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34 pages, 8018 KB  
Article
A Two-Stage GMFAMM Approximation for Joint Bias Correction of NASA POWER Hydroclimatic Data: The ColClim Web Application
by David Arango-Londoño, Delia Ortega-Lenis, Mauricio A. Mazo-Lopera and Paula Moraga
Sensors 2026, 26(13), 4301; https://doi.org/10.3390/s26134301 - 7 Jul 2026
Viewed by 126
Abstract
We propose and empirically evaluate a two-stage approximation to a Generalized Multivariate Functional Additive Mixed Model (GMFAMM) for the joint bias correction of five NASA POWER reanalysis variables: minimum and maximum temperature (Tmin, Tmax), relative humidity (RH), solar [...] Read more.
We propose and empirically evaluate a two-stage approximation to a Generalized Multivariate Functional Additive Mixed Model (GMFAMM) for the joint bias correction of five NASA POWER reanalysis variables: minimum and maximum temperature (Tmin, Tmax), relative humidity (RH), solar radiation (Rad), and precipitation occurrence (Pbin). Our primary contribution is the first operational-scale evaluation of such a framework (≈200,000 station–day observations, two orders of magnitude beyond previous studies) together with its deployment in an open-access web application. A systematic grid of more than 200 marginal configurations is evaluated on a strict chronological 70/30 hold-out (training 2016–2022; testing 2023–2025) to identify the optimal marginal specification per variable. Against a correctly specified marginal baseline, station-level linear calibration combined with the marginal GAMM removes the bulk of the systematic bias (RMSE reductions of ≈80%, 82% and 30% for Tmin, Tmax and RH). A shared latent step, using the first principal component of the marginal residual matrix as a scalar proxy for Λ0(t), yields additional but conditional out-of-sample reductions (≈17% Tmax, 10% RH, 9% Rad; negligible for Tmin, with precipitation occurrence retained in the shared representation but its joint gain treated as exploratory); because it requires co-located donor observations, at ungauged locations the deployed pipeline applies the marginal correction only, whose spatial transfer is confirmed by leave-one-station-out cross-validation. The residual cross-correlation structure is consistent with, though not in itself proof of, Clausius–Clapeyron coupling. The trained artefacts are deployed in ColClim, an open-access R Shiny application that queries the NASA POWER API and the Open-Meteo forecast service for any location in Colombia and delivers historical bias-corrected series and short-range (1–16 day) forecasts. Full article
(This article belongs to the Section Remote Sensors)
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27 pages, 12625 KB  
Article
Spectral Multi-Representation Fusion for Audio Deepfake Detection
by Dora Ballesteros, Daniel Suarez and Cesar Pachon
Algorithms 2026, 19(7), 549; https://doi.org/10.3390/a19070549 - 5 Jul 2026
Viewed by 110
Abstract
Audio deepfake detection systems often achieve excellent internal validation performance but fail to generalize under real-world inference conditions involving synthetic speech generated with previously unseen AI tools. To address this limitation, this work proposes the Spectral Multi-Representation Fusion (SMRF) framework, which integrates multiple [...] Read more.
Audio deepfake detection systems often achieve excellent internal validation performance but fail to generalize under real-world inference conditions involving synthetic speech generated with previously unseen AI tools. To address this limitation, this work proposes the Spectral Multi-Representation Fusion (SMRF) framework, which integrates multiple spectral representations and decision-level fusion strategies to improve robustness under cross-domain conditions. Additionally, a Stability-Aware Multi-Metric Selection (SAMMS) strategy is introduced to select architectures by jointly considering predictive performance and cross-representation stability. The proposed framework was evaluated using four spectral representations (log-magnitude spectrogram (LOG), Mel spectrogram (MEL), Discrete Wavelet Transform (DWT), and Constant-Q Transform (CQT)) combined with multiple convolutional architectures and complementary voting strategies. The experiments revealed that isolated models exhibiting validation metrics above 95% may still produce very poor synthetic-audio detection rates during external inference (even lower than 10%). In contrast, fusion-based strategies substantially improved robustness by exploiting complementary synthetic evidence across spectral domains. The results also demonstrated that both the voting strategy and the SAMMS stability parameter λ strongly affect the final behavior of the system. In particular, hybrid fusion using One-Hard Voting with two architectures selected using λ0.25 achieved the best balance between synthetic-audio detection and real-audio preservation, outperforming individual models under cross-domain inference conditions, with detection rates close to 75% for both synthetic and real audio. These findings suggest that stability-aware fusion strategies constitute a promising direction for improving robustness in realistic audio deepfake detection scenarios. Full article
(This article belongs to the Special Issue Machine Learning Algorithms for Signal Processing)
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21 pages, 4639 KB  
Article
A Refined 2D Lagrangian-Based Model for Joint Torque Estimation in Lower-Limb Exoskeleton Applications
by Chanoknan Boonlupyanan, Thitima Jintanawan and Gridsada Phanomchoeng
Mathematics 2026, 14(13), 2400; https://doi.org/10.3390/math14132400 - 4 Jul 2026
Viewed by 172
Abstract
Exoskeletons are widely utilized across various domains, including biomedical and rehabilitative engineering. In clinical applications, precise joint torque evaluation is critical to ensuring exoskeleton efficiency, especially when assisting patients with impaired mobility. This work presents a straightforward inverse-dynamics framework to compute human joint [...] Read more.
Exoskeletons are widely utilized across various domains, including biomedical and rehabilitative engineering. In clinical applications, precise joint torque evaluation is critical to ensuring exoskeleton efficiency, especially when assisting patients with impaired mobility. This work presents a straightforward inverse-dynamics framework to compute human joint torques using motion capture and force plate data. Estimating these torques is a key requirement for exoskeleton systems to deliver appropriate and individualized assistive support. A key innovation of the proposed model is the explicit integration of a three-link chain—comprising the thigh, shank, and foot—treated as a cohesive multi-segment limb. By formally incorporating the foot segment, the model enables a more rigorous representation of ground reaction forces (GRF) and the dynamic migration of the center of pressure (COP). The proposed framework was validated against OpenSim 4.0 using benchmark datasets involving walking, squatting, and drop-jump maneuvers. The results demonstrated strong agreement with OpenSim, yielding normalized root mean square errors of approximately 10% across major lower-limb joints during walking. In contrast, the squatting posture provided a significant magnitude offset, despite maintaining close temporal phase alignment. Beyond torque estimation, the results provide insight into the sensitive interplay among COP trajectories, foot geometry, and GRF orientation. The proposed framework offers a computationally efficient tool for biomechanical analysis and provides a practical foundation for future lower-limb exoskeleton and assistive robotic applications. Full article
(This article belongs to the Special Issue Applications of Mathematical Methods in Robotic Systems)
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21 pages, 387 KB  
Article
A Mathematical Theory of Phase-Consistent Information Bottleneck for Cross-Domain Generalization
by Feng Liu and Zheng Wang
Entropy 2026, 28(7), 764; https://doi.org/10.3390/e28070764 - 3 Jul 2026
Viewed by 138
Abstract
We propose a mathematical framework for domain generalization in medical image segmentation built on dual-tree complex wavelet transform (DTCWT) and variational information theory. The core premise is that, under adequate spatial normalization and acquisition-style shifts, DTCWT phase components are more closely associated with [...] Read more.
We propose a mathematical framework for domain generalization in medical image segmentation built on dual-tree complex wavelet transform (DTCWT) and variational information theory. The core premise is that, under adequate spatial normalization and acquisition-style shifts, DTCWT phase components are more closely associated with anatomical structure, whereas amplitude components are more sensitive to domain-specific intensity and style variations. We formulate this as a local phase–magnitude complementarity premise and construct an information bottleneck that operates on structured subband representations. The framework provides several key theoretical results under explicit structural assumptions: an information bound showing when DTCWT amplitude subbands better isolate domain-related information than global Fourier representations; a variational information bottleneck encoder that compresses domain-specific amplitude information into low-dimensional latent codes; a triple constraint mechanism (domain supervision, KL compression, and orthogonality) that controls domain–task information leakage; and a predictive feature modulation scheme with O(1) spatial complexity. We further analyze test-time adaptation via calibrated uncertainty, deriving a sufficient condition under which a two-pass inference strategy reduces the expected generalization gap. Finally, we include illustrative public-dataset checks on FeTS 2022 and BraTS 2023 to test the central phase–amplitude premise and the feasibility of DTCWT-front-end segmentation. All theorems are stated with their assumptions and verifiable conditions, offering a physically motivated approach to domain generalization in medical imaging. Full article
22 pages, 23544 KB  
Article
DualCDM: Dual-Domain Conditional Diffusion for SAR-to-Optical Translation with Spatial–Frequency Correlation and Adaptive Feature Recalibration
by Yaobin Ma, Hossein Aghababaei, Ling Chang and Jingbo Wei
Sensors 2026, 26(13), 4183; https://doi.org/10.3390/s26134183 - 2 Jul 2026
Viewed by 233
Abstract
Translating Synthetic aperture radar (SAR) images into optical images is intrinsically ill-posed because microwave backscatter and optical reflectance describe different physical properties of the observed scene. Although frequency-domain modeling has been introduced into diffusion-based translation, existing methods mainly rely on independent weighting of [...] Read more.
Translating Synthetic aperture radar (SAR) images into optical images is intrinsically ill-posed because microwave backscatter and optical reflectance describe different physical properties of the observed scene. Although frequency-domain modeling has been introduced into diffusion-based translation, existing methods mainly rely on independent weighting of individual Fourier coefficients and provide limited modeling of interactions among neighboring frequencies and feature channels. To address this limitation, we propose dualCDM, a conditional diffusion model that jointly exploits spatial- and frequency-domain representations. In the diffusion backbone, a spatial-frequency hybrid residual block (SFHRB) combines a spatial convolution branch with complex-valued convolution in the Fourier domain. The complex convolution aggregates neighboring Fourier coefficients across all input feature channels, enabling local cross-frequency and cross-channel modeling, while its response is modulated by the diffusion timestep. In the SAR conditional encoder, an adaptive frequency-domain feature recalibration block (AFFRB) predicts input-dependent real-valued gains from magnitude and trigonometric phase representations of intermediate GRD features. These gains adaptively recalibrate the complex frequency responses without introducing an additional phase shift, while the residual connection preserves the original conditional information. A dual-domain objective further constrains both the predicted diffusion noise and the one-step optical reconstruction in the spatial and frequency domains. We also construct the S1S2 dataset using 16-bit Sentinel-2 reflectance data, retaining the original 0–10,000 value range and including the near-infrared band. Experiments on SEN1-2 and S1S2 show that dualCDM improves radiometric accuracy, spectral consistency, and structural preservation over six representative methods. Paired statistical tests further confirm significant improvements over the strongest competing method across all six evaluation metrics on both datasets. Full article
(This article belongs to the Section Remote Sensors)
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20 pages, 12259 KB  
Article
Turbulent Flow–Thermal Field Prediction Around a Pin-Fin Using Geometry-Aware Multiscale Graph Neural Network
by Riddhiman Raut, Evan M. Mihalko and Amrita Basak
Int. J. Thermofluid Sci. Technol. 2026, 13(1), 3; https://doi.org/10.3390/ijtst13010003 - 30 Jun 2026
Viewed by 125
Abstract
Pin-fins are widely used to enhance heat transfer in compact heat exchangers, turbine cooling passages, and electronic devices, but their complex geometries make accurate thermal–fluid prediction computationally expensive. This paper presents a geometry-aware multiscale (GAMS) graph neural network (GNN) for predicting steady turbulent [...] Read more.
Pin-fins are widely used to enhance heat transfer in compact heat exchangers, turbine cooling passages, and electronic devices, but their complex geometries make accurate thermal–fluid prediction computationally expensive. This paper presents a geometry-aware multiscale (GAMS) graph neural network (GNN) for predicting steady turbulent flow and heat transfer in a two-dimensional channel containing arbitrarily shaped pin-fin geometries. An automated framework integrating geometry generation, meshing, and ANSYS Fluent simulations was developed to construct the training dataset. Pin-fin geometries were parameterized using piecewise cubic splines, generating 1000 unique configurations through Latin Hypercube Sampling. Each simulation was converted into a graph representation, where nodes contained spatial coordinates, normalized streamwise position, one-hot boundary indicators, and signed distance to the nearest wall. These graph-based features were used to train the GNN to predict the temperature, velocity magnitude, and pressure fields directly from geometry. The network achieved excellent predictive accuracy, successfully capturing boundary layers, recirculation zones, and upstream stagnation regions while reducing computational wall time by 2–3 orders of magnitude compared to conventional CFD simulations. Overall, the proposed GNN provides a fast, reliable surrogate modeling framework for complex thermal–fluid flow configurations. Full article
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23 pages, 311 KB  
Article
Evaluating Adversarial Robustness of Deepfake Audio Detectors and Vocoder Fingerprint Detectors Against Universal Adversarial Perturbations
by Quang Minh Tran, Wei Zong, Yang-Wai Chow and Willy Susilo
Future Internet 2026, 18(7), 344; https://doi.org/10.3390/fi18070344 - 29 Jun 2026
Viewed by 260
Abstract
Audio deepfake and vocoder fingerprint detectors are increasingly used to identify synthetic speech and attribute it to its generating model. However, their robustness against adversarial perturbations remains unclear across attack algorithms, perturbation domains, detector representations, and vocoder types. This paper presents a focused, [...] Read more.
Audio deepfake and vocoder fingerprint detectors are increasingly used to identify synthetic speech and attribute it to its generating model. However, their robustness against adversarial perturbations remains unclear across attack algorithms, perturbation domains, detector representations, and vocoder types. This paper presents a focused, quality-aware evaluation of four representative adversarial attacks, namely the Fast Gradient Sign Method (FGSM), Basic Iterative Method (BIM), Projected Gradient Descent (PGD), and Carlini–Wagner (CW) attack, against audio deepfake and vocoder fingerprint detectors. Each attack is implemented in both the waveform domain and the short-time Fourier transform (STFT) magnitude domain. All attacks are optimized against Audio Anti-Spoofing using Integrated Spectro-Temporal Graph Attention Networks (AASIST) under a targeted fake-to-real objective and are evaluated on synthetic speech generated by HiFi-GAN, Fullband MelGAN, StyleMelGAN, and Parallel WaveGAN. Attack performance is first measured on the source AASIST detector, after which black-box transferability is assessed on three target detector families: ResNet with Linear Frequency Cepstral Coefficient (LFCC) features, LCNN with Constant-Q Cepstral Coefficient (CQCC) features, and a bidirectional long short-term memory (BiLSTM) detector. The results show that adversarial effectiveness depends strongly on perturbation domain and detector representation. STFT-magnitude PGD transfers strongly to LFCC-based ResNet detectors but has limited effect on CQCC-based and recurrent detectors. In contrast, waveform-domain attacks produce broader transferability across feature-based detectors, with different attacks showing distinct ASR–quality trade-offs. Under the chosen waveform-domain budget, FGSM and BIM preserve transcription-level intelligibility while retaining meaningful black-box transferability, whereas CW provides the strongest overall source-detector and black-box attack performance. To distinguish effective adversarial perturbations from destructive signal degradation, we evaluate audio quality and intelligibility using word error rate (WER) and signal-to-noise ratio (SNR). Overall, the findings show that robustness claims in audio deepfake and vocoder fingerprint detection are limited when adversarial perturbations, black-box transferability, and audio quality are jointly considered. Full article
(This article belongs to the Special Issue Adversarial Attacks and Cyber Security)
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21 pages, 20819 KB  
Article
Nonlinear Correlation of POD and DMD Modal Coefficients in Reduced-Order Modeling of Flow Around a Cylinder in a Microchannel
by Bin Zuo, Xiaopei Yang, Haichun Wang and Qianhao Xiao
Micromachines 2026, 17(7), 778; https://doi.org/10.3390/mi17070778 - 26 Jun 2026
Viewed by 253
Abstract
Nonlinear correlations among modal coefficients enable interpretable reduced-order models (ROMs) for microfluidic flows. In this study, flow around a cylinder in a microchannel at Re = 100 is investigated using proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), and POD + DMD. The [...] Read more.
Nonlinear correlations among modal coefficients enable interpretable reduced-order models (ROMs) for microfluidic flows. In this study, flow around a cylinder in a microchannel at Re = 100 is investigated using proper orthogonal decomposition (POD), dynamic mode decomposition (DMD), and POD + DMD. The sparse identification of nonlinear dynamics (SINDy) is employed to identify nonlinear correlations among modal coefficients. The results show that the first POD mode contains 33% of the total kinetic energy, and the first 14 modes capture 99.2% of the energy. A minimal ROM with only two degrees of freedom is constructed, in which the real and imaginary parts of active modal coefficients differ in phase by π/2 and their magnitude equals the vortex-shedding fundamental frequency (1.067 Hz). Among sparse regression algorithms, the FROLS method yields the sparsest representation (sparsity rate 0.05), whereas other methods give sparsity rate > 0.3. Reducing the temporal resolution from 0.01 to 0.1 increases the manifold dynamics coefficient error from 0% to 0.56%. Only the ROMs built from POD + DMD and DMD preserve essential kinematic resolution. The POD-based ROM fails to maintain correct energy levels over long-time integration. Therefore, the nonlinear correlation between POD + DMD modal coefficients is recommended for developing ROMs in microchannel flows when accuracy, interpretability, and stability are considered together. Full article
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23 pages, 4039 KB  
Article
FAF-Net: A Lightweight Frequency-Auxiliary Fusion Network for Plant Disease Classification in Natural-Scene Images
by Chuqing Zhao and Fangling Sun
Appl. Sci. 2026, 16(13), 6380; https://doi.org/10.3390/app16136380 - 25 Jun 2026
Viewed by 151
Abstract
Plant disease classification in natural scenes remains challenging because disease symptoms are often localized and imaging conditions are complex, including cluttered backgrounds, illumination variations, scale changes, and fine-grained inter-class similarities. To address these challenges, this study proposes FAF-Net, a frequency-aware fusion network with [...] Read more.
Plant disease classification in natural scenes remains challenging because disease symptoms are often localized and imaging conditions are complex, including cluttered backgrounds, illumination variations, scale changes, and fine-grained inter-class similarities. To address these challenges, this study proposes FAF-Net, a frequency-aware fusion network with auxiliary supervision for plant disease classification in natural scenes. The proposed framework is built on EfficientNet-B3 and integrates three complementary strategies: CutMix augmentation, an FFT-based frequency branch, and a healthy/diseased auxiliary supervision branch. The RGB branch extracts spatial semantic features from natural-scene images, whereas the frequency branch converts the input image into a log-normalized Fourier magnitude spectrum and learns complementary texture representations. The auxiliary branch provides coarse-grained health-status supervision during training, encouraging the shared representation to capture disease-relevant features. Experiments were conducted on the PlantDoc dataset, which contains 2598 images from 27 healthy and diseased categories. Compared with the EfficientNet-B3 baseline, FAF-Net improved the classification accuracy from 69.49% to 74.58%, corresponding to a gain of 5.09 percentage points. Ablation results further indicate that CutMix, frequency-domain features, and auxiliary supervision provide complementary improvements. These results suggest that frequency-aware feature fusion and coarse-grained auxiliary supervision can enhance plant disease classification under natural-scene conditions. Full article
(This article belongs to the Section Agricultural Science and Technology)
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21 pages, 8895 KB  
Article
Registration Quality and the Limits of Statistical Shape Modeling Evaluation in Transtibial Residual Limb Modeling: A Cross-Sectional Shape Representation Framework
by Shinichiro Kon, Yukio Agarie, Hironori Suda, Hiroshi Otsuka, Kengo Ohnishi, Akihiko Hanahusa, Motoki Takagi and Shinichiro Yamamoto
Prosthesis 2026, 8(7), 65; https://doi.org/10.3390/prosthesis8070065 - 23 Jun 2026
Viewed by 323
Abstract
Background/Objectives: Statistical shape modeling (SSM) is used to describe transtibial residual-limb morphology for prosthetic socket design, simulation, and future structural testing. However, conventional intrinsic metrics such as compactness, generality, and specificity may not directly reflect geometric fidelity to the original shape. This [...] Read more.
Background/Objectives: Statistical shape modeling (SSM) is used to describe transtibial residual-limb morphology for prosthetic socket design, simulation, and future structural testing. However, conventional intrinsic metrics such as compactness, generality, and specificity may not directly reflect geometric fidelity to the original shape. This study examined the relationship between geometric fidelity and SSM evaluation and assessed a cross-sectional shape representation framework for transtibial residual limbs. Methods: Residual-limb surfaces were acquired from 62 adults with unilateral transtibial amputation using a structured-light 3D scanner while preserving habitual limb posture. Two surface-based registration methods, non-rigid iterative closest point and Bayesian coherent point drift, were compared with a cross-sectional representation in which proximal and distal regions were sectioned separately and reconstructed by strip triangulation. Geometric fidelity to the original mesh was quantified using average symmetric surface distance (ASSD). SSM performance was evaluated using compactness, generality, and specificity. Results: The optimal cross-sectional configuration was 60 sections × 72 points. The proposed method showed the best geometric fidelity (ASSD, 1.30 ± 0.14 mm), followed by Bayesian coherent point drift (1.33 ± 0.14 mm) and non-rigid iterative closest point (1.48 ± 0.48 mm). Compactness was highest for the proposed method, reaching 95% cumulative variance in four modes, compared with five and seven modes, respectively, for the two surface-based methods. In geometry-space evaluation, the proposed method showed the lowest specificity error, while differences in generality were statistically significant but small in magnitude. Conclusions: Intrinsic SSM metrics alone were insufficient to judge registration quality in transtibial residual-limb modeling. The cross-sectional representation preserved the original surface geometry more faithfully than the evaluated surface-based methods while maintaining competitive SSM performance. Full article
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19 pages, 7335 KB  
Article
MSA-DET: A Multi-Scale Attention Network with Adaptive Feature Fusion for SAR Ship Detection
by Sai Wan, Zhiyong Tao and Lu Chen
Sensors 2026, 26(13), 3970; https://doi.org/10.3390/s26133970 - 23 Jun 2026
Viewed by 272
Abstract
Synthetic aperture radar (SAR) ship detection faces three persistent challenges: coherent speckle noise that obscures target boundaries, heterogeneous background clutter in coastal and harbor scenes, and ship targets whose spatial extent varies by more than an order of magnitude within the same image. [...] Read more.
Synthetic aperture radar (SAR) ship detection faces three persistent challenges: coherent speckle noise that obscures target boundaries, heterogeneous background clutter in coastal and harbor scenes, and ship targets whose spatial extent varies by more than an order of magnitude within the same image. To address these issues jointly, this paper proposes MSA-DET, an improved SAR ship detection network built upon YOLOv11. In the backbone, a Multi-Scale Cross-axis Attention module (MSCAttention) runs horizontal and vertical axial attention branches in parallel across multiple receptive-field scales, sharpening feature representations for ship targets that vary widely in size and orientation. In the neck, the standard C3k2 block is redesigned as C3k2_SSA by embedding sparse self-attention, which selectively focuses on the most discriminative spatial tokens while suppressing speckle interference and reducing computational overhead. An Adaptive Spatial Feature Fusion detection head (ASFF) replaces fixed pyramid-level aggregation with learned per-pixel blending weights, resolving gradient conflicts across scales and improving localization consistency for both small and large ships. On the HRSID dataset, MSA-DET achieves an mAP@0.5:0.95 of 63.6% and mAP@0.5 of 88.1%, representing gains of 4.0% and 1.6% over the YOLOv11n baseline; on SSDD, it reaches 69.6% and 97.7%, surpassing the baseline by 7.2% and 2.1%, respectively. These results demonstrate that coordinated multi-stage redesign—rather than isolated module substitution—is an effective strategy for SAR-oriented ship detection. The accuracy gains are accompanied by a moderate increase in model size (8.9 M parameters versus 2.6 M for YOLOv11n) and computational cost (9.6 G FLOPs versus 6.3 G), a trade-off that is justified by the substantial improvement in detection quality. Full article
(This article belongs to the Section Remote Sensors)
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20 pages, 4611 KB  
Article
Research on Fault Type Identification for Distribution Networks with Distributed Power Sources Based on Improved CNN-BiGRU
by Lei Li and Weili Wu
Sensors 2026, 26(12), 3947; https://doi.org/10.3390/s26123947 - 21 Jun 2026
Viewed by 338
Abstract
The integration of distributed generation (DG) changes the fault current path, magnitude, direction, and transient characteristics of distribution networks, which increases the difficulty of fault type identification. In particular, weak fault features and high-frequency transient components may reduce the reliability of traditional feature-based [...] Read more.
The integration of distributed generation (DG) changes the fault current path, magnitude, direction, and transient characteristics of distribution networks, which increases the difficulty of fault type identification. In particular, weak fault features and high-frequency transient components may reduce the reliability of traditional feature-based diagnosis methods. To improve the representation and classification capability of fault signals, this paper proposes a fault type identification method based on wavelet packet transform and an improved CNN-BiGRU model with a channel attention mechanism. First, three-phase voltage, three-phase current, and zero-sequence voltage signals are decomposed by wavelet packet transform, and the corresponding time–frequency matrices are constructed. Then, these matrices are integrated and converted into time-frequency images, so that multi-source fault information can be represented in a unified form. On this basis, CNN is used to extract local spatial features from the time-frequency images, while BiGRU is employed to capture bidirectional dependency information of fault features. Furthermore, a channel attention mechanism is introduced to enhance informative feature channels and suppress redundant information, thereby improving the fault classification performance. Simulation results based on a 10 kV DG-integrated distribution network show that the proposed method achieves high recognition accuracy under different DG capacities and access configurations. Compared with CNN, BiGRU, and CNN-BiGRU models, the proposed CNN-BiGRU-Attention model shows better classification accuracy and adaptability, demonstrating its effectiveness for fault type identification in active distribution networks. Full article
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20 pages, 4211 KB  
Article
On the Role of Feature Extraction in Transformer PD Severity Classification: A Controlled Comparison of PCA and Autoencoder Models
by Lucas Thobejane and Bonginkosi Thango
Machines 2026, 14(6), 708; https://doi.org/10.3390/machines14060708 - 21 Jun 2026
Viewed by 265
Abstract
This paper applies the comparative PCA-ANN vs. Autoencoder-ANN framework to transformer partial discharge (PD) severity classification, using a 294-sample dataset spanning four severity classes: Normal, Low PD, Medium PD, and High PD. Two raw measurements of discharge magnitude (pC) and applied voltage (kV) [...] Read more.
This paper applies the comparative PCA-ANN vs. Autoencoder-ANN framework to transformer partial discharge (PD) severity classification, using a 294-sample dataset spanning four severity classes: Normal, Low PD, Medium PD, and High PD. Two raw measurements of discharge magnitude (pC) and applied voltage (kV) are expanded into a 15-dimensional physics-informed feature space. Both linear (PCA) and nonlinear (bottleneck Autoencoder) feature extraction are evaluated exhaustively across all latent dimensions k = 1–15, feeding an identical ANN classifier. PCA + ANN achieves perfect test accuracy of 100.0% at k = 9, while Autoencoder + ANN achieves 98.3% at k = 8. PCA + ANN demonstrates superior performance on this dataset, attributed to the low intrinsic dimensionality of the two-measurement PD feature space and the highly separable nature of PD severity classes in the engineered ratio feature space. The Autoencoder provides a more compact latent representation but introduces classification errors for the Normal class due to its extreme under-representation. Cross-validation confirms PCA + ANN stability (97.4 ± 0.9% vs. 97.0 ± 1.0%). These results, alongside the companion DGA study, provide the complete baseline for comparing linear and nonlinear feature extraction across two transformer diagnostic modalities. Full article
(This article belongs to the Special Issue Condition Monitoring and Fault Diagnosis)
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29 pages, 12456 KB  
Article
A Lightweight Drainage Pipe Defect Detection Method Based on an Improved YOLO11 Network
by Rui Xue, Hongtao Fu, Hui Zhao and Chongquan Wang
Information 2026, 17(6), 613; https://doi.org/10.3390/info17060613 - 21 Jun 2026
Viewed by 261
Abstract
Drainage pipe defect detection is essential for maintaining the normal operation of urban infrastructure. In recent years, deep learning-based object detection methods have provided an effective technical solution for drainage pipe defect recognition. Among them, YOLO-series models have demonstrated strong potential in visual [...] Read more.
Drainage pipe defect detection is essential for maintaining the normal operation of urban infrastructure. In recent years, deep learning-based object detection methods have provided an effective technical solution for drainage pipe defect recognition. Among them, YOLO-series models have demonstrated strong potential in visual detection tasks due to their end-to-end architecture and high inference efficiency. However, directly applying baseline YOLO models may still face challenges such as limited detection accuracy, relatively high model complexity, and insufficient adaptability for lightweight deployment scenarios. To address these issues, this paper proposes a lightweight drainage pipe defect detection method based on an improved YOLO11 network. Rather than treating detection enhancement and model compression as two separate procedures, the proposed method integrates feature enhancement, adaptive pruning, and distillation-based recovery into a unified lightweight detection framework. Specifically, an improved SimAM attention mechanism is introduced into the backbone and integrated with the C3k2 module to construct the C3K2_SWS module, aiming to enhance the representation capability of critical defect features. In the neck network, a focused diffusion pyramid network with a dimension-aware selective fusion structure, termed FDPN-DASI, is designed to strengthen multi-scale feature interactions. In addition, an adaptive-threshold focal loss (ATFL) is introduced to improve the learning capability for hard samples. For efficient deployment, the LAMP pruning algorithm is further improved, and an entropy-guided entropy-adaptive magnitude-based pruning method (EA-LAMP) is proposed to enable adaptive allocation of pruning ratios across different network layers. Moreover, BCKD knowledge distillation is applied after pruning to mitigate the accuracy degradation caused by model compression. Experimental results indicate that the proposed lightweight YOLO11-SFA+EA+BCKD framework achieves a precision of 92.4%, a recall of 88.5%, and an mAP50 of 93.3%, while maintaining a compact model size of 1.6 M parameters and 4.5 G FLOPs. Compared with the baseline model, the proposed method improves precision, recall, and mAP50 by 5.9%, 5.0%, and 4.7%, respectively, while reducing the number of parameters, FLOPs, and model size by 1.0 M, 1.8 G, and 2.1 M, respectively. These results suggest that the proposed framework can improve detection performance while reducing model complexity under the current experimental setting, indicating its potential for lightweight drainage pipe defect detection tasks. Full article
(This article belongs to the Section Artificial Intelligence)
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22 pages, 412 KB  
Article
On a Biparametric Appell Extension: Analytical Properties and Structural Analysis
by Hany Mostafa Ahmed
Axioms 2026, 15(6), 455; https://doi.org/10.3390/axioms15060455 - 17 Jun 2026
Viewed by 194
Abstract
This paper introduces and investigates a novel two-parameter sequence, termed the biparametric Appell extension (B-App-Ex) and denoted by Bn(x;λ,α). Standard classical Appell sequences often lack sufficient structural parameters, which can limit their operational flexibility [...] Read more.
This paper introduces and investigates a novel two-parameter sequence, termed the biparametric Appell extension (B-App-Ex) and denoted by Bn(x;λ,α). Standard classical Appell sequences often lack sufficient structural parameters, which can limit their operational flexibility in certain advanced spectral schemes. To address this limitation, we construct an enhanced operational framework by integrating a binomial structural kernel (1+w)λ with a linear exponential scaling eαxw entirely within the Appell class. We provide a rigorous logical deduction of the fundamental properties of this sequence, including its explicit power series representation, a characteristic three-term recurrence relation, and a governing second-order differential equation (DEq.). A significant contribution of this work is the establishment of analytically exact connection and inverse connection formulas between the B-App-Ex basis and various classical orthogonal polynomial (COP) families. Numerical verification via a collocation-based projection framework demonstrates that these algebraic kernels achieve near-machine epsilon precision (≈1015), remaining stable even for high-order approximations. Furthermore, by isolating the dilation factor α, we establish an O(N) computational complexity that offers a reduction in latency by approximately two orders of magnitude compared to classical matrix-based transformations. The results demonstrate that the proposed biparametric (Bip.) extension offers a versatile and highly optimized analytical template for modeling complex dynamic systems where structural shifting and spatial scaling must be tuned simultaneously. Full article
(This article belongs to the Section Mathematical Analysis)
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