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35 pages, 1866 KB  
Article
A Graph Convolutional Network Framework Integrating Nuclear Norm Minimization and Conditional Random Fields for Microbe–Disease Association Prediction
by Zhen Zhang, Xianjun Hu, Jiacheng Lai and Lei Wang
Algorithms 2026, 19(9), 763; https://doi.org/10.3390/a19090763 (registering DOI) - 5 Sep 2026
Abstract
Microbiota dysbiosis is closely associated with a wide range of human diseases, yet wet-lab validation remains costly and time-consuming. Therefore, this study aims to develop an efficient framework for predicting potential microbe–disease associations. We propose a novel predictive model, NNGCFCAE, which integrates Nuclear [...] Read more.
Microbiota dysbiosis is closely associated with a wide range of human diseases, yet wet-lab validation remains costly and time-consuming. Therefore, this study aims to develop an efficient framework for predicting potential microbe–disease associations. We propose a novel predictive model, NNGCFCAE, which integrates Nuclear Norm Minimization (NNM), an enhanced Graph Convolutional Network (GCF) with an energy-based Conditional Random Field (CRF) smoothing mechanism, and a multi-channel convolutional autoencoder (CAE) with residual connections to effectively infer latent microbe–disease associations. First, we construct a heterogeneous network by integrating known microbe–disease associations with Gaussian Interaction Profile (GIP) kernels and Hamming Interaction Profile (HIP) features. Subsequently, nuclear norm minimization is applied to complete the initial association matrix, yielding a preliminary prediction score matrix. The GCF module then extracts spatial structural features of microbe and disease nodes from the network, while the CAE module further learns attribute-based representations of these nodes. Finally, the prediction score matrix, topological features, attribute features, and multi-source information are fused to form a joint representation matrix, which is used to compute the final association scores between microbes and diseases. Experiments conducted on datasets such as HMDAD and Disbiome demonstrate that NNGCFCAE significantly outperforms several state-of-the-art methods in terms of AUC and AUPR. Ablation studies and case analyses on obesity, asthma, and ulcerative colitis further demonstrate its biological plausibility, highlighting its potential for uncovering latent microbe–disease associations. Full article
35 pages, 3527 KB  
Article
A Data–Physics Dual-Driven Intelligent Diagnostic Method for Downhole Drilling Risks
by Kun Shao, Lizhi Xiao, Yue Liu, Huihui Wang, Zhengzhi Zhou, Zhanjun Jia and Qichen Sun
Processes 2026, 14(17), 2845; https://doi.org/10.3390/pr14172845 - 4 Sep 2026
Abstract
Safe drilling in hydrate-bearing sediments is essential for environmentally responsible natural gas hydrate development. Complex pressure variations, fluid migration, and mechanical disturbances during drilling may increase the risks of gas influx, lost circulation, pipe sticking, and wellbore instability. To improve diagnostic robustness under [...] Read more.
Safe drilling in hydrate-bearing sediments is essential for environmentally responsible natural gas hydrate development. Complex pressure variations, fluid migration, and mechanical disturbances during drilling may increase the risks of gas influx, lost circulation, pipe sticking, and wellbore instability. To improve diagnostic robustness under heterogeneous and noisy drilling conditions while reducing dependence on large-scale manually labeled datasets, this study develops an adaptively coupled data–physics dual-driven diagnostic framework based on a self-organizing map (SOM) and a competitive classifier. Unlike a conventional one-way SOM–classifier cascade, changes in the downstream classification loss are fed back to adjust the SOM neighborhood radius, thereby coupling unsupervised feature mapping with supervised risk classification. In addition, class-conditional pressure-window and torque–drag consistency penalties are linked to the predicted class probabilities so that physical information directly participates in the optimization of applicable fluid-related and pipe-sticking risk predictions. Risk categories without an explicitly available physical residual remain primarily data-driven. Experiments on a hybrid measured–simulated dataset show that the proposed model achieves a test-set accuracy of 97.67%, outperforming representative baseline models. When 20% Gaussian noise is added, the accuracy decreases by only 4.20 percentage points. A three-layer data acquisition–edge-computing–cloud-monitoring early-warning system is implemented through MATLAB/VC integration. In a pilot field trial, a representative well-kick risk was identified 12 min earlier than by a conventional threshold-based alarm, and the missed-alarm rate decreased from 15% to 3%. The proposed method provides an engineering-oriented framework for improving drilling safety and environmental risk control during natural gas hydrate development. Full article
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19 pages, 35698 KB  
Article
Robust Display-to-Camera Communication via Location Error-Tolerant Deep Data Embedding
by Dae-Gyu Lee, Pankaj Singh and Sung-Yoon Jung
Appl. Sci. 2026, 16(17), 8767; https://doi.org/10.3390/app16178767 - 3 Sep 2026
Abstract
This paper proposes a location error-tolerant data embedding technique for display-to-camera (D2C) communication systems. The method is designed to enable robust data transmission while maintaining high image fidelity, facilitating simultaneous digital content display and data communication. To address the common issue of alignment [...] Read more.
This paper proposes a location error-tolerant data embedding technique for display-to-camera (D2C) communication systems. The method is designed to enable robust data transmission while maintaining high image fidelity, facilitating simultaneous digital content display and data communication. To address the common issue of alignment and localization inaccuracies in D2C systems, the proposed approach defines specific regions of interest to ensure robustness against object detection model location errors. The architecture employs an expanding and contracting network structure for the encoder to achieve seamless data integration, while the decoder utilizes a computationally efficient “thin” structure for rapid data extraction. To improve performance in diverse environments, various distortion models were integrated into the system training. The system’s effectiveness was evaluated by measuring the bit error rate under conditions of Gaussian noise, blur, simulated localization errors, and real-world distortions. Image quality was validated using peak signal-to-noise ratio and the structural similarity index measure. The results indicate that the proposed technique maintains superior image quality and achieves reliable data recovery even in the presence of significant localization errors. These findings suggest that the approach provides a stable and effective solution for practical mobile-based D2C communication. Full article
(This article belongs to the Special Issue Display-Based Optical Wireless Communication for IoT and 6G)
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14 pages, 5586 KB  
Article
Flat-Topped Lattice and Its Properties in Oceanic Turbulence
by Rui Cong, Dajun Liu, Yan Yin, Yaochuan Wang and Haiyang Zhong
J. Mar. Sci. Eng. 2026, 14(17), 1636; https://doi.org/10.3390/jmse14171636 - 3 Sep 2026
Abstract
In this paper, based on a theory given by Gori, we have introduced a flat-topped lattice named a multi-cosine-multi-Gaussian correlated beam (McMGCB); the coherence function of the McMGCB consists of a multi-cosine component and a multi-Gaussian component, and the array composed of flat-topped [...] Read more.
In this paper, based on a theory given by Gori, we have introduced a flat-topped lattice named a multi-cosine-multi-Gaussian correlated beam (McMGCB); the coherence function of the McMGCB consists of a multi-cosine component and a multi-Gaussian component, and the array composed of flat-topped beamlets can be realized by this McMGCB. Based on the extended Huygens-Fresnel integral, the propagation equation of such McMGCB is derived. The McMGCB with smaller δ will split into a beam array faster. And the number of beamlets is determined by Nx and Ny. The flatness of the beamlets is controlled by F. Moreover, the beamlets of such a McMGCB in stronger oceanic turbulence can overlap and merge into one spot. The characterizations of this flat-topped lattice with its adjustable parameters provide a method to generate a rectangular flat-topped beam array, which may have applications that demand a flat-topped array. Full article
(This article belongs to the Special Issue Propagation of Structured Light Beams in Oceanic Turbulence)
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33 pages, 7218 KB  
Article
TSP-Net: A Structure-Aware and Geometry-Constrained Network for Cherry-Tomato Truss Detection and Picking-Point Localization in Greenhouse Harvesting
by Yu Zhuang, Jiayuan Zhu, Zhanpeng Luo, Yahui Tian, Meng Yin, Haoyi Wang and Yijia Wang
Horticulturae 2026, 12(9), 1099; https://doi.org/10.3390/horticulturae12091099 - 3 Sep 2026
Viewed by 112
Abstract
During cherry-tomato-bunch harvesting, clustered fruits, thin stems, and ambiguous fruit–stem junctions cause missed detections and errors in picking-point localization. To address these challenges, we propose TSP-Net, a structure-aware and geometry-constrained detection network built on YOLOv11n, together with an ROI heat-map regression module for [...] Read more.
During cherry-tomato-bunch harvesting, clustered fruits, thin stems, and ambiguous fruit–stem junctions cause missed detections and errors in picking-point localization. To address these challenges, we propose TSP-Net, a structure-aware and geometry-constrained detection network built on YOLOv11n, together with an ROI heat-map regression module for picking-point localization. TSP-Net integrates the Truss-aware Multi-scale Ghost Cross Stage Partial (TMG-CSP) module into the backbone to strengthen structural features of fruit edges, small stems, and clusters. It introduces the Truss-oriented Axial-Local Attention (TALA) module during feature fusion to capture fruit-arrangement direction and local occlusion boundaries. We also design Physics-informed Truss Consistency (PTC) Loss to regularize detections by enforcing consistency with fruit-cluster morphology through constraints on center distribution, inter-fruit spacing, and scale continuity. For picking-point localization, local ROIs are extracted from detection outputs, Gaussian heat maps are predicted, and continuous coordinates are decoded using soft-argmax. In the controlled evaluation, TSP-Net attains precision 81.81%, recall 73.21%, mAP@50 79.53%, and mAP@50:95 64.83%, which exceed the corresponding YOLOv11n results by 0.83, 0.32, 1.29, and 1.03 percentage points, respectively. The model size is reduced from 5.23 MB to 5.08 MB, the parameter count falls from 2.59 M to 2.49 M, and computational cost declines from 6.4 to 6.0 GFLOPs. On the common valid-ROI test set, the proposed heat-map localization yields a mean localization error of 47.2 px, a median error of 24.2 px, and PCK@20, PCK@50, and PCK@100 of 45.1%, 68.4%, and 85.5%, respectively. Under identical ROI conditions, this heat-map method reduces the mean localization error by 11.3 px and raises PCK@20 by 14.9 percentage points compared with direct coordinate regression. In summary, the proposed approach enhances cherry-tomato-bunch detection and 2D picking-point candidate localization while meeting lightweight constraints, offering a structure-aware visual perception solution for greenhouse cherry-tomato harvesting. Full article
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23 pages, 1206 KB  
Article
A Cross-Validated Reassessment of Regression and Machine-Learning Models for AISI 1045 End Milling
by Prakash Marimuthu, Jana Petru and Thenarasu Mohanavelu
Machines 2026, 14(9), 1001; https://doi.org/10.3390/machines14091001 - 2 Sep 2026
Viewed by 67
Abstract
Machining-induced residual stress, cutting force, and temperature govern the fatigue life, dimensional stability, and surface integrity of milled components, yet predictive models for these responses are still routinely validated only in-sample, concealing overfitting on small, single-laboratory datasets. This study re-examines a published AISI [...] Read more.
Machining-induced residual stress, cutting force, and temperature govern the fatigue life, dimensional stability, and surface integrity of milled components, yet predictive models for these responses are still routinely validated only in-sample, concealing overfitting on small, single-laboratory datasets. This study re-examines a published AISI 1045 end-milling dataset (N = 24, combining one-factor-at-a-time and Taguchi L9 trials) using six regression paradigms: Multiple Linear Regression (MLR), random forest, gradient boosting, Support Vector Regression (SVR), Gaussian process regression (GPR), and a shallow neural network (ANN)—under leave-one-out cross-validation (LOO-CV). The previously reported in-sample R2 of 0.84 (from a smaller n = 9 subset) was substantially higher than the LOO-CV R2 of 0.167 obtained here on the full dataset; although this gap cannot be attributed to cross-validation alone, it shows a substantial in-sample/out-of-sample performance gap. SVR gave the strongest, bootstrap- and nested-CV-confirmed cross-validated residual-stress prediction (R2 = 0.575); its apparent force advantage (R2 = 0.558) was statistically indistinguishable from GPR and did not survive nested tuning, so it is reported cautiously. GPR was narrowly best for temperature (R2 = 0.492); the ANN and SVR underperformed the linear baseline there, though nested tuning traced this largely to a fixed hyperparameter rather than the kernel method itself. Random forest permutation importance identified feed rate as the dominant residual-stress predictor, consistent with the original ANOVA. The contribution is a cross-validated, multi-paradigm reassessment with explicit uncertainty and sensitivity analysis, together with a candidate low-cost screening surrogate for AISI 1045 process planning—not a replacement for XRD or FE—and a broader caution to match model complexity to sample size. Full article
(This article belongs to the Topic Digital Manufacturing Technology)
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43 pages, 1956 KB  
Review
Data-Driven Development of Biomedical Hydrogels for Controlled Drug Delivery: Clinical Applications and Emerging Machine-Learning Approaches
by Elham Eskandarnia, Ayah Binrajab, Adnan Alsaei, Fatema Rahimi, Nasser Alahmed, Ahmad Zarwi and G. Roshan Deen
J. Funct. Biomater. 2026, 17(9), 444; https://doi.org/10.3390/jfb17090444 - 2 Sep 2026
Viewed by 106
Abstract
Hydrogels are hydrated three-dimensional polymeric networks with biomedical potential because they can encapsulate therapeutic agents and provide localised, sustained, or stimulus-responsive drug delivery. Their performance is determined by interacting variables, including polymer composition, synthesis route, crosslinking chemistry, drug loading, swelling, degradation, and the [...] Read more.
Hydrogels are hydrated three-dimensional polymeric networks with biomedical potential because they can encapsulate therapeutic agents and provide localised, sustained, or stimulus-responsive drug delivery. Their performance is determined by interacting variables, including polymer composition, synthesis route, crosslinking chemistry, drug loading, swelling, degradation, and the biological microenvironment. This multidimensional design space often makes hydrogel development slow and dependent on trial-and-error experimentation. This review examines the data-driven development of biomedical hydrogels for controlled drug delivery, focusing on clinical applications and emerging machine-learning approaches that support material selection, formulation design, synthesis optimisation, and release prediction. The review first discusses natural and synthetic hydrogels, including alginate, chitosan, gelatin-based systems, hyaluronic acid, and polyethylene glycol, with emphasis on how their physicochemical properties influence biocompatibility, synthesis flexibility, and drug-release behaviour. Key applications are then considered, including wound healing, cancer therapy, glucose-responsive insulin delivery, and inflammatory disease management. Particular attention is given to injectable and stimuli-responsive hydrogels, where formulation conditions and synthesis parameters can be tuned to improve localisation, therapeutic exposure, and release control. The review evaluates machine-learning methods, including random forest, gradient boosting, artificial neural networks, Gaussian process regression, and active learning, for predicting hydrogel properties, modelling release profiles, optimizing synthesis and formulation variables, and prioritizing experimental candidates. Finally, translational challenges are addressed, including small non-standardised datasets, limited external validation, weak in vitro-clinical correlations, material safety, explainability, reproducibility, scalability, and regulatory requirements. By integrating clinical, materials, synthesis, and machine-learning perspectives, this review highlights opportunities for developing safer and clinically relevant hydrogel-based drug-delivery systems. Full article
(This article belongs to the Special Issue Biomedical Applications of Hydrogels: Current Status and Advances)
31 pages, 446 KB  
Article
Managing Load Uncertainty in Distribution Network Capacitor Planning: A Master–Slave Stochastic Optimization Framework
by Oscar Danilo Montoya, Luis Fernando Grisales-Noreña and Juan Manuel Sánchez-Céspedes
Electricity 2026, 7(3), 97; https://doi.org/10.3390/electricity7030097 - 2 Sep 2026
Viewed by 156
Abstract
This paper presents a novel master–slave stochastic optimization framework for the optimal siting and sizing of fixed-step capacitor banks in medium-voltage distribution networks, explicitly addressing the inherent variability of load demand that is typically neglected in conventional deterministic approaches. The proposed methodology integrates [...] Read more.
This paper presents a novel master–slave stochastic optimization framework for the optimal siting and sizing of fixed-step capacitor banks in medium-voltage distribution networks, explicitly addressing the inherent variability of load demand that is typically neglected in conventional deterministic approaches. The proposed methodology integrates a scenario-based stochastic optimization model with a Chu and Beasley genetic algorithm (CBGA) as the master stage, which handles discrete placement decisions, and a successive-approximation power flow method (SAPF) as the slave stage, which evaluates the technical and economic performance of each candidate solution under multiple load scenarios. To capture demand uncertainties, 365 daily load realizations are generated using independent Gaussian noise with a relative standard deviation of 10% applied to each load point. These are subsequently reduced to ten representative scenarios via k-means clustering, reducing the number of power-flow evaluations per candidate solution from 365 to 10 (a 36.5-fold reduction); the reduced scenarios exhibit a low mean absolute error (MAE: <2%) with respect to the original mean, indicating faithful representation of the average load behavior, while the silhouette score is modest (approximately 0.25), consistent with the unimodal nature of the generated data and implying that the clusters are not well separated. Extensive simulations on a 33-bus test feeder considering three energy-cost-escalation scenarios (0%, 10%, and 20%) over a 20-year planning horizon demonstrate that both the deterministic and stochastic approaches reduce the total net present cost by 16.52% to 17.34% compared to the uncompensated network; the stochastic approach consistently delivers solutions that are either superior or comparable to deterministic planning (yielding up to approximately 0.16% additional cost reduction) while offering enhanced robustness against load variability. The stochastic framework offers distinct advantages, including robust solutions across a wide range of operating conditions, an inherent ability to adjust investment levels in response to probabilistic load distributions, and the ability to quantify uncertainty in decision making, with the most significant benefits observed when energy costs are low and load variability is high. The convergence of both approaches at a 20% escalation level further validates the reliability of high-resolution deterministic modeling when economic factors strongly dominate the optimization objective. This study underscores the importance of probabilistic modeling for modern distribution network planning, providing a practical and computationally efficient decision-support tool for utility planners to enhance grid resilience and operational efficiency in the context of increasing demand variability and renewable energy integration. Full article
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38 pages, 35452 KB  
Article
A Lightweight Oriented Insulator Detection Method Based on Dual-Frequency Phase-Shift Angle Encoding and Gaussian Geometric Supervision
by Tianhao Gao, Ke Zhang, Xu Bai, Xiaotong Li, Xinguo Yan, Nan Wang and Shijie Wang
Mathematics 2026, 14(17), 3133; https://doi.org/10.3390/math14173133 - 31 Aug 2026
Viewed by 94
Abstract
In unmanned aerial vehicle inspection of transmission lines, insulators often exhibit arbitrary orientations and elongated shapes and are frequently embedded in complex backgrounds. Horizontal bounding boxes tend to include substantial redundant regions. Meanwhile, existing oriented object detection methods still suffer from angular discontinuities [...] Read more.
In unmanned aerial vehicle inspection of transmission lines, insulators often exhibit arbitrary orientations and elongated shapes and are frequently embedded in complex backgrounds. Horizontal bounding boxes tend to include substantial redundant regions. Meanwhile, existing oriented object detection methods still suffer from angular discontinuities at periodic boundaries, insufficient geometric supervision for rotated bounding boxes, and difficulties in lightweight deployment. To address these issues, this paper proposes a lightweight oriented object detection model, termed R-YOLOv8-PSGH, which integrates dual-frequency phase-shift encoding and Gaussian geometric supervision. Based on a lightweight R-YOLOv8 architecture, a rotated detection head is developed to decouple the predictions of object categories, bounding-box locations, and orientation angles. To improve the periodic continuity of angle representations and strengthen the geometric constraints on rotated bounding boxes, a dual-frequency phase-shift angle encoding strategy and a Gaussian geometric localization loss are designed. Specifically, the complementary relationship between periodic signals with periods of 180°and 90° is exploited to map orientation angles into continuous phase responses, thereby improving the stability of orientation prediction. Moreover, the spatial structure of each rotated bounding box is modeled as a two-dimensional Gaussian distribution, and overlap consistency, center distance, and shape discrepancy are jointly optimized. In this manner, the orientation representation and bounding-box-level geometric supervision are collaboratively enhanced. Experimental results demonstrate that the proposed method improves the detection accuracy and localization stability of rotated objects while maintaining favorable lightweight deployment capability, providing a new solution for lightweight object detection in complex scenarios. Full article
(This article belongs to the Special Issue Mathematical Modelling in Structural Dynamics)
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15 pages, 3139 KB  
Article
Freeform Mirror Design Based on Zonal Energy Mapping
by Fei Wang, Xin Zhang, Yunhai Tang, Yue He and Baohua Chen
Materials 2026, 19(17), 3682; https://doi.org/10.3390/ma19173682 - 30 Aug 2026
Viewed by 159
Abstract
In laser phase-transformation hardening and laser cladding processes, the inherent thermodynamic limitations of conventional intensity distributions severely restrict the uniformity of metallurgical reaction. Although programmable beam shaping devices offer flexibility in profile reconstruction, their transmissive structure results in a low laser-induced damage threshold [...] Read more.
In laser phase-transformation hardening and laser cladding processes, the inherent thermodynamic limitations of conventional intensity distributions severely restrict the uniformity of metallurgical reaction. Although programmable beam shaping devices offer flexibility in profile reconstruction, their transmissive structure results in a low laser-induced damage threshold (LIDT), making them unsuitable for long-term stable operation at kilowatt-level power. This study proposes a reflective freeform mirror design method based on the principle of zonal energy mapping. The method constructs energy mapping relations that correlate the irradiance distribution in every sub-region of the incident Gaussian beam with the desired M-shaped irradiance profile. Relying on such mappings, the local surface generatrices of all sub-regions are solved separately; these generatrices are subsequently assembled to yield an integrated mirror surface. Optical performance was verified through Zemax non-sequential ray tracing simulations. The mirror was precisely machined using single-point diamond turning (SPDT). The experimental results show that the measured intensity distribution on the observation screen exhibits a typical M-shaped profile, with a peak-to-valley ratio of 1.28, which is in good agreement with the design target. This method provides a technically feasible and engineering-robust solution for complex thermal flux control requirements in high-power laser material processing. Full article
(This article belongs to the Special Issue Functional Laser Materials)
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22 pages, 578 KB  
Article
A Joint Model for Longitudinal Data with Terminal Event: Integrating Time-Varying Coefficients, Residual Life Effects, and Censored Data
by Simeng Li and Dianliang Deng
Axioms 2026, 15(9), 647; https://doi.org/10.3390/axioms15090647 - 29 Aug 2026
Viewed by 130
Abstract
In longitudinal studies, a terminal event such as death typically halts data collection, and patients may exhibit marked changes as they approach the event. Existing methods face three related challenges: interpreting the effect of residual life on the longitudinal response, accommodating time-varying covariates [...] Read more.
In longitudinal studies, a terminal event such as death typically halts data collection, and patients may exhibit marked changes as they approach the event. Existing methods face three related challenges: interpreting the effect of residual life on the longitudinal response, accommodating time-varying covariates and coefficients, and retaining information from censored individuals. We propose a joint model that addresses these challenges in a unified likelihood framework. The longitudinal submodel includes an explicit residual-life effect g(Tit,ξ), time-varying covariates Xi(t) with time-varying coefficients β(t), and shared random effects. Exponential-decay and Gaussian-kernel specifications are considered for g(·). The survival submodel depends on the latent state mi(t)=Xi(t)β(t)+Zi(t)bi. The coefficient functions are approximated by B-splines, and the full observed-data likelihood is maximized numerically with random-effects integrals evaluated by Gauss–Hermite quadrature. Under the stated regularity conditions, we establish consistency, root-n asymptotic normality of the finite-dimensional parameters, and the sieve convergence rate of the time-varying coefficient functions. Simulation studies demonstrate accurate recovery of the coefficient and residual-life functions. In the MADIT application, the fitted hazard ratio for ICD implantation is 0.433, and the residual-life effect indicates an increase in medical costs approximately three weeks before death. Full article
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24 pages, 5494 KB  
Article
Passive Microwave Angular Sensor Based on Local Perturbation of a Split-Ring Resonator
by Yingzhou Chen, Zihe Cheng, Minyang Wu, Jingyuan Huang, Xingyu Liu, Peiying Lin and Jiangtao Huangfu
Electronics 2026, 15(17), 3897; https://doi.org/10.3390/electronics15173897 - 29 Aug 2026
Viewed by 186
Abstract
This work presents a microwave attitude sensing method and device based on localized perturbation of a split-ring resonator (SRR). The sensor comprises a planar SRR, parallel microstrip feed lines and a metallic disk that can move along a circular trajectory. When the sensor’s [...] Read more.
This work presents a microwave attitude sensing method and device based on localized perturbation of a split-ring resonator (SRR). The sensor comprises a planar SRR, parallel microstrip feed lines and a metallic disk that can move along a circular trajectory. When the sensor’s orientation is modified in a plane perpendicular to the ground, the metallic disk moves within the constrained structure under the influence of gravity and changes its position relative to the SRR, modulating the local near field and the microstrip coupling state. Consequently, variations in angle are observed across multiple S-parameter channels. The mechanism is validated through simulation and experimental measurements. The measured S-parameters are used to construct a circular residual mixture-of-experts Gaussian process regression (MoE-GPR) model, which is developed for 360° angle reconstruction. In leave-one-angle-out (LOAO) validation on data sampled at 2.5° intervals, the proposed reconstruction method achieves a mean absolute error (MAE) of 0.700°. When trained on data sampled at 10° intervals and tested on a dataset sampled at 2.5° intervals, the proposed method achieves an MAE of 1.125°, demonstrating its generalization across different angular sampling conditions. As no active electronics are required at the moving sensing element, the proposed configuration has potential for integration with RF sensing and communication platforms, as well as for inclination sensing referenced to gravity, orientation detection and structural health monitoring. Full article
(This article belongs to the Special Issue Trends and Prospects in Microwave Sensors)
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38 pages, 5009 KB  
Article
A Similarity-Enhanced Transformer-LSTM Framework with IPOA for Short-Term Photovoltaic Power Forecasting
by Xiaoxiao Wei, Tao Wang, Xu Wang, Ye Xu and Wei Li
Atmosphere 2026, 17(9), 842; https://doi.org/10.3390/atmos17090842 - 28 Aug 2026
Viewed by 176
Abstract
Accurate prediction of PV output is critical for optimizing its absorption potential and ensuring the safe, stable, and cost-effective operation of the power grid. Yet, due to the intermittent and stochastic nature of photovoltaic power generation, establishing a highly precise prediction model presents [...] Read more.
Accurate prediction of PV output is critical for optimizing its absorption potential and ensuring the safe, stable, and cost-effective operation of the power grid. Yet, due to the intermittent and stochastic nature of photovoltaic power generation, establishing a highly precise prediction model presents significant difficulties. In this study, a hybrid forecasting framework integrating WCSD, CEEMDAN-FE, IPOA, and Transformer-LSTM is developed to improve PV power forecasting accuracy. Firstly, a new training data sample generation method based on WCSD is developed for determining the historical days having similar meteorological conditions to the predicted day. Secondly, CEEMDAN is employed to decompose original output sequence into an ensemble of components with different amplitudes and frequencies, where they were recombined as new set including a handful of components with low-frequency variation characteristics based on FE index. Thirdly, the IPOA is proposed for the first time, which couples Gaussian mutation and enhanced circle chaotic mapping. Next, the prediction model for each component is formulated by aid of Transformer-LSTM algorithm, the optimal hyperparameter combination of which is determined by IPOA method. Finally, the predicted results are obtained as the sum of individual component predictions. The prediction performance of the designed model is tested and verified via experimental analysis located in Yunnan Province, China and the publicly available Australian DKASC dataset. The empirical findings demonstrate that, in contrast to alternative benchmark models, our developed hybrid prediction model consistently attains superior prediction accuracy. Full article
(This article belongs to the Special Issue Carbon Neutrality, Renewable Energy and Climate Change Impacts)
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30 pages, 11082 KB  
Article
Three-Dimensional Gravity Forward Modeling of Prismatic Models Using Gauss–Kronrod Numerical Integration
by Jieyu Su and Chunming Liu
Mathematics 2026, 14(17), 3101; https://doi.org/10.3390/math14173101 - 28 Aug 2026
Viewed by 123
Abstract
Three-dimensional gravity-anomaly forward modeling is a critical component in geophysical exploration for delineating subsurface geological structures and mineral resources. Conventional numerical-integration methods, however, often suffer from insufficient accuracy and low computational efficiency, particularly when dealing with complex density distributions and irregular geometries. To [...] Read more.
Three-dimensional gravity-anomaly forward modeling is a critical component in geophysical exploration for delineating subsurface geological structures and mineral resources. Conventional numerical-integration methods, however, often suffer from insufficient accuracy and low computational efficiency, particularly when dealing with complex density distributions and irregular geometries. To overcome these limitations, we introduce the Gauss–Kronrod numerical integration scheme, which combines high-order Gaussian quadrature with embedded error estimation. We derive the integral formulations for gravitational potential, gravity field, and gravity gradients under both constant-density and variable-density assumptions. A numerical algorithm is developed by applying the Gauss–Kronrod rule in three dimensions. Extensive synthetic model tests are conducted to evaluate the performance of the proposed method. The results show that our approach achieves substantial improvements in accuracy, with errors converging to the order of 10−12 for constant-density models, and significantly reduces computation time compared with the MATLAB R2024a built-in function integral3. The method effectively handles variable-density models and provides stable solutions for complex geological scenarios. This work offers a practical and efficient tool for high-precision gravity forward modeling, with potential applications in mineral exploration and geodynamic studies. Full article
(This article belongs to the Special Issue High-Performance Numerical Methods for Geophysical Field Modeling)
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46 pages, 53861 KB  
Article
Multi-Model Coupled Flood Risk Evaluation of Huaihe Anhui Reach for Sustainable Disaster Risk Reduction
by He Li, Chaojie Zheng, Yao Zhang, Lan Yang, Mi Wu, Hui Zhang, Benle Liu, Dandan Song, Yanfang Wang and Xin Li
Sustainability 2026, 18(17), 8830; https://doi.org/10.3390/su18178830 - 28 Aug 2026
Viewed by 154
Abstract
The Anhui reach of the Huaihe River Basin features low-lying terrain, dense river networks, and high flood risk spatial heterogeneity, restricting regional socio-ecological sustainability. Traditional flood risk assessments suffer from incomplete indicators, subjective grading, and one-sided outputs when adopting single empirical or unsupervised [...] Read more.
The Anhui reach of the Huaihe River Basin features low-lying terrain, dense river networks, and high flood risk spatial heterogeneity, restricting regional socio-ecological sustainability. Traditional flood risk assessments suffer from incomplete indicators, subjective grading, and one-sided outputs when adopting single empirical or unsupervised clustering models. Based on disaster system theory, this study constructed a 14-indicator evaluation system covering hazard susceptibility, environmental sensitivity, and hazard-bearing vulnerability. Subjective-objective weights from Analytic Hierarchy Process (AHP) and entropy weight were fused via game theory equilibrium to build the Game Theory-AHP-Entropy Weight Coupled FCE Model (GAE-FCE Model) for comprehensive flood risk quantification. Meanwhile, principal component analysis (PCA) was utilized for indicator dimensionality reduction, and two unsupervised clustering models, namely, K-Means and Gaussian Mixture Model (GMM), were developed. Confusion matrix, Adjusted Rand Index, and correlation analysis were used to compare four model outputs. Individual models display weak correlation due to distinct risk characterization mechanisms; the ensemble scheme compensates single-model defects, achieving AUC = 0.9161, Recall = 0.9231, and F1 = 0.8889 under optimal weights, and a multi-model coupling framework was further proposed to obtain integrated flood risk zoning. Results show that five dominant factors (Distance to rivers, Topographic Roughness, NDVI, Distance to lakes, and Population Density) contribute over 59.6% of total weight. GAE-FCE reflects inundation characteristics yet lacks natural-factor comprehensiveness; clustering methods capture natural background differentiation but ignore socio-economic vulnerability, whereas ensemble coupling offsets individual model defects. High-risk zones are concentrated along major rivers, and low-risk areas mainly distribute in southern mountainous regions. This multi-model framework provides scientific support for flood prevention and territorial spatial optimization, advancing sustainable disaster risk reduction for the Huaihe River Basin and similar plain basins. Full article
(This article belongs to the Section Environmental Sustainability and Applications)
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