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15 pages, 2195 KiB  
Article
A Novel Neural Network Framework for Automatic Modulation Classification via Hankelization-Based Signal Transformation
by Jung-Hwan Kim, Jong-Ho Lee, Oh-Soon Shin and Woong-Hee Lee
Appl. Sci. 2025, 15(14), 7861; https://doi.org/10.3390/app15147861 - 14 Jul 2025
Viewed by 97
Abstract
Automatic modulation classification (AMC) is a fundamental technique in wireless communication systems, as it enables the identification of modulation schemes at the receiver without prior knowledge, thereby promoting efficient spectrum utilization. Recent advancements in deep learning (DL) have significantly enhanced classification performance by [...] Read more.
Automatic modulation classification (AMC) is a fundamental technique in wireless communication systems, as it enables the identification of modulation schemes at the receiver without prior knowledge, thereby promoting efficient spectrum utilization. Recent advancements in deep learning (DL) have significantly enhanced classification performance by enabling neural networks (NNs) to learn complex decision boundaries directly from raw signal data. However, many existing NN-based AMC methods employ deep or specialized network architectures, which, while effective, tend to involve substantial structural complexity. To address this issue, we present a simple NN architecture that utilizes features derived from Hankelized matrices to extract informative signal representations. In the proposed approach, received signals are first transformed into Hankelized matrices, from which informative features are extracted using singular value decomposition (SVD). These features are then fed into a compact, fully connected (FC) NN for modulation classification across a wide range of signal-to-noise ratio (SNR) levels. Despite its architectural simplicity, the proposed method achieves competitive performance, offering a practical and scalable solution for AMC tasks at the receiver in diverse wireless environments. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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21 pages, 22475 KiB  
Article
Assessment of Spatiotemporal Wind Complementarity
by Dirk Schindler, Jonas Wehrle, Leon Sander, Christopher Schlemper, Kai Bekel and Christopher Jung
Energies 2025, 18(14), 3715; https://doi.org/10.3390/en18143715 - 14 Jul 2025
Viewed by 91
Abstract
This study investigates whether combining singular value decomposition with wavelet analysis can provide new insights into the spatiotemporal complementarity between wind turbine sites, surpassing previous findings. Earlier studies predominantly relied on various forms of correlation analysis to quantify complementarity. While correlation analysis offers [...] Read more.
This study investigates whether combining singular value decomposition with wavelet analysis can provide new insights into the spatiotemporal complementarity between wind turbine sites, surpassing previous findings. Earlier studies predominantly relied on various forms of correlation analysis to quantify complementarity. While correlation analysis offers a way to compute global metrics summarizing the relationship between entire time series, it inherently overlooks localized and time-specific patterns. The proposed approach overcomes these limitations by enabling the identification of spatially explicit and temporally resolved complementarity patterns across a large number of wind turbine sites in the study area. Because complementarity information is derived from orthogonal components obtained through singular value decomposition of a wind power density matrix, there is no need to adjust for phase shifts between sites. Moreover, the complementary contributions of these components to overall wind power density are expressed in watts per square meter, directly reflecting the magnitude of the analyzed data. This facilitates a site-specific, complementarity-optimized strategy for further wind energy expansion. Full article
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16 pages, 2159 KiB  
Article
A General Model Construction and Operating State Determination Method for Harmonic Source Loads
by Zonghua Zheng, Yanyi Kang and Yi Zhang
Symmetry 2025, 17(7), 1123; https://doi.org/10.3390/sym17071123 - 14 Jul 2025
Viewed by 178
Abstract
The widespread integration of power electronic devices and renewable energy sources into power systems has significantly exacerbated voltage and current waveform distortion issues, where asymmetric loads—including single-phase nonlinear equipment and unbalanced three-phase power electronic installations—serve as critical harmonic sources whose inherent nonlinear and [...] Read more.
The widespread integration of power electronic devices and renewable energy sources into power systems has significantly exacerbated voltage and current waveform distortion issues, where asymmetric loads—including single-phase nonlinear equipment and unbalanced three-phase power electronic installations—serve as critical harmonic sources whose inherent nonlinear and asymmetric characteristics increasingly compromise power quality. To enhance power quality management, this paper proposes a universal harmonic source modeling and operational state identification methodology integrating physical mechanisms with data-driven algorithms. The approach establishes an RL-series equivalent impedance model as its physical foundation, employing singular value decomposition and Z-score criteria to accurately characterize asymmetric load dynamics; subsequently applies Variational Mode Decomposition (VMD) to extract time-frequency features from equivalent impedance parameters while utilizing Density-Based Spatial Clustering (DBSCAN) for the high-precision identification of operational states in asymmetric loads; and ultimately constructs state-specific harmonic source models by partitioning historical datasets into subsets, substantially improving model generalizability. Simulation and experimental validations demonstrate that the synergistic integration of physical impedance modeling and machine learning methods precisely captures dynamic harmonic characteristics of asymmetric loads, significantly enhancing modeling accuracy, dynamic robustness, and engineering practicality to provide an effective assessment framework for power quality issues caused by harmonic source integration in distribution networks. Full article
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23 pages, 373 KiB  
Article
Few-Grid-Point Simulations of Big Bang Singularity in Quantum Cosmology
by Miloslav Znojil
Symmetry 2025, 17(6), 972; https://doi.org/10.3390/sym17060972 - 19 Jun 2025
Viewed by 301
Abstract
In the context of the current lack of compatibility of the classical and quantum approaches to gravity, exactly solvable elementary pseudo-Hermitian quantum models are analyzed, supporting the acceptability of a point-like form of the Big Bang. The purpose is served by a hypothetical [...] Read more.
In the context of the current lack of compatibility of the classical and quantum approaches to gravity, exactly solvable elementary pseudo-Hermitian quantum models are analyzed, supporting the acceptability of a point-like form of the Big Bang. The purpose is served by a hypothetical (non-covariant) identification of the “time of the Big Bang” with Kato’s exceptional-point parameter t=0. The consequences (including the ambiguity of the patterns of unfolding the singularity after the Big Bang) are studied in detail. In particular, singular values of the observables are shown to be useful in the analysis. Full article
(This article belongs to the Section Physics)
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27 pages, 4944 KiB  
Article
Study on Electric Power Fittings Identification Method for Snake Inspection Robot Based on Non-Contact Inductive Coils
by Zhiyong Yang, Jianguo Liu, Shengze Yang and Changjin Zhang
Sensors 2025, 25(11), 3562; https://doi.org/10.3390/s25113562 - 5 Jun 2025
Viewed by 449
Abstract
In power inspection fields, snake-like robots are often used for transmission line inspection tasks, requiring accurate identification of various power fittings. However, traditional visual sensors perform poorly under varying light intensity and complex background conditions. This paper proposes a non-visual perception method for [...] Read more.
In power inspection fields, snake-like robots are often used for transmission line inspection tasks, requiring accurate identification of various power fittings. However, traditional visual sensors perform poorly under varying light intensity and complex background conditions. This paper proposes a non-visual perception method for the high-precision classification of different power fittings (e.g., vibration dampers, suspension clamps, and tension clamps) in snake-like robot transmission line inspection for high-voltage lines. This method, unaffected by light intensity changes, uses machine learning to classify the magnetic induction electromotive force signals around the fittings. First, the Dodd–Deeds eddy current model is used to analyse the magnetic field changes around the transmission line fittings and determine the induction coil distribution. Then, the concept of condition number and singular value decomposition (SVD) are introduced to analyse the impact of detection position on classification accuracy, with optimal detection positions found using the particle swarm optimization algorithm. Finally, a BP neural network optimised by a genetic algorithm is used for power fitting identification. Experiments show that this method successfully identifies vibration dampers, tension clamps, suspension clamps, and transmission lines at detection distances of 5 cm, 10 cm, 15 cm, and 20 cm, with accuracies of 99.8%, 97.5%, 95.1%, and 92.5%, respectively. Full article
(This article belongs to the Section Electronic Sensors)
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22 pages, 2386 KiB  
Article
A Stochastic Framework for Saint-Venant Torsion in Spherical Shells: Monte Carlo Implementation of the Feynman–Kac Approach
by Behrouz Parsa Moghaddam, Mahmoud A. Zaky, Alireza Sedaghat and Alexandra Galhano
Symmetry 2025, 17(6), 878; https://doi.org/10.3390/sym17060878 - 4 Jun 2025
Viewed by 434
Abstract
This research introduces an innovative probabilistic method for examining torsional stress behavior in spherical shell structures through Monte Carlo simulation techniques. The spherical geometry of these components creates distinctive computational difficulties for conventional analytical and deterministic numerical approaches when solving torsion-related problems. The [...] Read more.
This research introduces an innovative probabilistic method for examining torsional stress behavior in spherical shell structures through Monte Carlo simulation techniques. The spherical geometry of these components creates distinctive computational difficulties for conventional analytical and deterministic numerical approaches when solving torsion-related problems. The authors develop a comprehensive mesh-free Monte Carlo framework built upon the Feynman–Kac formula, which maintains the geometric symmetry of the domain while offering a probabilistic solution representation via stochastic processes on spherical surfaces. The technique models Brownian motion paths on spherical surfaces using the Euler–Maruyama numerical scheme, converting the Saint-Venant torsion equation into a problem of stochastic integration. The computational implementation utilizes the Fibonacci sphere technique for achieving uniform point placement, employs adaptive time-stepping strategies to address pole singularities, and incorporates efficient algorithms for boundary identification. This symmetry-maintaining approach circumvents the mesh generation complications inherent in finite element and finite difference techniques, which typically compromise the problem’s natural symmetry, while delivering comparable precision. Performance evaluations reveal nearly linear parallel computational scaling across up to eight processing cores with efficiency rates above 70%, making the method well-suited for multi-core computational platforms. The approach demonstrates particular effectiveness in analyzing torsional stress patterns in thin-walled spherical components under both symmetric and asymmetric boundary scenarios, where traditional grid-based methods encounter discretization and convergence difficulties. The findings offer valuable practical recommendations for material specification and structural design enhancement, especially relevant for pressure vessel and dome structure applications experiencing torsional loads. However, the probabilistic characteristics of the method create statistical uncertainty that requires cautious result interpretation, and computational expenses may surpass those of deterministic approaches for less complex geometries. Engineering analysis of the outcomes provides actionable recommendations for optimizing material utilization and maintaining structural reliability under torsional loading conditions. Full article
(This article belongs to the Section Engineering and Materials)
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46 pages, 1989 KiB  
Review
Survey of Dense Video Captioning: Techniques, Resources, and Future Perspectives
by Zhandong Liu and Ruixia Song
Appl. Sci. 2025, 15(9), 4990; https://doi.org/10.3390/app15094990 - 30 Apr 2025
Viewed by 1532
Abstract
Dense Video Captioning (DVC) represents the cutting edge of advanced multimedia tasks, focusing on generating a series of temporally precise descriptions for events unfolding within a video. In contrast to traditional video captioning, which usually offers a singular summary or caption for an [...] Read more.
Dense Video Captioning (DVC) represents the cutting edge of advanced multimedia tasks, focusing on generating a series of temporally precise descriptions for events unfolding within a video. In contrast to traditional video captioning, which usually offers a singular summary or caption for an entire video, DVC demands the identification of multiple events within a video, the determination of their exact temporal boundaries, and the production of natural language descriptions for each event. This review paper presents a thorough examination of the latest techniques, datasets, and evaluation protocols in the field of DVC. We categorize and assess existing methodologies, delve into the characteristics, strengths, and limitations of widely utilized datasets, and underscore the challenges and opportunities associated with evaluating DVC models. Furthermore, we pinpoint current research trends, open challenges, and potential avenues for future exploration in this domain. The primary contributions of this review encompass: (1) a comprehensive survey of state-of-the-art DVC techniques, (2) an extensive review of commonly employed datasets, (3) a discussion on evaluation metrics and protocols, and (4) the identification of emerging trends and future directions. Full article
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18 pages, 7740 KiB  
Article
Study on Post-Stack Signal Denoising for Long-Offset Transient Electromagnetic Data Based on Combined Windowed Interpolation and Singular Spectrum Analysis
by Chuyang Lu, Xingbing Xie, Yang Xu, Lei Zhou and Liangjun Yan
Geosciences 2025, 15(4), 121; https://doi.org/10.3390/geosciences15040121 - 1 Apr 2025
Viewed by 357
Abstract
The long-offset transient electromagnetic (LOTEM) method, as a widely applied electromagnetic exploration technique, plays a significant role in mineral resource exploration, hydraulic fracturing monitoring, and fluid identification in oil and gas reservoirs. However, due to external interference, the signals acquired by this method [...] Read more.
The long-offset transient electromagnetic (LOTEM) method, as a widely applied electromagnetic exploration technique, plays a significant role in mineral resource exploration, hydraulic fracturing monitoring, and fluid identification in oil and gas reservoirs. However, due to external interference, the signals acquired by this method often contain substantial noise, which severely affects the reliability of subsequent inversion and interpretation. Therefore, denoising is a critical issue in LOTEM data processing. To address this problem, this paper proposes a denoising study for LOTEM post-stack signals based on a combination of windowed interpolation and singular spectrum analysis. First, the stacking method and windowed interpolation are employed to remove most of the random noise and power-line interference (including its harmonics). Then, singular spectrum analysis is applied to further suppress noise and obtain higher-quality signal data. Experimental results demonstrate that the proposed method performs well in denoising, effectively reducing the root mean square error (RMSE) of the signal and improving its signal-to-noise ratio (SNR). The method was validated using LOTEM data collected from Zhongjiang County, Sichuan Province. The validation results show that the method can effectively remove noise interference from underground media, providing essential technical support for inversion and interpretation. Full article
(This article belongs to the Section Geophysics)
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12 pages, 342 KiB  
Article
New Evidence for Asherata/Asherah
by Richard S. Hess
Religions 2025, 16(4), 397; https://doi.org/10.3390/rel16040397 - 21 Mar 2025
Viewed by 1312
Abstract
This paper examines the appearance of published West Semitic spellings of the name of the deity commonly referred to as Asherah. In light of new evidence from the Bronze Age Amorite sources, as well as the complete publication of the inscriptions at Kuntillet [...] Read more.
This paper examines the appearance of published West Semitic spellings of the name of the deity commonly referred to as Asherah. In light of new evidence from the Bronze Age Amorite sources, as well as the complete publication of the inscriptions at Kuntillet ʿAjrud, a review of the analysis and discussion concerning the identification of the deity is undertaken. The purpose will be to ascertain the significance of the witness of epigraphic Hebrew texts at Kuntillet ʿAjrud and Khirbet el-Qom in light of earlier Bronze Age evidence, the biblical attestations, the conceptualization of deity, and the understanding of Iron Age epigraphic Hebrew spellings of the feminine singular suffix, as well as pronominal suffixes. The more complete availability of textual witnesses provides a foundation on which to argue the degree of continuity across more than a thousand years of the appearance of the deity in the West Semitic world. Full article
(This article belongs to the Special Issue The Bible and Ancient Mesopotamia)
29 pages, 10427 KiB  
Article
Cultural Perception of Tourism Heritage Landscapes via Multi-Label Deep Learning: A Study of Jingdezhen, the Porcelain Capital
by Yue Cheng and Weizhen Chen
Land 2025, 14(3), 559; https://doi.org/10.3390/land14030559 - 6 Mar 2025
Viewed by 1526
Abstract
In the face of rapid progress in heritage preservation and cultural tourism integration, landscape planning in historic cities is pivotal to showcasing regional identities and disseminating cultural value. However, the complexity of cultural characteristic identification and the imbalance in planning often restrict the [...] Read more.
In the face of rapid progress in heritage preservation and cultural tourism integration, landscape planning in historic cities is pivotal to showcasing regional identities and disseminating cultural value. However, the complexity of cultural characteristic identification and the imbalance in planning often restrict the progress of urban development. Additionally, existing studies predominantly rely on subjective methods and focus on a single cultural attribute, highlighting the urgent need for research on diversified cultural perception. Using Jingdezhen, a renowned historic cultural city, as an example, this study introduces a multi-label deep learning approach to examine cultural perceptions in tourism heritage landscapes. Leveraging social media big data and an optimized ResNet-50 model, a framework encompassing artifacts, production, folk, and living culture was constructed and integrated with ArcGIS spatial analysis and diversity indices. The results show: (1) The multi-label classification model achieves 92.35% accuracy, validating its potential; (2) Heritage landscapes exhibit a “material-dominated, intangible-weak” structure, with artifacts culture as the main component; (3) Cultural perception intensity is unevenly distributed, with core areas demonstrating higher recognition and diversity; (4) Diversity indices suggest that comprehensive venues display stronger cultural balance, whereas specialized ones reveal marked cultural singularity, indicating a need for improved integration across sites. This research expands the use of multi-label deep learning in tourism heritage studies and offers practical guidance for global heritage sites tackling mass tourism. Full article
(This article belongs to the Special Issue Landscape Planning for Mass Tourism in Historical Cities)
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18 pages, 2393 KiB  
Article
Identification of Ship Maneuvering Behavior Using Singular Value Decomposition-Based Hydrodynamic Variations
by Cem Guzelbulut
J. Mar. Sci. Eng. 2025, 13(3), 496; https://doi.org/10.3390/jmse13030496 - 3 Mar 2025
Viewed by 1388
Abstract
Recent efforts on the decarbonization, autonomy, and safety of the maritime vehicles required comprehensive analyses and prediction of the behavior of the existing vessels and prospective adaptations. To predict the performance of vessels, a better understanding of ship hydrodynamics is necessary. However, it [...] Read more.
Recent efforts on the decarbonization, autonomy, and safety of the maritime vehicles required comprehensive analyses and prediction of the behavior of the existing vessels and prospective adaptations. To predict the performance of vessels, a better understanding of ship hydrodynamics is necessary. However, it is necessary to conduct dozens of experiments or computational fluid dynamics simulations to characterize the hydrodynamic behavior of the vessels, which require significant amounts of cost and time. Thus, system identification studies to characterize the hydrodynamics of ships have gained attention. The present study proposes a hybrid methodology that combines the existing hydrodynamic databases, and a prediction model of ship hydrodynamics based on motion indexes obtained by turning and zigzag tests. Firstly, singular value decomposition was applied to extract the main hydrodynamic variations, and an artificial yet realistic hydrodynamic behavior generation systematics was developed. Then, turning and zigzag tests were simulated to train artificial neural network models which predict how hydrodynamic behavior varies based on the motion indexes. Finally, the proposed methodology was applied to two vessels to predict the hydrodynamic behaviors of the target ships based on given motion indexes. It was found that the motion obtained via the predicted hydrodynamics showed a high correlation with the given motion indexes. Full article
(This article belongs to the Special Issue Advances in Ship and Marine Hydrodynamics)
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21 pages, 6452 KiB  
Article
CEEMDAN-SVD Motor Noise Reduction Method and Application Based on Underwater Glider Noise Characteristics
by Haotian Zhao and Maofa Wang
Symmetry 2025, 17(3), 378; https://doi.org/10.3390/sym17030378 - 1 Mar 2025
Viewed by 547
Abstract
When utilizing underwater gliders to observe submerged targets, ensuring the quality and reliability of the acquired target characteristic signals is paramount. However, the signal acquisition process is significantly compromised by noise generated from various motors on the platform, which severely contaminates the authentic [...] Read more.
When utilizing underwater gliders to observe submerged targets, ensuring the quality and reliability of the acquired target characteristic signals is paramount. However, the signal acquisition process is significantly compromised by noise generated from various motors on the platform, which severely contaminates the authentic target signal characteristics, thereby complicating subsequent research efforts such as target identification. Given the limited capability of wavelet transforms in processing complex non-stationary signals, and considering the non-stationary and non-linear nature of the signals in question, this study focuses on the denoising of hydroacoustic signals and the characteristics of motor noise. Building upon the traditional CEEMDAN-SVD approach, we propose an adaptive noise reduction method that combines the maximum singular value of motor noise with the differential spectrum of singular values. In particular, this paper delves into the symmetry between the noise subspace and the signal subspace in SVD decomposition. By analyzing the symmetric characteristics of their singular value distributions, the process of separating noise from signals is further optimized. The effectiveness of this denoising method is analyzed and validated through simulations and experiments. The results demonstrate that under a signal-to-noise ratio (SNR) of 3 dB, the improved CEEMDAN-SVD method reduces the mean square error by an average of 22.8% and decreases the absolute value of skewness by 27.8% compared to the traditional CEEMDAN-SVD method. These findings indicate that our proposed method exhibits superior noise reduction capabilities under strong non-stationary motor noise interference, effectively enhancing the SNR and reinforcing signal characteristics. This provides a robust foundation for improving the recognition rate of hydroacoustic targets in subsequent research. Full article
(This article belongs to the Section Engineering and Materials)
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13 pages, 5279 KiB  
Article
Nonlinear Control of a Permanent Magnet Synchronous Motor Based on State Space Neural Network Model Identification and State Estimation by Using a Robust Unscented Kalman Filter
by Sergio Velarde-Gomez and Eduardo Giraldo
Eng 2025, 6(2), 30; https://doi.org/10.3390/eng6020030 - 7 Feb 2025
Viewed by 893
Abstract
This work proposes a nonlinear modeling of a permanent magnet synchronous motor (PMSM) based on state space neural networks. The state space neural network is trained and the state variables (currents in a direct–quadrature frame and the rotational speed) are estimated by considering [...] Read more.
This work proposes a nonlinear modeling of a permanent magnet synchronous motor (PMSM) based on state space neural networks. The state space neural network is trained and the state variables (currents in a direct–quadrature frame and the rotational speed) are estimated by considering a robust Unscented Kalman Filter (UKF). Two contributions are presented in this work: the fist one is a nonlinear modeling structure for a PMSM based on a state space neural network that allows real-time parameter identification, and the second one is PMSM neural network training and state estimation based on a robust UKF. The robustness of the UKF is obtained by using a singular value decomposition of the covariance matrix. A comparison analysis is performed over a real PMSM motor by considering the proposed approach and a linear approximation of the nonlinear model where the states and parameters are computed by using an Extended Kalman Filter. The identified model is validated in closed loop by considering a nonlinear control strategy based on state feedback linearization. Full article
(This article belongs to the Special Issue Artificial Intelligence for Engineering Applications)
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32 pages, 11857 KiB  
Article
A Hybrid Dynamic Principal Component Analysis Feature Extraction Method to Identify Piston Pin Wear for Binary Classifier Modeling
by Hao Yang, Yubin Zhai, Mengkun Zheng, Tan Wang, Dongliang Guo, Jianhui Liang, Xincheng Li, Xianliang Liu, Mingtao Jia and Rui Zhang
Machines 2025, 13(1), 68; https://doi.org/10.3390/machines13010068 - 18 Jan 2025
Viewed by 631
Abstract
The wear condition of a piston pin is a main factor in determining the operational continuity and life cycle of a diesel engine; identifying its vibration feature is of paramount importance in carrying out necessary maintenance in the early wear stage. As the [...] Read more.
The wear condition of a piston pin is a main factor in determining the operational continuity and life cycle of a diesel engine; identifying its vibration feature is of paramount importance in carrying out necessary maintenance in the early wear stage. As the dynamic vibration features are susceptible to environmental disturbance during operation, an effective signal processing method is necessary to improve the accuracy and fineness of the extracted features, which is essential to build a reliable and precise binary classifier model to identify piston pin wear based on the features. Aiming at the feature extraction requirements of anti-noise, accuracy and effectiveness, this paper proposes a piston pin wear feature extraction algorithm based on dynamic principal component analysis (DPCA) combined with variational mode decomposition (VMD) and singular value decomposition (SVD). An orthogonal sensor layout is applied to collect the vibration signal under normal and worn piston pin conditions, which proved effective in reducing environmental vibration disturbance. DPCA is utilized to extract dynamical vibration features by introducing time lag. Then, the dynamic principal component matrix is further decomposed by VMD to obtain intrinsic mode functions (IMFs) as finer features and is finally decomposed by SVD to compress the features, thus improving the classification efficiency based on the features. To validate the significance of the features extracted by the proposed method, a support vector machine (SVM) is employed to model binary classifiers to evaluate the classification performance trained by different features. A modeling dataset containing 80 samples (40 normal samples and 40 worn samples) is employed, and five-round cross-validation is adopted. For each round, two binary classifier models are trained by features extracted by the proposed method and the empirical mode decomposition (EMD)–auto regressive (AR) spectrum method, fast Fourier transform (FFT) and continuous wavelet transform (CWT), respectively; the classification precision, recall ratio, accuracy and F1 ratio are obtained on the testing set by contrasting the overall performances of the five-round cross-validation, and the proposed method is proved to be more effective in noise reduction and significant feature extraction, which is able to improve the accuracy and efficiency of binary classification for piston pin wear identification. Full article
(This article belongs to the Section Machines Testing and Maintenance)
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17 pages, 1524 KiB  
Article
Discovering PDEs Corrections from Data Within a Hybrid Modeling Framework
by Chady Ghnatios and Francisco Chinesta
Mathematics 2025, 13(1), 5; https://doi.org/10.3390/math13010005 - 24 Dec 2024
Viewed by 722
Abstract
In the context of hybrid twins, a data-driven enrichment is added to the physics-based solution to represent with higher accuracy the reference solution assumed to be known at different points in the physical domain. Such an approach enables better predictions. However, the data-driven [...] Read more.
In the context of hybrid twins, a data-driven enrichment is added to the physics-based solution to represent with higher accuracy the reference solution assumed to be known at different points in the physical domain. Such an approach enables better predictions. However, the data-driven enrichment is usually represented by a regression, whose main drawbacks are (i) the difficulty of understanding the subjacent physics and (ii) the risks induced by the data-driven model extrapolation. This paper proposes a procedure enabling the extraction of a differential operator associated with the enrichment provided by the data-driven regression. For that purpose, a sparse Singular Value Decomposition, SVD, is introduced. It is then employed, first, in a full operator representation regularized optimization problem, where sparsity is promoted, leading to a linear programming problem, and then in a tensor decomposition of the operator’s identification procedure. The results show the ability of the method to identify the exact missing operators from the model. The regularized optimization problem was also able to identify the weights of the missing terms with a relative error of about 10% on average, depending on the selected use case. Full article
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