revolute joints. [...] Read more.
This work presents the kinematic analysis of a redundant planar parallel manipulator within the framework of screw theory. The main contribution of this work is the introduction and kinematic modeling of a novel redundant planar parallel manipulator topology composed exclusively of revolute joints. The proposed architecture is motivated by the search for structurally simple mechanisms with favorable analytical properties for screw-theoretic formulation and potential applications in robotic systems requiring compact and efficient planar motion. For completeness, the displacement analysis is included. Thanks to the simple topology of the otherwise complex mechanism, the inverse–forward displacement problem is resolved through straightforward quadratic equations. The velocity input–output relationship is derived without reliance on passive joint rate velocities, and the acceleration input–output equation is obtained independently of passive joint rate accelerations. These simplifications are achieved by exploiting reciprocal line properties. Numerical examples are provided to illustrate the robustness and effectiveness of the proposed kinematic analysis method across the main topics addressed in this contribution. Full article
53 pages, 21010 KB  
Article
Developed Model-Updating Technique for Structures Equipped with Various Supplemental Dampers
by Neda Godarzi and Farzad Hejazi
Mathematics 2026, 14(13), 2247; https://doi.org/10.3390/math14132247 (registering DOI) - 23 Jun 2026
Abstract
Recent advancements in structural engineering have driven the development of sophisticated damping mechanisms aimed at reducing the detrimental effects of structural vibrations. As a result, accurate numerical modeling and analytical evaluation have become essential for assessing structural stability and enhancing seismic resilience. This [...] Read more.
Recent advancements in structural engineering have driven the development of sophisticated damping mechanisms aimed at reducing the detrimental effects of structural vibrations. As a result, accurate numerical modeling and analytical evaluation have become essential for assessing structural stability and enhancing seismic resilience. This study introduces a model-updating framework to develop analytical constitutive models for structural damping systems. The proposed approach employs a genetic algorithm (GA) to calibrate model parameters by minimizing the discrepancy between analytical predictions and experimental responses. Experimental force–displacement hysteresis data and displacement time-history records are used at both the element and system levels for model calibration. The methodology is applied to a rubber isolator, a 10-story structure equipped with Pall friction dampers, and a 6-story structure with friction dampers to evaluate its performance under different dynamic characteristics and damping mechanisms. The results indicate that the proposed approach achieves very high accuracy, with prediction errors reduced to negligible levels for both force and displacement responses in all cases. Consistent performance is observed using both global and local displacement measures in friction-damped systems, indicating the robustness of the proposed method. Overall, the findings indicate that the GA-based model-updating framework provides an efficient and reliable tool for improving the predictive capability of analytical models of structures with nonlinear damping devices and is suitable for practical structural engineering applications. Full article
(This article belongs to the Special Issue Numerical Analysis and Algorithms in Structural Mechanics)
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22 pages, 447 KB  
Article
Parity Bifurcation, PIII(D6) Topology, and a Stieltjes Framework to Jensen Polynomial Hyperbolicity
by Michel Planat
Mathematics 2026, 14(13), 2240; https://doi.org/10.3390/math14132240 (registering DOI) - 23 Jun 2026
Abstract
We investigate the onset of hyperbolicity in Jensen polynomials Jd,n associated with the Riemann Ξ-function and identify a robust parity-driven bifurcation with a natural geometric interpretation. Numerical analysis for degrees 5d16 reveals two distinct regimes. [...] Read more.
We investigate the onset of hyperbolicity in Jensen polynomials Jd,n associated with the Riemann Ξ-function and identify a robust parity-driven bifurcation with a natural geometric interpretation. Numerical analysis for degrees 5d16 reveals two distinct regimes. For even d, the roots form a compact complex cluster whose imaginary extent decreases smoothly, and the transition to hyperbolicity is governed by a single complex-conjugate pair, consistent with a low-dimensional (tame) geometric structure. For odd d, a hierarchy of more intricate onset mechanisms emerges, including single-event transitions (d=11) and intermittent regimes (d13) with decoupled geometric invariants, suggestive of dynamics on decorated (wild) character varieties. We interpret this dichotomy through a connection with the PIII(D6) tau-function arising in the Painlevé confluence diagram. Defining τ(t)=Ξ(12+t)/Ξ(12), we construct a generating function B(w)=j0bjwj from the cumulants of logΞ(12+z) using high-precision Cauchy/DFT methods (280–400-digit arithmetic), without explicit use of the zero expansion. Two independent numerical diagnostics indicate that B exhibits Stieltjes-type behavior: (i) positivity of Hankel determinants up to order N=30 and (ii) Padé approximants whose poles converge to γk2 (squares of Riemann-zero ordinates) with stabilizing residues. These results provide strong evidence that the parity bifurcation observed in Jensen polynomial onset reflects a finite-dimensional manifestation of an underlying moment-based positivity structure. Motivated by this correspondence, we formulate a conjecture relating the Stieltjes nature of B(w) to the eventual hyperbolicity of Jensen polynomials. This conjecture suggests a bridge between finite-dimensional root geometry and an infinite-dimensional kernel-based positivity framework, while leaving open the problem of establishing such positivity independently of the zero expansion. Full article
(This article belongs to the Special Issue Special Functions, Representations and Applications)
36 pages, 3020 KB  
Article
An Enhanced Equilibrium Optimizer Based on Rural Tourism Inspiration Strategy for Global Optimization and Engineering Applications
by Zhiwang Xu, Hui Xie and Chengpeng Li
Systems 2026, 14(7), 728; https://doi.org/10.3390/systems14070728 (registering DOI) - 23 Jun 2026
Abstract
As the complexity, scale, and nonlinearity of modern engineering optimization problems continue to increase, traditional optimization algorithms face significant challenges in achieving high solution accuracy, fast convergence, and robust performance. To address these issues, this paper proposes a Rural Tourism Migration-based Improved Equilibrium [...] Read more.
As the complexity, scale, and nonlinearity of modern engineering optimization problems continue to increase, traditional optimization algorithms face significant challenges in achieving high solution accuracy, fast convergence, and robust performance. To address these issues, this paper proposes a Rural Tourism Migration-based Improved Equilibrium Optimizer (RTM-IEO), aiming to enhance the global search capability and adaptive balance between exploration and exploitation. Specifically, an adaptive lens imaging opposition-based learning strategy is introduced to effectively expand the search space and maintain population diversity. A dynamic elite-guided elimination mechanism is designed to strengthen exploitation capability and accelerate convergence by reconstructing inferior individuals using high-quality solutions. In addition, a multi-stage rural tourism migration strategy is developed to dynamically regulate the search behavior across different optimization phases, enabling a more flexible and efficient search process. The effectiveness of the proposed algorithm is comprehensively validated on the CEC2021 and CEC2022 benchmark suites, where RTM-IEO demonstrates superior performance in terms of convergence accuracy, convergence speed, and robustness compared with several representative state-of-the-art algorithms. The statistical superiority of the proposed method is further confirmed through Friedman mean ranking and Wilcoxon rank-sum tests. To further evaluate its practical applicability, RTM-IEO is applied to the sustainable economic dispatch problem of a microgrid integrating renewable energy sources, including wind power and photovoltaic generation, along with energy storage systems and controllable units. The optimization objective simultaneously considers economic cost minimization and sustainable operation requirements, such as improving renewable energy utilization and reducing dependence on fossil-fuel-based generation. Experimental results indicate that the proposed method achieves a significant reduction in daily operating cost (exceeding 52% compared with benchmark algorithms), while effectively promoting low-carbon energy utilization and enhancing overall system sustainability. Overall, the proposed RTM-IEO provides an efficient and reliable optimization framework for addressing complex global optimization problems, particularly in scenarios requiring a coordinated balance between economic performance and sustainable development. Full article
23 pages, 109510 KB  
Article
Efficiency-Aware Group Size Optimization for GRPO via Multi-Fidelity Bayesian Optimization
by Taehyeon Kim and Kyung-Taek Lee
AI 2026, 7(7), 234; https://doi.org/10.3390/ai7070234 (registering DOI) - 23 Jun 2026
Abstract
Group Relative Policy Optimization (GRPO) streamlines the alignment of Large Language Models (LLMs) and Vision–Language Models (VLMs) by eliminating the Critic model. However, its efficiency heavily depends on the group size, G. While a larger G improves reward estimation and stabilizes the [...] Read more.
Group Relative Policy Optimization (GRPO) streamlines the alignment of Large Language Models (LLMs) and Vision–Language Models (VLMs) by eliminating the Critic model. However, its efficiency heavily depends on the group size, G. While a larger G improves reward estimation and stabilizes the Advantage, Ai, it drastically increases VRAM usage and reduces throughput. Standard heuristics like a fixed G of 64 create significant bottlenecks in resource-constrained settings. This paper introduces an Efficiency-Aware optimization framework utilizing Multi-fidelity Bayesian Optimization and Hyperband (BOHB) to dynamically identify the optimal group size, G*. The method uses a multi-objective function that balances reward accuracy, Ai variance, and hardware utilization, applying z-score normalization. By employing Successive Halving to quickly evaluate candidates at low fidelity, the framework reduces search costs by up to 74% compared with random search. Tested across text-only LLMs (Qwen2.5-7B/1.5B) and multimodal VLMs (Qwen2.5-VL-3B), the framework demonstrates that the discovered G* saves up to 72.5% in VRAM compared with the baseline of 64, while maintaining reward accuracy within 5.8%. Sensitivity analyses on hyperparameters like λ, α, and β confirm the framework’s robustness. Rather than treating group size as a mere engineering heuristic, this study establishes a principled methodological advance by formalizing the trade-off between statistical estimation stability and hardware constraints into a unified optimization framework for resource-efficient RLHF. Full article
(This article belongs to the Section AI Systems: Theory and Applications)
17 pages, 5457 KB  
Article
A Hybrid Ensemble System for Time-Series Anomaly Detection in Automated Quality Control of Medical Equipment
by Ziheng Zhang, Defeng Cai, Zhuo Deng, Zhicheng Du, Fuxing Zhang and Lan Ma
Diagnostics 2026, 16(13), 1953; https://doi.org/10.3390/diagnostics16131953 (registering DOI) - 23 Jun 2026
Abstract
Background/Objectives: The accuracy and reliability of automated clinical analyzers are fundamental to patient safety and effective medical decision-making. Traditional quality control (QC) methods, which rely on periodic manual calibration and reactive maintenance, are inherently limited by high latency and labor costs; furthermore, they [...] Read more.
Background/Objectives: The accuracy and reliability of automated clinical analyzers are fundamental to patient safety and effective medical decision-making. Traditional quality control (QC) methods, which rely on periodic manual calibration and reactive maintenance, are inherently limited by high latency and labor costs; furthermore, they fail to provide continuous, real-time monitoring. This paper introduces a novel hybrid ensemble learning framework for the automated quality inspection of medical devices through the analysis of time-series reaction curves. Methods: Our system integrates three heterogeneous anomaly detection paradigms: an Enhanced Dynamic Time Warping (DTW) detector for robust non-linear pattern matching, a Shape Template Matching (STM) detector that mimics expert clinical logic by analyzing morphological features in a normalized shape space, and a specialized Time-series Variational Autoencoder (TimeVAE) for deep representation learning. The outputs of these detectors are fused using a weighted ensemble strategy, which is specifically designed to prioritize the minimization of false negatives—a critical requirement in medical diagnostics. Results: We evaluate our framework on a comprehensive, multi-center real-world dataset comprising seven distinct biochemical assays. Experimental results demonstrate that our proposed method achieves superior performance, attaining a 0% false negative rate on CRE and DBIL assays and outperforming all baseline methods on the other five datasets. An ablation study confirms the model’s robustness even with limited training data, and a comparative analysis against eight state-of-the-art baseline methods further validates the effectiveness of our domain-optimized ensemble approach. Conclusions: The system provides a robust, interpretable, and highly automated solution for transitioning from reactive maintenance to proactive, real-time quality assurance in clinical laboratories. Full article
(This article belongs to the Special Issue Artificial Intelligence for Health and Medicine—2nd Edition)
30 pages, 6708 KB  
Article
Dynamics and Experimental Validation of a UAV-Borne Flexible Net for Intercepting Low, Slow, and Small Targets
by Kunlin Han, Yiming Liu, Ziming Xiong, Jiafeng Hu, Hao Lu, Minqian Sun and Tongxin Zhang
Drones 2026, 10(7), 478; https://doi.org/10.3390/drones10070478 (registering DOI) - 23 Jun 2026
Abstract
The escalating security risks associated with unauthorized unmanned aerial vehicles (UAVs) in advancing smart cities necessitate the development of robust active countermeasures. This work presents a novel approach centered on a UAV-borne flexible net system and provides a rigorous investigation into its complex [...] Read more.
The escalating security risks associated with unauthorized unmanned aerial vehicles (UAVs) in advancing smart cities necessitate the development of robust active countermeasures. This work presents a novel approach centered on a UAV-borne flexible net system and provides a rigorous investigation into its complex nonlinear dynamics. This study establishes a lumped-mass, semi-spring–damper dynamic model of the flexible capture net, characterizing its key dynamic properties, including deployment performance, aerodynamic attitude, and the high-impact phenomena of collision and entanglement with the target UAV. To verify the reliability of the proposed method, numerical simulations are combined with field tests for systematic validation. Comparative analysis reveals excellent quantitative agreement, with over 80% conformity in the net’s spatial configuration between simulated and experimental results. This paper illuminates the fundamental principles governing energy dissipation and transient tension dynamics pre- and post-capture. This study provides preliminary evidence for the feasibility of the proposed method and identifies key directions for future investigation. The findings offer guidance for the design and optimization of future systems intended to neutralize low, slow, and small (LSS) aerial threats. Full article
75 pages, 13072 KB  
Article
Business Management Improvement Enterprise Development Optimization Algorithm for Numerical Optimization and Its Application
by Liyun Deng and Antong Li
Symmetry 2026, 18(7), 1069; https://doi.org/10.3390/sym18071069 (registering DOI) - 23 Jun 2026
Abstract
Complex optimization problems are widely encountered in engineering design, intelligent manufacturing, communication systems, and wireless sensor network deployment. However, the original Enterprise Development Optimization Algorithm (EDOA) still suffers from insufficient population diversity, weak search guidance, and limited adaptability in balancing exploration and exploitation [...] Read more.
Complex optimization problems are widely encountered in engineering design, intelligent manufacturing, communication systems, and wireless sensor network deployment. However, the original Enterprise Development Optimization Algorithm (EDOA) still suffers from insufficient population diversity, weak search guidance, and limited adaptability in balancing exploration and exploitation when solving high-dimensional and multimodal optimization problems. To address these issues, this paper proposes a Multi-Strategy Improved Enterprise Development Optimization Algorithm (MIEDOA). First, a Strategic Diversification Initialization (SDI) strategy is developed by integrating Sobol sequence sampling, random initialization, and Gaussian perturbation to improve the diversity and distribution quality of the initial population. Second, an Organizational Synergy Learning (OSL) mechanism is introduced to enhance search guidance through the collaborative utilization of elite information, population mean information, and peer interaction. Third, an Adaptive Governance with Feedback Regulation (AGFR) strategy is designed to dynamically regulate the exploration–exploitation behavior according to the current population fitness state. The proposed MIEDOA is evaluated on the CEC2017 and CEC2020 benchmark suites and compared with representative EDOA variants, CEC winner algorithms, and other advanced optimization methods. The experimental results indicate that MIEDOA generally achieves competitive performance in terms of solution quality, convergence behavior, and robustness across different benchmark scenarios. In addition, strategy effectiveness analysis, parameter sensitivity analysis, and statistical tests further provide evidence supporting the effectiveness of the proposed strategies. Finally, MIEDOA is applied to a three-dimensional wireless sensor network deployment problem. The results suggest that the proposed algorithm can obtain competitive deployment solutions and satisfactory coverage performance under different node scales, demonstrating its potential applicability to practical engineering optimization problems. Full article
(This article belongs to the Special Issue Symmetry in Optimization Algorithms and Applications)
25 pages, 2938 KB  
Article
GP-Driven Adaptive Tube MPC for Communication-Preserving Navigation of Mobile Relay Robots in Indoor Disaster Environments
by Dongju Kim, Sungjae Kim and Jin-Ho Suh
Sensors 2026, 26(13), 3981; https://doi.org/10.3390/s26133981 (registering DOI) - 23 Jun 2026
Abstract
Maintaining reliable communication while ensuring collision-free motion is a central challenge for mobile relay robots operating in indoor disaster environments, where abrupt non-line-of-sight (NLOS) degradation and narrow structural bottlenecks can severely disrupt multi-hop connectivity. To address this problem, this paper proposes a Gaussian [...] Read more.
Maintaining reliable communication while ensuring collision-free motion is a central challenge for mobile relay robots operating in indoor disaster environments, where abrupt non-line-of-sight (NLOS) degradation and narrow structural bottlenecks can severely disrupt multi-hop connectivity. To address this problem, this paper proposes a Gaussian Process-Driven Adaptive Tube Model Predictive Control (GP-ATMPC) framework for communication-preserving relay navigation. Gaussian process regression (GPR) is used to construct a probabilistic spatial radio map from sparse received signal strength indicator (RSSI) measurements, providing both the predicted channel mean and its uncertainty over unvisited regions. Motion uncertainty is represented by an adaptive ellipsoidal error tube whose radius varies with translational motion, angular motion, and localization uncertainty. Based on this tube model, both obstacle and communication constraints are tightened over the full closed-loop state tube via a tube-tightened lower confidence bound (LCB) that jointly accounts for radio-prediction and motion-tracking uncertainty. Across two indoor disaster environments and 50 Monte Carlo runs each, the proposed method attains the highest connectivity satisfaction rate among controllers that preserve a safe motion margin, with significantly fewer end-to-end connectivity violations than nominal and heuristic adaptive-margin MPC by a paired Wilcoxon test, while maintaining millisecond-level online solve times. A reactive connectivity-first baseline reaches slightly higher raw connectivity but at three to four times the near-collision rate and without feasibility or stability guarantees. The radio-prediction layer is further validated in a higher-fidelity Gazebo environment and on real indoor RSSI measurements, where it reconstructs the measured channel with a mean absolute error of about 2.1 dB. These results indicate that coupling spatial radio prediction with adaptive tube-based robust control provides an effective framework for resilient communication-aware relay navigation in degraded indoor environments. Full article
(This article belongs to the Section Sensors and Robotics)
21 pages, 13902 KB  
Article
A Hybrid Method of Binary Grey Wolf Optimization and Equilibrium Optimization for Feature Selection in Diagnosing Bearing Faults
by Chun-Yao Lee, Kuan-Yu Huang, Truong-An Le, Guang-Lin Zhuo, Mu-Ze Li and Chung-Hao Huang
Mathematics 2026, 14(13), 2244; https://doi.org/10.3390/math14132244 (registering DOI) - 23 Jun 2026
Abstract
Diagnosing bearing faults remains a crucial challenge, particularly in effectively extracting fault information and achieving high diagnostic accuracy. To address this issue, this study presents a model for diagnosing bearing faults, which comprises three primary stages: feature extraction, feature selection, and classification. In [...] Read more.
Diagnosing bearing faults remains a crucial challenge, particularly in effectively extracting fault information and achieving high diagnostic accuracy. To address this issue, this study presents a model for diagnosing bearing faults, which comprises three primary stages: feature extraction, feature selection, and classification. In the feature extraction stage, features are extracted from raw motor signals using empirical mode decomposition (EMD) and fast Fourier transform (FFT). In the feature selection stage, an effective method based on binary grey wolf optimization (BGWO) and the equilibrium optimizer (EO) is developed to remove redundant and irrelevant features. Finally, k-nearest neighbours (KNNs) and support vector machine (SVM) classifiers are used to identify bearing fault conditions. The proposed model is evaluated using four datasets: the University of California, Irvine (UCI) benchmark datasets, a motor bearing fault current-signal dataset, the Case Western Reserve University (CWRU) benchmark dataset, and the Machinery Failure Prevention Technology (MFPT) benchmark dataset. The experimental results show that the proposed method improves bearing fault diagnosis accuracy and demonstrates strong robustness compared with conventional methods. Full article
(This article belongs to the Special Issue Mathematical Models for Fault Detection and Diagnosis)
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