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22 pages, 5652 KB  
Article
Building Energy Assessment of Thermal and Electrical Properties for Compact Cities: Case Study of a Multi-Purpose Building in South Korea
by Jaeho Lee and Jaewan Suh
Buildings 2025, 15(17), 3023; https://doi.org/10.3390/buildings15173023 (registering DOI) - 25 Aug 2025
Abstract
This study conducts a simulation-based assessment of a recently commissioned office building in the Republic of Korea, representing a typical public office facility. The building was modeled using EnergyPlus 23.1.0 after construction, although no validation was performed due to the absence of metered [...] Read more.
This study conducts a simulation-based assessment of a recently commissioned office building in the Republic of Korea, representing a typical public office facility. The building was modeled using EnergyPlus 23.1.0 after construction, although no validation was performed due to the absence of metered consumption data. Previous approaches relying on simplified methods such as the Radiant Time Series (RTS), which neglect dynamic building behavior, have often led to overestimated cooling and heating loads. This has emerged as a major obstacle in designing energy-efficient buildings within the context of compact and smart cities pursuing carbon neutrality. Consequently, the trend in building performance analysis is shifting toward dynamic simulations and digital twin-based design methodologies. Furthermore, electrification of buildings without adequate thermal load assessment may also contribute to overdesign, irrespective of urban environmental characteristics. From an urban planning standpoint, there is a growing need for performance criteria that reflect occupant behavior and actual usage patterns. However, dynamics-based building studies remain scarce in the Republic of Korea. In this context, the present study demonstrates that passive design strategies, implemented through systematic changes in envelope materials, HVAC operational standards, and compliance with ASHRAE 90.1 criteria, can significantly enhance thermal comfort and indoor air quality. The simulation results show that energy consumption can be reduced by over 36.21% without compromising occupant health or comfort. These findings underscore the importance of thermal load understanding prior to electrification and highlight the potential of LEED-aligned passive strategies for achieving high-performance, low-energy buildings. Full article
(This article belongs to the Special Issue Study on Building Energy Efficiency Related to Simulation Models)
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24 pages, 10666 KB  
Article
Three-Dimensional Path Planning for UAV Based on Multi-Strategy Dream Optimization Algorithm
by Xingyu Yang, Shiwei Zhao, Wei Gao, Peifeng Li, Zhe Feng, Lijing Li, Tongyao Jia and Xuejun Wang
Biomimetics 2025, 10(8), 551; https://doi.org/10.3390/biomimetics10080551 - 21 Aug 2025
Viewed by 171
Abstract
The multi-strategy optimized dream optimization algorithm (MSDOA) is proposed to address the challenges of inadequate search capability, slow convergence, and susceptibility to local optima in intelligent optimization algorithms applied to UAV three-dimensional path planning, aiming to enhance the global search efficiency and accuracy [...] Read more.
The multi-strategy optimized dream optimization algorithm (MSDOA) is proposed to address the challenges of inadequate search capability, slow convergence, and susceptibility to local optima in intelligent optimization algorithms applied to UAV three-dimensional path planning, aiming to enhance the global search efficiency and accuracy of UAV path planning algorithms in 3D environments. First, the algorithm utilizes Bernoulli chaotic mapping for population initialization to widen individual search ranges and enhance population diversity. Subsequently, an adaptive perturbation mechanism is incorporated during the exploration phase along with a lens imaging reverse learning strategy to update the population, thereby improving the exploration ability and accelerating convergence while mitigating premature convergence. Lastly, an Adaptive Individual-level Mixed Strategy (AIMS) is developed to conduct a more flexible search process and enhance the algorithm’s global search capability. The performance of the algorithm is evaluated through simulation experiments using the CEC2017 benchmark test functions. The results indicate that the proposed algorithm achieves superior optimization accuracy, faster convergence speed, and enhanced robustness compared to other swarm intelligence algorithms. Specifically, MSDOA ranks first on 28 out of 29 benchmark functions in the CEC2017 test suite, demonstrating its outstanding global search capability and conver-gence performance. Furthermore, UAV path planning simulation experiments conducted across multiple scenario models show that MSDOA exhibits stronger adaptability to complex three-dimensional environments. In the most challenging scenario, compared to the standard DOA, MSDOA reduces the best cost function fitness by 9% and decreases the average cost function fitness by 12%, thereby generating more efficient, smoother, and higher-quality flight paths. Full article
(This article belongs to the Section Biological Optimisation and Management)
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16 pages, 3508 KB  
Article
Metabolomic Profiling Reveals Dynamic Changes in Organic Acids During Zaolajiao Fermentation: Correlation with Physicochemical Properties and CAZymes
by Ju Chen, Xueya Wang, Wenxin Li, Jianwen He, Yong Yin, Min Lu and Yubing Huang
Fermentation 2025, 11(8), 479; https://doi.org/10.3390/fermentation11080479 - 20 Aug 2025
Viewed by 238
Abstract
Zaolajiao (ZLJ) is a traditional national specialty fermented condiment in Guizhou, and organic acid is one of its main flavor substances. In the study, we used metabolomics and multivariate analysis to identify differential organic acids (DOAs) during ZLJ fermentation and explored their correlations [...] Read more.
Zaolajiao (ZLJ) is a traditional national specialty fermented condiment in Guizhou, and organic acid is one of its main flavor substances. In the study, we used metabolomics and multivariate analysis to identify differential organic acids (DOAs) during ZLJ fermentation and explored their correlations with physicochemical indices and CAZymes. Eight DOAs were detected, with citric acid prominent early and lactic acid dominant late in fermentation. Citric acid exhibited a highly significant negative correlation (p < 0.01, |r| > 0.955) with AA3, GT4, and CE1, while showing significant positive correlation (p < 0.05) with GH1, soluble sugars, and total acids. Lactic acid exhibited a highly significant positive correlation with total acid, AA3, and GT4 (p < 0.05, |r| > 0.955). Conversely, it showed a significant negative correlation with soluble sugar (p < 0.05) and a highly significant negative correlation with GH1 (p < 0.05, |r| > 0.955). The most significant metabolic pathway for DOAs enrichment was the citrate cycle (TCA cycle). Full article
(This article belongs to the Section Fermentation for Food and Beverages)
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25 pages, 7795 KB  
Article
Outlier-Robust Three-Element Non-Uniform Linear Arrays Design Strategy for Direction of Arrival Estimation in MIMO Radar
by Andrea Quirini, Fabiola Colone and Pierfrancesco Lombardo
Sensors 2025, 25(16), 5062; https://doi.org/10.3390/s25165062 - 14 Aug 2025
Viewed by 233
Abstract
This paper presents a novel design strategy for outlier-robust, three-element non-uniform linear array (NULA) configurations optimized for multiple-input multiple-output (MIMO) radar systems aimed at target direction of arrival (DoA) estimation. The occurrence of outliers, i.e., ambiguous estimates, is a well-known issue in DoA [...] Read more.
This paper presents a novel design strategy for outlier-robust, three-element non-uniform linear array (NULA) configurations optimized for multiple-input multiple-output (MIMO) radar systems aimed at target direction of arrival (DoA) estimation. The occurrence of outliers, i.e., ambiguous estimates, is a well-known issue in DoA estimation based on the maximum likelihood (ML), which is caused by the local maxima of the likelihood function. Specifically, we study how the positioning of both transmitters and receivers affects both presence of outliers and accuracy of ML DoA estimation. By leveraging a theoretical prediction of the DoA mean squared error (MSE), we propose a design strategy to jointly optimize the positions of NULA array of three transmitting and receiving elements, only inside a subspace which guarantees that the outlier probability remains below a specified threshold. Compared to NULA configurations with a single transmitter, the proposed designs achieve superior estimation accuracy due to two key factors: improved asymptotic performance resulting from a narrower mainlobe, and enhanced robustness against outliers due to reduced sidelobes. Furthermore, the proposed approach is well-suited for practical implementation in low-cost radars using only 3 × 3 or 2 × 3 MIMO configurations, as it also incorporates practical design constraints such as minimum inter-element spacing to account for the physical dimensions of the antennas, and tolerance in the installation accuracy. Full article
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26 pages, 1722 KB  
Article
Accelerating Broadband DOA Estimation: A Real-Valued and Coherent Sparse Bayesian Approach for 5G Sensing
by Xin Tong, Yinzhe Hu, Zhongliang Deng and Enwen Hu
Electronics 2025, 14(16), 3174; https://doi.org/10.3390/electronics14163174 - 9 Aug 2025
Viewed by 255
Abstract
For applications like smart cities and autonomous driving, high-precision direction-of-arrival (DOA) estimation for 5G broadband signals is essential. A primary obstacle for existing methods is the spatial incoherence caused by multi-frequency propagation. We present a sparse Bayesian learning (SBL) algorithm specifically designed to [...] Read more.
For applications like smart cities and autonomous driving, high-precision direction-of-arrival (DOA) estimation for 5G broadband signals is essential. A primary obstacle for existing methods is the spatial incoherence caused by multi-frequency propagation. We present a sparse Bayesian learning (SBL) algorithm specifically designed to resolve this issue while also minimizing computational load. The algorithm synergistically combines three key components: first, a multiple-signal classification (MUSIC)-like focusing technique ensures a coherent sparse model; second, a real-valued transformation significantly cuts down on computational complexity; and third, an optimized variational Bayesian inference accelerates convergence via root-finding. Validation against MUSIC and rootSBL confirms our method’s marked superiority in low-SNR, limited-snapshot, and multipath conditions delivering both higher accuracy and faster convergence. This work, thus, contributes an effective and practical solution for real-time 5G DOA sensing. Full article
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19 pages, 2504 KB  
Article
TSNetIQ: High-Resolution DOA Estimation of UAVs Using Microphone Arrays
by Kequan Zhu, Tian Jin, Shitong Xie, Zixuan Liu and Jinlong Sun
Appl. Sci. 2025, 15(15), 8734; https://doi.org/10.3390/app15158734 - 7 Aug 2025
Viewed by 384
Abstract
With the rapid development of unmanned aerial vehicle (UAV) technology and the rise of the low-altitude economy, the accurate tracking of UAVs has become a critical challenge. This paper considers a deep learning-based localization scheme that combines microphone arrays for audio source reception. [...] Read more.
With the rapid development of unmanned aerial vehicle (UAV) technology and the rise of the low-altitude economy, the accurate tracking of UAVs has become a critical challenge. This paper considers a deep learning-based localization scheme that combines microphone arrays for audio source reception. The microphone array is utilized to capture sound source reception from various angles. The proposed TSNetIQ combines elaborately designed Transformer and convolutional neural networks (CNN) modules, and the raw in-phase (I) and quadrature (Q) components of the audio signals are used as input data. Hence, the direction of arrival (DOA) estimation is treated as a regression problem. Experiments are conducted to evaluate the proposed method under different signal-to-noise ratios (SNRs), sampling frequencies, and array configurations. The results demonstrate that TSNetIQ can effectively estimate the direction of the sound source, outperforming conventional architectures trained with the same dataset. This study offers superior accuracy and robustness for real-time sound source localization in UAV applications under dynamic scenarios. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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18 pages, 2227 KB  
Article
Adaptive Array Shape Estimation and High-Resolution Sensing for AUV-Towed Linear Array Sonar During Turns
by Junxiong Wang, Xiang Pan, Lei Cheng and Jianbo Jiao
Remote Sens. 2025, 17(15), 2690; https://doi.org/10.3390/rs17152690 - 3 Aug 2025
Viewed by 299
Abstract
The deformation of the array shape during the turning process of an autonomous underwater vehicle (AUV)-towed line array sonar can significantly degrade its remote sensing performance. In this paper, a method for circular arc array modeling and dynamic deformation estimation is proposed. By [...] Read more.
The deformation of the array shape during the turning process of an autonomous underwater vehicle (AUV)-towed line array sonar can significantly degrade its remote sensing performance. In this paper, a method for circular arc array modeling and dynamic deformation estimation is proposed. By treating the array shape as a hyperparameter, an adaptive central angle (shape) marginal likelihood maximization (ASMLM) algorithm is derived to jointly estimate the array shape and the directions of arrival (DOAs) of sources. The high-resolution ASMLM algorithm is used to improve the DOA estimation performance, effectively suppress left–right ambiguity and significantly reduce computational complexity, making it suitable for AUV platforms with limited computational resources. Experimental results from sea trials in the South China Sea are used to validate the superior performance of the proposed method over existing methods. Full article
(This article belongs to the Section Ocean Remote Sensing)
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21 pages, 4522 KB  
Article
A Method Integrating the Matching Field Algorithm for the Three-Dimensional Positioning and Search of Underwater Wrecked Targets
by Huapeng Cao, Tingting Yang and Ka-Fai Cedric Yiu
Sensors 2025, 25(15), 4762; https://doi.org/10.3390/s25154762 - 1 Aug 2025
Viewed by 282
Abstract
In this paper, a joint Matching Field Processing (MFP) Algorithm based on horizontal uniform circular array (UCA) is proposed for three-dimensional position of underwater wrecked targets. Firstly, a Marine search and rescue position model based on Minimum Variance Distortionless Response (MVDR) and matching [...] Read more.
In this paper, a joint Matching Field Processing (MFP) Algorithm based on horizontal uniform circular array (UCA) is proposed for three-dimensional position of underwater wrecked targets. Firstly, a Marine search and rescue position model based on Minimum Variance Distortionless Response (MVDR) and matching field quadratic joint Algorithm was proposed. Secondly, an MVDR beamforming method based on pre-Kalman filtering is designed to refine the real-time DOA estimation of the desired signal and the interference source, and the sound source azimuth is determined for prepositioning. The antenna array weights are dynamically adjusted according to the filtered DOA information. Finally, the Adaptive Matching Field Algorithm (AMFP) used the DOA information to calculate the range and depth of the lost target, and obtained the range and depth estimates. Thus, the 3D position of the lost underwater target is jointly estimated. This method alleviates the angle ambiguity problem and does not require a computationally intensive 2D spectral search. The simulation results show that the proposed method can better realise underwater three-dimensional positioning under certain signal-to-noise ratio conditions. When there is no error in the sensor coordinates, the positioning error is smaller than that of the baseline method as the SNR increases. When the SNR is 0 dB, with the increase in the sensor coordinate error, the target location error increases but is smaller than the error amplitude of the benchmark Algorithm. The experimental results verify the robustness of the proposed framework in the hierarchical ocean environment, which provides a practical basis for the deployment of rapid response underwater positioning systems in maritime search and rescue scenarios. Full article
(This article belongs to the Special Issue Sensor Fusion in Positioning and Navigation)
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28 pages, 4107 KB  
Article
Channel Model for Estimating Received Power Variations at a Mobile Terminal in a Cellular Network
by Kevin Verdezoto Moreno, Pablo Lupera-Morillo, Roberto Chiguano, Robin Álvarez, Ricardo Llugsi and Gabriel Palma
Electronics 2025, 14(15), 3077; https://doi.org/10.3390/electronics14153077 - 31 Jul 2025
Viewed by 286
Abstract
This paper introduces a theoretical large-scale radio channel model for the downlink in cellular systems, aimed at estimating variations in received signal power at the user terminal as a function of device mobility. This enables applications such as direction-of-arrival (DoA) estimation, estimating power [...] Read more.
This paper introduces a theoretical large-scale radio channel model for the downlink in cellular systems, aimed at estimating variations in received signal power at the user terminal as a function of device mobility. This enables applications such as direction-of-arrival (DoA) estimation, estimating power at subsequent points based on received power, and detection of coverage anomalies. The model is validated using real-world measurements from urban and suburban environments, achieving a maximum estimation error of 7.6%. In contrast to conventional models like Okumura–Hata, COST-231, Third Generation Partnership Project (3GPP) stochastic models, or ray-tracing techniques, which estimate average power under static conditions, the proposed model captures power fluctuations induced by terminal movement, a factor often neglected. Although advanced techniques such as wave-domain processing with intelligent metasurfaces can also estimate DoA, this model provides a simpler, geometry-driven approach based on empirical traces. While it does not incorporate infrastructure-specific characteristics or inter-cell interference, it remains a practical solution for scenarios with limited information or computational resources. Full article
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20 pages, 6694 KB  
Article
Spatiotemporal Assessment of Benzene Exposure Characteristics in a Petrochemical Industrial Area Using Mobile-Extraction Differential Optical Absorption Spectroscopy (Me-DOAS)
by Dong keun Lee, Jung-min Park, Jong-hee Jang, Joon-sig Jung, Min-kyeong Kim, Jaeseok Heo and Duckshin Park
Toxics 2025, 13(8), 655; https://doi.org/10.3390/toxics13080655 - 31 Jul 2025
Viewed by 437
Abstract
Petrochemical complexes are spatially expansive and host diverse emission sources, making accurate monitoring of volatile organic compounds (VOCs) challenging using conventional two-dimensional methods. This study introduces Mobile-extraction Differential Optical Absorption Spectroscopy (Me-DOAS), a real-time, three-dimensional remote sensing technique for assessing benzene emissions in [...] Read more.
Petrochemical complexes are spatially expansive and host diverse emission sources, making accurate monitoring of volatile organic compounds (VOCs) challenging using conventional two-dimensional methods. This study introduces Mobile-extraction Differential Optical Absorption Spectroscopy (Me-DOAS), a real-time, three-dimensional remote sensing technique for assessing benzene emissions in the Ulsan petrochemical complex, South Korea. A vehicle-mounted Me-DOAS system conducted monthly measurements throughout 2024, capturing data during four daily intervals to evaluate diurnal variation. Routes included perimeter loops and grid-based transects within core industrial zones. The highest benzene concentrations were observed in February (mean: 64.28 ± 194.69 µg/m3; geometric mean: 5.13 µg/m3), with exceedances of the national annual standard (5 µg/m3) in several months. Notably, nighttime and early morning sessions showed elevated levels, suggesting contributions from nocturnal operations and meteorological conditions such as atmospheric inversion. A total of 179 exceedances (≥30 µg/m3) were identified, predominantly in zones with benzene-handling activities. Correlation analysis revealed a significant relationship between high concentrations and specific emission sources. These results demonstrate the utility of Me-DOAS in capturing spatiotemporal emission dynamics and support its application in exposure risk assessment and industrial emission control. The findings provide a robust framework for targeted management strategies and call for integration with source apportionment and dispersion modeling tools. Full article
(This article belongs to the Section Air Pollution and Health)
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34 pages, 3535 KB  
Article
Hybrid Optimization and Explainable Deep Learning for Breast Cancer Detection
by Maral A. Mustafa, Osman Ayhan Erdem and Esra Söğüt
Appl. Sci. 2025, 15(15), 8448; https://doi.org/10.3390/app15158448 - 30 Jul 2025
Cited by 1 | Viewed by 658
Abstract
Breast cancer continues to be one of the leading causes of women’s deaths around the world, and this has emphasized the necessity to have novel and interpretable diagnostic models. This work offers a clear learning deep learning model that integrates the mobility of [...] Read more.
Breast cancer continues to be one of the leading causes of women’s deaths around the world, and this has emphasized the necessity to have novel and interpretable diagnostic models. This work offers a clear learning deep learning model that integrates the mobility of MobileNet and two bio-driven optimization operators, the Firefly Algorithm (FLA) and Dingo Optimization Algorithm (DOA), in an effort to boost classification appreciation and the convergence of the model. The suggested model demonstrated excellent findings as the DOA-optimized MobileNet acquired the highest performance of 98.96 percent accuracy on the fusion test, and the FLA-optimized MobileNet scaled up to 98.06 percent and 95.44 percent accuracies on mammographic and ultrasound tests, respectively. Further to good quantitative results, Grad-CAM visualizations indeed showed clinically consistent localization of the lesions, which strengthened the interpretability and model diagnostic reliability of Grad-CAM. These results show that lightweight, compact CNNs can be used to do high-performance, multimodal breast cancer diagnosis. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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33 pages, 16026 KB  
Article
Spatiotemporal Analysis of BTEX and PM Using Me-DOAS and GIS in Busan’s Industrial Complexes
by Min-Kyeong Kim, Jaeseok Heo, Joonsig Jung, Dong Keun Lee, Jonghee Jang and Duckshin Park
Toxics 2025, 13(8), 638; https://doi.org/10.3390/toxics13080638 - 29 Jul 2025
Viewed by 619
Abstract
Rapid industrialization and urbanization have progressed in Korea, yet public attention to hazardous pollutants emitted from industrial complexes remains limited. With the increasing coexistence of industrial and residential areas, there is a growing need for real-time monitoring and management plans that account for [...] Read more.
Rapid industrialization and urbanization have progressed in Korea, yet public attention to hazardous pollutants emitted from industrial complexes remains limited. With the increasing coexistence of industrial and residential areas, there is a growing need for real-time monitoring and management plans that account for the rapid dispersion of hazardous air pollutants (HAPs). In this study, we conducted spatiotemporal data collection and analysis for the first time in Korea using real-time measurements obtained through mobile extractive differential optical absorption spectroscopy (Me-DOAS) mounted on a solar occultation flux (SOF) vehicle. The measurements were conducted in the Saha Sinpyeong–Janglim Industrial Complex in Busan, which comprises the Sasang Industrial Complex and the Sinpyeong–Janglim Industrial Complex. BTEX compounds were selected as target volatile organic compounds (VOCs), and real-time measurements of both BTEX and fine particulate matter (PM) were conducted simultaneously. Correlation analysis revealed a strong relationship between PM10 and PM2.5 (r = 0.848–0.894), indicating shared sources. In Sasang, BTEX levels were associated with traffic and localized facilities, while in Saha Sinpyeong–Janglim, the concentrations were more influenced by industrial zoning and wind patterns. Notably, inter-compound correlations such as benzene–m-xylene and p-xylene–toluene suggested possible co-emission sources. This study proposes a GIS-based, three-dimensional air quality management approach that integrates variables such as traffic volume, wind direction, and speed through real-time measurements. The findings are expected to inform effective pollution control strategies and future environmental management plans for industrial complexes. Full article
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20 pages, 4960 KB  
Article
A Fault Diagnosis Method for Planetary Gearboxes Using an Adaptive Multi-Bandpass Filter, RCMFE, and DOA-LSSVM
by Xin Xia, Aiguo Wang and Haoyu Sun
Symmetry 2025, 17(8), 1179; https://doi.org/10.3390/sym17081179 - 23 Jul 2025
Viewed by 235
Abstract
Effective fault feature extraction and classification methods serve as the foundation for achieving the efficient fault diagnosis of planetary gearboxes. Considering the vibration signals of planetary gearboxes that contain both symmetrical and asymmetrical components, this paper proposes a novel feature extraction method integrating [...] Read more.
Effective fault feature extraction and classification methods serve as the foundation for achieving the efficient fault diagnosis of planetary gearboxes. Considering the vibration signals of planetary gearboxes that contain both symmetrical and asymmetrical components, this paper proposes a novel feature extraction method integrating an adaptive multi-bandpass filter (AMBPF) and refined composite multi-scale fuzzy entropy (RCMFE). And a dream optimization algorithm (DOA)–least squares support vector machine (LSSVM) is also proposed for fault classification. Firstly, the AMBPF is proposed, which can effectively and adaptively separate the meshing frequencies, harmonic frequencies, and their sideband frequency information of the planetary gearbox, and is combined with RCMFE for fault feature extraction. Secondly, the DOA is employed to optimize the parameters of the LSSVM, aiming to enhance its classification efficiency. Finally, the fault diagnosis of the planetary gearbox is achieved by the AMBPF, RCMFE, and DOA-LSSVM. The experimental results demonstrate that the proposed method achieves significantly higher diagnostic efficiency and exhibits superior noise immunity in planetary gearbox fault diagnosis. Full article
(This article belongs to the Special Issue Symmetry in Fault Detection and Diagnosis for Dynamic Systems)
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17 pages, 3725 KB  
Article
Robust Low-Snapshot DOA Estimation for Sparse Arrays via a Hybrid Convolutional Graph Neural Network
by Hongliang Zhu, Hongxi Zhao, Chunshan Bao, Yiran Shi and Wenchao He
Sensors 2025, 25(15), 4563; https://doi.org/10.3390/s25154563 - 23 Jul 2025
Viewed by 337
Abstract
We propose a hybrid Convolutional Graph Neural Network (C-GNN) for direction-of-arrival (DOA) estimation in sparse sensor arrays under low-snapshot conditions. The C-GNN architecture combines 1D convolutional layers for local spatial feature extraction with graph convolutional layers for global structural learning, effectively capturing both [...] Read more.
We propose a hybrid Convolutional Graph Neural Network (C-GNN) for direction-of-arrival (DOA) estimation in sparse sensor arrays under low-snapshot conditions. The C-GNN architecture combines 1D convolutional layers for local spatial feature extraction with graph convolutional layers for global structural learning, effectively capturing both fine-grained and long-range array dependencies. Leveraging the difference coarray technique, the sparse array is transformed into a virtual uniform linear array (VULA) to enrich the spatial sampling; real-valued covariance matrices derived from the array measurements are used as the network’s input features. A final multi-layer perceptron (MLP) regression module then maps the learned representations to continuous DOA angle estimates. This approach capitalizes on the increased degrees of freedom offered by the virtual array while inherently incorporating the array’s geometric relationships via graph-based learning. The proposed C-GNN demonstrates robust performance in noisy, low-data scenarios, reliably estimating source angles even with very limited snapshots. By focusing on methodological innovation rather than bespoke architectural tuning, the framework shows promise for data-efficient DOA estimation in challenging practical conditions. Full article
(This article belongs to the Section Communications)
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15 pages, 441 KB  
Article
Efficient Nyström-Based Unitary Single-Tone 2D DOA Estimation for URA Signals
by Liping Yuan, Ke Wang and Fengkai Luan
Mathematics 2025, 13(15), 2335; https://doi.org/10.3390/math13152335 - 22 Jul 2025
Viewed by 220
Abstract
We propose an efficient Nyström-based unitary subspace method for low-complexity two-dimensional (2D) direction-of-arrival (DOA) estimation in uniform rectangular array (URA) signal processing systems. The conventional high-resolution DOA estimation methods often suffer from excessive computational complexity, particularly when dealing with large-scale antenna arrays. The [...] Read more.
We propose an efficient Nyström-based unitary subspace method for low-complexity two-dimensional (2D) direction-of-arrival (DOA) estimation in uniform rectangular array (URA) signal processing systems. The conventional high-resolution DOA estimation methods often suffer from excessive computational complexity, particularly when dealing with large-scale antenna arrays. The proposed method addresses this challenge by combining the Nyström approximation with a unitary transformation to reduce the computational burden while maintaining estimation accuracy. The signal subspace is approximated using a partitioned covariance matrix, and a real-valued transformation is applied to further simplify the eigenvalue decomposition (EVD) process. Furthermore, the linear prediction coefficients are estimated via a weighted least squares (WLS) approach, enabling robust extraction of the angular parameters. The 2D DOA estimates are then derived from these coefficients through a closed-form solution, eliminating the need for exhaustive spectral searches. Numerical simulations demonstrate that the proposed method achieves comparable estimation performance to state-of-the-art techniques while significantly reducing computational complexity. For a fixed array size of M=N=20, the proposed method demonstrates significant computational efficiency, requiring less than 50% of the running time compared to conventional ESPRIT, and only 6% of the time required by ML methods, while maintaining similar performance. This makes it particularly suitable for real-time applications where computational efficiency is critical. The novelty lies in the integration of Nyström approximation and unitary subspace techniques, which jointly enable efficient and accurate 2D DOA estimation without sacrificing robustness against noise. The method is applicable to a wide range of array processing scenarios, including radar, sonar, and wireless communications. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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